Biomedical Engineering Reference
In-Depth Information
6.4 Wavefront Aberration Simulation for a cylindrical object
he. simulation. model. for. wavefront. aberrations. of. cylindrical. objects. is. very. similar. to. that. used. for.
spherical.objects..Again,.we.would.like.to.ind.the.pupil.function.
P
(
r
,θ).of.Equation.6.1,.depending.on.
the.focal.position.and.the.geometry.of.the.specimen..A.sketch.of.the.simulation.model.is.depicted.in.
Figure. 6.6.. he. unit. direction. vector. w. deines. the. direction. of. the. cylinder. axis,.
C
. is. a. point. on. the.
cylinder.axis,.
R
.denotes.the.radius,.and. ∆ =
n
n
n
c c
0
.is.the.absolute.diference.in.refractive.index.of.the.
cylinder.in.respect.to.the.immersion.medium..he.unit-direction.vector.
t
.again.describes.the.direction.
of.the.traced.ray.and.is.obtained.from.the.polar.coordinates.of.the.pupil.plane.using.Equation.6.4..he.
vector.denoted.by.
m
.points.from.the.focus.
P
.to.
C
.on.the.cylinder.axis..If.
a
(
m
,
t
,
w
).denotes.the.distance.
the.ray.travels.within.the.cylinder,.we.ind
−
2
R
−
m t w
t w
d
(
,
,
)
2
2
for
d R
<
.
.
(6.8)
a
(
m t w
,
,
)
=
|
×
|
0
otherwise
Here,.
d
.refers.to.the.distance.between.the.passing.ray.and.the.axis.of.the.cylinder..If,.furthermore,.the.
vector.
w
.is.normalized.to.unity,.the.distance.
d
.is.given.by
|
m w t
w t
·(
×
) |
.
d
=
.
(6.9)
|
×
|
Using.the.vector.components,.we.get
(
m w t
(
−
w t
))
2
+
(
m w t
(
−
w t
))
2
+
(
m w t
(
−
w t
))
2
x
y z
z y
y
z x
x z
z
x
y
y x
.
d
=
.
(6.10)
(
w t
−
w t
)
2
+
(
w t
−
w t
)
2
+
(
w t
−
w
y
t
)
2
y z
z y
z x
x z
x y
Now.the.set.of.Equations.6.2,.6.4,.6.8,.and.6.10.allows.one.to.calculate.the.phase.function.that.con-
tains.the.aberration.due.to.the.wavefront.distortions.imposed.by.the.object.
Pupil function
P
(
r
,
θ
)
in the pupil plane
of the lens
θ
r
Objective lens
β
γ
Beam focused to the
bottom of the sample
Embedding medium
of refractive index
n
0
Single ray that is traced
t
w
Cylindrical region of
radius
R
and
refractive index
n
c
Microscope slide
R
C
m
Scan
P
FIGuRE 6.6
Model.for.the.calculation.of.the.aberrations.caused.by.a.cylindrical.object.
