傅里叶光学 信息光学课件

n
I ( p) Ii ( p) i 1
3/ ""
1 2 /
1 ----
2cos/sin----V(x)=f(x+d)=f(x)
f
(
x)
0
2
i 1
an
cos(2x
n a
)
bn
sin(2x
bn)
3eix
f (x) F (x) ei2fdf
LSI 1----/
t s(t) s'(t)
rect( x)
1
a
a
0
a
x
2
2
OTF
1-|x|/a |x|a
tri(x/a)=
0
a<0,2a
tri(x/a)tri(y/b)
tri( x ) a
1
a 0 a
x
Sinc
sin( x)
a
Sincx/a= x x=�na n=�1,�2,...
a
Sincx/aSinCy/b
sin c( x ) a
-3a
-a
-2a
a
3a
2a
x
Gaus( x ) exp[ ( x )2 ]
a
a
1
a 1,Gaus(x) exp( x2 )
Gaus( x )Gaus( y ) exp{[( x )2 ( y )2 ]}
a
b
ab
Gaus(r) exp( r2 )
1
Gaus( x ) a
x
-a
a
1
circ( x2 y2 ) =
step(x)
sgn(x)
2.3
1 x>0 Stepx= � x=0
0 x<0
step(x)
1
0
step(x-x0),x0
x
1 x>0 Sgnx= 0 x=0
-1 x<0
Sgn(x)=2step(x)-1
sgn(x)
1
x
0
1
1 |x|a/2
rect(x/a)=
0
a1
rect(x/a)rect(y/b)
:SW
SW=A0Af
A0: Af
SW
N=Nx �Ny= x � yBx �By
Nx=
x�Bx=
x
x
Bx � x =1
1FT
2
3
4
5
Fourier Fourier
x
-- combx rectx sincX
Fourier
2.1 2.2 2.3 2.4 2.5 2.6Fourier 2.7fourier 2.8LSI
Fourier Fourier
""
:
Uxy
I (x, y)
1
2
3
1
= =
2--
Ex, y, z; t=A cos(k�r-�t)
3
4 It
1.22 D
5
TW
TWt� � t =1
t
TW= t
2.1
()
1 2/ 3 4----
5
u i u j u k u x y z
2
2 x 2
2 y 2
2 z 2
, , FL
S (t) FT S ( f )
1/ :
a s a n
i
(t)
i
n
i s'i(t )
i1
i1
2
E E1( p) E2( p)
n
Up=Ui ( p) i 1
2 h(x, y;0, 0) h(x, y; ,)
3
h(x, y) h(x, y;,), h
x
L
x
h(x, y; x0, y0) :
00
(x0 , y0 )
y'
h(x, y)
h(x x0, y y0)
y
g(x) { f (x)}
fx
f
(x)
f
( )
(x
)d
g(x)
{
f
() (x
,
y
)dd
1
(x)
0
h(x, 0)
x
f (x) (x)
g(x) { f (x)} { (x)} h(x,0)
(x xi)
h(x, xi )
0 xi
0 xi
h(x, xi ) { (x, xi )}
h(x, y;0, 0) { (x, y)} h(x, y; ,) { (x , y )}
)d}
f
( )h( x, )d
g(x,
y)
f
( , )h( x,
y; , )dd
g(x, y) f (,)h(x , y )dd f (x, y) h(x, y)
g(x) f ()h(x )d
f(x)h(x)
rect(x)
rect(x)rect(y)
Circ(r)
comb(x)
1/2 1
x
h(x)
1/2
1/2 1
x
1
h(x)= rect(x-1/2)
2
g(x) f ()h(x )d f (x) h(x)
x , h() h()
h() x0h(x0 )
x0 x0
f ()h(x0 )
x0 g(x0 )
f()
h(x0 )
g(x) f ()h(x )d f (x) h(x) g(x)
t s(t ) s'(t )
2
f (x) g(x) f (x x0) g(x x0)
f (x x0) g(x x0)
2.2
1 2
(x, y) 0 x 0 y 0
(x,
y)dxdy
1
(
x,
y)
(x,
y)dxdy
(0,0)
3
(x) 0
1/2
x 0
1
2
h(x)
(x+x0) (x-x1)
f(x)=rect(x/a)
x
a
x0
x1
h(x)= 1 comb( x )
d
d
g
(
x)
rect
(
x d
)
[(x+x0
)+(x-x1
)]
d
x d
x0
x1
g(x) rect( x ) 1 comb( x )
12 3
f (x)
x
f
( x0)
(x
x0 )
f
( x)dx
f
( x1)
(x
x1)
f
( x)dx
f
( x2)
(x
x2)
f
( x)dx
.
.
.
f
( xn)
(x
xn)
f
( x)dx
(x )
wenku.baidu.com
f
( )
f
(x)
(x
)dx
x
f
(x)
(
x)
f
( )d
(x
)
f
( )d
f
(x,
y)
f
( ,) (x
A (x x1)
x2
x1
x
B (x x2)
4
(x
x0,
y
y0) ( x,
y)dxdy
( x0
,
y0)
(ax) 1 (x)
a
a1
h( x,
y)
(x
x
,
0
y
y) 0
h( x
x
,
0
y
y) 0
rect( x) a
a
x
(x x0)
x0
x
x0
x
f (x)
x x x x 0
r0
0
x2 y2 1
circ(r/r0)
x2 y2
circ(
)
r0
y
1
x 0 r0
2.4
:
g(x) f ()h(x )df (x) h(x)
g(x,
y)
f
(,)h(x ,
y
)dd
f
(x,
y) h( x,
y)
Ut=U0h(h)
It=I0hI (hI)
f(x)
1
f(x)=rect(x-1/2)