Biomedical Engineering Reference
In-Depth Information
Circular pupil stop
Focal
plane
x
u
z
z
E
(
u
)
=
P
(
u
)
Ae
i
2
πz
/
λ
p
(
x
)
=
F{
P
(
u
)
}
FIGuRE 1.22
Fourier.transform.relation.of.incoming.wave.to.the.ield.at.the.image.plane..Here.
u
.is.the.position.
in.the.aperture.plane,.
E
(
u
).is.the.electric.ield.at.the.aperture,.
P
(
u
).is.the.pupil.function.(one.inside.the.aperture,.zero.
outside.the.aperture),.and.
p
(
x
).is.the.electric.ield.at.the.focal.plane.
Image
plane
Object
plane
x
x
'
z
z
FIGuRE 1.23
Two-lens.system.that.produces.an.image.of.sources.in.the.object.plane.
not.the.case..A.laser-illuminated.scene.will.exhibit.“speckle”.due.to.the.rough.surface,.causing.random.
reinforcement.and.cancellation.of.coherent.waves.
Assuming.the.incoherent.source.ield
2
(
)
(
)
=
(
)
(
)
o x o x
′
*
′′
o x
′
δ
x
′ − ′′
x
.
t
2
2
2
2
( )
(
)
(
)
( )
⊗
( )
∫
i x
=
p x
− ′
x
o x
′
d
x
′ =
PSF
x
o x
t
that.is,.the.distribution.of.intensity.in.the.image.plane.is.the.convolution.of.intensity.in.the.object.plane.
with.the.PSF..he.PSF.is
{
}
=
{
}
2
.
( )
=
( )
=
∫
(
)
(
)
( )
PSF
x
p x
F
P u P u u
−
′
d
u
F
OTF
u
′
′
he.OTF,.deined.as
(
)
(
)
.
∫
OTF
( ) :
u
=
P u P u u
′
− ′
d
u
′
