Possible Optical Detection of the Anomalous X-ray Pulsar CXOU J010043.1-721134

合集下载

Gamma-rays From Neutralino Annihilation in Milky Way Substructure What Can We Learn

a r X i v :a s t r o -p h /0309516v 1 18 S e p 2003Gamma-rays From Neutralino Annihilation in Milky Way Substructure:What Can We Learn?Savvas M.Koushiappas Department of Physics,The Ohio State University,Columbus,OH 43210,USAsmkoush@Andrew R.ZentnerDepartment of Physics,The Ohio State University,Columbus,OH 43210,USAPresent Address:Center for Cosmological Physics,The University of Chicago,Chicago,IL 60637,USATerrence P.WalkerDepartment of Physics,The Ohio State University,Columbus,OH 43210,USADepartment of Astronomy,The Ohio State University,Columbus,OH 43210,USAAbstract.We estimate the probability of detecting gamma-rays from the annihilation of neutralino dark matter in the substructure of the Milky Way.We characterize substructure statistically based on Monte Carlo realizations of the formation of a Milky Way-like halo using semi-analytic methods that have been calibrated against N-body simulations.We ﬁnd that it may be possible for the upcoming GLAST and VERITAS experiments,working in concert,to detect gamma-rays from dark matter substructure if M χ<∼100GeV,while for M χ>∼500GeV such a detection seems unlikely.We investigate the eﬀects of the underlying cosmological model and ﬁnd that the probability of detection is sensitive to the primordial power spectrum of density ﬂuctuations on small (galactic and sub-galactic)scales.We conclude that the lack of such a detection reveals little about the supersymmetric parameter space due to the uncertainties associated with the properties of substructure and cosmological parameters.1Introduction In the currently popular ΛCDM cosmological model,the Universe is composed of ∼4%baryonic matter and ∼26%cold,collisionless dark matter (CDM),and is made ﬂat by a cosmological constant(Λ)[1].The growth of structure is seeded by a nearly scale-invariant spectrum of density ﬂuctuations,supposedly generated during an early epoch of inﬂation.Within this framework,structure forms hierarchically,with small objects collapsing ﬁrst and subsequently merging into larger structures over time.This paradigm for structure formation predicts the presence of a large number of self-bound subhalos within Milky Way-sized halos (e.g.,[2])and it is possible that the these substructures may give rise to a gamma-ray signal due to annihilations of dark matter particles in their dense inner regions [4].This is based on the assumption that the dark matter is a weakly-interacting massive particle (WIMP)that annihilates into photons.Such a WIMP candidate is provided by supersymmetry (SUSY).In the most popular SUSY models,R-parity conservation guarantees that the lightest SUSY particle (LSP)is stable.Additionally,a large region of SUSY parameter space provides an LSP with the requisite relic abundance to serve as the CDM.In the constrained minimal supersymmetric extension to the standard model (MSSM),this particle is typically the lightest neutralino,or lightest mass eigenstate formed from the two CP-even Higgsinos,the W 3ino and the Bino.In this Proceeding,we explore the idea that neutralino annihilations in Milky Way (MW)substruc-ture may teach us about SUSY and/or structure formation.In particular,we estimate the probability that the gamma-ray signal from neutralino annihilations in substructure will be detected by the up-coming GLAST and VERITAS experiments,assuming the the majority of the CDM is in the form of neutralinos.Further,we investigate the type of information that may be gleaned from such a gamma-ray detection,or lack thereof.The results that we summarize here are based on the work of Ref.[3],to which we refer the reader for details.2Milky Way SubstructureTo begin with,we describe the matter density proﬁles of halos using the result of Navarro,Frenk,and White(NFW)[5]:ρ(r)=ρs(r/r s)−1(1+r/r s)−2.This description of CDM halos is supported by the most recent numerical studies[6].To estimate the properties of substructure in the MW,we adopt the simple,semi-analytic model described in Ref.[7].Weﬁrst generate Monte Carlo realizations of the merger history of a Milky Way-sized host halo using the extended Press-Schechter formalism[8]. We then track the orbit of the subhalo in the host potential in order to determine whether or not the subhalo is destroyed by tidal forces and to estimate itsﬁnal position.This model produces substructure radial distributions,mass functions,and velocity functions that are in approximate agreement with the results of high-resolution N-body simulations.This method allows us to account approximately for known correlations between the density structure and collapse histories of subhalos,to model substructure in a simple way that is inherently free of resolution eﬀects,and to generate statistically signiﬁcant results for a variety of input parameters by examining a large number of realizations of MW-like host halos.3The Gamma-ray Signal From SubstructureWe calculate the number of gamma-ray photons originating from neutralino annihilations in the central regions of subhalos by assuming the best-case-scenario for detection.We choose toﬁx the annihilation cross section into all intermediate states that subsequently decay and/or hadronize to yield photons to σ|v| h=5×10−26cm3s−1and the annihilation cross section into the2-photon and Z0-photonﬁnal states to be σ|v| γγ,γZ0=10−28cm3s−1.These values are representative of the maximum achievable cross sections within the context of the constrained MSSM.We include the contributions from the cosmic ray electron[9],hadron[10],and the diﬀuse gamma-ray backgrounds[11]in our calculation of competing backgrounds.We adopt a liberal deﬁnition of a detection at a signiﬁcance of S>3 and note that due to detector speciﬁcations,the signiﬁcance is a function of threshold energy and neutralino mass.In accord with our strategy of optimizing the likelihood for detecting the gamma-ray signal from substructure,we concentrate on observations at a threshold energy and neutralino mass where the signiﬁcance is ing the speciﬁcations of the atmosphericˇCerenkov telescope (ACT)VERITAS1,weﬁnd that the signiﬁcance is maximized at a neutralino mass of Mχ≃500GeV, with a threshold energy of E th≃50GeV.We take GLAST2as an example of a space-based detector. In this case,the signiﬁcance is maximized at a neutralino mass just above experimental bounds, Mχ≃40GeV,and at a threshold E th≃4GeV.4ResultsOurﬁrst results deal with the likelihood of a detection by the VERITAS instrument.Figure4shows results for the most optimistic case for VERITAS,namely,Mχ=500GeV observed above a threshold of E th=50GeV.We have assumed a generous exposure time of t exp=250hours.In Fig.4,we show the cumulative number of visible subhalos in the entire sky as a function of an adopted lower mass cut-oﬀ,M min.In practice,there is likely a cut-oﬀin CDM substructure at some low mass,well beyond the regime where N-body simulations can probe.Our results indicate that reducing M min, adding more low-mass subhalos,does not necessarily lead to a dramatic increase in the number of visible subhalos.Our model suggests that the number of detectable subhalos per mass interval scales as d N total/d ln M∼M−0.02at low mass.Weﬁnd that with M min=104M⊙,we expect N total∼17 detectable subhalos,with fewer than N total∼25detectable at95%.This means that,on average,an ACT like VERITAS will have to survey∼1/20of the sky toﬁnd one subhalo.Considering the small ﬁeld of view of VERITAS and the fact that ACTs can,on average,observe∼6hours per night,the prospects for detection must rely heavily on serendipity,even in the best of circumstances.Note that for neutralino masses higher or lower than Mχ∼500GeV,there are fewer detectable subhalos.If we are to learn about SUSY and/or structure formation from such experiments,we must inves-tigate the sensitivity of these results to cosmological parameters.In Figure4,we show the results ofFigure1:Left:The cumulative number of subhalos on the entire sky with mass M≥M min that are detectable at S≥3by VERITAS after an exposure time of250hours.The neutralino mass is Mχ=500GeV and E th=50GeV,yielding the highest probability for detection.The solid line represents the mean over100model realizations in theΛCDM cosmological model with scale-invariant primordial power spectrum.The dashed line represents the mean over100realizations in aΛCDM model with a running power law power spectrum,d n/d ln k=−0.03with n(k=0.05Mpc−1)≃0.93 andσ8≃0.84.In both cases,the error bars correspond to the64%range of the predictions(symmetric about the median).The down arrows indicate that more than18%of the realizations had zero visible halos in the corresponding mass bin.Right:The cumulative number of visible subhalos detectable at S≥3,with mass M≥M min,after a one year exposure with GLAST in standardΛCDM.The threshold energy is E th=3GeV.Solid lines represent the mean over100model realizations for a neutralino with mass Mχ=40GeV,while dashed lines represent a neutralino with Mχ=100GeV. The error bars are as in the left panel.a calculation based on aΛCDM model with a nonstandard power spectrum.We show a model with a running power law index,d n/d ln k=−0.03,as suggested by the recent analysis of the WMAP team[1].In this case,the mean number of visible subhalos is reduced by more than an order of mag-nitude.This can be explained by examining the eﬀects of reduced small-scale power on the properties of substructure populations[7]and shows that predictions for the gamma-ray signal from WIMP annihilations in substructure are sensitive the power spectrum on sub-galactic scales.We now turn our attention to the space-based GLAST detector.In Figure4,we show the number of subhalos that would be detectable after a year long exposure with GLAST.The most optimistic number of detectable subhalos is N total∼14,corresponding to roughly two subhalos per GLASTﬁeld of view;however,one must be cautious.Consider the energy scales involved in this calculation.The optimum neutralino mass for a GLAST detection is at the lower limit of current experimental searches, Mχ∼40GeV.Increasing the neutralino mass results in fewer visible halos due to the limited eﬀective area of GLAST and a rapidly decreasing subhalo luminosity.A key ingredient in this calculation is the matter distribution in the very central regions of subhalos. In the absence of any other eﬀect,subhalos may exhibit a central,constant density core established by the competition between the rate of neutralino annihilations and the rate of infalling material. Due to the signiﬁcant uncertainty in the mass densities achieved in the central regions of dark matter halos,we investigate the eﬀect of the size of the core region on subhalo detectability.In Figure4,we show how our results vary as a function of core radius,parameterized byβ≡r c/r c,0,where r c,0is the core radius assigned by equating the annihilation rate inside the core to the rate of material infall (see[3]),and r c is a new core radius deﬁned as a multiple of r c,0.Clearly,the precise choice of the core radius aﬀects our results only weakly over many orders of magnitude.Notably,makingβ<1Figure2:Left:The cumulative number of subhalos with mass M≥M min as a function of M min for diﬀerent values of the core parameterβ=˜r c/˜r c,0.The solid,long-dashed and dash-dotted lines correspond to means over all realizations in aΛCDM cosmological model forβ=10−2,107and5×107 respectively.Error bars are as in Figure4.Right:The cumulative number of visible subhalos with a mass M≥M min for the standardΛCDM cosmological model(solid),a model with a spectral index of primordialﬂuctuations n=1.1(σ8≃1.2;long-dashed),and a model where the density proﬁles of subhalos are described by the Moore et al.proﬁle(short-dashed).does not have a signiﬁcant eﬀect on N total.Eventually,whenβ>∼5×107,the number of detectable subhalos decreases signiﬁcantly as the angles subtended by typical subhalo cores become comparable to the detector resolution.In general the luminosity and therefore detectability of a subhalo is given by integrating the square of the mass density of the subhalo along the line-of-sight to the subhalo.It is of interest to test the robustness of our results by investigating the change in N total when diﬀerent mass density proﬁles are assumed.For this purpose,we show in Figure4the number of detectable objects when the Moore et al.proﬁle[12](withρ(r)∝r−3/2at small radii)is assumed.As expected,the number of detectable subhalos increases dramatically(a factor of∼10).5ConclusionsWe investigated the possible detection of the MW substructure via the detection of gamma-rays from neutralino annihilations in otherwise dark subhalos.We chose the most optimistic SUSY parameters in order to maximize the probability of detection.We also employed a realistic,yet still optimistic from the standpoint of predicting observable signals from substructure,model for the population of subhalos in the MW.Our main results were:⋆If the neutralino is relatively light(Mχ<∼100GeV),then GLAST and VERITAS,working in concert,may be able to detect the gamma-ray signal.In this case,GLAST with its largeﬁeld of view can be used to identify sources in the sky and direct subsequent VERITAS observations,which can search for line-emission at E=Mχ,the smoking gun of neutralino annhilations.For example,if Mχ∼75GeV,then,in the case of optimal coupling to photons,there will be∼1detectable subhalo per GLASTﬁeld of view,on average.In this case,subsequent,directed observations with VERITAS should be able to conﬁrm the line-emission feature after an exposure time of t exp∼450hr.⋆For neutralino masses in the range100GeV<∼Mχ<∼500GeV,detection requires an instrument with a large eﬀective area,like VERITAS;however,such a detection must rely on serendipity due tothe small number of potentially detectable objects and VERITAS’comparably smallﬁeld of view.⋆For Mχ>∼500GeV it seems unlikely that gamma-rays from neutralino annihilations in dark subhalos will be detectable with VERITAS or GLAST.What can be learned by the lack of such a detection?The lack of such a detection certainly will not lead to a bonanza of constraints on the MSSM or SUSY in general.Even after choosing the optimal MSSM parameters for detection,the likelihood of a detection is small for most of the viable range of Mχ.Moreover,the number of detectable objects depends upon the uncertain shape of density proﬁles in the innermost regions of dark matter halos.These uncertainties can signiﬁcantly inﬂuence our predictions.Moreover,their are additional uncertainties that are not associated with our lack of knowledge of density proﬁles and subhalo populations.The predictions of the expected gamma-ray ﬂux are strongly dependent upon poorly-constrained cosmological parameters.We showed in Fig. 4that adopting the best-ﬁtting power spectrum from the WMAP group reduces the probability of detection by more than an order of magnitude relative to a model with a standard,scale-invariant primordial power spectrum.Of course,a detection would yield a great deal of information.First and foremost,it would be evidence for neutralino(or some other WIMP that annihilates into photons)dark matter,it would suggest the presence of dark subhalos within the MW,it would indicate that such subhalos do achieve extremely high densities in their central regions,and it may also yield information about the survival rates and accretion histories of dark matter subhalos.Nevertheless,it will be diﬃcult to“measure”SUSY from such a detection.As we demonstrated above,cosmological parameters play a role in predicting the gamma-ray signal and,as we show in Fig.4,adopting a“blue tilted”power spectrum with n=1.1,COBE-normalized toσ8≃1.2,can boost the expected number of detectable subhalos by a factor of∼3.Such uncertainties must be marginalized over and a model similar to the one we presented here may be able to play an important role in this regard.Further,theﬂux from a particular subhalo depends upon subhalo distance and there is no obvious way to determine reliably the distance to an otherwise dark subhalo.Our model attempts to take this uncertainty into account by calculating“likely”realizations of the substructure population of the MW.References[1]Spergel,D.et al.,2003,astro-ph/0302209.[2]Klypin,A.A.et al.,1999,ApJ522,82;Moore,B.et al.1999,ApJL524,L19;Stoehr,F.et al. 2002,MNRAS,335,L84.[3]Koushiappas,S.M.,Zentner,A.R.&Walker,T.P.,2003,Phys.Rev.D,submitted,astro-ph/0309464.[4]Bergstr¨o m,L.et al,1999,PRD59,043506;Baltz,E.A.et al.,1999,PRD61,023514;Calc´a neo-Rold´a n,C.&Moore,B.,2000,PRD62,123005;Tasitsiomi,A.&Olinto,A.,2002,PRD66, 083006;Aloisio,R.,Blasi,P.&Olinto,A.V.,2002,astro-ph/0206036;Taylor,J.E.and Silk,J., 2003,MNRAS339,505;Stoehr,F.et al.,2003,astro-ph/0307026.[5]Navarro,J.F.,Frenk,C.S.,&White,S.D.M.,1997,ApJ490,493[6]Power,C.et al.2003,MNRAS,338,14.[7]Zentner,A.R.&Bullock,J.S.,2003,ApJ,598,in press.[8]Bond,J.R.et al.1991,ApJ,379,440;Lacey,C.&Cole,S.1993,MNRAS,262,627;Somerville, R.S.&Kolatt,T.S.1999,305,1.[9]Nishimura,J.et al.1980,ApJ238,394.[10]Ryan,M.J.,Orme,J.F.,&Balasubrahmanyan,V.K.,1972,PRL28,985.[11]Sreekumar,P.et al.,1998,ApJ494,523.[12]Moore,B.et al.,1999,MNRAS,310,1147.。

高三英语天文观测设备单选题50题

高三英语天文观测设备单选题50题1. An ______ is a building or place equipped with telescopes and other instruments for observing astronomical objects.A. observatoryB. laboratoryC. factoryD. library答案：A。

