lecture072FPN

Lecture Notes7Fixed Pattern NoiseEE392B Handout#20 Prof.A.El Gamal and H.-S.P.Wong Spring05•Definition•Sources of FPN•Analysis of FPN in PPS and APS•Total Noise Model•Correlated Double SamplingEE392B:Fixed Pattern Noise7-1Fixed Pattern Noise(FPN)•FPN(also called nonuniformity)is the spatial variation in pixel outputvalues under uniform illumination due to device and interconnectparameter variations(mismatches)across the sensor•It isfixed for a given sensor,but varies from sensor to sensor,so if v o isthe nominal pixel output value(at unifrom illumination),and the output pixel values(excluding temporal noise)from the sensor are v ij for1≤i≤n and1≤j≤m,then thefixed pattern noise is the set of values ∆v oij=v oij−v o•FPN consists of offset and gain components–increases with illumination, but causes more degradation in image quality at low illumination•FPN for CCD image sensors appears random•CMOS(PPS and APS)sensors have higher FPN than CCDs and sufferfrom column FPN,which appears as“stripes”in the image and can result in significant image quality degradationEE392B:Fixed Pattern Noise7-2FPN ImagesFor CCD sensor For CMOS sensorEE392B:Fixed Pattern Noise7-3Sources of FPN•CCD image sensors only suffer from pixel FPN due to spatial variation in photodetector device parameters and dark current–neither the CCDs nor the output amplifier(which is shared by all pixels)cause FPN(additional nonuniformity can result if more than one output amplifier is used,however)•In CMOS image sensors pixel transistors cause additional pixel FPN and column amplifiers cause column FPN.As a result FPN is in general higher than in CCDsEE392B:Fixed Pattern Noise7-4•Main sources of FPN in PPS:i dcA D v T ,C olv ov REF +v op osC f◦Pixel FPN is mainly due to the variation in the photodetectorparameters (e.g.,area A D )and dark current◦Column FPN is due to the variation in the column amplifierparameters,e.g.,offset voltage v op os ,feedback capacitor value,resettransistor threshold voltage and overlap capacitance value C olEE 392B:Fixed Pattern Noise 7-5•InAPSi dcA DoC D v ◦In addition to variation in the photodetector parameters and dark current,pixel FPN is caused also by variations in transistorparameters◦Column FPN is mainly due to variation i biasEE 392B:Fixed Pattern Noise 7-6PPS and APS FPN•APS suffers from higher pixel FPN than PPS but PPS generally suffersfrom higher column FPNPPS APSEE392B:Fixed Pattern Noise7-7Quantifying FPN•FPN is quantified by the standard deviation of the spatial variation inpixel outputs under uniform illumination(not including temporal noise).It is typically reported as a%of voltage swing(or well capacity)◦FPN standard deviation values of<0.1%to>4%of well capacityhave been reported•Experimentally,FPN is measured as follows:◦Set a constant uniform illumination level(including no illumination)◦Take many images◦For each pixel compute the average output value(to average outtemporal noise)◦Estimate the standard deviation of the average pixel values◦Repeat the procedure for several uniform illumination levelsEE392B:Fixed Pattern Noise7-8Analysis of FPN•Suppose we are given the standard deviation of each parameter that casues FPN,we now show how to compute its contribution to the total FPN•Assume the parameter values to be random variables Z1,Z2,...,Z k expressed asZ i=z i+∆Z i,where z i is the mean of Z i(i.e.,nominal value of the device parameter) and∆Z i is the variation of Z i from its mean,and has zero mean and standard deviationσZi•Assuming sufficiently small device parameter variations,we can approximate the pixel output voltage(for a given illumination)as a function of the device parameters using the Taylor series expansion,asV o(Z1,Z2,...,Z k)≈v o(z1,z2,...z k)+ki=1∂v o∂z i z1,z2,...z k·∆Z iEE392B:Fixed Pattern Noise7-9 where v o(z1,z2,...z k)is the nominal output voltage and∂v o/∂z i is thesensitivity of v o w.r.t.the i th parameter(evaluated at the nominalparameter values)•So the variation in V o can be represented by the random variable∆V o=ki=1∂v o∂z i z1,z2,...z k·∆Z i•To quantify FPN,wefind the standard deviation of the output voltage,σVo,i.e.,the standard deviation of the r.v.