314
4 Speckle-Optical Methods and Devices for Studying …
form incoherently (I); surface roughness is small (II); the total number of elementary waves is small, and application of the central limit theorem is not possible (III).
Besides, non-Gaussian statistics emerges in the case of multiple light diffusion [31].
Such a situation occurs in experimental praxis, for example, if diffusing object is
illuminated by scattered illumination.
It was noticed that longitudinal shift of the diffuser can significantly influence
the change of speckle-field causing decrease of determination accuracy of lateral
deformations, vibrations, velocity, up to full inappropriateness of methods. In addition to that knowledge of laws of 3D speckle transformation is of great interest for
development of new ways of determination of complex spatial shifts.
As it was mentioned earlier, most widespread description of speckle-fields is an
approach based on the analysis of correlated functions, and significant role is played
by correlated amplitude functions [32–34] as well as correlated intensity functions of
intensity, which give the possibility to describe the measured parameters of speckles,
contrast, longitudinal and transversal sizes, shift, degree of decorrelation, lifetime,
etc. [35].
As a rule, two main methods of intensity correlation studying are used. In the
first one, the correlated intensity function is determined as squared absolute value of
amplitude correlated function; in the second one—expression for complex amplitude
of specific field realization in the given optical scheme is obtained in a form of integral
transformation, then the amplitude correlated function as well as correlated intensity
function is calculated through ensemble averaging, as well as correlated intensity
function. Ensemble averaging gives the possibility to analyze features of the field,
in particular its temporal and spatial stationarity.
If the diffuser velocity is zero, then expressions for parameters of static specklefield formed by stationary diffuser should follow in a natural way, which was
studied in the work [1] for transverse coordinated, and for the longitudinal ones
—in the work [36].
In holographic and speckle-interferometry and laser anemometry, diffusive
surface is illuminated in a number of cases not with a Gaussian beam, but with
diffusive coherent radiation. If laser illumination preliminarily passes through phase
chaotic screen, turbulent medium, multi-mode waveguide, then a secondary specklestructure is formed on the object as a result of scattering. Correlation features of
secondary speckles depend significantly on the distribution of field amplitude on the
diffusive object, as well as on its spatial and time coherence, and in common case
they are not identical to the features of primary speckles [37].
In the work [29], the results of the calculation for phase screen with a right-angled
mask are given, which give the possibility to find out main laws of changing correlated
functions and judge about the character of speckle movement. It was shown that the
secondarily speckle-field will not experience shift, and its changing is accompanied
only by “boiling”.
Static case of light diffusing with two stationary surfaces due to the speckle-field
theory was first examined in the work [38] and was experimentally studied in the
work [39]. It was shown that the amplitude probability density is described by Kdistribution, which is characterized by great fluctuation value comparing to normal
4 Speckle-Optical Methods and Devices for Studying …
form incoherently (I); surface roughness is small (II); the total number of elementary waves is small, and application of the central limit theorem is not possible (III).
Besides, non-Gaussian statistics emerges in the case of multiple light diffusion [31].
Such a situation occurs in experimental praxis, for example, if diffusing object is
illuminated by scattered illumination.
It was noticed that longitudinal shift of the diffuser can significantly influence
the change of speckle-field causing decrease of determination accuracy of lateral
deformations, vibrations, velocity, up to full inappropriateness of methods. In addition to that knowledge of laws of 3D speckle transformation is of great interest for
development of new ways of determination of complex spatial shifts.
As it was mentioned earlier, most widespread description of speckle-fields is an
approach based on the analysis of correlated functions, and significant role is played
by correlated amplitude functions [32–34] as well as correlated intensity functions of
intensity, which give the possibility to describe the measured parameters of speckles,
contrast, longitudinal and transversal sizes, shift, degree of decorrelation, lifetime,
etc. [35].
As a rule, two main methods of intensity correlation studying are used. In the
first one, the correlated intensity function is determined as squared absolute value of
amplitude correlated function; in the second one—expression for complex amplitude
of specific field realization in the given optical scheme is obtained in a form of integral
transformation, then the amplitude correlated function as well as correlated intensity
function is calculated through ensemble averaging, as well as correlated intensity
function. Ensemble averaging gives the possibility to analyze features of the field,
in particular its temporal and spatial stationarity.
If the diffuser velocity is zero, then expressions for parameters of static specklefield formed by stationary diffuser should follow in a natural way, which was
studied in the work [1] for transverse coordinated, and for the longitudinal ones
—in the work [36].
In holographic and speckle-interferometry and laser anemometry, diffusive
surface is illuminated in a number of cases not with a Gaussian beam, but with
diffusive coherent radiation. If laser illumination preliminarily passes through phase
chaotic screen, turbulent medium, multi-mode waveguide, then a secondary specklestructure is formed on the object as a result of scattering. Correlation features of
secondary speckles depend significantly on the distribution of field amplitude on the
diffusive object, as well as on its spatial and time coherence, and in common case
they are not identical to the features of primary speckles [37].
In the work [29], the results of the calculation for phase screen with a right-angled
mask are given, which give the possibility to find out main laws of changing correlated
functions and judge about the character of speckle movement. It was shown that the
secondarily speckle-field will not experience shift, and its changing is accompanied
only by “boiling”.
Static case of light diffusing with two stationary surfaces due to the speckle-field
theory was first examined in the work [38] and was experimentally studied in the
work [39]. It was shown that the amplitude probability density is described by Kdistribution, which is characterized by great fluctuation value comparing to normal