解析：本题考查名词词义辨析。

observatory意为天文台，是配备望远镜等仪器用于观测天文物体的建筑或场所，符合题意。

laboratory是实验室，主要用于科学实验；factory是工厂，用于生产制造；library是图书馆，用于藏书和供人阅读学习，这三个选项均不符合天文观测场景的描述。

2. The ______ is an important tool for astronomers to observe the stars and galaxies far away.A. microscopeB. telescopeC. magnifierD. binoculars答案：B。

解析：本题考查天文观测工具相关的名词。

telescope望远镜是天文学家观测遥远恒星和星系的重要工具。

microscope是显微镜，用于观察微小的物体，如细胞等；magnifier是放大镜，主要用于放大近距离的小物体；binoculars是双筒望远镜，虽然也可用于观测，但在天文观测中telescope更为专业和常用。

3. In the observatory, the ______ of the telescope needs to be adjusted precisely to get a clear view of the celestial bodies.A. lensB. buttonC. handleD. box答案：A。

解析：本题考查名词在天文观测设备中的部件。

Review article Linear optical quantum computing

a r X i v :q u a n t -p h /0512071v 2 14 M a r 2006Linear optical quantum computingPieter Kok,1,2,∗W.J.Munro,2Kae Nemoto,3T.C.Ralph,4Jonathan P.Dowling,5,6and burn 41Department of Materials,Oxford University,Oxford OX13PH,UK2Hewlett-Packard Laboratories,Filton Road Stoke Giﬀord,Bristol BS348QZ,UK3National Institute of Informatics,2-1-2Hitotsubashi,Chiyoda-ku,Tokyo 101-8430,Japan 4Centre for Quantum Computer Technology,University of Queensland,St.Lucia,Queensland4072,Australia5Hearne Institute for Theoretical Physics,Department of Physics and Astronomy,LSU,Baton Rouge LA,70803,USA6Institute for Quantum Studies,Department of Physics,Texas A&M University,77843-4242,USA(Dated:February 1,2008)Linear optics with photon counting is a prominent candidate for practical quantum computing.The protocol by Knill,Laﬂamme,and Milburn [Nature 409,46(2001)]explicitly demonstrates that efﬁcient scalable quantum computing with single photons,linear optical elements,and projective measure-ments is possible.Subsequently,several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation.We review the original theory and its improvements,and we give a few examples of experimental two-qubit gates.We discuss the use of realistic components,the errors they induce in the computation,and how these errors can be corrected.PACS numbers:03.67.Hk,03.65.Ta,03.65.UdContentsI.Quantum computing with light 1A.Linear quantum optics2B.N port interferometers and optical circuits 4C.Qubits in linear optics4D.Early optical quantum computers and nonlinearities 6II.A new paradigm for optical quantum computing8A.Elementary gates8B.Parity gates and entangled ancillæ10C.Experimental demonstrations of gates 11D.Characterisation of linear optics gates 13E.General probabilistic nonlinear gates14F.Scalable optical circuits and quantum teleportation 15G.The Knill-Laﬂamme-Milburn protocol 16H.Error correction of the probabilistic gates 18III.Improvements on the KLM protocol19A.Cluster states in optical quantum computing 19B.The Yoran-Reznik protocol 21C.The Nielsen protocol22D.The Browne-Rudolph protocol22E.Circuit-based optical quantum computing revisited 24IV .Realistic optical components and their errors25A.Photon detectors 25B.Photon sources27C.Circuit errors and quantum memories 32V .General error correction33A.Correcting for photon loss33B.General error correction in LOQC 35VI.Outlook:beyond linear optics36Acknowledgements 37References382The difﬁculty with this technique is that such optical quantum gates are probabilistic:More often than not, the gate fails and destroys the information in the quan-tum computation.This can be circumvented by using an exponential number of optical modes,but this is by deﬁnition not scalable(see also section I.D).In2001, Knill,Laﬂamme,and Milburn(KLM2001)constructed a protocol in which probabilistic two-photon gates are teleported into a quantum circuit with high probabil-ity.Subsequent error correction in the quantum circuit is used to bring the error rate down to fault-tolerant levels. We describe the KLM protocol in detail in section II. Initially,the KLM protocol was designed as a proof that linear optics and projective measurements allow for scalable quantum computing in principle.However, it subsequently spurred on new experiments in quan-tum optics,demonstrating the operation of high-ﬁdelity probabilistic two-photon gates.On the theoretical front, several improvements of the protocol were proposed, leading to ever smaller overhead cost on the computa-tion.A number of these improvements are based on cluster-state quantum computing,or the one-way quan-tum computer.Recently,a circuit-based model was shown to have similar scaling properties as the best-known cluster state model.In section III,we describe the several improvements to linear optical quantum in-formation processing in considerable detail,and in sec-tion IV,we describe the issues involved in the use of realistic components such as photon detectors,photon sources and quantum memories.Given these realistic components,we discuss loss tolerance and general er-ror correction for Linear Optical Quantum Computing (LOQC)in section V.We will restrict our discussion to the theory of single-photon implementations of quantum information pro-cessors,and we assume some familiarity with the ba-sic concepts of quantum computing.For an introduc-tion to quantum computation and quantum informa-tion,see e.g.,Nielsen and Chuang(2000).For a re-view article on optical quantum information process-ing with continuous variables,see Braunstein and Van Loock(2005).In section VI we conclude with an outlook on other promising optical quantum informa-tion processing techniques,such as photonic band-gap structures,weak cross-Kerr nonlinearities,and hybrid matter-photon systems.We start our review with a short introduction to linear optics,N port optical interferome-ters and circuits,and we deﬁne the different versions of the optical qubit.A.Linear quantum opticsThe basic building blocks of linear optics are beam split-ters,half-and quarter-wave plates,phase shifters,etc. In this section we will describe these devices mathemat-ically and establish the convention that is used through-out the rest of thepaper.n|n−1 andˆa†|n =√Physically,a phase shifter is a slab of transparent mate-rial with an index of refraction that is different from thatof free space.Another important component is the beam splitter(see Fig.1).Physically,it consists of a semi-reﬂective mir-ror:when light falls on this mirror,part will be reﬂected and part will be transmitted.The theory of the lossless beam splitter is central to LOQC,and was developed by Zeilinger(1981)and Fearn and Loudon(1987).Lossybeam splitters were studied by Barnett et al.(1989).The transmission and reﬂection properties of general dielec-tric media were studied by Dowling(1998).Let the two incoming modes on either side of the beam splitter be denoted byˆa in andˆb in,and the outgoing modes byˆa out andˆb out.When we parameterise the probability ampli-tudes of these possibilities as cosθand sinθ,and the relative phase asϕ,then the beam splitter yields an evo-lution in operator formˆa†out=cosθˆa†in+ie−iϕsinθˆb†in,ˆb†=ie iϕsinθˆa†in+cosθˆb†in,(4) outThe reﬂection and transmission coefﬁcients R and T of the beam splitter are R=sin2θand T=1−R=cos2θ. The relative phase shift ie±iϕensures that the transfor-mation is unitary.Typically,we choose eitherϕ=0or ϕ=π/2.Mathematically,the two parametersθandϕrepresent the angles of a rotation about two orthogonal axes in the Poincar´e sphere.The physical beam splitter can be described by any choice ofθandϕ,provided the correct phase shifts are applied to the outgoing modes. In general the Hamiltonian H BS of the beam splitter evolution in Eq.(4)is given byH BS=θe iϕˆa†inˆb in+θe−iϕˆa inˆb†in.(5) Since the operator H BS commutes with the total number operator,[H BS,ˆn]=0,the photon number is conserved in the lossless beam splitter,as one would expect.The same mathematical description applies to the evolution due to a polarisation rotation,physically im-plemented by quarter-and half-wave plates.Instead of having two different spatial modes a in and b in,the two incoming modes have different polarisations.We write ˆa in→ˆa x andˆb in→ˆa y for some orthogonal set of coor-dinates x and y(i.e., x|y =0).The parametersθandϕare now angles of rotation:ˆa†x′=cosθˆa†x+ie−iϕsinθˆa†y,ˆa†y′=ie iϕsinθˆa†x+cosθˆa†y.(6) This evolution has the same Hamiltonian as the beam splitter,and it formalises the equivalence between the so-called polarisation and dual-rail logic.These trans-formations are sufﬁcient to implement any photonic single-qubit operation(Simon and Mukunda1990). The last linear optical element that we highlight here is the polarising beam splitter(PBS).In circuit diagrams,5of choice is usually taken to be a single photon that has the choice of two different modes|0 L=|1 ⊗|0 ≡|1,0 and|1 L=|0 ⊗|1 ≡|0,1 .This is calleda dual-rail qubit.When the two modes represent the internal polarisation degree of freedom of the photon (|0 L=|H and|1 L=|V ),we speak of a polari-sation qubit.In this review we will reserve the term “dual rail”for a qubit with two spatial modes.As we showed earlier,these two representations are mathe-matically equivalent,and we can physically switch be-tween them using polarisation beam splitters.In addi-tion,some practical applications(typically involving a dephasing channel such as aﬁbre)may call for so-called time-bin qubits,in which the two computational qubit values are“early”and“late”arrival times in a detec-tor.However,this degree of freedom does not exhibit a natural internal SU(2)symmetry:Arbitrary single-qubit operations are very difﬁcult to implement.In this review we will be concerned mainly with polarisation and dual-rail qubits.In order to build a quantum computer,we need both single-qubit operations as well as two-qubit operations. Single-qubit operations are generated by the Pauli op-eratorsσx,σy,andσz,in the sense that the operator exp(iθσj)is a rotation about the j-axis in the Bloch sphere with angleθ.As we have seen,these operations can be implemented with phase shifters,beam splitters, and polarisation rotations on polarisation and dual-rail qubits.In this review,we will use the convention that σx,σy,andσz denote physical processes,while we use X,Y,and Z for the corresponding logical operations on the qubit.These two representations become inequiva-lent when we deal with logical qubits that are encoded in multiple physical qubits.Whereas single-qubit operations are straightforward in the polarisation and dual-rail representation,the two-qubit gates are more problematic.Consider,for exam-ple,the transformation from a state in the computational basis to a maximally entangled Bell state:|H,H ab→12(|H,V cd+|V,H cd).(13)This is the type of transformation that requires a two-qubit gate.In terms of the creation operators(and ig-noring normalisation),the linear optical circuit that is supposed to create Bell states out of computational ba-sis states is described by a Bogoliubov transformation of both creation operatorsˆa†Hˆb†H→ ∑k=H,Vαkˆc†k+βkˆd†k ∑k=H,Vγkˆc†k+δkˆd†k =ˆc†Hˆd†V+ˆc†Vˆd†H.(14)It is immediately clear that the right-hand sides in both lines cannot be made the same for any choice ofαk,βk,γk,andδk:The top line is a separable expression in the creation operators,while the bottom line is an entangled expression in the creation operators.Therefore,linear optics alone cannot create maximal polarisation entan-glement from single polarised photons in a determinis-tic manner(Kok and Braunstein2000a).Entanglement that is generated by changing the deﬁnition of our sub-systems in terms of the globalﬁeld modes is inequiv-alent to the entanglement that is generated by apply-ing true two-qubit gates to single-photon polarisation or dual-rail qubits.Note also that if we choose our representation of the qubit differently,we can implement a two-qubit transformation.Consider the single-rail qubit encoding |0 L=|0 and|1 L=|1 .That is,the qubit is given by the vacuum and the single-photon state.We can then implement the following(unnormalised)transfor-mation deterministically:|1,0 →|1,0 +|0,1 .(15) This is a50:50beam splitter transformation.However, in this representation the single-qubit operations cannot be implemented deterministically with linear optical el-ements,since these transformations do not preserve the photon number(Paris2000).This implies that we can-not implement single-qubit and two-qubit gates deter-ministically for the same physical representation.For linear optical quantum computing,we typically need the ability to(dis-)entangleﬁeld modes.We therefore have to add a non-linear component to our scheme.Two possible approaches are the use of Kerr nonlinearities, which we brieﬂy review in the next section,and the use of projective measurements.In the rest of this review,we concentrate mainly on linear optical quantum comput-ing with projective measurements,based on the work by Knill,Laﬂamme,and Milburn.Finally,in order to make a quantum computer with light that can outperform any classical computer,we need to understand more about the criteria that make quantum computers“quantum”.For example,some simple schemes in quantum communication require only superpositions of quantum states to distinguish them from their corresponding classical ones.However, we know that this is not sufﬁcient for general computa-tional tasks.First,we give two deﬁnitions.The Pauli group P is the set of Pauli operators with coefﬁcients {±1,±i}.For instance,the Pauli group for one qubit is{11,±X,±Y,±Z,±i11±iX,±iY,±iZ,}where11is the identity matrix.The Pauli group for n qubits consists of elements that are products of n Pauli operators,in-cluding the identity.In addition,we deﬁne the Clifford group C of transformations that leave the Pauli group in-variant.In other words,for any element of the Clifford group c and any element of the Pauli group p,we havecpc†=p′with p′∈P.(16) Prominent members of the Clifford group are the Hadamard transformation,phase transformations,and8can be achieved with a single two-level atom in a one-sided cavity.The cavity effectively enhances the tiny nonlinearity of the atom.The losses in this system are negligible.In sectionVI we will return to systems in which (small)phase shiftscanbe generated using nonlinear optical interactions,but the principal subject of this re-view is how projective measurements can induce enough of a nonlinearity to make linear optical quantum com-puting possible.II.A NEW PARADIGM FOR OPTICAL QUANTUM COMPUTINGIn 2000,Knill,Laﬂamme,and Milburn proved that it is indeed possible to create universal quantum computers with linear optics,single photons,and photon detection (Knill et al.2001).They constructed an explicit protocol,involving off-line resources,quantum teleportation,and error correction.In this section,we will describe this new paradigm,which has become known as the KLM scheme ,starting from the description of linear optics that we developed in the previous section.In sections II.A,II.B and II.C,we introduce some elementary probabilis-tic gates and their experimental realizations,followed by a characterisation of gates in section II.D,and a gen-eral discussion on nonlinear unitary gates with projec-tive measurements in section II.E.We then describe how to teleport these gates into an optical computational cir-cuit in sections II.F and II.G,and the necessary error correction is outlined in section II.H.Recently,Myers and Laﬂamme (2005)published a tutorial on the origi-nal “KLM theory.”A.Elementary gatesPhysically,the reason why we cannot construct deter-ministic two-qubit gates in the polarisation and dual-rail representation,is that photons do not interact with each other.The only way in which photons can directly in-ﬂuence each other is via the bosonic symmetry relation.Indeed,linear optical quantum computing exploits ex-actly this property,i.e.,the bosonic commutation rela-tion [ˆa,ˆa †]=1.To see what we mean by this statement,consider two photons in separate spatial modes inter-acting on a 50:50beam splitter.The transformation will be|1,1 ab =ˆa †ˆb †|0 →12ˆc †2−ˆd †2 |0 cd =12(|2,0 cd −|0,2 cd ).