Using of a 2D and 3D Hilbert transform for reconstruction of the phase distribution of the intensity of a speckle field is proposed. It is shown that the advantage of this approach consists in the invariance of a phase map to a change of the position of the kernel of transformation and in a possibility to reconstruct the structure-forming elements of the skeleton of an optical field, including singular points and saddle points. We demonstrate the possibility in real time to reconstruct the equi-phase lines within a narrow confidence interval, and introduce a new algorithm for solving the phase problem for random 2D intensity distributions.
An analysis of a "window" 2D/3D Hilbert transform for reconstruction of the phase distribution of the intensity of a speckle field has been carried out. It is shown that the advantage of these approaches consists in the invariance of a phase map to a change of the position of the kernel of transformation and in a possibility to reconstruct the structure forming elements of the skeleton of an optical field. Within the framework of the approach based on the use of the discrete 2D "window" Hilbert transform, we have demonstrated the feasibility for reconstructing the phase of random 2D objects in real time.
The influence of an evanescent field formed by two evanescent waves under the total internal reflection on the dynamics of motion of separate erythrocyte into blood plasma is demonstrated. Computer simulation of red blood cell motion into evanescent field and experimental demonstration of rotational and rectilinear motion expand the possibilities of using optical evanescent waves in applied tasks of nanophysics and biomedicine. The vertical spin produced by the illumination of a cell by the linearly polarized wave with the azimuth of polarization 45º demonstrates unique ability to control transverse motion of the nanoobject that is not characterized to the action of spin momentum inherent to the classical circular polarized optical beam.
Using of a “window” 2D Hilbert transform for reconstruction of the phase distribution of the intensity of a speckle field is proposed. It is shown that the advantage of this approach consists in the invariance of a phase map to a change of the position of the kernel of transformation and in a possibility to reconstruct the structure-forming elements of the skeleton of an optical field, including singular points and saddle points. We demonstrate the possibility in real time to reconstruct the equi-phase lines within a narrow confidence interval, and introduce a new algorithm for solving the phase problem for random 2D intensity distributions.
The paper presents principal approaches to diagnosing the structure forming skeleton of the complex optical field. An analysis of optical field singularity algorithms depending on intensity discretization and image resolution has been carried out. An optimal approach is chosen, which allows to bring much closer the solution of the phase problem of localization speckle-field special points. A possible approach to diagnosing the signs of zero amplitudes was offered.
To analyze the coordinate-like structure of Stokes-parametric and Mueller-matrix images of optically anisotropic components of biological tissues, the two-point polarization-correlational approach was applied. On this basis parameters the method of cross-correlational definition of parameters (average sizes, asymmetry factor) of correlational contour was developed, which defines the topographical structure of the characteristic meanings of Stokes-parametric and Mueller-matrix images of histological sections of biological tissues.
A method of polarization mapping of the optico-anisotropic polycrystalline networks of the blood plasma albumin and globulin proteins with adjusted spatial-frequency filtering of the coordinate distributions of the azimuth and ellipticity of the polarization of laser radiation in the Fourier plane is proposed and substantiated. Comparative studies of the effectiveness of direct methods of mapping and a spatial-frequency selection in differentiating polarization azimuth and ellipticity maps of the field of laser radiation converted by the networks of albumin - globulin crystals of the blood plasma in healthy people and patients with prostate cancer have been carried out.
Among various opticophysical methods [1 - 3] of diagnosing the structure and properties of the optical
anisotropic component of various biological objects a specific trend has been singled out - multidimensional
laser polarimetry of microscopic images of the biological tissues with the following statistic, correlative and
fractal analysis of the coordinate distributions of the azimuths and ellipticity of polarization in approximating
of linear birefringence polycrystalline protein networks [4 – 10]. At the same time, in most cases,
experimental obtaining of tissue sample is a traumatic biopsy operation. In addition, the mechanisms of
transformation of the state of polarization of laser radiation by means of the opticoanisotropic biological
structures are more varied (optical dichroism, circular birefringence). Hereat, real polycrystalline networks
can be formed by different types, both in size and optical properties of biological crystals. Finally, much more
accessible for an experimental investigation are biological fluids such as blood, bile, urine, and others. Thus,
further progress of laser polarimetry can be associated with the development of new methods of analysis and
processing (selection) of polarization- heterogeneous images of biological tissues and fluids, taking into
account a wider set of mechanisms anisotropic mechanisms.
