316
4 Speckle-Optical Methods and Devices for Studying …
study of changes of subjective speckle-fields. On the other hand, the knowledge of
characteristics of objective dynamic speckles significantly helps to study subjective
speckle-fields. As analyses showed behavior of speckles formed by the optical system
can be studied using two equivalent ways: (a) by examining actual transformation of
speckles in image space during longitudinal movement of an object; (b) by formally
calculating all the values in the space of objects, and then moving on to real values
in image space taking into account changes of phase correlation with a lens, which
in fact will come to heterogeneous transformation of object space into image space
using a lens, as well as influence of aperture.
If the detection plane is situated behind the focal plane, then speckles “scatter”
from the axis when the diffuser approaches the objective and when it moves away they
gather. This effect is conditioned by the change of magnification under longitudinal
movement.
For the first time, the usage of speckle-field correlation for determining longitudinal shifts was mentioned in the work [53].
The method is based on radial “scattering” of speckles in the image plane,
obtaining double-exposure speckle-photographs and forming not traditional equidistant fringes but characteristic system of rings [8]. The upper limit of measurements is
restricted by the depth of objective focus used during recording of speckle-structures.
This method was further developed in the works [44, 54, 55] where in particular it is
suggested that ring diaphragms should be used to increase the quantity and contrast
of the observed rings, and manifestation of speckle fine structure is investigated.
But in speckle-interferometry of longitudinal shift, there are a number of problems, which require further study of connected with coherent-optical processing of
specklograms, study of optimal conditions of spatial filtration, determination of localization area of speckle-interferograms and extension of measurement range. During
the analysis of a specklogram, which reflects the transverse shift of the object, Fourier
transformation of specklogram is conducted, and equidistant fringes are observed,
which are equivalent to Jung’s fringes.
In this case instead of pulse response of the objective, it is necessary to put
the expression, which responses to Fourier transformation. This particular case was
analyzed in detail in literature, for instance in the works [56–63].
Interferograms of longitudinal shift have the appearance of concentric rings and
are observed under other circumstances [53].
Interferograms appearing under optic coherent processing of specklograms, on
which pairs of speckles are registered, shifted on the same value are registered, have
direct analogy in transverse direction with interference experiments on two pin holes
and are named Jung’s fringes.
Specklograms of longitudinal shift have another structure [64, 65]. They have
symmetry center, each pair of identical spectrums is situated on a radius, and value
of separation between them is in direct proportion to distance from the center. Under
plane wave diffraction on this specially obtained diffuser, completely different type
of interference phenomena appears, which is not well-investigated.
Schemes for obtaining speckle-interferograms using pin hole diaphragms were
empirically established [66, 67], and their elementary geometrooptical interpretation
4 Speckle-Optical Methods and Devices for Studying …
study of changes of subjective speckle-fields. On the other hand, the knowledge of
characteristics of objective dynamic speckles significantly helps to study subjective
speckle-fields. As analyses showed behavior of speckles formed by the optical system
can be studied using two equivalent ways: (a) by examining actual transformation of
speckles in image space during longitudinal movement of an object; (b) by formally
calculating all the values in the space of objects, and then moving on to real values
in image space taking into account changes of phase correlation with a lens, which
in fact will come to heterogeneous transformation of object space into image space
using a lens, as well as influence of aperture.
If the detection plane is situated behind the focal plane, then speckles “scatter”
from the axis when the diffuser approaches the objective and when it moves away they
gather. This effect is conditioned by the change of magnification under longitudinal
movement.
For the first time, the usage of speckle-field correlation for determining longitudinal shifts was mentioned in the work [53].
The method is based on radial “scattering” of speckles in the image plane,
obtaining double-exposure speckle-photographs and forming not traditional equidistant fringes but characteristic system of rings [8]. The upper limit of measurements is
restricted by the depth of objective focus used during recording of speckle-structures.
This method was further developed in the works [44, 54, 55] where in particular it is
suggested that ring diaphragms should be used to increase the quantity and contrast
of the observed rings, and manifestation of speckle fine structure is investigated.
But in speckle-interferometry of longitudinal shift, there are a number of problems, which require further study of connected with coherent-optical processing of
specklograms, study of optimal conditions of spatial filtration, determination of localization area of speckle-interferograms and extension of measurement range. During
the analysis of a specklogram, which reflects the transverse shift of the object, Fourier
transformation of specklogram is conducted, and equidistant fringes are observed,
which are equivalent to Jung’s fringes.
In this case instead of pulse response of the objective, it is necessary to put
the expression, which responses to Fourier transformation. This particular case was
analyzed in detail in literature, for instance in the works [56–63].
Interferograms of longitudinal shift have the appearance of concentric rings and
are observed under other circumstances [53].
Interferograms appearing under optic coherent processing of specklograms, on
which pairs of speckles are registered, shifted on the same value are registered, have
direct analogy in transverse direction with interference experiments on two pin holes
and are named Jung’s fringes.
Specklograms of longitudinal shift have another structure [64, 65]. They have
symmetry center, each pair of identical spectrums is situated on a radius, and value
of separation between them is in direct proportion to distance from the center. Under
plane wave diffraction on this specially obtained diffuser, completely different type
of interference phenomena appears, which is not well-investigated.
Schemes for obtaining speckle-interferograms using pin hole diaphragms were
empirically established [66, 67], and their elementary geometrooptical interpretation