2.1 Holographic Microscopy for the Study of Phase, Diffusive …
75
that corresponds to the result in [125]. In spite of the results in [125], (2.16) shows
that in general the contrast depends on the object transverse shift as well as on the
defocusing value. Let us consider the private case of (2.15) when d z = 0 and
d x = 0.
The function h(0, d z ) describes the change of the field amplitude in the observing
plane center during the shift of the point source along the axis at a distance d z . In
this case,
γ =
sin c
2πq
2 d z M
2
λρ
2
i
,
(2.16)
where q is the output pupil radius, and interference pattern contrast becomes zero
under
d z M
2
=
λ
2
ρ
2
i
q 2 .
(2.17)
The result gives the possibility to explain it simply. As the value
δ = λ
p
2
i
q 2
(2.18)
determines the speckle average size along the observing axis, and d z M
2 is the separation of the image planes in the result of the object shift, then for the interference pattern
disappearance, it is enough that the distance between two speckle-fields V 1 and V 2
will be more than the speckle size, and correlation between them will disappear.
Passing in (2.17) from the value q/ρ i to the object input aperture A, it is possible
to write interference pattern condition in the following way
|d z | <
λ
2 A 2
(2.19)
Equation (2.19) shows the general regularity: The increase of the objective
resolving power leads to the decrease of measurement limits. But, for example,
for A = 0.2, it is possible to produce about 30 fringes with the contrast of 0.5 that is
quite sufficient in many supplements during the studies of microobjects, for example,
thermal deformations of semiconductor elements [55–68]. The character of change
of interference pattern with the increase of d z is shown in Fig. 2.5b, where the dotted
line is the visibility dependence and the solid line is the normalized interference
pattern rate (ensemble averaged) for A = 0.6. Negative visibility values indicate the
inversion of interference fringe contrast. It should be noticed that it is necessary
to be more careful if A is increased by (2.16). It is connected with the fact that if
diffusivity character does not change ρ 1 ( x 0 )ρ 1
x
0
= δ
x 0 − −
x
0
(i.e., the number
of scatterers, which are situated at a distance equal to objective resolving power
remains high), and the allowed distance itself approaches to wavelength, then the
diffusive object becomes a mirror object. In other words, with the decrease of the
75
that corresponds to the result in [125]. In spite of the results in [125], (2.16) shows
that in general the contrast depends on the object transverse shift as well as on the
defocusing value. Let us consider the private case of (2.15) when d z = 0 and
d x = 0.
The function h(0, d z ) describes the change of the field amplitude in the observing
plane center during the shift of the point source along the axis at a distance d z . In
this case,
γ =
sin c
2πq
2 d z M
2
λρ
2
i
,
(2.16)
where q is the output pupil radius, and interference pattern contrast becomes zero
under
d z M
2
=
λ
2
ρ
2
i
q 2 .
(2.17)
The result gives the possibility to explain it simply. As the value
δ = λ
p
2
i
q 2
(2.18)
determines the speckle average size along the observing axis, and d z M
2 is the separation of the image planes in the result of the object shift, then for the interference pattern
disappearance, it is enough that the distance between two speckle-fields V 1 and V 2
will be more than the speckle size, and correlation between them will disappear.
Passing in (2.17) from the value q/ρ i to the object input aperture A, it is possible
to write interference pattern condition in the following way
|d z | <
λ
2 A 2
(2.19)
Equation (2.19) shows the general regularity: The increase of the objective
resolving power leads to the decrease of measurement limits. But, for example,
for A = 0.2, it is possible to produce about 30 fringes with the contrast of 0.5 that is
quite sufficient in many supplements during the studies of microobjects, for example,
thermal deformations of semiconductor elements [55–68]. The character of change
of interference pattern with the increase of d z is shown in Fig. 2.5b, where the dotted
line is the visibility dependence and the solid line is the normalized interference
pattern rate (ensemble averaged) for A = 0.6. Negative visibility values indicate the
inversion of interference fringe contrast. It should be noticed that it is necessary
to be more careful if A is increased by (2.16). It is connected with the fact that if
diffusivity character does not change ρ 1 ( x 0 )ρ 1
x
0
= δ
x 0 − −
x
0
(i.e., the number
of scatterers, which are situated at a distance equal to objective resolving power
remains high), and the allowed distance itself approaches to wavelength, then the
diffusive object becomes a mirror object. In other words, with the decrease of the