∆V o•Assuming that the∆Z i s are uncorrelated(may not be a good assumption in general),we can writeσVo= k i=1 ∂v o∂z i z1,z2,...z k 2·σ2Z iEE392B:Fixed Pattern Noise7-10Column and Pixel FPN•For a CMOS(PPS or APS)image sensor,let the column device parameters be Z1,Z2,...,Z l and the rest be the pixel device parameters, we can define the column variation asY=li=1∂v o∂z i z1,z2,...z k·∆Z iand the pixel variation asX=ki=l+1∂v o∂z i z1,z2,...z k·∆Z i•We quantify column FPN byσY and pixel FPN byσX(vary withillumination)•Since(by assumption)X and Y are uncorrelatedσ2Vo=σ2Y+σ2XEE392B:Fixed Pattern Noise7-11Offset and Gain FPN•The pixel output voltage v o and FPNσVovary with illumination •The nominal output voltage from a pixel can be expressed in terms of the photocurrent density asv o=hj ph+v oswhere h is the pixel gain in V·cm2/A(not to be confused with sensorconversion gain g)and v os is the pixel offset(which includes the dark signal as well as the offset voltages due to the amplifiers used,e.g.,v op os for PPS)•Assuming all photodetectors have the same QE,and thus under uniform illumination,they have the same photocurrent density,we can now write the pixel output voltage variation as∆V o= k i=1∂h∂z i z1,z2,...z k∆Z i j ph+ k i=1∂v os∂z i z1,z2,...z k∆Z i=∆H j ph+∆V osEE392B:Fixed Pattern Noise7-12•We quantify offset FPN byσVand gain FPN byσH·j phos•Offest FPN is reported as%of well capacity•Gain FPN is referred to as Pixel Response Nonuniformity(PRNU)and is reported as%of gain factor variation,i.e.,100σH/h•Note that∆H and∆V os are not necessarily uncorrelated,since somedevice parameters can affect both offset and gainEE392B:Fixed Pattern Noise7-13Analysis of FPN in PPS•Thefigure shows the device parameters consideredi dcA D v,C olTC fv ov REF+v oposA D is the photodiode area,i dc is its dark current,v op os is the opamp offsetvoltage,C ol is the overlap capacitance,and v T is the threshold voltageEE392B:Fixed Pattern Noise7-14•The output voltage in steady state is given byv o=(Q+C ol v T)·1C f+v REF+v op os,where C ol v T is the“feedthrough”charge(when the reset transistor isturned off),and the charge Q accumulated on the photodiode capacitanceQ=(j ph A D+i dc)t int•The following table lists the absolute values of the parameter senitivities ∂v oiand effect on FPNParameter Sensitivity Effect on FPNA D t intC f·j ph pixel/gaini dc t intC fpixel/offsetv op os1column/offsetC f i dc t int+C ol v TC2fcolumn/offset+A D t intC2f·j ph column/gainv T C olC fcolumn/offsetC ol v TC fcolumn/offsetEE392B:Fixed Pattern Noise7-15•Offset FPNσVos= t int fσi dc 2+σ2v op os+ i dc t int+C ol v T2f σC f 2+ v T fσC ol 2+ C ol fσv T 2•Gain FPNσH·j ph=j ph t int C fσA D 2+ A D t int C2fσC f 2•Pixel FPNσX= j ph t int C fσA D 2+ t int C fσi dc 2•Column FPNσY= σ2v op os+ i dc t int+C ol v T+A D j ph t int2f σC f 2+ v T fσC ol 2+ C ol fσv T 2•Note that the FPN varianceσ2V o=σ2X+σ2Y can be written as the sum of three terms,a term that is independent of the signal,a term thatincreases linearly with the signal,and a term that increases quadratically with the signalEE392B:Fixed Pattern Noise7-16Example•Assume the following device parameter means,standard deviations,and that t int=30msParameter MeanσSensitivityA D50µm20.4%A D15×103j ph V/µm2i dc5fA2%i dc1.5mV/fAv op os0V2mV1C f20fF0.2%C f11.6×1011V/F37500j ph V/fFv T R0.8V0.2%v T R0.02C ol0.4fF0.4%C ol0.04V/fFEE392B:Fixed Pattern Noise7-17•Offset FPNParameter Contribution toσVosi dc0.15mVv op os2mVC f0.0464mVv T R0.032mVC ol0.064mVand≈2mV,σVosvaluewhich is basically equal to the opamp offsetσv opos•Gain FPN at j ph=2.64×10−6A/cm2(high illumination)Parameter Contribution toσH·j phA D7.92mVC f3.96mVandσH·j ph=8.85mVEE392B:Fixed Pattern Noise7-18•The followingfigure plots total FPNσVo,pixel FPNσX,and column FPN σY,assuming monochromatic illumination F0photons/cm2.s at quantum efficiency QE=0.3EE392B:Fixed Pattern Noise7-19Analysis of FPN in APSi dcA DC D•In steady state and assuming soft reset,the output voltage is given byv o=v DD−v T R−QC D− v T F+ F k n W F i bias , where the charge accumulted on the photodiode is given byQ=(A D j ph+i dc)t int+C olR v DDThe C olR v DD term is the“feedthrough”charge(when the reset transistor is turned off)EE392B:Fixed Pattern Noise7-20Example•Consider the following parameter means and standard deviations parameter meanσeffect