Multifractal Algorithms for 3D Digital Holographic Jones-Matrix Microscopy in Soft Matter Biological Films Diagnostics

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.