(22)It is clear (from the second and third line)that the bosonic nature of the electromagnetic ﬁeld gives rise toCZ |0 |0,0|1 |0,1 |1|1,0|1 |1,0(24)which is identical to|q 1,q 2 →CZ (−1)q 1q 2|q 1,q 2 (25a)|q 1,q 2→CNOT|q 1,q 2⊕q 1 .(25b)FIG.7The nonlinear sign (NS)gate according to Knill,Laﬂamme and Milburn.The beam splitter transmission am-plitudes are η1=η3=1/(4−2√2.2,then the output state isa maximally entangled state.The overall probability of this CZ gate p CZ =p 2NS .It is immediately clear that we cannot make the NS gate with a regular phase shifter,because only the state |2 picks up a phase.A linear optical phase shifter would also induce a factor i (or −i )in the state |1 .How-ever,it is possible to perform the NS-gate probabilistically using projective measurements.The fact that two NS gates can be used to create a CZ gate was ﬁrst realized by Knill,Laﬂamme,and Milburn (2001).Their proba-bilistic NS gate is a 3-port device,including two ancil-lary modes the output of which is measured with perfect photon-number discriminating detectors (see Fig.7).The input states for the ancillæare the vacuum and a single-photon,and the gate succeeds when the detec-tors D 1and D 2measure zero and one photons,respec-tively.For an arbitrary input state α|0 +β|1 +γ|2 ,this occurs with probability p NS =1/4.The gen-eral upper bound for such gates was found to be 1/2(Knill 2003).Without any feed-forward mechanism,the success probability of the NS gate cannot exceed 1/4.It was shown numerically by Scheel and L ¨utkenhaus (2004)and proved analytically by Eisert (2005)that,in general,the NS N gate deﬁned byN∑k =0c k |k→NS NN −1∑k =0c k |k −c N |N (28)can be implemented with probability 1/N 2[see alsoScheel and Audenaert (2005)].Several simpliﬁcations of the NS gate were reported shortly after the original KLM proposal.First,a 3-port NS gate with only marginally lower success probability p ′NS =(3−√√√Detecting no photons in the ﬁrst output port yieldsα+βcos σˆa †H +γ2cos 2σˆa †2H ˆb †V |0 ,after which we apply the second polarisation rotation:ˆaH →cos θˆa H +sin θˆa V and ˆa V →−sin θˆa H +cos θˆa V .This gives the output stateα+βcos σ cos θˆa†H +sin θˆa †V +γ2cos 2σ cos θˆa †H +sin θˆa †V 2 −sin θˆa †H +cos θˆa †V |0 .After detecting a single vertically polarised photon in the second output port,we have|ψout =αcos θ|0 +βcos σcos 2θ|1 +γcos 2σcos θ(1−sin 23θ)|2 .When we choose σ≃150.5◦and θ≃61.5◦,thisyields the NS gate with the same probability cos 2θ=(3−√ing pulsed parametric down conversion.The target qubit is generated by an attenuated laser pulse where the pulse is branched off the pump laser.The pulse is converted by a frequency doubler to generate entangled photon pairs at the same frequency as the photon con-stituting the target qubit.The CNOT gate is then im-plemented as follows:The action of the polarising beam splitters on the control,target and ancilla qubits trans-forms them according to|ψ out∝|H a U C|ψ in+|V a U C|ψ in+√3(that is,a beam splitter with a reﬂec-tivity of3313are introduced in one of the control and target modes.The gate works as follows:If the control qubit is in the state where the photon occupies the top mode c0there is no interaction between the control and the target qubit.On the other hand,when the control photon is in the lower mode, the control and target photons interfere non-classically√at the central beam splitter with cosθ2=1/FIG.16Schematic diagram of the four-photon CNOT gate by Gasparoni et al.(2004).A parametric down conversion source is used to create the control and target input qubits in the spa-tial modes a1and a2,as well as a maximally entangled ancilla pair in the spatial modes a3and a4.Polarisingﬁlters(Pol)can be used to destroy the initial entanglement in a1and a2if nec-essary.15When we deﬁne d (ρ)≡TrQAU (ρ⊗σ)U †P k ,we ﬁnd that M is unitary if and only if d (ρ)is independent of ρ.We can then construct a test operator ˆT=TrA σU †P k U .The induced operation on the qubits in HQ is then uni-tary if and only if ˆTis proportional to the identity,or ˆT =Tr A σU †P k U ∝11⇔d (ρ)=d .(33)Given the auxiliary input state σ,the N port transforma-tion U and the projective measurement Pk ,it is straight-forward to check whether this condition holds.The suc-cess probability of the gate is given by d .In Eq.(32),the projective measurement was in fact aprojection operator (P 2k =P k).However,in general,we might want to include generalised measurements,commonly known as Positive Operator-Valued Mea-sures,or POVMs.These are particularly useful when we need to distinguish between nonorthogonal states,and they can be implemented with N ports as well (Myers and Brandt 1997).Other optical realizations of non-unitary transformations were studied by Bergou et al.(2000).The inability to perform a deterministic two-qubit gate such as the CNOT with linear optics alone is inti-mately related to the impossibility of complete Bell mea-surements with linear optics (L ¨utkenhaus et al.1999;Vaidman and Yoran 1999;Calsamiglia 2002).Since quantum computing can be cast into the shape of single-qubit operations and two-qubit projections (Nielsen 2003;Leung 2004),we can approach the prob-lem of making nonlinear gates via complete discrimina-tion of multi-qubit bases.Van Loock and L ¨utkenhaus gave straightfor-ward criteria for the implementation of com-plete projective measurements with linear optics (van Loock and L ¨utkenhaus 2004).Suppose the basis states we want to identify without ambiguity are given by {|s k },and the auxiliary state is given by |ψaux .Applying the unitary N port transformation yields the state |χk .If the outgoing optical modes are denoted bya j ,with corresponding annihilation operators ˆaj ,then the set of conditions that have to be fulﬁlled for {|χk }to be completely distinguishable areχk |ˆa †j ˆaj |χl =0∀jχk |ˆa †j ˆa j ˆa †j ′ˆa j′|χl =0∀j ,j ′χk |ˆa †j ˆa j ˆa †j ′ˆa j ′ˆa †j ′′ˆa j′′|χl =0∀j ,j ′,j ′′......(34)Furthermore,when we keep the speciﬁc optical im-plementation in mind,we can use intuitive physicalprinciples such as photon number conservation and group-theoretical techniques such as the decomposition of U (N )into smaller groups.This gives us an insight into how the auxiliary states and the photon detection affects the (undetected)signal state (Scheel et al.2003).16that uses N such gates succeeds with probability p N. For large N and small p,this probability is minuscule.As a consequence,we have to repeat the calculation on the order of p−N times,or run p−N such systems in par-allel.Either way,the resources(time or circuits)scaleexponentially with the number of gates.Any advantage that quantum algorithms might have over classical pro-tocols is thus squandered on retrials or on the amount of hardware we need.In order to do useful quantum computing with probabilistic gates,we have to take the probabilistic elements out of the running calculation.In1999,Gottesman and Chuang proposed a trick thatremoves the probabilistic gate from the quantum circuit, and places it in the resources that can be prepared off-line(Gottesman and Chuang1999).It is commonly re-ferred to as the teleportation trick,since it“teleports the gate into the quantum circuit.”Suppose we need to apply a probabilistic CZ gate to two qubits with quantum states|φ1 and|φ2 respec-tively.If we apply the gate directly to the qubits,we are very likely to destroy the qubits(see Fig.20).However, suppose that we teleport both qubits from their initial mode to a different mode.For one qubit,this is shown in Fig.21.Here,x and z are binary variables,denoting the outcome of the Bell measurement,which determine the unitary transformation that we need to apply to the output mode.If x=1,we need to apply theσx Pauli op-erator(denoted by X),and if z=1,we need to applyσz (denoted by Z).If x,z=0we do not apply the respec-tive operator.For teleportation to work,we also need the entangled resource|Φ+ ,which can be prepared off-line.If we have a suitable storage device,we do not have to make|Φ+ on demand:we can create it with a proba-bilistic protocol using several trials,and store the output of a successful event in the storage device.When we apply the probabilistic CZ gate to the out-put of the two teleportation circuits,we effectively have again the situation depicted in Fig.20,except that now our circuit is much more complicated.Since the CZ gate is part of the Clifford group,we can commute it through the Pauli operators X and Z at the cost of more Pauli operators.This is good news,because that means we can move the CZ gate from the right to the left, and only incur the optically available single-qubit Pauli gates.Instead of preparing two entangled quantum channels|Φ+ ,we now have to prepare the resource 11⊗U CZ⊗11|Φ+ ⊗|Φ+ (see Fig.22).Again,with a suitable storage device,this can be done off-line with a probabilistic protocol.There are now no longer any probabilistic elements in the computational circuit.G.The Knill-Laﬂamme-Milburn protocol Unfortunately,there is a problem with the teleporta-tion trick when applied to linear optics:In our qubit representation the Bell measurement(which is essential to quantum teleportation)is not complete,andworksn+1n∑j=0|1 j|0 n−j|0 j|1 n−j,(35)where|k j≡|k 1⊗...⊗|k j.We can then teleport the stateα|0 +β|1 by applying an n+1-point discrete quantum Fourier transform(QFT)to the input mode and theﬁrst n modes of|t n ,and count the number of photons m in the output mode.The input state will then be teleported to mode n+m of the quantum channel (see Fig.23).The discrete quantum Fourier transform F n can be written in matrix notation as:(F n)jk=1nexp 2πi(j−1)(k−1)1718and the one-photon state is replaced with a vertically polarised photon,|1 →|V .There are now2n rather than n photons in the state|t n .The teleportation pro-cedure remains the same,except that we now count the total number of vertically polarised photons.The ad-vantage of this approach is that we know that we should detect exactly n photons.If we detect m=n photons, we know that something went wrong,and this therefore provides us with a level of error detection(see also section V).Of course,having a near-deterministic two-qubit gate is all very well,but if we want to do arbitrarily long quantum computations,the success probability of the gates must be close to one.Instead of making larger teleportation networks,it might be more cost effective or easier to use a form of error correction to make the gates deterministic.This is the subject of the next sec-tion.H.Error correction of the probabilistic gatesAs we saw in the previous section the probability of success of teleportation gates can be increased arbitrar-ily by preparing larger entangled states.However the asymptotic behaviour to unit probability is quite slow as a function of n.A more efﬁcient procedure is to encode against gate failure.This is possible because of the well-deﬁned failure mode of the teleporters.We noted in the previous section that the teleporters fail if zero or n+1 photons are detected because we can then infer the log-ical state of the input qubit.In other words the failure mode of the teleporters is to measure the logical value of the input qubit.If we can encode against accidental measurements of this type then our qubit will be able to survive gate failures and the probability of eventually succeeding in applying the gate will be increased. KLM introduced the following logical encoding over two polarisation qubits:|0 L=|HH +|VV|1 L=|HV +|VH (38)This is referred to as parity encoding as the logical zero state is an equal superposition of the even parity states and the logical one state is an equal superposition of the odd parity states.Consider an arbitrary logical qubit:α|0 L+β|1 L.Suppose a measurement is made on one of the physical qubits returning the result H.The effect on the logical qubit is the projection:α|0 L+β|1 L→α|H +β|V (39)That is,the qubit is not lost,the encoding is just reduced from parity to polarisation.Similarly if the measure-ment result is V we have:α|0 L+β|1 L→α|V +β|H (40)Again the superposition is preserved,but this time a bit-ﬂip occurs.However,the bit-ﬂip is heralded by the mea-surement result and can therefore be corrected. Suppose we wish to teleport the logical value of a par-ity qubit with the t1teleporter.We attempt to teleport one of the polarisation qubits.If we succeed we mea-sure the value of the remaining polarisation qubit and apply any necessary correction to the teleported qubit. If we fail we can use the result of the teleporter failure (did weﬁnd zero photons or two photons?)to correct the remaining polarisation qubit.We are then able to try again.In this way the probability of success of teleporta-tion is increased from1/2to3/4.At this point we have lost our encoding in the process of teleporting.How-ever,this can beﬁxed by introducing the following en-tanglement resource:|H |0 L+|V |1 L(41) If teleportation is successful,the output state remains encoded.The main observation is that the resources re-quired to construct the entangled state of Eq.(41)are much less than those required to construct|t3 .As a re-sult,error encoding turns out to be a more efﬁcient way to scale up teleportation and hence gate success.Parity encoding of an arbitrary polarisation qubit can be achieved by performing a CNOT gate between the arbitrary qubit and an ancilla qubit prepared in the di-agonal state,where the arbitrary qubit is the target and the ancilla qubit is the control.This operation has been demonstrated experimentally(O’Brien et al.2005).In this experiment the projections given by Eqs.(39)and (40)were conﬁrmed up toﬁdelities of96%.In a subse-quent experiment by Pittman et al.,the parity encoding was prepared in a somewhat different manner and,in order to correct the bit-ﬂip errors,a feed-forward mech-anism was implemented(Pittman et al.2005).To boost the probability of success further,we need to increase the size of the code.The approach adopted by Knill,Laﬂamme and Milburn(2001)was to concatenate the code.At theﬁrst level of concatenation the parity code states become:|0 (4)L=|00 L+|11 L|1 (4)L=|01 L+|10 L(42) This is now a four-photon encoded state.At the second level of concatenation we would obtain an eight-photon state etc.At each higher level of concatenation,cor-responding encoded teleportation circuits can be con-structed that operate with higher and higher probabil-ities of success.If we are to use encoded qubits we must consider a universal set of gates on the logical qubits.An arbi-trary rotation about the x-axis,deﬁned by the opera-tion Xθ=cos(θ/2)I−i sin(θ/2)X,is implemented on a logical qubit by simply implementing it on one of the constituent polarisation qubits.However,to achieve ar-。