on FPNi dc5fA2%i dc pixel/offsetA D50µm20.4%A D pixel/gainC D20fF0.4%CD pixel/offset,gainv T R 1.1V0.2%v T R pixel/offsetC olR0.4fF0.4%C olR pixel/pffsetv T F0.9V0.2%v T F pixel/offsetW F L F 420.2%W FFpixel/offseti bias1.88µA1%i bias column/offset•You will compute the FPN component values in the homeworkEE392B:Fixed Pattern Noise7-21Image Sensor Total Noise Model•Combining temporal noise and FPN,we can express the total inputreferred noise charge asQ n=Q shot+Q reset+Q readout+Q fpn,where◦Q shot is the r.v.representing the noise charge due to photodetectorphoto and dark current shot noise and is Gaussian with zero meanand variance1q(i ph+i dc)t int electrons2◦Q reset is the r.v.representing the reset noise and is basicallyindependent of the signal◦Q readout is the r.v.representing the readout circuit noise(possiblyincluding quantization)and is basically independent of the signalEE392B:Fixed Pattern Noise7-22◦Q fpn is the r.v.representing FPN(in electrons),and can be represented either as a sum of pixel and column componentsQ fpn=1g(X+Y)where g is the sensor conversion gain in V/electron, or offset and gain componentsQ fpn=1g(∆Hj ph+∆V os)Thus it has one component that is independent of signal and onethat grows with the signal◦The noise components are assumed independent•Thus the total average noise power is the sum of three components:◦One that does not depend on the signal(due to reset and readoutnoise and offset FPN)◦One that increases linearly with the signal(i ph or j ph)(due to shotnoise and gain FPN)◦One that increases quadratically in the signal(due to gain FPN)EE392B:Fixed Pattern Noise7-23 Noise as Function of PhotocurrentEE392B:Fixed Pattern Noise7-24Correlated Double Sampling (CDS)•CDS is a multiple sampling technique commonly used in image sensors to reduce FPN and reset noise •You sample the output twice;once right after reset and a second time with the signal present.The output signal is the difference between the two samples◦CDS only reduces offset FPN (does not reduce gain FPN)◦CDS does not cancel offset FPN due to dark current variation ◦In CCDs,PPS,photogate and pinned diode APS,CDS cancels reset noise.In photodiode APS it increases itEE 392B:Fixed Pattern Noise 7-25CDS inPPSReset SR oSoRWord,SSEE 392B:Fixed Pattern Noise7-26•Cancells,v T,and C ol◦FPN due to v oposand V2o3in our analysis)◦Temporal noise due to reset(terms V2o2◦Readout noise due to op-amp1/f noise•Does not cancel◦Offset FPN due to i dc variation.This is called Dark SignalNon-uniformity(DSNU)◦Gain FPN(or PRNU)◦Other temporal noise components•Addsterm)◦Opamp noise due to reset read(Vo4◦KTnoise due to SS and SR transistorsCEE392B:Fixed Pattern Noise7-27•To summarize,the total noise charge for the two samples are given by:Q n1=Q reset+Q read1+Q fpn1Q n2=Q shot+Q reset+Q readout2+Q fpn2Note that Q fpn1is simply an offset FPN whereas Q fpn2is the sum of offset and gain FPN(PRNU).However,Q fpn1does not include the offset FPN due to dark current variation(DSNU),whereas the offset part of Q fpn1includes itThe difference between the two samples is thus:Q n2−Q n1=Q shot+(Q readout2−Q readout1)+Q prnu+Q dsnuEE392B:Fixed Pattern Noise7-28PPS FPN With and Without CDS•The following figure plots PPS FPN with and without CDS (assumingthat v op,v T ,and C ol are eliminated)EE 392B:Fixed Pattern Noise 7-29PPS Offset FPN With and Without CDS102030405060102030405060102030405060102030405060without CDS with CDSEE 392B:Fixed Pattern Noise 7-30CDS in 3TAPSWord ResetReset SS SRoSoREE 392B:Fixed Pattern Noise7-31•Cancells◦All offset FPN terms involving v T R ,v T F ,C olR ,W F L F ,and i bias•Does not cancel◦DSNU ◦Reset noise ◦PRNU ◦Readout noise •Adds◦Reset noise kT 2C D (reset noise component during reset readout independent of that during signal readout)◦Readout noise during reset readout ◦kT Cdue to SS and SR transistorsEE 392B:Fixed Pattern Noise 7-32•To summarize,the total noise charge for the two samples are given by:Q n1=Q shot+Q reset1+Q readout1+Q fpn1Q n2=Q reset2+Q readout2+Q fpn2The difference is:Q n1−Q n2=Q shot+(Q reset1−Q reset2)+(Q read1−Q read2)+Q prnu+Q dsnu•An important advantage of photogate and pinned diode APS is that reset noise is eliminated using CDS instead of doubledEE392B:Fixed Pattern Noise7-33。