Iryna V. Soltys

A complex polarization-interference Jones-matrix polarimetry approach with digital holographic reconstruction and phase scanning of coherent speckle fields is proposed for the analysis of optically anisotropic architectonics in dehydrated biological fluid films. The method enables reconstruction of complex-amplitude Jones-matrix images and differential mapping of the scalar magnitudes of linear birefringence and linear dichroism, together with circular birefringence and circular dichroism, which characterize the local strength of structural anisotropy and optical activity in supramolecular polycrystalline networks. A phase-selection procedure based on depolarization control is used to isolate the minimally scattered, predominantly ballistic component of the speckle field, thereby improving the physical correspondence between reconstructed Jones-matrix parameters and local mechanisms of optical anisotropy. The obtained anisotropy maps were analyzed using statistical, wavelet, and multifractal descriptors to quantify the spatial hierarchy, scale-dependent heterogeneity, and singular structure of biological soft-matter networks. Experimental approbation was performed on limited diagnostically verified sample sets of dehydrated blood, synovial fluid, bile, and saliva films, representing different biochemical compositions and pathological conditions. The results indicate that multifractal analysis of reconstructed optical-anisotropy maps provides the highest discriminatory potential, particularly under low-scattering conditions, and reveals pathology-associated rearrangements of supramolecular architecture that are less accessible to conventional intensity-based polarimetric approaches. The reported diagnostic indicators should be interpreted as a proof-of-concept assessment of the analytical and biophysical sensitivity of the proposed method within verified sample sets, rather than as completed clinical validation. The developed framework provides a basis for further validation of Jones-matrix, phase-resolved, and multifractal polarimetric biomarkers in larger independent cohorts.

The paper presents a new approach to biological diagnostics based on 3D Jones matrix mapping. An approach to analyzing the multifractal structure of optically anisotropic soft matter films formed during dehydration self-organization of biofluids has been developed and experimentally validated. Theoretical basis: Analytical relationships have been established between the phase anisotropy parameters (linear and circular birefringence) of supramolecular networks and the components of the Jones matrix elements. This has enabled an objective quantitative description of the optical properties of biopreparations. Methodology: Using synovial fluid films as an example, patterns in the transformation of the statistical and topographic structure of phase-reconstructed images have been revealed. It has been established that the architecture of self-organized networks of biochemical crystals exhibits the property of scaling self-similarity. Diagnostic markers: A set of invariant parameters - statistical moments of the 3rd and 4th orders - have been determined, exhibiting maximum sensitivity to changes in the orientation-phase multifractal structure of polycrystalline networks. Validation: The effectiveness of the method has been confirmed in the study of films of various compositions (whole blood, lavage solution). The accuracy of differentiation of pathological conditions (inflammatory and oncological processes) was 94.9%-97.4%. Conclusion: The developed 3D Jones matrix mapping technology is a highly accurate tool for differential diagnostics in biomedicine, allowing for an objective assessment of structural rearrangement of biological tissues at the microlevel.

The paper examines the possibilities of applying the method of laser image phasometry to study the optical-anisotropic structure of biological fluids, specifically human knee joint synovial fluid. The relevance of using new informational parameters to enhance the effectiveness of pathological state diagnostics is substantiated, as traditional laser polarimetry methods lack sufficient sensitivity for optically thin media. An approach for forming coordinate distributions of phase shifts in laser images is proposed, allowing for the generation of phase maps of the synovial fluid's polycrystalline structure. Based on the analysis of these maps, it was established that the statistical characteristics of phase distributions differ significantly across various pathological states of the knee joint, including rheumatoid arthritis, postoperative synovitis, and septic arthritis. The results confirm the high sensitivity and specificity of the phasometry method for the clinical diagnosis of traumatic and inflammatory joint diseases