The BeppoSAX spectrum of the composite galaxy Mrk609

a r X i v :a s t r o -p h /0204514v 1 30 A p r 2002Mon.Not.R.Astron.Soc.000,000–000(0000)Printed 1February 2008(MN L A T E X style ﬁle v1.4)The BeppoSAX spectrum of the composite galaxy Mrk609A.Pappa 1,2,I.Georgantopoulos 3,M.Ward 1,A.L.Zezas 41Departmentof Physics and Astronomy,University of Leicester,Leicester,LE17RH,UK1Institute for Astronomy,University of Edinburgh,Royal Observatory,Blackford Hill,Edinburgh EH93HJ,UK3Institute of Astronomy &Astrophysics,National Observatory of Athens,Lofos Koufou,Palaia Penteli,15236,Athens,Greece 4Harvard-Smithsonian Center for Astrophysics,60Gardes St.,Cambridge,MA 02138,USA1February 2008ABSTRACTWe present BeppoSAX observations of the starburst/Seyfert composite galaxy Mrk609.This enigmatic object has an optical spectrum dominated by the features of starburst galaxies,yet its X-ray luminosity (6.3×1042erg s −1)is typical of an AGN.The X-ray spectrum of Mrk609can be parameterised by a single power-law model with a photon index Γ∼1.6±0.1and no evidence for signiﬁcant absorption above the Galactic value.Long term variability in both the 0.1-2keV and 2-10keV energy bands is detected,again suggesting that the X-ray emission is dominated by an AGN.The observed broad Ha component is a factor of 40below that predicted by the X-ray ﬂux implying a deﬁcit of ionizing UV photons.Key words:galaxies:AGN –galaxies:starburst -X-rays:galaxies1INTRODUCTIONMoran,Halpern &Helfand (1996),after careful spectroscopy of a sample based on the cross-correlation of the IRAS PSC and ROSAT All Sky Survey,reported the discovery of an “anomalous”class of objects.The optical spectra of these sources are dominated by the features of starburst galaxies,based on the emission line diagnostic diagrams (Veilleux &Osterbrock 1987),yet their X-ray luminosities are typical of Seyfert 2galaxies.Close examination of their optical spectra reveals some weak Seyfert-like features:[OIII]signiﬁcantly broader than all other narrow lines in the spectrum and in some cases a weak broad H αcomponent.The authors desig-nated these objects “starburst/Seyfert composite”galaxies and presented them as a new class of X-ray luminous source.Similar ”composite”objects have also been noticed by Veron et al.(1997).Indeed,they presented observations of 15ob-jects with transition spectra ie showing the simultaneous presence of a strong star-forming component and an active nucleus and they showed that fall either on the starburst region or on the borderlines between the diﬀerent classes.Hereafter,we will refer to these objects as composite galax-ies and we will distinguish them from the Sy2/Starburst galaxies that show emission from both components at all wavelengths.The composite galaxies bear close resemblance to the narrow-line X-ray galaxies (NLXGs)detected in large num-bers in deep ROSAT surveys (eg Boyle et al.1995,Griﬃths et al.1996).These NLXGs again have spectra composite of Seyfert and starburst galaxies (Boyle et al.1995)with lumi-nosities L 2−10keV ∼1042−43erg s −1.Unfortunately the faintﬂuxes of these NLXGs do not allow their detailed study in either optical or X-ray wavelengths.Although it is unclear whether these nearby “composites”are the same class of ob-jects as those found in ROSAT deep ﬁeld NLXGs,their high luminosities need to be explained.It is unclear how their in-tense X-ray emission can be reconciled with weak or absent Seyfert characteristics.1.1Composite galaxies in X-raysOnly a few composite galaxies have been studied so far in X-rays.Speciﬁcally,IRAS00317-2142(Georgantopoulos 2000)has been observed with ASCA and is the most luminous object (L x =∼1043erg s −1in the 0.1-2keV band)in the Moran et al.(1996)sample.The spectrum is represented by a power-law with Γ∼1.76and there is no evidence for absorption above the Galactic value.Strong variability in the 1-2keV band (by a factor of three)is detected between the ROSAT and ASCA observations.These characteristics indicate an AGN origin for the X-ray emission.However no iron line is detected and the 90per cent upper limit on the equivalent width is 0.9keV.The ratio f HX /f [OIII ]∼2.5rule out the Compton thick interpretation for IRAS00317-2142.However,the precise nature of this object and the relative contribution of the starburst and AGN components could not be determined.A further composite object studied in X-rays with ROSAT and ASCA is AXJ1749+684(Iwasawa et al.1997).AXJ1749+684was serendipitously detected with the ASCAc0000RAS2 A.Pappa,I.Georgantopoulos,M.Ward and A.L.ZezasGIS.Its X-ray spectrum isﬂat(Γ=1.23+0.21−0.27).Theﬂat-ness is attributed by the authors to absorption mainly be-cause of the:(a)large Balmer decrement in the narrow line region,Hα/Hβ=7.32and(b)lack of signiﬁcant X-ray de-tection at<0.4keV.On the other hand,the optical coun-terpart of AXJ1749+684is detected in the Kiso Schmidt Survey of UV-excess galaxies.Iwasawa et al.(1997)claimed that the UV emission is due to large-scale starburst activ-ity,however in this case strong far infrared emission should be expected,which is inconsistent with the non-detection of this source by IRAS.They concluded that the X-ray spectrum of AXJ1749+684is wellﬁtted by an obscured(N H=2.1+6.2−2.1×1021cm−2)Seyfert nucleus embeddedwithin a star-forming galaxy.Recently Levenson et al.2001,examined NGC6221as a further example of a composite galaxy.They proposed that the X-ray spectrum of this object is characterised by a Seyfert1like spectrum.They detect an iron line and con-tinuum variability on short-and long-term timescales.The source has a column density of N H=1022cm−2.They pro-posed that the central region is obscured by a surrounding starburst.Thus the optical spectrum has the characteristics of the starburst component alone.1.2Mrk609Mrk609is at a redshift of0.034.The optical position of the object is032525.3,-060839(J2000)and the Galactic absorption is N H=4.41×1020cm−2.The Hβproﬁle is∼110 km sec−1wide,while the[OIII]lines are∼4times wider.In addition,the broad blueshifted wings seen on the[OIII]lines are completely missing in Hβ(Heckman et al.1981).The UV spectrum show strong contribution from hot stars(Rudy et al.1988)indicating the presence of an intense starburst component in Mrk609.The broad Hα/Hβvalue is7.8(Osterbrock1981).In a later observation,Rudy et al.(1988)obtained a value for the broad Hα/Hβ=5.The discrepancy was attributed to continuum variability.The high broad Hα/Hβvalue was attributed by Osterbrock1981to reddening of the broad line region.However the broad Lyα/Hβvalue is16,which is large for Seyfert1galaxies,ruling out obscuration(see Rudy et al.1988for a detailed discussion).2OBSER V ATIONS AND DATA REDUCTION Mrk609was observed by BeppoSAX three times.Theﬁrst observation was carried out on20/01/2000for∼18ksec (LECS exposure7.13ksec),the second one on14/02/2000 for∼2.5ksec(LECS exposure1.4ksec)and the third one on4/03/2000for∼28ksec(LECS exposure6668ksec).It should be reminded here,that the exposure time for the LECS is lower than the MECS because it is limited by stronger operational constraints to avoid UV light contam-ination,thus it is operated during Earth dark time only. Spectra and light curves of Mrk609have been extracted from circular regions centered on the source.We used a circular extraction cell of4and6arcminutes in radius for MECS and LECS data respectively.The background spectra were extracted from blank deepﬁeld exposures,using the same region of the detector in each case.Table1.χ2for the long-term light curves.0.1-2keV8.16(2) 1.7×10−22-5keV30.08(2) 2.9×10−75-10keV 2.76(2)0.432-10keV45(2) 1.4×10−10BeppoSAX spectrum of Mrk6093(a)(b)(c)(d)Figure 1.The long term light curves for Mrk609;(a)the 0.1-2keV,(b)2-5keV,(c)5-10keV,(d)2-10keV curves.spectral ﬁtting results is given in Table 2.In the following analysis all three BeppoSAX observations are ﬁtted together.Throughout this paper values of H o =75km s −1Mpc −1and q o =0.5are assumed.4.1The AGN modelsWe ﬁrst ﬁt the data with a single power-law model (PL).We obtain an acceptable ﬁt (χ2=98.89for 82dof)with Γ=1.57+0.10−0.10,and N H ≤1.32×1021cm−2.This model together with the data points and the data to model ratio are plotted in Figure 2.The observed ﬂux in the 2-10keV band for this model is 2.86×10−12erg s −1cm −2,which corresponds to aluminosity of 6.3×1042erg s −1in the same band.If the slope of the power-law model is ﬁxed at the 1.9value,the nominal value for the Seyfert 1galaxies (Nandra &Pounds 1994),the model yields an unacceptable ﬁt (χ2=119.26for 83dof)with N H =2.03+1.5−1.8×1021cm −2.Although Seyfert galaxies show strong narrow iron K αemission lines,no such line is detected in Mrk609.However an upper limit of ∼283eV is obtained,consistent with values seen in Seyfert galaxies.In the context of the uniﬁed models we expect to see some faction of the primary emission through the torus,with a component superimposed upon this that represents a fraction of emission scattered back into our line of sight byc0000RAS,MNRAS 000,000–0004 A.Pappa,I.Georgantopoulos,M.Ward and A.L.ZezasFigure2.The BeppoSAX time averaged spectrum,when the single power-law model is applied to the data.Theﬁlled squares represent the LECS data points and the stars the MECS data points.The top panel shows the data with the model and the bottom panel shows the data/model ratiomaterial lying above the torus.This model is representingby two power-laws with the same photon index but diﬀer-ent normalisations and absorptions-the scattering model.When this model is applied to the data,the normalisationsof the two power-laws are comparable,whereas no excess ab-sorption above the Galactic is required and thus this modeleﬀectively is the same as the single power-law model.There-fore it is evident that the scattering model does not providea good representation of the data.Finally,an ionised warm absorber model in additionto the Galactic column density wasﬁtted to the data(PL+warm).The temperature of the absorber isﬁxed atT=105K(Brandt et al.1999).The model provides an ac-ceptableﬁt(χ2=98.84for81dof)but does not represent astatistically signiﬁcant improvement to the single power-lawmodel.The bestﬁt parameters areΓ=1.60+0.16−0.12and warmcolumn density N H w=6.73+25.47−6.73×1021cm−2,while theionisation parameter is practically unconstrained,possiblybecause of the poor statistics of the data.4.2The composite modelGiven the composite classiﬁcation of this object,it is nat-ural to investigate a model in which X-ray emission origi-nates from both a starburst and an AGN.A power-law plusa Raymond-Smith model(PL+RS)with the temperatureﬁxed at0.8keV is adopted.The power-law component isallowed to have additional absorption over and above thatof the thermal component.This model yields an acceptableﬁt(χ2=99.81for81dof)withΓ=1.57+0.09−0.11,whereas noexcess absorption above the Galactic is required.When thetemperature of the thermal component is a free parameter,weﬁnd kT>18keV andΓ=2.81+2.59−0.96(χ2=95.00for80dof).However,the temperature of the thermal componentis far too high for a starburst and thus this model cannotprovide a physical description of the data.4.3The pure starburst modelFor completeness we have also investigated pure starburstmodels.Firstly a single Raymond-Smith model(RS)wasﬁt-ted to the data.An acceptableﬁt was obtained(χ2=108.94for83dof)with kT1=18.92+10.15−6.02keV.No starbursts withsuch a high temperature have been found as yet.Then a two Raymond-Smith model representing ther-mal emission from a pure starburst galaxy following Zezaset al.(1998)was utilised.The soft emission is parameterisedby a thermal component with kT1≤1keV and the emissionin the hard band by kT2=21.8+14.33−7.69keV,again too high fora starburst.Therefore it is obvious that this model cannotprovide a physical description of the data.From the above it is evident that the pure starburstmodel is ruled out,whereas the composite model does notprovide a physically accepted model.5SPECTRAL V ARIABILITYMrk609was observed three times with BeppoSAX,allow-ing us to examine whether there is spectral variability.Inparticular it is interesting to see whether the drop in theﬂux during the second observation is related to a change inthe spectrum of Mrk609and examine whether the X-ray be-haviour is similar to that of black hole candidates(BHC)inour galaxy during their high and low states.For this analysisonly the single power-law is applied to the MECS data.In addition any spectral variability at soft energies willbe examined by comparing the ROSAT PSPC and LECSc 0000RAS,MNRAS000,000–000BeppoSAX spectrum of Mrk6095 Table2.The spectralﬁts results on the BeppoSAX data.single PL1.57+0.10−0.10≤1.32---98.89(82)1.9f2.03+1.53−0.98119.26(83)PL+warm1.60+0.16−0.12g≤369.11≥0-97.90(81)PL+RS1.57+0.09−0.11g--0.8f99.00(81)RS-g--18.92+10.05−6.02108.94(83)2RS-g--≤1105.57(80)21.81+14.33−7.696 A.Pappa,I.Georgantopoulos,M.Ward and A.L.Zezasmodel NGC6221is a Seyfert1galaxy which is surrounded by a starburst component.The starburst accounts for the X-ray obscuration(N H∼1022)cm−2and its characteristics dominate the optical spectrum.Although in principal this model can explain qualitatively the optical appearance of the composite galaxies it doesn’t seem toﬁt the X-ray ob-servations of Mrk609.Our object does not show concrete ev-idence for signiﬁcant X-ray absorption.In addition the soft X-ray variability and the high luminosity at low energies (L0.5−2keV∼2×1042erg s−1)probably rule out a dusty ob-scuring circumnuclear starburst.We note here that the spec-tral X-ray properties of Mrk609are similar to the composite IRAS00317-2142(Georgantopoulos et al.2000).Again this galaxy has a low column density,consistent with the Galac-tic,and thus the obscuring starburst model cannot explain the properties of IRAS00317-2142.Although the single power-law model yields a good rep-resentation of the Mrk609spectrum the X-ray long term variability indicates that the spectrum of Mrk609consists of more than one components.An AGN covered by a warm ab-sorbing screen could provide an explanation for the observed long term variability.In this case changes in the X-ray con-tinuumﬂux,will be followed by changes in the ionisation state of the warm absorber resulting in changes in the emis-sion in the soft band.However,the quality of the data does not allow to examine the viability of the model to Mrk609.Given the composite nature of Mrk609it is natural to investigate whether emission from starburst regions con-tribute to the X-ray wavelengths.In principle,in a compos-ite starburst-AGN model,the power-law component is heav-ily absorbed,and thus the star-forming component,which is located outside the obscuring screen,dominates the soft emission.However,when this model is applied to Mrk609 data,no excess absorption above the Galactic is required by the data for the power-law component.In addition the poor quality of the data at energies below∼2keV do not allow us to constrain the temperature of the thermal emission and make an unambiguous estimate of the starburst contribu-tion to the X-ray emission.The strength of the star-forming component can be indirectly estimated from the observed IRﬂux.The expected X-ray contribution from stars was calculated using the empirical relationship between infrared and X-ray luminosity(equation[2]David,Jones&Forman 1992)found in a sample of IRAS galaxies.However,note that some of the infrared(IR)ﬂux could arise from nuclear reprocessed emission from the obscuring medium.Thus any starburst contribution to the X-rayﬂux derived using the above relation may be overestimated and the derivedﬂux should only be treated as an upper limit.First we calcu-lated the IR luminosities using theﬂuxes IRASﬂuxes at 60µm and100µm and equation[1]from David,Jones et al. 1992.Weﬁnd that the upper limit of the expected contribu-tion of a starburst in the0.5-4keV band is2.75×1042erg s−1. The luminosity in the same band derived by the spectral ﬁtting is∼4.7×1042erg s−1,indicating that about half of the soft emission may be due to an intense starburst com-ponent.However,the variable soft X-ray emission clearly argues that any starburst contribution in soft energy band should be low.To further test the AGN interpretation of Mrk609 the broad Hαline and the2-10keVﬂux were compared. Ward et al.(1988)found a strong correlation between the two quantities in a sample of IRAS selected Seyfert 1galaxies.The observed luminosity of the broad Hαis L(Hα)=8.4×1039erg s−1,whereas the2-10keV luminosity is ∼7.5×1042erg s−1.According to the above relation the pre-dicted broad Hαluminosity should be∼40times higher.The above discrepancy between the optical and X-ray spectrum could be explained by variability.Possibly the AGN was weaker during the optical observation(1984),but bright-ened over the∼15years timescale between the optical and X-ray observations.Alternatively the source may have un-usually low UV emission.Then the photoionised emission lines would have lowerﬂuxes than those typical for AGNs. To examine this possibility the Mrk609spectral energy dis-tribution(SED)was computed.This is shown in Figure3. It is indeed clear that Mrk609lacks a big blue bump(BBB). This feature is characteristic of high luminosity unobscured AGNs and is thought to be a signature of the presence of a cold accretion disk around the black hole(see Koratkar &Blaes1999).We note here that lack of ultraviolet ex-cess has also been observed in a sample of low-luminosity AGN(Ho1999).Low accretion rate models have been em-ployed to account for the absence of the BBB feature.Note that Mrk609has a very strong Lyαline(Rudy et al.1988). The abnormally strong Lyαline and anomalous emission line strengths in Mrk609could be explained if the optical depth and ionisation parameter in the region where the lines form is signiﬁcantly less than believed typical for Seyfert-1 galaxies.In this scenario the discrepancy between the op-tical and X-ray spectrum could be ing Paβspectroscopy Goodrich(1990)and Rix et al.(1990)showed that Mrk609line properties are indeed well explained by the optical depth/ionisation parameter theory.As mentioned in the introduction the optical spectrum of the composite objects like Mrk609bear close resemblance to the narrow line X-ray galaxies detected in ROSAT sur-veys.The X-ray spectrum of these sources isﬂat(Almaini et al.1996)but it is unclear whether theﬂatness of the spectrum is intrinsic or due to obscuration.On the other hand,our observations show that Mrk609has a relatively steep X-ray spectrum and no signiﬁcant X-ray absorption. If the narrow line X-ray galaxies detected in ROSAT surveys have X-ray spectra similar to Mrk609then they should not contribute signiﬁcantly to the XRB.7SUMMARYWe have analysed BeppoSAX data of the composite galaxy Mrk609.The spectrum is described by a power-lawΓ=1.6 with negligible absorption.The absence of absorption is con-sistent with the small Balmer decrement and the large Ly a ﬂux observed(Rudy et al.1988).The absence of an ob-scuring column clearly does notﬁt the absorbed starburst model proposed by Levenson et al.2001to explain the mul-tiwavelength properties of the composite galaxy NGC6221. The detection of signiﬁcant soft and hard X-ray variability, clearly suggests that the AGN emission dominates the X-ray spectrum.Any starburst contribution to the X-ray emission should be small.In addition Mrk609does not follow the L Hα−L x correlation of bright AGN(Ward et al.1988), showing a weak broad Hαcomponent(∼40times less than predicted by the X-rayﬂux).The discrepancy between thec 0000RAS,MNRAS000,000–000BeppoSAX spectrum of Mrk6097Figure3.The spectral energy distribution of Mrk609,from far infrared to hard X-rays.optical and X-ray spectrum can be explained as a deﬁcit ofUV ionising photons.This is supported by the SED,whichshows no upturn of the spectrum below3000A,implying theabsence of a UV bump.Alternatively,as the optical and theX-ray observations were taken15years apart,dramatic vari-ability in the X-rayﬂux could result in a low L Hα−L x ratio.Finally the above discrepancy and anomalous line proper-ties could be explained by small optical depth and ionisationparameter in the line emitting regions.8ACKNOWLEDGMENTSWe would like to thank the referee Dr.J.Halpern for usefulcomments and suggestions and A.Burston for producing theSED of Mrk609.REFERENCESAlmaini O.,Shanks T.,Boyle B.J.,Griﬃths R.E.,Roche N.,Stewart G.C.,Georgantopoulos I.,1996,MNRAS,282,295Boyle B.J.,McMahon R.G.,Wilkes B.J.,Elvis,M.,1995,MN-RAS,276,315Brandt W.N.,Fabian A.C.,Takahashi K.,Fujimoto R.,Ya-mashita A.,Inoue H.,Ogasaka Y.,1997,MNRAS,290,617David L.P.,Jones C.,Forman W.,1992,APJ,181,1513Georgantopoulos,I.2000,MNRAS,315,77Goodrich R.W.,1990,ApJ,355,88Griﬃths R.E.,Georgantopoulos I.,Boyle B.J.,Stewart G.C.,Shanks T.,della Ceca R.,1996,MNRAS,275,77Heckman T.M.,Miley G.K.,van Breugel W.J.M,.Butcher H.R,1981,ApJ,247,403Iwasawa K.,Fabian A.C.,Brandt W.N.,Crawford C.S.,AlmainiO.,1997,MNRAS,291,L17Koratkar A.&Blaes O.,1999,PASP,111,1Levenson N.A.,Cid Fernandes R.Jr.,Weaver K.A.,HeckmanT.M.,Storchi-Bergmann T.,2001,astro-ph/0104316Moran E.,Halpern J.P,Helfand D.J.,1996,ApJS,106,341Nandra K.&Pounds K.,1994,MNRAS,268,405Osterbrock D.E.,1981,ApJ,249,462Rix H-W.,Carleton N.P.,Rieke G.,Rieke M.,1990,ApJ,363,480Rudy,R.J.,Cohen R.D.,Ake T.B.,1988,ApJ,332,172Veilleux S.,Osterbrock D.E.,1987,ApJS,63,295Veron P.,Goncalves A.C.,Veron-Cetty M.-P.,1997,A&A,319,52Ward M.J.,Done C.,Fabian A.C.,Tennant A.F.,Shafer R.A.,1988,Apj,324,767c 0000RAS,MNRAS000,000–000。

《现代传感器》课件Lecture11

Garlic and enchiladas produce a slightly different collective response in the entire set of sensors in your nose, and your brain has stored an extensive collection of these patterns which are used for comparisons.
An important lesson is that a multi-functional system will probably need to use a small set of distinct sensors and a pattern-matching algorithm to identify odors accurately.
A responsive matrix
Pattern-Matching algorithm
Identify Odors
Department of ptical Engineering
Zhejiang University
Detectors of Particular Molecules
If a chemical sensing application requires detection of a particular molecule, several techniques are available. These techniques are based on the unique properties of particular molecules.
Metal oxide sensors are more accurate and are the common type of sensor employed in home models. This type of sensor uses solid state tin-dioxide circuits, which clear quickly and continually monitor the air for presence of carbon monoxide.

