4.5 Correlation of Speckle-Fields Formed by Diffuse …
345
γ I =
4(d 2 /d 1 )
2
1 + (d 2 /d 1 )
2
2
(4.72)
Decrease of the correlation under d 2 ≈ d 1 can be explained by the fact that the
resolution of the objective changes when the observation aperture changes, and other
parts of the surface participate in the formation of a separate speckle. The resulting
coherent sum of waves scattered by elementary diffusers will differ from the initial
one and correlation will sink. When observation points, in which meeting condition
in (4.71) lies in the planes P 1 and P 2 characterized by identical defocusing parameter
ε 1 = ε 2 , then decorrelation with α alteration comes much faster. If planes P 1 and P 2
are connected by the ratio ε 1 /ε 2 = const, then for any defocusing ε 1, there are two
planes D 1 and D 2 , for which intensities correlation does not alter, does not depend
on the quantity, and its value is determined by the condition d
2
2 ε 2 = d
2
1 ε 1 .
In conclusion, it is worth mentioning that (4.68) can be easily proved in experiments with speckle-photography and directly used for the development of new
methods for determination of shifts and longitudinal velocities components.
4.6 Experimental Study of the Movement of Subjective
Speckle-Fields Under Longitudinal Shift of the Diffuse
Object
Methods of speckle-photography give the possibility to determine both longitudinal
and transversal shifts of surfaces of biological and other diffuse objects [8, 44]. In one
of the first works on speckle-interferometry [53], an efficient way of determination
of axial shift was demonstrated, which is based on radial recession of the specklestructure and obtaining of annular interferograms. Dependence of the contrast of such
interferograms on the aperture was discussed in the works [44, 54], and in the work
[84] correlation characteristics of the field were investigated, which was scattered
by the moving along with the axis diffuser in the neighborhood of the plane image.
According to these publications, the range of the determined shifts is limited by the
depth of the focus of the objective.
In Sect. 4.5, speckle-fields correlation in two random points of image space is
considered. In particular, it was shown that caused by the longitudinal shift, decorrelation of speckle-fields comes much more slowly if they are registered not in the fixed
plane as it was before, but in planes conjugated with the initial and the shifted positions of the object. Dependencies of optimal distribution of registration planes under
defocusing during the first exposition were obtained. The possibility of obtaining
interferograms was experimentally investigated. The interferograms correspond to
the longitudinal shifts of the object exceeding the depth of the field of the objective.
As follows from the work [118], radial shift of speckles is connected with the
initial and the final position of the object d 1 and d 2 by the ratio
345
γ I =
4(d 2 /d 1 )
2
1 + (d 2 /d 1 )
2
2
(4.72)
Decrease of the correlation under d 2 ≈ d 1 can be explained by the fact that the
resolution of the objective changes when the observation aperture changes, and other
parts of the surface participate in the formation of a separate speckle. The resulting
coherent sum of waves scattered by elementary diffusers will differ from the initial
one and correlation will sink. When observation points, in which meeting condition
in (4.71) lies in the planes P 1 and P 2 characterized by identical defocusing parameter
ε 1 = ε 2 , then decorrelation with α alteration comes much faster. If planes P 1 and P 2
are connected by the ratio ε 1 /ε 2 = const, then for any defocusing ε 1, there are two
planes D 1 and D 2 , for which intensities correlation does not alter, does not depend
on the quantity, and its value is determined by the condition d
2
2 ε 2 = d
2
1 ε 1 .
In conclusion, it is worth mentioning that (4.68) can be easily proved in experiments with speckle-photography and directly used for the development of new
methods for determination of shifts and longitudinal velocities components.
4.6 Experimental Study of the Movement of Subjective
Speckle-Fields Under Longitudinal Shift of the Diffuse
Object
Methods of speckle-photography give the possibility to determine both longitudinal
and transversal shifts of surfaces of biological and other diffuse objects [8, 44]. In one
of the first works on speckle-interferometry [53], an efficient way of determination
of axial shift was demonstrated, which is based on radial recession of the specklestructure and obtaining of annular interferograms. Dependence of the contrast of such
interferograms on the aperture was discussed in the works [44, 54], and in the work
[84] correlation characteristics of the field were investigated, which was scattered
by the moving along with the axis diffuser in the neighborhood of the plane image.
According to these publications, the range of the determined shifts is limited by the
depth of the focus of the objective.
In Sect. 4.5, speckle-fields correlation in two random points of image space is
considered. In particular, it was shown that caused by the longitudinal shift, decorrelation of speckle-fields comes much more slowly if they are registered not in the fixed
plane as it was before, but in planes conjugated with the initial and the shifted positions of the object. Dependencies of optimal distribution of registration planes under
defocusing during the first exposition were obtained. The possibility of obtaining
interferograms was experimentally investigated. The interferograms correspond to
the longitudinal shifts of the object exceeding the depth of the field of the objective.
As follows from the work [118], radial shift of speckles is connected with the
initial and the final position of the object d 1 and d 2 by the ratio