Biomedical Engineering Reference
In-Depth Information
We. can. use. this. paraxial. approximation. to. ind. the. travel. times. for. light. along. the. diferent. paths.
shown.in.
Figure.2.3
.
.he.travel.times.along.the.paths.from.point.
O
.to.
P
.and.from.point.
P
.to.
I
.are.given.by
n
c
OP t
n
c
PI
1
2
t
=
=
OP
PI
.
he.travel.times.along.the.path.from.point.
O
.to.
I
.are.given.by
n
c
OV t
n
c
VQ t
n
c
QC t
n
c
CI
t
=
1
=
2
=
2
=
2
OV
VQ
QC
CI
.
hen,.the.total.travel.times.along.the.paths.
OPI
.and.
OI
.are.as.follows:
n
c
OP
n
c
PIs
t
=
1
+
2
OPI
n
c
OV
n
c
(
)
t
=
1
+
2
VQ QC CI
+
+
OI
.
We.can.then.use.the.paraxial.equation.to.simplify.this.equation:
OP OQ
=
+
∆
=
OV VQ
+
+
∆
1
1
h
s
2
=
OV VQ
+
+
2
1
PI QI
=
+
∆
=
QC CI
+
+
∆
2
2
h
s
2
=
QC CI
+
+
2
.
2
he.diference.in.the.travel.times.along.the.two.routes.would.be
n
c
n
c
(
)
+
(
)
1
2
t
−
t
=
OP OV
−
PI VQ QC CI
−
−
−
OPI
OI
+
n
c
h
s
2
n
c
h
s
2
=
1
VQ
+
2
−
VQ
2
2
.
1
2
For.the.travel.times.along.the.two.routes.to.be.equal,.we.need
n
c
h
s
=
n
c
h
s
2
2
1
2
VQ
+
VQ
−
2
2
1
2
n
c
h
s
n
c
h
s
VQ
n
c
n
c
2
2
1
+
2
=
2
−
1
2
2
1
2
n
s
n
s
VQ
h
2
(
)
1
1
+
2
2
=
n
−
n
1
2
2
.
