Biomedical Engineering Reference
In-Depth Information
he.imaging.process.in.luorescence.mode.is.completely.diferent,.because.the.coherence.is.destroyed.
during.the.process.of.excitation.and.emission.of.the.dye.molecule..Let.
f
.denote.the.distribution.of.the.
luorescent.dye..hen.the.excitation.creates.an.incoherent.luorescent.ield.of.an.intensity.|
h
1
|
2
f
..Following.
Wilson.and.Sheppard.(1984).and.Wilson.(1989),.the.successive.incoherent.imaging.of.this.ield.yields
I
fluorescence
=
|
h u v
( ,
, )
φ
h u
(
/
β
,
v
/
β φ
, ) |
2
⊗
f
.
.
(3.12)
1
2
where. β λ λ
=
2 1
. is. the. ratio. between. the. emitted. luorescence. wavelength.
λ
2
. and. the. excitation.
.wavelength.
λ
1
..Again,.the.imaging.process.is.modeled.by.a.convolution.of.some.efective.PSF.and.the.
object. function.. his. insight. is. the. starting. point. for. so-called. deconvolution. techniques. that. aim. to.
.calculate. a. closer. approximation. of. the. object. by. taking. into. account. the. properties. of. the. imaging.
device,.that.is,.the.PSF.
3.5 PSF for an ideal Lens and Diffraction Limited imaging
Let.us.consider.a.symmetric.pupil.function.
P
(
r
1
).for.an.ideal.lens.that.has.uniform.phase.and.uniform.
amplitude.and.is.unity.for.a.radius.of.
r
1
.≤.
a
..Using.Equation.3.7,.we.can.state.the.radial.variation.of.the.
intensity.distribution.in.the.focal.plane.of.the.lens.as
2
| (
h r
) |
2
2
J
( )
ν
∝
2
1
I r
(
)
=
.
.
(3.13)
2
λ
f
ν
2
2
Here.
J
1
(.).denotes.the.irst-order.Bessel.function.of.the.irst.kind.(Abramowitz.and.Stegun.1972)..his.
radially. symmetric. intensity. distribution. is. also. known. as. the. Airy. pattern. and. is. plotted. in. the. let.
panel.of.Figure.3.4.
he.axial.intensity.distribution.for.an.ideal.lens.may.also.be.calculated.from.Equation.3.7,.and.has.
the.form
2
∝
sin( / ))
/
u
u
4
4
.
I
( , ) | ( ,
0
u
=
h u
0 0
, )|
2
.
(3.14)
and.is.shown.in.the.right.panel.of.Figure.3.4..Again.the.deinition.(3.9).for.the.axial.normalized.optical.
coordinate.was.used.
1
1
0.8
0.8
0.6
0.6
Lateral
Axial
0.4
0.4
0.2
0.2
0
0
0
2
4
6
8
10
0
5
10
15
20
25
30
35
Normalized optical coordinate
u
Normalized optical coordinate
v
FIGuRE 3.4
Intensity. distribution. in. the. focal. region. of. an. ideal. lens.. Let:. lateral. proile. through. focus.. his.
function. is. also. known. as. Airy. pattern.. Right:. axial. proile. through. focus.. For. the. deinition. of. the. normalized.
optical.coordinates,.see.Equations.3.8.and.3.9.