Background: Modern methods of Mueller matrix polarimetry are aimed at determining the criteria and practical application of such markers in the differential diagnosis of pathological and necrotic changes in biological tissues of human organs. At the same time, little-studied and relevant are the issues related to matrix studies of another class of objects – dehydrated (dried) films of biological fluids (BF), the polycrystalline structure of which is associated with the composition and ratio of dissolved substances. Polarimetric analysis of the BF dehydrated film at the macroscopic level enables the retrieval of information about its molecular microstructure. In addition, BF are more easily accessible and do not require traumatic, sometimes dangerous, biopsy. Objectives: Development and experimental testing of the diagnostic efficiency of a new technique of polarization-interference reconstruction and layer-by-layer phase scanning of object fields of complex amplitudes with algorithmic reproduction of the real and imaginary components of Jones matrix images of polycrystalline films of dehydrated bile from healthy donors and patients with cholelithiasis. Materials and methods: Polarization interferometry, digital phase scanning and statistical analysis of algorithmically reproduced real and imaginary components of Jones matrix images of dehydrated bile films were used. Results: The results of the statistical analysis of the polarization-interference mapping method with digital Fourier reconstruction and phase scanning of complex amplitude distributions and algorithmic calculation of the real and imaginary components of Jones matrix images of bile film samples are presented and physically analyzed. Statistical markers that are most sensitive to changes in the polycrystalline structure of dehydrated bile films are established and high accuracy (97.6%) of differential diagnosis of cholelithiasis is demonstrated. Conclusions: General scenarios for the transformation of the statistical structure of the set of Jones matrix images, which are reproduced in different phase planes of the object field of dehydrated bile films, are established. A set of structures of self-assembled molecular networks (hereinafter referred to as supramolecular networks) formed during the dehydration of bile films, which are diagnostic markers most sensitive to pathological changes, has been identified. They turned out to be asymmetry and kurtosis, which characterize the coordinate distributions of the values of the real and imaginary components of the Jones matrix.

To date, visual analysis is mainly used to evaluate images of dehydrated films (facies) of biological fluids—microscopy at various magnifications, illumination with white or polarized light, as well as using a dark field. At the same time, important information on the architectonics of optically anisotropic supramolecular networks of facies is unknown (inaccessible). In our work, a model of optical anisotropy of the architectonics of supramolecular networks of blood facies is proposed. Algorithms and a methodology for a new multifunctional method of polarization-interference visualization of the Jones matrix and digital layer-by-layer phase reconstruction of optical anisotropy maps (theziograms) have been developed. As a result, statistically significant markers of oncological changes in the polycrystalline architectonics of supramolecular networks of blood facies samples from healthy donors and patients with papillary thyroid cancer at different stages of the oncological process have been determined and physically analyzed. A comparative study of the diagnostic efficiency of Jones matrix theziography (JT) and Mueller matrix diffusion tomography (MDT) of blood facies samples was conducted within the framework of evidence-based medicine. The main advantages of the Jones matrix method are shown: its multifunctionality (complex detection of birefringence and dichroism), high accuracy of early (stage 1: JM—90.4% and MDT—78.8%) and current (stage 2: JM—96.2% and MDT—88.5%) cancer diagnostics and an excellent level (JM—94.2% and MDT—84.6%) of differentiation of papillary thyroid cancer stages.

The results of the theoretical substantiation and experimental validation of a novel laser polarization-interference method for Jones matrix mapping with digital phase layer-by-layer scanning of the object field of polycrystalline bile films are presented. Statistical analysis of the layer-by-layer maps of the real and imaginary components of the Jones matrix images has revealed a set of diagnostic markers – skewness and kurtosis – sensitive to variations in the linear and circular birefringence of the polycrystalline structure within the supramolecular networks of dehydrated bile films.