Magnetic photonic crystals

Magnetic photonic crystals
I L Lyubchanskii1,4 , N N Dadoenkova1 , M I Lyubchanskii1 , E A Shapovalov2 and Th Rasing3
1 Donetsk Physical and Technical Institute of the National Academy of Sciences of Ukraine, 72, R. Luxemburg St., 83114 Donetsk, Ukraine 2 Department of Physics, Donetsk National University, 24, Universitetskaya St., 83055 Donetsk, Ukraine 3 NSRIM Institute, University of Nijmegen, 6525 ED, Nijmegen, The Netherlands
INSTITUTE OF PHYSICS PUBLISHING J. Phys. D: Appl. Phys. 36 (2003) R277–R287
JOURNAL OF PHYSICS D: APPLIED PHYSICS PII: S0022-3727(03)58197-9
TOPICAL REVIEW
0022-3727/03/180277+11$30.00
© 2003 IOP Publishing Ltd
Printed in the UK
Topical Rs a result, the light polarization properties undergo modiﬁcations. In this paper we present a short review of MPCs. The paper is organized as follows. In section 2 we discuss the MPCs in the microwave region. Section 3 is devoted to MPCs in the near infrared and visible regions. In section 4 we present the results on PBG effects in magnetic liquids and magnetic colloids. Magnetic ﬁlms with regular domain structures such as MPCs are considered in section 5. Finally, nonlinear optical effects in MPCs are presented in section 6. A perspective on the use of magnetic materials as MPCs is given in section 7.

Modern Application of mooc课后章节答案期末考试题库2023年

Modern Application of Optoelectronic Technology_南京邮电大学中国大学mooc课后章节答案期末考试题库2023年1.Reconstructive spectrometer is based on compressive sensing theory.参考答案:正确2.Photoconductive detector gain depends on the difference of electron andhole drift speed参考答案:正确3.As tandem structure can increase solar cell efficiency, so we can add as manycells as possible to increase the overall absorption and energy conversionefficiency.参考答案:错误4.The solar cell performance can be degraded by参考答案:Series resistance_Defects in semiconductors_Shunt resistance5.The optical transition in silicon devices is usually indirect参考答案:正确6.Write the bandgap (300k) of silicon _______ eV.参考答案:1.117.The commercial solar cell panels are still dominated by silicon photovoltaics.参考答案:正确D means __________________________参考答案:charge coupled device9._____________________are the study and application of _________________ devices andsystems that source, detect and control ______________.参考答案:Optoelectronics, electronic, photon##%_YZPRLFH_%##Optoelectronics, electronic, light10.Which of the following factors affect the LED output spectrum？参考答案:Operation temperature_Semiconductor bandgap_Dopingconcentration_Applied voltage/current11.Conventional spectrometers used in laboratories are参考答案:Based on dispersive optics_High resolution12.Some typical research results show that graphene hybrid photodetectors can参考答案:Cover a wide detection bandwidth from UV to MIR._Have highresponsivity_Use both planar and vertical heterostructures._Have high detectivity13.The equation to express photoelastic effect is【图片】, which means therefractive index changes with strain参考答案:正确14.What are the four typical layers of optical fibers?____________,___________,____________,_____________.参考答案:core, cladding, protective polymeric coating, buffer tube15.Second harmonic generation happens when an intense light beam offrequency ω passing through an appropriate crystal (e.g., quartz) generates a light beam of half the frequency, 1/2ω参考答案:错误16.The two regimes in acousto-optic modulators are Raman-Nath regimeand___________参考答案:Bragg regime17.Optically anisotropic crystals are called __________ because an incident lightbeam may be doubly refracted. There is also a special direction in abirefringent crystal, called the optic axis.参考答案:birefringent18._____________ is the rotation of the plane of polarization by a substance参考答案:optical activity19.What efficiency is typical of a commercial PERC solar panel?参考答案:20%20.The advantages of perovskite materials include参考答案:High quantum yields_Low-cost_High quantum yields21.Typical optoelectronic process includes参考答案:Light transmission_Light modulation_Light detection_Light generation22.The two operation principles of photonic crystal fibers are ___________________and _____________________.参考答案:total internal reflection, photonic bandgap23.The propagation modes in waveguide can be classified in terms of____________________(TE) mode and ____________________(TM) mode?参考答案:transverse electric field, transverse magnetic field24.Kerr effect can be used to induce birefringence参考答案:正确25.The lattice constant of AlGaAs alloy follows nonlinear mixing rule参考答案:错误26.Which of the following is not a challenge for 2D semiconductor technology?参考答案:Materials choice27.In the space charge region, a high doping concentration results a shortdepletion width参考答案:正确28.CMOS means __________________________参考答案:complementary metal oxide semiconductor29.Photodetectors convert ___________________ to an electrical signal such asa____________________.参考答案:light, voltage or current##%_YZPRLFH_%##photon, voltage or current。

Exploring the Optical Properties of Quantum Dots

Exploring the Optical Properties ofQuantum DotsQuantum dots (QDs) are semiconductor crystals with a diameter of a few nanometers, which exhibit unique optical and electronic properties. They have the potential to revolutionize fields such as optoelectronics, energy conversion, and biomedical imaging. The optical properties of QDs, in particular, have attracted considerable attention due to their strong and tunable fluorescence. In this article, we explore the optical properties of QDs and their potential applications in various fields.Optical Properties of Quantum DotsQDs exhibit size-dependent optical properties due to the confinement of charge carriers within the semiconductor crystal. As the diameter of the QD decreases, the energy levels become quantized, resulting in discrete electronic states. The size dependence of the energy levels leads to a unique set of optical properties such as strong fluorescence, broad absorption bands, and a narrow emission spectrum.One of the most notable optical properties of QDs is their strong and tunable fluorescence. The fluorescent emission of QDs arises from the recombination of electrons and holes confined within the crystal. The energy bandgap of the QD determines the emission wavelength, which can be systematically tuned by varying the size of the QD. Additionally, QDs exhibit a high quantum yield, which refers to the ratio of emitted photons to absorbed photons. This property makes them useful in applications such as bioimaging and sensing.Another characteristic optical property of QDs is their broad absorption spectrum. This property arises due to the presence of multiple electronic states within the QD. As a result, QDs can absorb light across a broad range of wavelengths, making them ideal for use in solar cells and other energy conversion technologies.Applications of Quantum DotsThe unique optical properties of QDs have led to their potential use in a wide range of applications. Some of the most notable applications of QDs include bioimaging, sensing, optoelectronics, and energy conversion.In bioimaging, QDs are used as fluorescent probes due to their high quantum yield, photostability, and tunable emission wavelength. QDs have been used to visualize cellular structures, track drug delivery, and monitor cellular events in real-time. Additionally, QDs have been used in biosensing applications, where they can detect target molecules with high sensitivity and specificity.In optoelectronics, QDs are used in the development of advanced light-emitting diodes (LEDs), photovoltaics, and lasers. QDs can be incorporated into LED devices to tune the emission wavelength and improve the efficiency of the device. Additionally, QDs have been used in solar cells to improve the spectral response and increase the efficiency of the device.In energy conversion, QDs are used in the development of advanced photovoltaic devices and photocatalysts. QDs can be incorporated into solar cells to improve the spectral response and increase the efficiency of the device. Additionally, QDs have been used as photocatalysts for the dissociation of water and other molecules, which may have applications in hydrogen production and other energy conversion technologies.ConclusionIn conclusion, the optical properties of QDs make them unique and attractive materials for a wide range of applications. Their strong and tunable fluorescence, broad absorption spectrum, and high quantum yield have led to their use in bioimaging, sensing, optoelectronics, and energy conversion. Ongoing research on QDs is expected to lead to further advances in these fields and the development of new applications for QDs in the future.。

光学专业英语50句翻译

光学专业英语50句翻译1.The group's activities in this area have concentrated on the mechanicaleffects of angular momentum on a dielectric and on the quantum properties of orbital angular momentum.在这个研究领域，这个研究组主要集中在电介质中的角动量的机械效应和轨道角动量的量子属性。

2. Experimental realization of entanglement have been restricted totwo-state quantum systems. In this experiment entanglement exploiting the orbital angular momentum of photons, which are states of the electromagnetic field with phase singularities (doughnut modes).纠缠的实验认识还只停留在二维量子系统。

在这实验中，利用了光子的轨道角动量的纠缠是具有相位奇点（暗中空模式）的电磁场的状态。

3. Laguerre Gaussian modes with an index l carry an orbital angular momentum of per photon for linearly polarized light that is distinct from the angular momentum of the photons associated with their polarization对线偏振光来说，具有因子l的LG模式的每个光子能携带的轨道角动量，这是与偏振态相关的光子的角动量是截然不同的。

光电信息专业英语

⏹Light detectors(光探测器）⏹Light can be detected by the eye. The eye is not suitable for modern fiber眼睛可以探测到光。

但是眼睛不适合用在现在的光线通信上因为它的反应太慢了。

communications because its response is too slow, its sensitivity to low-level signals is它的敏感度对于低频信号来说太不足了，而且对于电子接收器进行调幅解码还有其他信号处理也不是很简单。

inadequate, and it is not easily connected to electronic receivers for amplification,decoding, or other signal processing. Furthermore, the spectral response of the eye is而且眼睛的光谱响应仅限于0.4和0.7UM 之间的波长，而这也正是光损失最多的波长。

limited to wavelengths between 0.4 and 0.7 u m, where fibers have high loss.Nonetheless, the eye is very useful when fibers are tested with visible light. Break and虽然如此，眼睛在用光纤探测可见光时是非常有用的。

终止和打断能够通过观察散射的光观察到discontinuities can be observed by viewing the scattered light.⏹System, such as couplers and connectors, can be visually aligned with the visiblesource before the infrared emitter is attached. The remainder of this chapter is confined to an investigation of devices that directly convert optic radiation to electrical signals (either current or voltage) and that respond quickly to changes in the optic power level.⏹Principles of Photodetection⏹We will look at two distinct photodetection mechanisms. The first is the externalphotoelectric effect, in which electrons are freed from the surface of a metal by the energy absorbed from an incident stream of photons. The vacuum photodiode and the photomultiplier tube are based on this effect. A second group of detectors are semiconductor junction devices in which free charge carriers (electrons and holes) are generated by absorption of incoming photons. This mechanism is sometimes called the internal photoelectric effect.⏹hree common devices using this phenomenon are the pn junction photodiode, the最常用的应用这个现象的手段是pn节光电二极管，pin二极管，还有雪崩二极管PIN photodiode, and the avalanche photodiode.⏹Important detector properties are responsivity, spectral response, and rise time. The重要的探测要素有敏感度，光谱响应，还有回升时间。

采用电磁波偏振方法探测极高频残余引力波

∗ †
supported by the CNSF, SRFDP, and CAS. yzh@
1ct GWs of very high frequencies from MHz to GHz, employing various techniques, such as laser beam [8]. One interesting method proposed by Cruise uses linearly polarized electromagnetic waves (EWs) [9, 10]. When GWs pass through the region of waveguide, the direction of polarization vector (PV) of EWs will generally experience a rotation [9]. A prototype gravitational waves detector has been built by Cruise’s group [10], which consists mainly of one, or several, annular waveguide of a shape of torus. As a merit of this method, depending upon the size of the waveguide, GWs in a very high frequency range ν (106 , 109 ) Hz can be detected, which is not covered by the laser interferometer method. Note that the GWs in the frequency range (106 , 109 ) Hz are generally not generated by usual astrophysical processes, such as binary neutron stars, binary black holes, merging of neutron stars or black holes, and collapse of stars [11] [12]. However, the background of relic gravitational waves (RGWs) has a spectrum stretching over a whole range of (10−18 , 1011 ) Hz [13] [14]. Depending on the frequency ranges, its diﬀerent portions can be detected by diﬀerent method. For instance, the very low frequency range (10−18 , 10−16 ) Hz can be detected by the curl type of polarization in CMB [7], the low frequency range (10−3 , 10−2 ) Hz can be detected by LISA, the mediate frequency range (102 , 103 ) Hz is covered by LIGO, and the very high frequency range (106 , 109 ) Hz can be the detection object of Cruise’s EWs polarization method. Therefore, one of the main object of detection by the annular waveguide is the very high frequency RGWs. The detection of high frequency RGWs from MHz to GHz is in complimentary to the usual detectors working in the range of (10−4 , 104 ) Hz. RGWs is a stochastic background that are generated by the inﬂationary expansion of the early Universe [13, 14, 15, 16, 17], and its spectrum depends sensitively on the inﬂationary and the subsequent reheating stages. Besides, the currently accelerating expansion also aﬀects both the shape and the amplitude of the RGW spectrum [13, 14, 17]. RGWs carry take a valuable information about the Universe, therefore, their detection is much desired and will provide a new window of astronomy. In this paper we give a comprehensive study of the rotations of PV of EWs in a conducting torus caused by incident GWs, and explore the feasibility and limitation of Cruise’s method of detecting GWs by polarized EWs in the annular waveguide. Firstly, we brieﬂy review the RGWs in the currently accelerating universe. Secondly, we shall present detailed calculations of rotations of the PV of EWs in the waveguide caused by the incoming GWs from from various directions and in various polarization states, thereby we analyze the multiple-cycling accumulating eﬀect and the resonance when the circling frequency of EWs is nearly equal to that of GWs. Thirdly, we shall examine the possible detection of the RGWs by the annular waveguide system around 100 MHz, comparing the predicted spectrum of RGWs in the accelerating Universe with the sensitivity of the detector [10]. Finally, we give the conclusions and possible ways of improvements for detection.

