4 Speckle-Optical Methods and Devices for Studying …
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about shift and deformation of the object are reflected. If correlated functions of the
field amplitude play an important part in holographic interferometry, then in speckleinterferometry intensity correlated functions get main importance. Though process
of speckle-interferogram formation can be described with elementary models, when
speckles are represented by apertures of the same size on non-transparent display [8],
then usage of mathematical apparatus of coherent optics appears to be more convenient, as it gives the opportunity to obtain additional information about decorrelation
of speckle-fields [9, 10]. Shift of the peak of correlated function reflects the shift,
which in its turn determines orientation and period of fringes [11]. Recently, study
of not only spatial but also spatial and temporal correlated functions has become
more interesting. These functions can be measured using special electronic device.
The latter is more informative and gives the possibility to study the dynamics of the
process and in a particular case to describe characteristics of speckle-interferograms.
To do this, it is enough to know the duration of exposures and interval between them.
Correlated approach to the research of dynamic speckles, which began in the works
[12, 13], was applied to the study of scattering of a laser Gaussian beam on a moving
diffusing surface [14–20] and analysis of subjective speckles in the area of image
of one- [21, 22] and double-lens [23] optical systems. Main results of these works
establish connections between parameters of the object, which moves perpendicular
to the optical axis, and characteristics of the speckles: quantity and direction of
their shift, size, contrast, degree of decorrelation, lifetime and spatial spectrum of
intensity. Two substantially different types of speckle movement were found out: shift
and “boiling,” and the optical system of observation can cause significant changes
in the movement of speckle-structure. Time spectrum of power of diffused radiation
was studied by the authors of the works [24, 25]. In other works, it was mentioned
that the incidence rate of correlated intensity functions integrated in time and space
speckle-structures [26–28].
As a result of analyses of spatial and temporal correlated functions of amplitude
and intensity of dynamic speckle-field for two arbitrary space points of images in the
work [29], it was established that mechanical trajectory of speckles is three dimensional. Along with lifetime, they are the most important characteristics of dynamic
speckles. Depending on the selection of initial point of observation trajectories can be
either straight passing through the focus or curved of the second order. Two reasons
of decorrelation were quantitatively determined: changing the number of elementary
diffusers, which are engaged in formation of a separate speckle and changing phase
difference between elementary diffused waves. Influence of these processes on the
“boiling” of speckles is significantly different for various areas. The first process
prevails in the area of images and the second one—in the area of great defocusing.
Gaussian statistics of speckle-field amplitude is supposed in most experimental
studies [1, 30]. Correlated functions of the first-order bear information about such a
field, and though they do not transmit significant information about the structure of
the diffuser, they almost fully describe its movement. In this case, correlated function of intensity fluctuation is determined by squared absolute value γ v . A number of
speckle-optical methods for object velocity determination are based on this assumption. In a number of cases, this model cannot be applied [20], when elementary waves
313
about shift and deformation of the object are reflected. If correlated functions of the
field amplitude play an important part in holographic interferometry, then in speckleinterferometry intensity correlated functions get main importance. Though process
of speckle-interferogram formation can be described with elementary models, when
speckles are represented by apertures of the same size on non-transparent display [8],
then usage of mathematical apparatus of coherent optics appears to be more convenient, as it gives the opportunity to obtain additional information about decorrelation
of speckle-fields [9, 10]. Shift of the peak of correlated function reflects the shift,
which in its turn determines orientation and period of fringes [11]. Recently, study
of not only spatial but also spatial and temporal correlated functions has become
more interesting. These functions can be measured using special electronic device.
The latter is more informative and gives the possibility to study the dynamics of the
process and in a particular case to describe characteristics of speckle-interferograms.
To do this, it is enough to know the duration of exposures and interval between them.
Correlated approach to the research of dynamic speckles, which began in the works
[12, 13], was applied to the study of scattering of a laser Gaussian beam on a moving
diffusing surface [14–20] and analysis of subjective speckles in the area of image
of one- [21, 22] and double-lens [23] optical systems. Main results of these works
establish connections between parameters of the object, which moves perpendicular
to the optical axis, and characteristics of the speckles: quantity and direction of
their shift, size, contrast, degree of decorrelation, lifetime and spatial spectrum of
intensity. Two substantially different types of speckle movement were found out: shift
and “boiling,” and the optical system of observation can cause significant changes
in the movement of speckle-structure. Time spectrum of power of diffused radiation
was studied by the authors of the works [24, 25]. In other works, it was mentioned
that the incidence rate of correlated intensity functions integrated in time and space
speckle-structures [26–28].
As a result of analyses of spatial and temporal correlated functions of amplitude
and intensity of dynamic speckle-field for two arbitrary space points of images in the
work [29], it was established that mechanical trajectory of speckles is three dimensional. Along with lifetime, they are the most important characteristics of dynamic
speckles. Depending on the selection of initial point of observation trajectories can be
either straight passing through the focus or curved of the second order. Two reasons
of decorrelation were quantitatively determined: changing the number of elementary
diffusers, which are engaged in formation of a separate speckle and changing phase
difference between elementary diffused waves. Influence of these processes on the
“boiling” of speckles is significantly different for various areas. The first process
prevails in the area of images and the second one—in the area of great defocusing.
Gaussian statistics of speckle-field amplitude is supposed in most experimental
studies [1, 30]. Correlated functions of the first-order bear information about such a
field, and though they do not transmit significant information about the structure of
the diffuser, they almost fully describe its movement. In this case, correlated function of intensity fluctuation is determined by squared absolute value γ v . A number of
speckle-optical methods for object velocity determination are based on this assumption. In a number of cases, this model cannot be applied [20], when elementary waves