Biomedical Engineering Reference
In-Depth Information
Traced ray
t
a(
m,t
)
C
d
L
Radius
R
v
m
P
(Focal point)
FIGuRE 6.2
Illustration.of.the.plane.that.contains.the.center.
C
.of.the.sphere.and.the.traced.ray.passing.the.focal.
point.
P
.in.a.direction.deined.by.the.vector.
t
.
t
=
=
r
sin( )cos( )
sin( )sin( )
γ
θ
x
.
t
r
γ
θ
.
(6.3)
y
t
=
1
−
r
2
sin
2
( )
γ
z
he.value.of.
a
,.which.is.the.section.the.ray.travels.within.the.sphere,.can.be.calculated.from.the.dis-
tance.
d
.between.the.ray.and.the.center.
C
.of.the.sphere.by
.
2
R
2
−
d
2
(
m t
, )
for
otherwise
d R
<
.
(6.4)
(
, )
m t
=
0
From.Figure.6.2.we.see.that.
d
.follows.from
.
d
=
|
LC
| |
=
m v m t m t
−
| |
=
−
·(
· ) |
.
(6.5)
If.the.vector.
m
.has.the.components.(
m
x
,
m
y
,
m
z
),.we.get
d
=
(
m t m t m t m t
m t m t m t m t
m t m t m t m t
−
(
+
+
))
2
2
x
x
x x
y y
z z
.
.
(6.6)
+
(
−
(
+
+
))
2
y
y
x x
y y
z z
+
(
−
(
+
+
))
2
z
z
x x
y y
z z
Now. the. phase. function. ψ(
r
,θ). can. be. calculated. using. Equations. 6.2. through. 6.6.. he. scanning.
across. the. virtual. sample. may. be. implemented. by. altering. the. coordinates. of. the. center.
C
. of. the.
sphere,.and.the.focusing.depth.can.be.changed.by.modifying.the.coordinates.of.the.focal.point.
P
.of.
the.model.