CO2激光刻印系统维护指南说明书

Maintaining your laser system: regular cleaning makes for a long laser life By Mike Dean, vice-president of sales and marketing, Epilog LaserAs with most pieces of equipment, preventive maintenance is an important part of owning any CO2 laser engraving sys tem. This month we’ll discuss common maintenance techniques that will keep your laser system performing at its peak. Please keep in mind that every laser manufacturer is a little different, so the following tips are more general in nature. You should reference the laser engraving guide/manual supplied by your provider for complete instructions.It’s actually very easy to keep your laser system running its best if you always keep it clean. That includes ensuring the area around the laser is free of clutter, combustible materials, explosives, or volatile solvents such as acetone, alcohol, or gasoline.Below are the common materials that will be used to remove the smoke and vapor from the table, X-beam and anywhere else that collects dirt and debris.Materials for regular system cleaning:∙Soft cloth∙Mild household solvent like Isopropyl alcohol∙Cotton swabsThe top six maintenance techniques we’re about to cover will give your laser and long, happy and productive life. Most manufacturers include some cleaning instructions in their manual, and you should refer to your specific manual for the best instructions.Cleaning OpticsThe optics in your system includes all lenses and mirrors. We recommend inspecting them weekly, and cleaning as necessary for optimum performance. Keep in mind that your exhaust flow may affect your cleaning schedule. If you have low exhaust flow, you may not be getting rid of all of smoke and debris, and you may need to modify your cleaning schedule. Luckily, a simple visual inspection is all that’s needed to determine if your optics need cleaning.The two optical components most likely to require cleaning are the focus lens and the mirror directly above it.Look at your optics to determine if they are dirty. Normally, most optics are a clear gold color and are bright and shiny. If the optics are cloudy, or have smudges or debris on them, they need to be cleaned. If there is a cover over your optics, remove the cover to inspect the optics. Don’t letthe cover fool you! Dirt and debris are still is able to get into most lens chambers and i f you don’t clean your optics, they can degrade your engraving and can even crack the lens.To clean the focus lens and the mirror that is directly above it, use a cotton swab that is soaked with optics cleaning fluid. Gently swab the optics to remove dust and debris. Wet the cotton swab thoroughly with the solvent, and then blot it against a piece of cotton so that it is no longer soaking-wet. Then dab the optic gently, rotating the swab after each dab to expose clean cotton to the surface, until the optic is free of visible contamination. At that point, prepare a fresh swab and clean the surface with a gentle zigzag motion across it. Avoid any hard "scrubbing" of the surface, especially while there are visible particles on it. When you are done, be careful to remove any cotton threads that may have snagged on the mountings. Allow the optics to dry before you operate your engraver.It might sound odd, but if you should run out of the optics cleaning fluid supplied by your laser manufacturer, pure ethyl (grain) alcohol is a highly recommended substitute because of its pure nature and because it is readily available.Cleaning your Vector Grid/TableWhenever you are vector cutting there is the potential for small pieces to fall through the vector grid and collect in the table tray. These small pieces present a very dangerous fire hazard, especially if they are allowed to collect over time. Since most users cut wood and acrylic, these small pieces that fall into the table tray act just like kindling and can ignite and start a fire. To clean your tray, remove the vector grid and clean out the table tray using a small brush or vacuum cleaner. Completely remove the debris in the bottom of the tray on a regular basis.Cleaning and the Bearing RailsThe bearing system in your laser system should be inspected on a regular basis and cleaned as necessary. Use a soft cloth or cotton swab with isopropyl alcohol or similar mild solvent to clean all of the bearing tracks. For many systems cleaning the bearings is not a necessary part of a frequent maintenance schedule, but they should occasionally be inspected and cleaned per the manufacturers instructions.Cleaning the Auto Focus FeatureThe auto focus mechanism is typically mounted at the back of the carriage that holds the focus lens. It is usually about a quarter inch in diameter, and about two inches long. If you work with materials that leave a greater amount of debris and/or residue (such as wood) the auto focus feature should be periodically cleaned for accurate focusing.Use a soft cotton cloth and some mild household cleaner or isopropyl alcohol to gently wipe the auto focus plunger until it is clean.Cleaning Optical Strip and Linear EncoderWith laser systems that use linear encoders, you occasionally may need to clean the optical strip and encoder in your machine. The optical strip and encoder are likely located under the protective cover of the X-beam assembly. The optical encoder provides precise positioning for the x-axis carriage. To clean the optical strip remove the protective X-beam cover and wipe off theoptical strip using isopropyl alcohol and a soft cotton cloth or swab.Cleaning the ExhaustMake sure the exhaust blower you are using receives proper maintenance. Periodically clean the exhaust blower and duct system to remove built-up debris. If you detect odor while engraving, or if the smoke in the cabinet is visible in the area of the lens carriage, inspect the exhaust system for leaks and obstructions. Ensure all connections are properly secured. Also check for loose or broken duct connections.Inspect and clean the exhaust ports in your machine to ensure there are no obstructions within the machine itself. Use a wire brush to clean the plenum and exhaust port of your machine.As you can see, all of the maintenance techniques are simple and easy to perform. Spending just a few minutes on a regular basis inspecting and cleaning your machine will add life andproductivity to your equipment and in turn, to your business.。

OPTICAL INSPECTION

专利名称：OPTICAL INSPECTION 申请号：AU4375272申请日：19720622公开号：AU471611B2公开日：19760429专利内容由知识产权出版社提供摘要：1392448 Television NATIONAL RESEARCH DEVELOPMENT CORP 7 June 1972 [22 June 1971] 29213/71 Heading H4F [Also in Division G2] Comparison of an object with another object or with the same object after changes have occurred (e.g. in surface characteristics), is effected by forming respective images of the object(s) simultaneously or sequentially, using coherent light illumination, on a photosensitive screen, which is scanned to provide two video signals which are correlated. In the arrangement of Fig. 1, two surfaces 3, 4 the latter of which is a reference are illuminated by laser light 1. The "speckle" patterns representing the two surfaces (each pattern or image having such speckle or granularity due to random interferences) are superimposed and interfere at TV camera screen 7. Alternatively an image intensifier plus TV camera may be used, in which case pulsed operation to give a stroboscopic effect is possible. The video signal after one frame scan is stored in recording device 9, e.g. magnetic disc or tape, or a storage C.R.T. Surface 3 is then deformed, and the subsequent frame scan compared with the stored one by means of differencing circuit 10. Rectification in detector circuit 11 provides a unidirectional signal which can be displayed on C.R.T. monitor 12, scanned in synchronism with the camera. In a modification of the arrangement of Fig. 1, the video signals before and after a change, are both recorded, to enable more accurate synchronization of the two for correlation purposes than is possible in Fig. 1, but at theexpense of real-time monitoring. In the arrangement of Fig. 2 (not shown), instead of a reference surface image being interfered with the test surface image, a smooth reference wavefront (direct from the laser) is used. Otherwise, operation as is in Fig. 1. In Fig. 3 (not shown), only the test surface is used, but two speckle patterns are provided by illuminating the surface from two different angles, and only in-plane displacements can be monitored. The comparison of a test surface to be checked against a "master" is possible using the apparatus of Fig. 4. An argon laser emitting 4965 Š and 4880 Š is used and a beam splitting and wavelength filtering system used in the camera, which has two screens 27, 28, so that the simultaneous video outputs, represent superimposition speckle patterns for two wavelengths. Differencing circuit 32, and detector 33 feed the display monitor 34. In the arrangement of Fig. 5 (not shown), two wavelengths of light are again used, but the camera has a single screen, in front of which is a two filter wheel, whose rotation is synchronized with the frame scan and the switching of the output on alternate frames to a delay device (41). A contour map of a surface may be obtained by using the apparatus of Fig. 1 to compare patterns from the surface obtained at two different wavelengths. The Figs. 4 and 5 arrangements may also be used for this purpose by the use of divergent radiation and selective blanking off of surfaces 21, 22.更多信息请下载全文后查看。

眼科规培英语试题及答案

眼科规培英语试题及答案一、选择题（每题2分，共20分）1. Which of the following is the most common cause of blindness in the world?A. CataractB. GlaucomaC. Age-related macular degenerationD. Diabetic retinopathy2. The primary function of the cornea is to:A. Focus lightB. Adjust the size of the pupilC. Protect the eyeD. Provide oxygen to the retina3. What is the medical term for the condition where the lens of the eye becomes cloudy?A. GlaucomaB. MyopiaC. HyperopiaD. Cataract4. The process of adjusting the eye's lens to focus on objects at varying distances is known as:A. AccommodationB. ConvergenceC. RefractionD. Pupil dilation5. Which of the following is not a type of strabismus?A. EsotropiaB. ExotropiaC. HypertropiaD. Diplopia6. The optic nerve is responsible for:A. Transmitting visual information to the brainB. Adjusting the size of the pupilC. Focusing light onto the retinaD. Providing nutrients to the eye7. Which of the following is a common symptom of dry eye syndrome?A. RednessB. PainC. Excessive tearingD. All of the above8. The term "myopia" refers to:A. FarsightednessB. NearsightednessC. BlindnessD. Color blindness9. Which of the following is a risk factor for developing age-related macular degeneration?A. SmokingB. Regular exerciseC. Healthy dietD. All of the above10. The procedure used to remove a cataract is known as:A. PhacoemulsificationB. VitrectomyC. RetinopexyD. Keratoplasty答案：1-5 A D D C C6-10 A D B A A二、填空题（每题1分，共10分）11. The ________ is the clear, protective outer layer of the eye.12. The ________ is the part of the eye that changes shape to focus on objects at different distances.13. The ________ is the central part of the retina responsible for detailed vision.14. The ________ is a condition where the eye produces too much aqueous humor or does not drain it properly, leading to increased intraocular pressure.15. The ________ is a condition characterized by the eye growing too long from front to back, causing distant objects to appear blurry.16. The ________ is a type of eye surgery that correctsvision by reshaping the cornea using a laser.17. The ________ is a condition where the eye does not grow long enough, causing near objects to appear blurry.18. The ________ is a procedure that involves removing the natural lens of the eye and replacing it with an artificiallens.19. The ________ is a condition where the eye does not align properly, causing double vision or misalignment of the eyes.20. The ________ is a condition where the cornea is not perfectly smooth and causes light to scatter, leading to blurry vision.答案：11. Cornea12. Lens13. Fovea14. Glaucoma15. Myopia16. LASIK17. Hyperopia18. Cataract surgery19. Strabismus20. Astigmatism三、简答题（每题5分，共30分）21. 简述青光眼的主要治疗方法。

Amplification of polarization NOON states

NOON states are path entangled states which can be exploited to enhance phase resolution in interferometric measurements. In the present paper we analyze the quantum states obtained by optical parametric ampliﬁcation of polarization NOON states. First we study, theoretically and experimentally, the ampliﬁcation of a 2-photon state by a collinear Quantum Injected Optical Parametric Ampliﬁer (QIOPA). We compared the stimulated emission regime with the spontaneous one, studied by Sciarrino et al. (PRA 77, 012324), ﬁnding comparable visibilities between the two cases but an enhancement of the signal in the stimulated case. As a second step, we show that the collinear ampliﬁer cannot be successfully used for amplifying N-photon states with N>2 due to the oscillation pattern of the crystal. To overcome this limitation, we propose to adopt a intrinsic λ 4 scheme for the ampliﬁcation of a generic state based on a non-collinear QIOPA and we show that λ the state obtained by the ampliﬁcation process preserves the N feature and exhibits a high resilience to losses. Furthermore, an asymptotic unity visibility can be obtained when correlation functions with suﬃciently high order M are analyzed.

