78
2 Holographic Microscopy of Phase and Diffuse Objects …
It is easy to notice that in (2.22) exponent tends to zero at ε → ∞, and moreover,
it is equal to zero at the condition
1 −
2R 0 A
εq 2 B
= 0.
(2.23)
Equation (2.23) amounts to cubic equation relative to ε and has the root ε =
4R 0 /3q
2 . Considering that the exponent is approximately equal to zero, it is possible
to show that at |ε| > 5R 0 /dq the exponent is almost equal to zero. As, as a rule,
5R 0 /dq < 4R 0 /3q
2 , then the case of |ε| > 5R 0 /dq is further considered and at that
the contrast is transformed into:
γ =
1 +
ππR
λ
2
−
1
4
.
(2.24)
If γ ≥ 0.1, then R/λ < 100/π . Thus, in all planes, which satisfy the condition
of |ε| > 5R 0 /dq, for object areas corresponding to |x| < R 0 /4 and at the deformation
of R/λ < 100/π , the interference pattern will be observed with the contrast
more than 0.1, and this contrast does not depend on the coordinates in the recording
plane and reveals as the function of only deformation value R (Fig. 2.6b). Phase
correlation at ε = −5R 0 /dq . . . will lead to the formation of dark and light fringes:
2
X
M
2
625π R
2
0
R
λ
1 −
25π
2
4
R
λ
2 q
d
2
− 4π
R
λ
=
2π n
−light fringes
(2n + 1)π −dark fringes
For example, n-th fringe will be in the point position with the coordinate
X n = 25π R 0 M
n + 2
R
λ
1 −
25π 2
4
R
λ
2 q
d
2
R
λ
.
(2.25)
Thus, the calculation shows the limits of holographic recording of cylinder object
radial deformation and allows calculating its value by the interference pattern [71].