Our research is aimed at developing experimental method of the Fourier polarimetry and a spatialfrequency
selection for distributions of the azimuth and the ellipticity polarization of blood plasma laser
images with a view of diagnosing prostate cancer.
A model of generalized optical anisotropy of human bile is suggested and a method of polarimetric of
the module and phase Fourier of the image of the field of laser radiation is analytically substantiated, that is
generated by the mechanisms of linear and circular birefringence of polycrystalline networks with a diagnosis
and differentiation of cholelithiasis against a background of chronic cholecystitis.
The optical model of polycrystalline networks of histological sections of rectum wall is suggested. The
results of investigating the interrelation between the values of statistical (statistical moments of the 1st-4th
order) parameters are presented. They characterize the coordinate polarization distributions of Fourier
transforms of laser images of blood plasma and oncological changes. The diagnostic criteria of rectum cancer
are determined.
Our research is aimed at designing an experimental method of Fourier laser polarization phasometry of the layers of human effusion for an express determining the potentialities of diagnostics of pathological changes in mammary gland basing on polarization analysis of laser images of the biopsy of the uterine wall tissue in order to differentiate benign (fibromioma) and malignant (adenocarcinoma).
An additional possibility for estimating the degree of coherence of interacting fields when classic methods of diagnostics
cannot be applied is offered.
The complex technique of the concerted polarization-phase and spatial-frequency filtering of blood plasma laser images
has been suggested. The possibility of obtaining separately the coordinate distributions of phases of linearly and
circularly birefringent protein networks of blood plasma has been presented. The diagnostically sensitive parameters of a
pathological change of the birefringence of blood plasma polycrystalline networks were determined. The effectiveness of
the developed technique for detecting the change of birefringence of the blood plasma smears in diagnostics and
differentiation of the acute and gangrenous appendicitis (exudate) is shown.
The paper presents a new method for determining the degree of coherence of superposing plane linearly polarized waves
converging at the angle of 900. The spatial modulation of polarization, which causes the spatial modulation of the
averaged values of the Poynting vector, presets the modulation of the volume energy density. Such an inhomogeneous
optical field can affect nanosize particles, randomly caught in this field. It is shown that the maximum velocity of
“trapping” the particles into the regions of maximum averaged values of the Poynting vector determines the degree of
coherence of interacting waves.
The paper proposes for consideration an additional possibility to evaluate the degree of coherence of superposing
mutually orthogonal linearly-polarized in the incidence plane waves. When analyzing the behavior of various-type
particles (Mie and Rayleigh) in the inhomogeneously polarized optical field and in the inhomogeneous field of the
averaged values of the Poynting vector, we obtain an additional tool for defining the degree of coherence of interacting
fields. The spatial modulation of polarization in the observation plane shapes the spatial modulation of the energy
density volume, which changes the velocity of the particle motion according to the coherence characteristics of the
superposing fields and to the resulting optical force that causes the motion and trapping of the tested particles.
The feasibilities for optical correlation diagnostics of a rough surface with large surface inhomogeneities by determining the
transformations of the longitudinal coherence function of the field scattered by such surface are substantiated and
implemented. The algorithm of computer processing of the interferograms for reconstruction of the relief of regular surfaces
with resolution 0.5 nm is represented.
Optical correlation methods for diagnostics of slightly rough surfaces are proposed, which are based on the model of an infinitely extended random phase object. All spatial frequency components associated with the phase structure of the object are assumed to contribute to formation of the radiation field resulting from interaction with the object. The object phase dispersion is assumed to be less than unity, and the inhomogeneity correlation radius of the random phase object larger than the incident wavelength.
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