2.1 Holographic Microscopy for the Study of Phase, Diffusive …
77
Fig. 2.6 a The scheme of interference pattern recording at radial expansion of the cylinder
object: 1—the object; 2—the divider; 3—the diaphragm; 4—the lens; P—the recording plane.
b Dependence of interference pattern contrast on deformation value. Reprinted from [136] with
permission
|γ | =
R 0
−R 0
exp
i
4π
λ
R
2
0 − x 2 + i
4π
λ
(1 + β)
R
2
0 − x 2
+ i
π
λ
x
2
d
+
X
2
p
−
x
d
−
X
p
2
λ 2
πq 2 − i
λ
π
ε
−
(1+β)x
d
−
X
p
2
λ 2
π 2 q 2 + i
λ
π
ε
−i
π
λ
(1 + β)
2 x
2
d
+
X
2
p
dx
(2.21)
Let us simplify, considering that
R
2
0 − x 2 ≈ R 0 − x
2
/2R 0 , and substitute
the reflection function for exp(−x
2
/R
2
0 ). But stated assumptions are reasonable for
cylinder radial expansion in the range |x| ≤ R 0 /4.
Then, transformed integral is taken accurately within infinite limits, and under
normalization β = 0, the module γ will be written in the following way:
|γ | =
1 +
kβ R o A
2B
2
−
1
4
exp
⎧
⎪ ⎪ ⎨
⎪ ⎪ ⎩
−
k
6 q
8
β
2 R
2
0 X
2
ε
2
8d 2
4 + k 2 ε 2 q 4
M 2 B
1 −
2R 0 A
4q 2 B
2
1 +
kβ R 0 A
2B
2
⎫
⎪ ⎪ ⎬
⎪ ⎪ ⎭
,
(2.22)
where
A = d
2
4 + k
2
ε
2 q
4
+ R 0 k
2
εq
4
;
B = d
2
4 + k
2
ε
2 q
4
+ R
2
0 k
2 q
2
,
where M = p/d.