4 Speckle-Optical Methods and Devices for Studying …
315
distribution. Along with this, the obtained results can be used for elimination of noises
in speckle-interferometry using light guides [40, 41], for increase of image quality in
microscopy [42], further development of methods of roughness determination [43].
Further behavior was examined of the speckle-field, which is formed as a result
free light diffraction on one or two diffusers, when elementary waves diffused by the
whole object surface participate in formation of a separate speckle.
At the same time, presence of optical lens system can significantly change character of forming and motion of speckles. Firstly, intensity in some point of an image
is determined by the result of coherent addition of elementary waves scattered in the
area around the image point, the size of which is equal to the order of resolution limit.
A rather huge number of elementary diffusers must be in this area to form a developed speckle-structure. Secondly, real speckle shift will be determined not only by
shift of the object, but also by extension of the optical system. Moreover, correlation
of speckle intensity will change depending on aperture, aberrations and objective
resolution [21, 44–46]. View of speckle movement can significantly change under
different positions of observation plane: from pure movement to “boiling”. These
factors lead to the fact that observation of speckle-fields formed by optical systems
became an independent part of speckle-optics, and such speckles were named subjective. Now the study of impact of longitudinal movement of the diffuser on changing
the structure of the spotted field is almost absent, though the impact of the transverse
shift is studied rather fully [23, 47–50].
The great practical value of speckle-photography methods, on the one hand, and
their maximal sensitivity to transverse shift, on the other hand, caused rather detailed
study of influence of transverse shift of the object on behavior of speckle-fields.
Unlike transverse movement of the diffuser [11, 51, 52] where decorrelation is
determined by the fact that some areas of the diffuser leave the illuminated area, and
other replace them, during longitudinal movement either new areas are added to the
illuminated ones or some of them disappear. That is why γ I can be calculated in
different ways. During transverse movement, it can be calculated as a ratio of superposed pupils’ area (the initial one and shifted at the value equal to shift of speckles)
to the whole area of the pupil. During longitudinal movement, γ I is determined
with some other, symmetrized relative to r 2 and r 1 expression, and decrease as well
as increase of r 2 equally leads to decorrelation (where r i = 1.2 can be interpreted as an
effective area of the diffuser, which participates in formation of a separate speckle).
Depending on the illumination conditions and observation “boiling” or shift of
the speckle-structure can prevail.
For double-lens optical systems, the dependence of areas of translation and
“boiling” of speckles from geometric parameters is considered in the work [22].
Notion “speckle lifetime” τ 0 is introduced for characterizing a dynamic speckleimage [47]. This notion characterizes full decorrelation of compared speckle-images,
i.e., disappearance of the peak of correlation function. It was shown above that on
the one hand speckle-fields occurring as a result of free diffraction can be considered
as a particular case of speckles formed in lens systems, and correlated functions
of subjective speckle-fields can be used for their description. On the other hand,
the knowledge of properties of optical dynamic speckles significantly helps in the
315
distribution. Along with this, the obtained results can be used for elimination of noises
in speckle-interferometry using light guides [40, 41], for increase of image quality in
microscopy [42], further development of methods of roughness determination [43].
Further behavior was examined of the speckle-field, which is formed as a result
free light diffraction on one or two diffusers, when elementary waves diffused by the
whole object surface participate in formation of a separate speckle.
At the same time, presence of optical lens system can significantly change character of forming and motion of speckles. Firstly, intensity in some point of an image
is determined by the result of coherent addition of elementary waves scattered in the
area around the image point, the size of which is equal to the order of resolution limit.
A rather huge number of elementary diffusers must be in this area to form a developed speckle-structure. Secondly, real speckle shift will be determined not only by
shift of the object, but also by extension of the optical system. Moreover, correlation
of speckle intensity will change depending on aperture, aberrations and objective
resolution [21, 44–46]. View of speckle movement can significantly change under
different positions of observation plane: from pure movement to “boiling”. These
factors lead to the fact that observation of speckle-fields formed by optical systems
became an independent part of speckle-optics, and such speckles were named subjective. Now the study of impact of longitudinal movement of the diffuser on changing
the structure of the spotted field is almost absent, though the impact of the transverse
shift is studied rather fully [23, 47–50].
The great practical value of speckle-photography methods, on the one hand, and
their maximal sensitivity to transverse shift, on the other hand, caused rather detailed
study of influence of transverse shift of the object on behavior of speckle-fields.
Unlike transverse movement of the diffuser [11, 51, 52] where decorrelation is
determined by the fact that some areas of the diffuser leave the illuminated area, and
other replace them, during longitudinal movement either new areas are added to the
illuminated ones or some of them disappear. That is why γ I can be calculated in
different ways. During transverse movement, it can be calculated as a ratio of superposed pupils’ area (the initial one and shifted at the value equal to shift of speckles)
to the whole area of the pupil. During longitudinal movement, γ I is determined
with some other, symmetrized relative to r 2 and r 1 expression, and decrease as well
as increase of r 2 equally leads to decorrelation (where r i = 1.2 can be interpreted as an
effective area of the diffuser, which participates in formation of a separate speckle).
Depending on the illumination conditions and observation “boiling” or shift of
the speckle-structure can prevail.
For double-lens optical systems, the dependence of areas of translation and
“boiling” of speckles from geometric parameters is considered in the work [22].
Notion “speckle lifetime” τ 0 is introduced for characterizing a dynamic speckleimage [47]. This notion characterizes full decorrelation of compared speckle-images,
i.e., disappearance of the peak of correlation function. It was shown above that on
the one hand speckle-fields occurring as a result of free diffraction can be considered
as a particular case of speckles formed in lens systems, and correlated functions
of subjective speckle-fields can be used for their description. On the other hand,
the knowledge of properties of optical dynamic speckles significantly helps in the