Computing Optical Flow with Physical Models of Brightness Variation ￡

Computing Optical Flow with Physical Models of Brightness VariationHorst W.Haussecker David J.FleetXerox Palo Alto Research Center,3333Coyote Hill Road,Palo Alto,CA94304hhaussec,ﬂeet@AbstractThis paper exploits physical models of time-varying brightness in image sequences to estimate opticalﬂow and physical parameters of the scene.Previous approaches han-dled violations of brightness constancy with the use of ro-bust statistics or with generalized brightness constancy con-straints that allow generic types of contrast and illumina-tion changes.Here,we consider models of brightness vari-ation that have time-dependent physical causes,namely, changing surface orientation with respect to a directional illuminant,motion of the illuminant,and physical models of heat transport in infrared images.We simultaneously es-timate the opticalﬂow and the relevant physical parame-ters.The estimation problem is formulated using total least squares(TLS),with conﬁdence bounds on the parameters.1.IntroductionThis paper uses physical models of time-dependent brightness variation in image sequences to estimate optical ﬂow and physical parameters of the scene.Physical causes of brightness variation include changing surface orientation with respect to a directional illuminant,motion of the illu-minant,and physical models of heat transport in infrared images such as diffusion and decay.We wish to estimate opticalﬂow and the relevant physical parameters.Many computer vision applications require accurate esti-mates of the opticalﬂowﬁeld.Although studied extensively [1,11],reliable opticalﬂow computation still remains difﬁ-cult in many cases.Problems arise from the complex physi-cal processes involved in scene illumination,surface reﬂec-tion,and the transmission of radiation through surfaces and the atmosphere[12,24,19].Without a model of image for-mation it is not possible to unambiguously relate spatiotem-poral brightness to motion.Part of this work was performed while HWH was with the Interdisci-plinary Center for Scientiﬁc Computing,Heidelberg University,Germany. Portions of this work were supported by the‘Deutsche Forschungsgemein-schaft’(Image Sequence Analysis to Investigate Dynamic Processes).The authors thank M.Black,B.J¨a hne,A.Jepson,and O.Nestares for helpful discussions,and C.Garbe for providing the rotating sphere sequence.a bcFigure1.Illustration of errors in the opticalﬂow esti-mation due to brightness changes.(a)constant brightness (correctﬂowﬁeld),(b)exponential decay,(c)diffusion.Common opticalﬂow techniques assume brightness con-stancy.For graylevel images x,where x,the tracking of points of constant brightness amounts toﬁnding a path x along which image brightness is constant,i.e.,x(1)for some constant.Taking the total temporal derivative of both sides of(1)yields the well-known brightness change constraint equation(BCCE)[12]:dd(2)where v d d d d is the opticalﬂow that we wish to estimate,and denotes the partial deriva-tive of with respect to the coordinate.Be-cause(2)provides one constraint in two unknowns it is common to combine constraints at neighboring pixels,as-suming that the opticalﬂowﬁeld is locally constant or afﬁne [1,2].This produces a system of linear equations that can be solved using standard(weighted)least squares[14],or total least squares(TLS)[25,26].To further constrain the estimates,the regions can be extended into time if v is smooth within local temporal windows[7,27].For the en-hanced brightness change models(Section3)we consider here,it is very important that the neighborhoods are ex-tended to more than two frames.With only two frames,one can only model brightness changes that are linear in time.2IEEE Conference on“Computer Vision and Pattern Recognition(CVPR)”,Hilton Head Island,SC,June2000If brightness is not conserved,then the opticalﬂowﬁeld estimated from(2)can be severely biased[4,17,18,24, 3,20,9,19].Causes of brightness variation include moving illumination envelopes,changing orientation of surfaces un-der directional illumination,and atmospheric inﬂuences in outdoor applications.Other instances occur in scientiﬁc ap-plications that quantitatively investigate dynamic processes [13].Figure1illustrates the inﬂuence of brightness changes on opticalﬂow estimation with two examples of physical transport processes in infrared images,namely,exponential decay and diffusion;although the surface translates in each case,theﬂowﬁeld that conserves brightness may converge or diverge.This paper describes a generalized framework for in-corporating brightness changes into motion analysis using physical models.Brightness changes are either parameter-ized as time-varying analytical functions or by the differen-tial equations that model the underlying physical processes. We only require that the brightness variation be linear in the model parameters,not in the image brightness or in the spatiotemporal coordinates.With this,we obtain a linear system of equations that constitutes a straightforward gen-eralization of the brightness constancy assumption.Estimates of the parameters can then be obtained using TLS.We show that this produces improved opticalﬂow es-timates,and it allows us to estimate additional information that characterizes the physical processes.TLS error covari-ance matrices[21]are used to quantify the accuracy of the opticalﬂow and the brightness change parameters.2.Previous WorkBrightness variations have been modeled by[4,17,18, 24,3,20,9].A general framework is proposed in[20] where the brightness change between two frames consists of a multiplier and an offsetﬁeld:(3) where,for notational convenience,denotes a space-time3D vector.It is certainly true that all changes between two images can be modeled according to(3). However,this approximation only yields the instantaneous brightness change,which does not allow us to discriminate different physical causes of brightness changes,or to con-strain the estimation to satisfy particular physical models.In related work on target tracking,Hager and Belhumeur [9]combine illumination changes and pose-dependent geo-metric image distortions into a parameterized model.They use robust area-based regression toﬁt the image to a linear combination of basis templates(eigenmodels).One disad-vantage of the approach is that the basis set must be com-puted from the target,under varying illumination,prior to the tracking.Also,the resulting parameters specify a lo-cation in the eigenspace of training images,rather than aFigure2.Illustration of the generalized model that allows the object brightness to change within a few images.Solu-tions of the brightness constancy assumption are conﬁned to the gray plane(x x).physical model of the brightness variation.Black et al.[3] express the change between two frames of an image se-quence as a mixture of causes,including both motion and illumination effects.But they have not considered realis-tic,time-varying,physical models.Moreover,their use of mixture models,robust statistics,and the EM algorithm are computationally expensive compared to the linear solution developed here.The techniques mentioned above are conﬁned to bright-ness changes between two images;they do not exploit the physical nature of brightness variation over more than two frames.Our approach generalizes the temporal brightness changes in ways governed by the underlying physical pro-cess.By conﬁning the classes of permitted solutions to those of physical relevance we constrain the solutions and simultaneously estimate the parameters of interest.3.Physics-Based Brightness VariationGiven a physical model,constraints on brightness varia-tions can be speciﬁed by a functional relation or,more di-rectly,by differential equations that relate temporal bright-ness changes to the spatial image structure.As a general-ization of brightness conservation(1),shown in Fig.2,we deﬁne a temporal trajectory x along which brightness can change according to a parameterized function,:x(4) where x denotes the image at time,anddenotes a-dimensional parameter vec-tor for the brightness change model.Without loss of gener-ality,we choose a parameterization such that a produces the identity transformation,a.While a is assumed to be constant within small temporal windows,is expressed as a function of time to be able to capture nonlinear temporal brightness changes.Taking the total derivative of both sides of(4)yields aHaussecker&Fleet:Computing Optical Flow with Physical Models of Brightness Variation3generalized brightness change constraint equation:a(5) where is deﬁned as:a dda(6)With the constant brightness model(1),,and(5)re-duces to(2).Given constraints like that in(5),our goal is to estimate the parameters of the opticalﬂowﬁeld v,and the parameters a of the physical model.In(5)we used a constantﬂow model for which theﬂow parameters are and.But it is straightforward to use other linear parame-terized models such as afﬁne motion[6].Finally,there are two different ways to specify the form of.One can compute by(6)using a known analytical form of,or one can choose according to the differential equations of the underlying physical processes.We will il-lustrate this below in Sections3.1-3.4,before returning to the general formulation in Section3.5.3.1.Exponential DecayIn certain instances,brightness in infrared images is well modeled using exponential decay.This occurs in applica-tions where heat is removed from the thin layer on an ob-ject surface that infrared cameras are imaging.In many such cases the brightness function in(4)has the analytical form(7)In this case,the parameter vector a reduces to a scalar decay constant,.Therefore,from(6)it follows thatx(8)This is the well known differential equation of exponential decay.It states that the rate of change at any time is propor-tional to the current value.Because is linear in,we can estimate v and using linear methods(see Section4).3.2.DiffusionAnother elementary physical transport process,used to model brightness changes in infrared image sequences is diffusion.If the brightness change can be modeled as isotropic diffusion in the image coordinates,then it depends on the spatial image structure according to the well known diffusion equation:(9)where is the scalar diffusion constant.Because is linear ,we can use linear methods to estimate v and(Sec.4).3.3.Moving Illumination EnvelopeBrightness changes caused by moving,non-uniform il-lumination envelopes have been considered in the2-frame case[20].Here we focus on illuminants with a relatively narrow envelope,such asﬂashlights or spotlights.Diffuse shadows provide another case of interest when they are cast on a surface the motion of which we wish to estimate.We model the image as the product of an underlying sur-face albedo function that translates with image velocity v,and an illumination envelope(surface irradiance)that translates with velocity u:x x v x u(10) The brightness variation of is caused by the relative mo-tion between the envelope and the surface reﬂectance.To characterize this brightness transformation it is convenient to use a coordinate frame of reference that isﬁxed on the underlying surface reﬂectance,i.e.,x x v.The mo-tion of the envelope relative to this reference frame is given by u u v and the image brightness becomesx x v x x u(11)where x is a warped version of x for which the motion of the surface reﬂectance is stabilized.To parameterize the brightness variation through time, we approximate x u by a Taylor series,up to second order with respect to time,about the point x:x u x u u u(12)where and are the gradient and Hessian of at x.Substituting(12)into(11)yields a brightness func-tion:u u u(13) Then,from(6),the brightness change,,is given by(14) where u and u u.The bright-ness change is linear in the parameters a.When the moving envelope can be approximated by(12) the quadratic time-varying model in(13)reduces the bias in opticalﬂow estimates.By comparison,if the envelope were nearly linear,aﬁrst-order temporal model for,and hence a constant model for,would sufﬁce.In either case, solving for the polynomial coefﬁcients of the model in a does not allow us to separate the exact shape of from its motion u.However,it does provide information about the combined impact of both.4IEEE Conference on“Computer Vision and Pattern Recognition(CVPR)”,Hilton Head Island,SC,June20003.4.Changing Surface OrientationThe last case we address here concerns brightness vari-ations caused by surface rotation under directional illumi-nation.As is well known,even Lambertian surfaces exhibit brightness changes if the angle between the surface normal n and the direction of incident illumination l changes with time.Although one might attempt to evenly illuminate a scene to avoid these effects,directional illumination cannot be avoided in most cases.Examples include outdoor scenes in direct sunlight,indoor illumination through a single win-dow,and exploration of dark scenes using a collimated light source.In some applications one might intentionally use a directional source to enhance edges while simultaneously tracking surface properties.Given a combination of ambient illumination and aﬁxed, distant,point light source from direction l(where l), the surface radiance from a Lambertian surface with unit normal n can be expressed as n l,where is the am-bient component and is proportional to surface albedo.If we assume a rotating body,then we can write the surface normal at time as n n,where is a3D rota-tion matrix and n is the normal at time.Then,the time-varying radiance becomes n l.The extent to which the radiance changes with time de-pends on the angle between the light source direction l and the axis of rotation l.To see this,let l l l,where l l,l l,and.With this,one can show that the time varying radiance becomesn l n l(15) Finally,with some manipulation of the second term,one can show that this reduces to the general form of(16) where n l,,and denotes the frequency of the temporal modulation which depends directly on the rate of object rotation.It is obvious from(16)that radiance,and hence image brightness,is not linear in parameters of interest. However,all possible angles between visible(opaque)sur-faces and the illumination direction are conﬁned to the inter-val.Within this interval the cosine can be ap-proximated by a second-order polynomial,which provides our brightness function that is linear in its parameters:(17) where the parameters and are functions of and. Using(17),can be approximated by(18) which is linear in the parameters.Once an approximate pa-rameter set,and,is estimated using(18)in(5),the quadratic approximation of can beﬁtted to(16)to esti-mate the parameters and.3.5.Generalized FormulationIn Sections3.1-3.3the parametric brightness change models were linear in the parameters a.For the cosinu-soidal brightness change in Section3.4we approximated the brightness function,,with a second-order polynomial in.In general,all smoothly varying functions can be lo-cally expanded by a Taylor series and approximated by a polynomial of order,and therefore we can assume that is analytic in a set of parameters awithout loss of generality.Accordingly,remembering that a,we can expand as a Taylor series about a:(19)Using(19)we can express,the temporal brightness vari-ation deﬁned in(6),asa daddd(20)where is assumed to be constant through time within lo-cal windows of temporal support.As is analytic in a we can exchange the order of differentiation to obtain the gen-eral form of our constraints:a a a(21)That is,can be written as scalar product of the parameter vector a,and a vector containing the partial derivatives of with respect to the parameters.putational FrameworkIn each of the above formulations we obtain linear con-straints that relate the variables of interest and noisy mea-surements.The general form of the constraints,assuming a constant opticalﬂow model,can be expressed asd p with d a(22)and p p p a v where p contains the parameters of interest(theﬂowﬁeld parameters and the brightness parameters of),and p de-notes the homogeneous counterpart of p.The-dimensional vector d combines the image derivative mea-surements and the gradient of with respect to the param-eters a.This form of constraint is easily generalized from a constant model to higher-order parameterized motion mod-els[2,6],such as an afﬁne model.Equation(22)is just one constraint in several unknowns. To further constrain the parameters,p,we assume that p is constant within a local space-time region.We then use aHaussecker&Fleet:Computing Optical Flow with Physical Models of Brightness Variation5 collection of such constraints at neighboring pixels in theregion to obtain a linear system:p with d d(23)Assuming IID Gaussian noise in the measurement matrix,a maximum likelihood estimate of p is given by the TLSestimator[21,23],often formulated as the minimum ofp pp p(24)In practice,errors in measuring temporal image deriva-tives are often larger than errors in measuring the spa-tial derivatives.Also,derivative measurements at adjacentpixels are often correlated.Thus,one must renormalizethe constraints before using TLS to avoid bias in the esti-mates[15,16].Although not always referred to as such,many recent approaches to opticalﬂow computation(e.g.,[5,8,22,18,26])are based on TLS or related techniques.To quantify the measurement error in terms of an errorcovariance matrix,we use the Hessian of the negative log-likelihood evaluated at the TLS estimate,p p.In[21],this is shown to beH p M p p D p Ip p D p p p M p A b p(25)where D is a matrix,contains theﬁrst columns of,b is the last column of, M,and I denotes a iden-tity matrix.The factor is deﬁned as, where denotes the variance of the expected distribution of gradients in,and I is the covariance of the IID Gaussian noise.If the signal to noise ratio(SNR)is high ,then.The error covariance matrix sug-gested by[21],is then given by.5.Experimental ResultsWe have applied the technique to both synthetic and nat-ural images sequences.These include scientiﬁc applica-tions with infrared image sequences,as well as more con-ventional computer vision applications.In each case we measure the opticalﬂow and the brightness change param-eters.We also compute error covariance matrices,given above in Sec.4,that serve as conﬁdence bounds on the es-timates[21].5.1.Changing Surface OrientationFigures3(a,b)show two frames from a computer gener-ated image sequence of a randomly textured3D sphere un-der directional illumination.The sphere was rendered to be illuminated under an angle of with respect to viewing direction,and it was rotating about a vertical axis through abFigure3.Rotating sphere under directional illumination.(a,b)Frames1and5.(c,d)Opticalﬂow estimates and uncertainty ellipses for the constant and quadratic temporal brightness models.its center.The angular velocity of the sphere was varied in several experiments,staying within the spatiotemporal sam-pling limits imposed by the scale of the spatial texture(this allowed us to avoid the need for a coarse-to-ﬁne estimation strategy in the current experiments).The temporal bright-ness function was modeled with the quadratic approxima-tion to the cosinusoidal relationship in(17),as described in Section3.4.For comparison,we also obtained estimates using a local linear approximation(3)and the brightness constancy model(2).In this and other experiments,we found that the con-stant brightness model performed poorly compared to the linear and quadratic models.For slow rotations the lin-ear and quadratic temporal change models produced very similar results.Fast motions produce faster brightness changes,which then show differences between the linear and quadratic models.To illustrate this while obeying sam-pling limits,we let the sphere rotate in one direction while the light source rotated in the other direction.Figure3(c,d)shows the opticalﬂow estimates with un-certainty ellipses.The error ellipses satisfy e eto capture90%of the expected errors,where is the2D error covariance matrix for and,and e is the optical ﬂow error.For convenience,we only displayﬂow estimates when the norm of is less than a liberal threshold.It is easy to see in Figure3(b,c)that theﬂowﬁeld estimated with the6IEEE Conference on“Computer Vision and Pattern Recognition(CVPR)”,Hilton Head Island,SC,June2000abcFigure4.A human arm,under directional illumination, is rotating about its main axis towards the left while slightly translating to the right.(a)Full image indicating the area displayed in the lower images.(b,c)Frames1and3.(d,e)Opticalﬂow estimates and uncertainty ellipses for theconstant and quadratic temporal brightness models. quadratic model is more accurate than that found with theconstantmodel.Another example of brightness variation caused by changing surface orientation is shown in Figure4.Here,a human arm was illuminated by light through a window in a workplace environment.The arm was turning with respect to the direction of the illumination.Due to the complex structure of non-rigid motion of the skin,the surface normal exhibited fast changes leading to brightness changes.Figure 4shows the opticalﬂow estimates based on the quadratic model described in Section3.4.By comparison one can see that the estimates with the brightness constancy model are severely biased.a bfFigure5.Synthetic moving illumination envelope.The underlying texture and the envelope move with velocities v and u pixels/frame respectively.(a,b)Frames2and6.(c,d,e)Difference between the true and estimatedﬂow,with the uncertainty ellipses,for the constant,linear,and quadratic temporal brightness models respectively.(f)Estimated parameter of the combined curvature and motion of the envelope(see Eqn.(14)).5.2.Moving IlluminantTo generate a synthetic example of a moving illuminant, we simply multiplied a sample of smoothed white noise with a Gaussian envelope.As described in Section3.3,both signals translate with constant velocity.The Gaussian sim-ulates the illumination envelope,and it is the motion of the noise signal that we wish to estimate.Figure5shows results for different temporal brightness models,namely,the constant(2),linear(3),and quadratic (13)models.Because the synthetic sequence provides ground truth,we plot the difference vectors e between theHaussecker&Fleet:Computing Optical Flow with Physical Models of Brightness Variation7 abfFigure6.Movingﬂashlight illuminates a carpet.Theenvelope moves right while the carpet texture remains al-most stationary.(a,b)Frames2and6.(c,d)Opticalﬂowestimates and uncertainty ellipses for constant and linearbrightness models.(e,f)Flow estimates with the quadraticmodel,and an image of estimates of parameter whichdepends on the curvature and motion of the envelope.ﬂow estimates and ground truth.Due to the shape of the il-lumination envelope,no part of the moving pattern remainsat constant brightness along its path.Consequently,the con-stant brightness model fails to predict the true velocity overthe entire image(Fig.5c).The linear model correctly ac-counts for brightness changes in regions where theinstanta-neous motion of the illumination envelope is mainly parallelto its level contours(Fig.5d).In these regions the param-eter in(14)exceeds the parameter and the temporalbrightness changes are nearly linear.However,the linearmodel fails in regions of high positive or negative valuesof the combined motion/curvature parameter(dark anda bc de fFigure7.Exponentially decaying heat spot on a wavywater surface.(a,b,c):Frames1,3and5.(d)Decayrate threshold by the conﬁdence measure.(e,f)Opticalﬂow estimates and uncertainty ellipses estimated with theconstant brightness model and the exponential decay model.bright regions in Figure5f.The quadratic brightness changemodel allows us to accurately estimate the motion of thepattern(Fig.5e).The next example shows an image sequence taken as amoving observer shone aﬂashlight on a dark textured carpet(Fig.6).Negahdaripour[20]investigated a similar exam-ple of a non-uniform illumination pattern in an underwaterscene.He showed that the linear brightness change model(3)performs well in estimating the correct opticalﬂow ascompared to the bias that occurs with the constant bright-ness model.However,in his case the illuminant was sta-tionary with respect to the camera.Weﬁnd the same result;for small u v,the linear model performs as well as aquadratic model.For faster motions u v the quadraticterms in(13)become more signiﬁcant,so the quadraticmodel yields better results(compare Figs.6d,e).This isclearest in regions with high envelope curvature(Fig.6f).5.3.Heat Transport in Infrared ImagesFigure7shows an application example from physicaloceanography.The scientiﬁc task was to estimate the decayrate of an exponentially decaying heat spot on the water sur-face in a wind/wave tank.The broader goal is to estimatethe transfer velocity of heat across the air/water interface,which is known to be related to the heat decay rate on thewater surface.In addition to the exponential decay,the im-age is expected to deform due to the underlying turbulentﬂowﬁeld,another important parameter of air/sea interac-8IEEE Conference on“Computer Vision and Pattern Recognition(CVPR)”,Hilton Head Island,SC,June2000tion.Thus,both the decay rate and theﬂowﬁeld need to be estimated.In Figure7,the images show an area of about55cm. If we assume brightness constancy then the estimatedﬂow (Fig.7e),especially the convergentﬂow in the center,is unrealistic.In fact the heat spot is sheared and elongated from one frame to the ing the exponential bright-ness change model theﬂow(Fig.7f)is accurately estimated together with the thermal decay rate(Fig.7d).Further examples of heat transport in infrared images, including further examples of heat decay and examples of heat diffusion can be found in[10].6.ConclusionsThis paper presents a new approach to quantitatively esti-mating motion and physical parameters of image sequences. We use physical models of brightness change to facilitate the estimation of both opticalﬂow and physical param-eters of the scene.Previous approaches have accommo-dated violations of brightness constancy with the use of ro-bust statistics or with generalized brightness constancy con-straints that allow generic types of contrast change.Here, we consider models of brightness variation that have time-dependent physical causes,including changing surface ori-entation with respect to a directional illuminant,motion of the illuminant,and physical models of heat transport(diffu-sion and decay)in infrared images.The new technique is a straightforward extension of the standard brightness change constraint equation to incorpo-rate the spatiotemporal signature of particular dynamic pro-cesses.With our formulation,the resulting problems have linear solutions using total-least-squares.With the use of an error covariance,we show that the method provides both accurate opticalﬂow estimates,and accurate estimates of the relevant physical parameters.The usual sensitivity of total-least-squares to measurement noise and conditioning is mitigated with the use of the error covariance. References[1]J.L.Barron,D.J.Fleet,and S.S.Beauchemin.Performanceof opticalﬂow techniques.IJCV,12(1):43–77,1994. [2]J.Bergen,P.Anandan,K.Hanna and R.Hingorani.Hier-archical model-based motion estimation.Proc.ECCV,pp.237–252.Springer-Verlag,1992.[3]M.J.Black,D.J.Fleet,and Y.Yacoob.Robustly estimatingchanges in image appearance.CVIU78:8–31,2000.[4]N.Cornelius and T.Kanade.Adapting opticalﬂow to mea-sure object motion in reﬂectance and x-ray image sequences.In ACM Workshop on Motion,pp.50–58,Toronto,1983. [5] B.Duc.Feature design:applications to motion analysisand identity veriﬁcation.PhD thesis,´Ecole Polytechnique F´e d´e rale de Lausanne,1997.[6] D.Fleet,M.Black,Y.Yacoob,and A.Jepson.Designand use of linear models for image motion analysis.IJCV 36:169–191,2000.[7] D.J.Fleet and ngley.Recursiveﬁlters for opticalﬂow.IEEE Trans.PAMI,17:61–67,1995.[8]L.Florac,W.Niessen,and M.Nielsen.The intrinsicstructure of opticalﬂow incorporating measurement duality.IJCV,27(3):263–286,1998.[9]G.D.Hager and P.N.Belhumeur.Efﬁcient region trackingwith parametric models of geometry and illumination.IEEE Trans.PAMI,27(10):1025–1039,1998.[10]H.Haussecker.Simultaneous estimation of opticalﬂowand heat transport in infrared image sequences.Proc.IEEE Workshop on Computer Vision Beyond the Visible Spectrum, (submitted),Hilton Head,2000.[11]H.Haussecker and H.Spies.Motion.In Handbook of Com-puter Vision and Applications.B.J¨a hne,H.Haussecker,and P.Geissler(eds),Academic Press,pp.309–396.1999. [12] B.K.Horn and B.G.Schunck.Determining opticalﬂow.AI,17:185–204,1981.[13] B.J¨a hne,H.Haussecker,H.Spies, D.Schmundt,andU.Schurr.Study of dynamical processes with tensor-based spatiotemporal image processing techniques.Proc.ECCV, pp.322–335.Springer-Verlag,1998.[14] B.Lucas and T.Kanade.An iterative image registrationtechnique with an application to stereo vision.Proc.DARPA IU Workshop,pp.121–130,1981.[15]W.J.MacLean.Removal of translation bias when usingsubspace methods.Proc.ICCV,pp.753–758,Corfu,1999.[16]M.M¨u hlich and R.Mester.A considerable improvementin pure parameter estimation using TLS and equilibration.Proc.Conf.Stat.Methods for Image Proc.,1999.[17]N.Mukawa.Estimation of shape,reﬂection coefﬁcients andillumination direction from image sequences.Proc.IEEE ICCV,pp.507–512,Osaka,1990.[18]H.-H.Nagel.On a constraint equation for the estimation ofdisplacement rates in image sequences.IEEE Trans.PAMI, 11(1):13–30,1989.[19]S.K.Nayar and G.Narasimhan.Vision in bad weather.Proc.IEEE ICCV,pp.820–827,Corfu,1999.[20]S.Negahdaripour.Revised deﬁnition of opticalﬂow:in-tegration of radiometric and geometric clues for dynamic scene analysis.IEEE Trans.PAMI,20(9):961–979,1998.[21]O.Nestares,D.J.Fleet,and D.J.Heeger.Likelihood func-tions and conﬁdence bounds for total-least-squares estima-tion.Proc.IEEE CVPR,(this volume),Hilton Head,2000.[22]N.Ohta.Opticalﬂow detection using a general noise model.IEICE Trans.Inf.&Syst.,E79-D(7):951–957,1996. [23]S.Van Huffel and S.Vandewalle.The Total Least SquaresProblem:Computational Aspects and Analysis.SIAM, Philadelphia,1991.[24] A.Verri and T.Poggio.Motionﬁeld and opticalﬂow:qual-itative properties.IEEE Trans.PAMI,11(5):490–498,1989.[25]S.Wang,V.Markandey,and A.Reid.Total least squaresﬁt-ting spatiotemporal derivatives to smooth opticalﬂowﬁelds.In SPIE:Signal and Data Processing of Small Targets,pp.42–55,1992.[26]J.Weber and J.Malik.Robust computation of opticalﬂow ina multiscale differential framework.IJCV,15:67–81,1995.[27]L.Zelnik-Manor and M.Irani.Multi-frame alignment ofplanes.Proc.IEEE CVPR,Fort Collins,pp.151–156,2000.。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

