4 Speckle-Optical Methods and Devices for Studying …
317
was given [8]. However, theoretical attempts to explain the origin of ring interferograms and optimize conditions of their obtaining [68] contradict the accumulated
experimental data, in particular dependence of rings period on the radius. Later it
was experimentally found that annular speckle-interferograms can be obtained in
lens systems as well. In practice, they appeared to be more effective. Now it is clear
that they are more high aperture, give the possibility to alter the scale and increase the
number of fringes and their contrast. But there are a number of conditions and limitations for location of lens elements and aperture. Their usage requires knowledge
of interferograms localization and optimal conditions of their obtaining.
It is worth mentioning that experimental test of speckles trajectories is rather
easy to realize during the study of transversal shift of speckles using doubleexposure speckle-photography method [69]. But standard methods are inapplicable
for studying longitudinal shift.
In the method developed below, three-dimensional character of speckle trajectories was used for estimation of longitudinal components that means that longitudinal
shift of speckles is firmly connected to their radial “recession”.
Transversal shift of diffuser leads to shift of interference rings from the axis
that is why contrast of fringes can be enhanced through the application of annular
diaphragms, and speckle-interferograms can be used for determination of shift
d, which were obtained during reconstruction of specklograms with a thin laser
beam [44].
It should also be mentioned that the obtained results can be useful while
making speckle-interferometers, which use longitudinal correlation of speckle-fields,
including real-time ones [70–74]. Analysis of correlated function of intensity fluctuations gives the possibility to find basic laws of changing subjective speckle-image
and obtain correlations, which underlie methods to determine velocity of solids
moving perpendicular to the optical axis [8, 75–77], frequency-contrast characteristics of optical systems [8, 78], determination of optical parameters of an eye [8, 79]
and measurement of deformations and shifts using speckle-interferometry methods
[8, 80–83].
Some information about correlation of speckle-fields is contained in a number of
works on speckle-interferometry of longitudinal shift. The articles [36, 47] theoretically examine theoretically dependence of the speckle-field on small defocusing and
determines longitudinal sizes of speckles. More fully decorrelation of the specklepattern near image plane is examined in the work [84] with the help of correlation
functions apparatus.
The works [85–87] are dedicated to theory and practical application of new
methods based on speckle-images obtained in coherent light. Such methods open
new possibilities concerning measurement of shifts, deformations, vibrations,
determination of shape and quality of diffused objects and image processing.
The works [87, 88] analyze the methods of quantitative determination of density
fields velocity, temperature of flows of gases, liquids, plasma, including turbulent flows using new experimental technical instruments based on double-exposure
speckle-photography and speckle-interferometry. Basic formulae are given, which
characterize statistic properties of speckle-fields. Experimental setups and apparatus
317
was given [8]. However, theoretical attempts to explain the origin of ring interferograms and optimize conditions of their obtaining [68] contradict the accumulated
experimental data, in particular dependence of rings period on the radius. Later it
was experimentally found that annular speckle-interferograms can be obtained in
lens systems as well. In practice, they appeared to be more effective. Now it is clear
that they are more high aperture, give the possibility to alter the scale and increase the
number of fringes and their contrast. But there are a number of conditions and limitations for location of lens elements and aperture. Their usage requires knowledge
of interferograms localization and optimal conditions of their obtaining.
It is worth mentioning that experimental test of speckles trajectories is rather
easy to realize during the study of transversal shift of speckles using doubleexposure speckle-photography method [69]. But standard methods are inapplicable
for studying longitudinal shift.
In the method developed below, three-dimensional character of speckle trajectories was used for estimation of longitudinal components that means that longitudinal
shift of speckles is firmly connected to their radial “recession”.
Transversal shift of diffuser leads to shift of interference rings from the axis
that is why contrast of fringes can be enhanced through the application of annular
diaphragms, and speckle-interferograms can be used for determination of shift
d, which were obtained during reconstruction of specklograms with a thin laser
beam [44].
It should also be mentioned that the obtained results can be useful while
making speckle-interferometers, which use longitudinal correlation of speckle-fields,
including real-time ones [70–74]. Analysis of correlated function of intensity fluctuations gives the possibility to find basic laws of changing subjective speckle-image
and obtain correlations, which underlie methods to determine velocity of solids
moving perpendicular to the optical axis [8, 75–77], frequency-contrast characteristics of optical systems [8, 78], determination of optical parameters of an eye [8, 79]
and measurement of deformations and shifts using speckle-interferometry methods
[8, 80–83].
Some information about correlation of speckle-fields is contained in a number of
works on speckle-interferometry of longitudinal shift. The articles [36, 47] theoretically examine theoretically dependence of the speckle-field on small defocusing and
determines longitudinal sizes of speckles. More fully decorrelation of the specklepattern near image plane is examined in the work [84] with the help of correlation
functions apparatus.
The works [85–87] are dedicated to theory and practical application of new
methods based on speckle-images obtained in coherent light. Such methods open
new possibilities concerning measurement of shifts, deformations, vibrations,
determination of shape and quality of diffused objects and image processing.
The works [87, 88] analyze the methods of quantitative determination of density
fields velocity, temperature of flows of gases, liquids, plasma, including turbulent flows using new experimental technical instruments based on double-exposure
speckle-photography and speckle-interferometry. Basic formulae are given, which
characterize statistic properties of speckle-fields. Experimental setups and apparatus