The paper proposes the use of multifractal analysis by algorithmic implementation of coordinate reconstructed distributions of linear birefringence magnitude and obtaining a spectrum of fractal dimensions of dehydrated polycrystalline blood films. The results of the diagnostic application of laser Jones matrix theziography methods of multifractal structure of polycrystalline networks of dehydrated films of blood for differential diagnostics of inflammatory and pathological conditions – "norm – sepsis" are presented. For dehydrated blood films, histograms and maps of the amplitude distributions of wavelet coefficients of theziograms of optical anisotropy and multifractal spectra of theziograms of optical anisotropy of polycrystalline supramolecular networks are given. Tables of the values of the central statistical moments of the 1st – 4th orders, which the Jones matrix characterize, wavelet and multifractal parameters of theziograms of phase anisotropy of dehydrated blood films, are systematized, and the set of statistical parameters more sensitive to changes in the polycrystalline structure of biological samples – diagnostic markers – is determined. Within the framework of statistical analysis of multifractal spectra and wavelet maps, it was determined that the algorithmically reconstructed birefringence theziogram allows identifying the most sensitive markers to changes in the anisotropic optical structure of blood caused by septic manifestations.

This study focuses on the topographic structure of optical anisotropy maps (theziograms) of dehydrated blood plasma films (facies) to identify and utilize markers for diagnosing self-similarity (multifractality) in the birefringence parameters of supramolecular protein networks. The research is based on the Jones-matrix analytical framework, which describes the formation of polarization-structural speckle fields in polycrystalline blood plasma facies. In the proposed model, algorithms were developed to relate the real and imaginary parts of the complex elements of the Jones matrix to the theziograms of linear and circular birefringence. To experimentally implement these algorithms, a novel optical technology was introduced for polarization-interference registration and phase scanning of the laser speckle field of blood plasma facies. The laser-based Jones-matrix layer-by-layer theziography relies on polarization filtration and the digital recording of interference patterns from microscopic images of blood plasma facies. This process includes digital 2D Fourier reconstruction and phase-by-phase scanning of the object field of complex amplitudes, enabling the acquisition of phase sections of laser polarization-structural speckle field components scattered with varying multiplicities. Jones-matrix images of supramolecular networks, along with their corresponding theziograms of linear and circular birefringence, were obtained for each phase plane. The experimental data derived from laser layer-by-layer Jones-matrix theziography were quantitatively analyzed using two complementary approaches: statistical analysis (central moments of the 1st to 4th orders) and multifractal analysis (spectra of fractal dimension distributions). As a result, the most sensitive markers—namely asymmetry and kurtosis—were identified, highlighting changes in the statistical and scale self-similar structures of the theziograms of linear and circular birefringence in blood plasma facies. The practical aspect of this work is to evaluate the diagnostic potential of the Jones-matrix theziography method for identifying and differentiating changes in the birefringence of supramolecular networks in blood plasma facies caused by the long-term effects of COVID-19. For this purpose, a control group (healthy donors) and three experimental groups of patients, confirmed to have had COVID-19 one-to-three years prior, were formed. Within the framework of evidence-based medicine, the operational characteristics of the method—sensitivity, specificity, and accuracy—were assessed. The method demonstrated excellent accuracy in the differential diagnosis of the long-term effects of COVID-19. This was achieved by statistically analyzing the spectra of fractal dimensions of Jones-matrix theziograms reconstructed in the phase plane of single scattering within the volume of blood plasma facies.

The article presents the materials of diagnostic application of the method of differential Mueller-matrix mapping of optically anisotropic architectonics of the layers of soft matter of the female reproductive sphere – histological sections of uterine biopsy. The efficiency and accuracy of differential diagnostics of benign and precancerous conditions of endometrial tissue are considered using statistical analysis of algorithmically reproduced maps of average values of linear and circular birefringence and dichroism parameters of optically anisotropic architectonics of representative samples of native histological sections of the uterine wall. The values of the balanced accuracy of differential diagnostics are presented by using the technique of statistical analysis of coordinate distributions of the mean values of the optical anisotropy parameters.

This paper explores the potential of artificial intelligence (AI) technologies in the field of digital image processing, analyzing current applications and future prospects. AI-based image processing techniques, such as noise reduction, super-resolution, inpainting, and image generation, are transforming traditional approaches, offering new levels of accuracy, efficiency, and creative potential. The paper examines AI applications across various fields, including healthcare for medical diagnostics, cultural heritage for art restoration, industry for quality control, and marketing for content creation.