a r X i v :a s t r o -p h /0506512v 1 21 J u n 2005Possible Optical Detection of the Anomalous X-ray PulsarCXOU J010043.1−721134Martin Durant and Marten H.van KerkwijkDepartment of Astronomy and Astrophysics,University of Toronto60St.George St,Toronto,ONM5S 3H8,CanadaABSTRACTArchival Hubble Space Telescope Wide Field/Planetary Camera 2observa-tions of the Small Magellanic Cloud serendipitously reveal a possible counterpart to the Anomalous X-ray Pulsar CXOU J010043.1−721134.The candidate is faint,but its location and strange colours make it an interesting object.We esti-mate,that the probability of such a detection being due to a non-physical source is less than 1.5%.We have tried to conﬁrm the identiﬁcation with Gemini-South and Magellan,but the conditions were insuﬃciently favourable.If conﬁrmed,the object will allow the ﬁrst detailed studies of the optical and ultraviolet emission of magnetars.Subject headings:pulsars:individual (CXOU J010043.1−721134)1.IntroductionThe anomalous X-ray pulsars (AXPs)are a class of neutron stars,numbering about half a dozen,which are radio-quiet,with periods of the order ∼10s and estimated ages of 103to 105yr.Like the soft gamma-ray repeaters,they are thought to be magnetars ,whose emission is powered by the decay of a super-strong magnetic ﬁeld (∼1015G).See Woods &Thompson (2004)for a review of the known magnetars and their properties.While energetically,the emission at X-ray energies dominates,optical and infrared pho-tometry of AXPs is giving interesting constraints on the physical processes of the stellar magnetospheres.Particularly intriguing is that for the brightest object,4U 0142+61,the optical spectral energy distribution is not just a power law.It shows,unique among neutron stars,a spectral break between V and B (Hulleman et al.,2004).Unfortunately,because of the uncertainty in the high amount of reddening,the precise shape cannot be measured.In the magnetar model,the optical emission could be dues to ion cyclotron emission. If so,the spectral break should be a general feature(C.Thompson,2004,priv comm.)due to the existence of a cooling radius in the magnetar magnetosphere from within which ions do not radiate(for a brief discussion,see Hulleman et al.,2004).The∼5other AXPs known so far are,unfortunately,too highly reddened to be detected in V or B.Another prediction is that the spectra of diﬀerent AXPs should be similar,but again uncertainties in the reddening do not allow us to test this(e.g.Durant&van Kerkwijk,2005).As an alternative model,Eichler et al.(2002),considered the possibility of coherent optical and infrared emission from the lower magnetosphere of a magnetar,in analogy to some radio pulsar models.Unfortunately,no clear predictions for the spectral shape were made.For the purposes of investigating the optical spectra of AXPs,the recent discovery of an AXP in the Small Magellanic Cloud(SMC),CXOU J010043.1−721134(Lamb et al.,2002; Majid et al.,2004)is particularly interesting.It is the only AXP found so far,that is not conﬁned to the disc of the Milky Way.The reddening to this source is,therefore,much less than for the other AXPs.Furthermore,its distance is relatively well known at60.6(1.0)kpc (e.g.Hilditch et al.,2005).It thus presents a unique opportunity to study an AXP in the blue/UV.2.Archival Observation and AnalysisSeeking imaging data on CXOU J010043.1−721134,we searched all the archives avail-able t us.We found that theﬁeld was observed on20April2004with the Wide Field and Planetary Camera2(WFPC2)on board the Hubble Space Telescope(HST),as part of a snapshot programme for three-colour photometry of several patches of the SMC(Tolstoy, 1999).Single exposures were taken of230s in the near-ultraviolet F300W,180s in the“broad V”F606W and300s in Cousins I-like F814Wﬁlters.The position of our object of interest is on chip WF2of the WFPC2array.We determined an astrometric solution by matching sources oﬀthe WF2image to objects in the USNO B1.0catalogue(Monet et al.,2003),andﬁtting for oﬀset,rotation and scale.Eight stars were matched,after rejecting7objects which had poorly measured positions or which corresponded to multiple sources on the WF2image.With these eight√sources,the uncertainty in the astrometricﬁt is0.′′19/Note that the latter is from the nominal Chandra performance,despite being somewhatoﬀ-axis(Lamb et al.,2002).The above numbers,combined in quadrature,give a totaluncertainty in the AXP’s position on our images of r=0.′′72at90%conﬁdence.Photometrywas performed using HSTphot1.1(Dolphin,2000).Figure1shows the F606W image of theﬁeld immediately around CXOU J010043.1−721134,with the positional error circle indicated.Stars X and Y have positions consistent with thatof the AXP,with Star Z being a nearby,much brighter source.Their positions and mag-nitudes are listed in Table1,and indicated in a colour-magnitude diagramme of all starsdetected in the WFPC2images in Figure2.From the photometry,Star Y is consistent with being a G5V star at the distance andreddening of the SMC,and Star Z an early B-type star.The colours and magnitudes of StarX do not correspond to any known stellar type,and make it a clear out-lier in Figure2,suggesting a very blue,possibly hot object.Based on its position and unusual colours,wetherefore consider Star X a likely counterpart to CXOU J010043.1−721134.As a caveat,however,it should be remembered that this measurement is based ona single F606W exposure.The source in Figure1does not appear like a cosmic ray hit,and the HSTphotχand Sharp parameters are within reasonable limits for a point source:χ=1.18(goodness ofﬁt parameter;reasonable values:<2.5)and Sharp=−0.425(where0corresponds to a stellar point spread function,positive values to more peaked proﬁles andnegative values to more diﬀuse ones;reasonable values:-0.5–0.5).There were no bad pixelswithin Star X’s proﬁle.In order to test the robustness of this identiﬁcation,we estimated the likelihood of sucha detection in an error circle of this size at any point on this chip of the detector.Wesearched the photometry for all objects in the F606W image which are classiﬁed as stellar(χ<2.5,−0.5<sharp<0.5),and with m606−m814<−0.3,i.e.at least as blue as Star X.Forty such objects are found on the same chip as Star X(including those near Star X inFigure2),giving the probability of one falling within a circle of radius0.′′72of≈1.5%.Wenote that the majority of these are within3pixels of brighter sources in the F814W image,and consequently were not detected in that band.Since this does not apply to Star X,andthere do not appear to be any artifacts close to it(i.e.the location of Star X appears likesky in the F814W image),the chance of it being a false detection is somewhat smaller,buthow much smaller is hard to quantify.We also calculated the likelihood of our putative detection being due to a cosmic rayhit or instrumental eﬀects.We searched for objects which are classiﬁed as stars in terms oftheir Chi and Sharp parameters as above,which were detected in F300W but not in F606W.Fig.1.—WFPC2images of theﬁeld of CXOU J010043.1−721134,in F606W(top),F300W (bottom left)and F814W(bottom right).Star X is the proposed counterpart,and Stars Y and Z its nearest neighbours.The circle shows the uncertainty in the Chandra position at 90%conﬁdence.Weﬁnd thirteen objects,which implies that the probability of Star X being due to a cosmic rays hit or purely instrumental eﬀects is0.4%(after correcting for the diﬀerence in exposure time between F300W and F606W).Seeking to conﬁrm this detection,we searched other archives for optical images.We found a V-band image from the Wide Field Imager(WFI)on the2.2m ESO telescope, La Silla,Chile.This demonstrated that the area of sky was very crowded,and extremely good seeing would be required to separate and securely detect Star X.In this case,the seeing was poor.We also obtained Gemini DDT observations with GMOS-S(Crampton &Murowinski,2004)at Cerro Pachon,Chile.Unfortunately,the seeing was also not good enough in these images to distinguish between the sources in the crowdedﬁeld.A proposal was also accepted at Magellan,Las Campanas,Chile,but conditions have not been good enough to obtain images so far.Unfortunately,the presence of Star Z means that only the most exceptional seeing conditions will allow further measurements of this object from the ground.3.Discussion and ConclusionsTaking Star X as the true optical counterpart,CXOU J010043.1−721134has an X-ray to opticalﬂux ratio F X/F V=1.0×10−13/5.5×10−15=18(un-absorbed X-rayﬂux in the2–10keV range from Woods&Thompson,2004;visualνFνﬂux is de-reddened using A V=0.3[Hilditch et al.,2005],and assumes m606=V).This compares with F X/F V=460 for4U0142+61(for A V=5.1,the nominal reddening),the only other AXP with an optical detection(Hulleman et al.,2004).Clearly the two ratios are very diﬀerent.It has been observed that infrared to X-rayﬂux ratios are similar for those AXPs with secure measurements(4U0142+61,1E1048.1−5937and1E2259+586;Durant&van Kerkwijk,2005).Variations have,however,been observed to be very large,of orders of magnitude in some cases.For example the transient AXP XTE J1810-197(Ibrahim et al, 2004)increased dramatically in both X-rays and infraredﬂux before slowly dimming again.It is possible that the diﬀerence in V-band to X-rayﬂux ratio above arises because the measurements for CXOU J010043.1−721134were not simultaneous;the AXP could have been brighter by a large factor at the time of the HST observation.CXOU J010043.1−721134 was observed to be sim50%brighter in X-rays by Majid et al.(2004)than Lamb et al. (2002),but they attribute this to the diﬀerent instruments used to make the observations rather than genuine variability.4U0142+61has been the most stable of the AXPs in both X-ray and opticalﬂux(Hulleman et al.,2004).This could,in principle,mean that theintrinsic spectra of the two objects are very diﬀerent,possibly indicating diﬀering magnetic ﬁeld conﬁgurations.The limit in F814W already provides some constraints on the shape of the optical spectrum.Whilst a Rayleigh-Jeans formνFν∼νn,n=3is possible,aﬂat spectrum (n=0)is excluded.The90%conﬁdence limit is n≥2.Since the spectrum should not increase steeper than Rayleigh-Jeans(in the absence of an emission feature),we predict that the I-band magnitude is not much below the limit we have established.The F300W limit is not constraining in this respect.In summary,we present Star X,with m606=24.19(15),as the probable optical counter-part to CXOU J010043.1−721134.It is at the right location and has colours unlike normal stellar sources.Although based on a detection in a single exposure,HSTphot diagnostics point to it being a real detection,with only a 1.5%probability of a false detection.If conﬁrmed,this discovery will enable the measurement of AXP properties in the blue and UV.Acknowledgements:This work made use of archival observations made with the NASA/ESA Hubble Space Telescope and with observations from ESO Telescopes at the La Silla Obser-vatories.We thank Slavek Rucinski and the Gemini Observatories for attempting follow-up observations.We thank an anonymous referee for very useful comments which much im-proved the presentation of our results.We acknowledgeﬁnancial support from NSERC.REFERENCESCrampton,D.&Murowinski,R.,2004,SPIE,5492,181Dolphin,A.,2000,PASP,112,1383Durant,M.,&van Kerkwijk,M.,2005,ApJ,in pressEichler,D.,Gedalin,M.,Lyubarsky,Y.,2002,ApJ,578,L121Ibrahim,A.,Markwardt,C.,Swank,J.,Ransom,S.,Roberts,M.,Kaspi,V.,Woods,P., Saﬁ-Harb,S.,Balman,S.,Parke,W.,Kouveliotou,C.,Hurley,K.,Cline,T.,2004, ApJ,609,L21IHilditch,R.,Howarth,I.,Harries,T.,2005,MNRAS,357,304Hulleman,F.,van Kerkwijk,M.,&Kulkarni,S.,2004,A&A,416,1037Lamb,R,Fox,D.,Macomb,D.,Prince,T.,2002,ApJ,574,L29Majid,W.,Lamb,R.,Macomb,D.,2004,ApJ,609,133Monet,D.et al.,2003,AJ,416,1037Tolstoy,E.,1999,IAU Symposium192,ASP,eds Whitelock,P.and Cannon,R. Woods,P.,&Thompson,C.,2004,in“Compact Stellar X-ray Sources”eds Lewin W.and van der Klis,M.Table1.Astrometry and photometry of stars near CXOU J010043.1−721134 Star R.A.J2000Dec J2000m300m606m814m606−m814M V aNote.—Limits are at the3σlevel.a Calculated using(m−M)0=18.9and A V=0.3(Hilditch et al.,2004)and assuming m606≃Vb Proposed counterpart to CXOU J010043.1−721134,which has position R.A.=01:00:43.14,dec=−72:11:33.8。