Jones Matrix Tomography Research Articles

Coincidence imaging for Jones matrix with a deep-learning approach

Coincidence measurement has become an emerging technique for optical imaging. Based on measuring the second-order coherence g2, sample features such as reflection/transmission amplitude and phase delay can be extracted with developed algorithms pixel-by-pixel. However, an accurate measurement of g2 requires a substantial number of collected photons which becomes difficult under low-light conditions. Here, we propose a deep-learning approach for Jones matrix imaging using photon arrival data directly. A variational autoencoder (β-VAE) is trained using numerical data in an unsupervised manner to obtain a minimal data representation, which can be transformed into an image with little effort. We demonstrate as few as 88 photons collected per pixel on average to extract a Jones matrix image, with accuracy surpassing previous semi-analytic algorithms derived from g2. Our approach not only automates formulating imaging algorithms but can also assess the sufficiency of information from a designed experimental procedure, which can be useful in equipment or algorithm designs for a wide range of imaging applications.

Optical Sensor System for 3D Jones Matrix Reconstruction of Optical Anisotropy Maps of Self-Assembled Polycrystalline Soft Matter Films.

Our work uses a polarization matrix formalism to analyze and algorithmically represent optical anisotropy by open dehydration of blood plasma films. Analytical relations for Jones matrix reconstruction of optical birefringence maps of protein crystal networks of dehydrated biofluid films are found. A technique for 3D step-by-step measurement of the distributions of the elements of the Jones matrix or Jones matrix images (JMI) of the optically birefringent structure of blood plasma films (BPF) has been created. Correlation between JMI maps and corresponding birefringence images of dehydrated BPF and saliva films (SF) obtained from donors and prostate cancer patients was determined. Within the framework of statistical analysis of layer-by-layer optical birefringence maps, the parameters most sensitive to pathological changes in the structure of dehydrated films were found to be the central statistical moments of the 1st to 4th orders. We physically substantiated and experimentally determined the sensitivity of the method of 3D polarization scanning technique of BPF and SF preparations in the diagnosis of endometriosis of uterine tissue.

The informativeness of the Johns-matrix image of laser autofluorescence in blood plasma films for early diagnosis of endometriosis associated with infertility

We used Jones-matrix images of protein networks of blood plasma films obtained from laser autofluorescence and determined the sensitivity, specificity, accuracy, and prognostication of positive and negative results. Our study aimed (1) to develop and substantiate new approaches for the diagnosis of endometriosis by improving the methods of Jones-matrix mapping of laser-induced auto-fluorescence and (2) to develop statistical approaches for analyzing the distribution of values of the true component of Jones-matrix images of blood plasma. Biological preparations were performed for two groups: 35 samples from control group 1 (women with infertility of unknown origin) and 85 samples from group 2 with endometriosis (women with infertility and endometriosis). The strength of the Jones-matrix method of autofluorescence mapping of plasma proteins taken from both groups was maximal for the decisions determined based on the calculation of the statistical moment of the 4th order, for statistical moment Z4, characterizing the sharpness of the peak distribution of the polycrystalline component of the plasma film. Comparison with the similar informative data of the Jones-matrix laser autofluorescence method of histological sections of the endometrial biopsy under conditions of blind endometriosis diagnosis revealed this method of analysis highly informative. Therefore, this technique can be used in screening studies to form a risk group.

Jones-matrix imaging based on two-photon interference

Abstract Two-photon interference is an important effect that is tightly related to the quantum nature of light. Recently, it has been shown that the photon bunching from the Hong–Ou–Mandel (HOM) effect can be used for quantum imaging in which sample properties (reflection/transmission amplitude, phase delay, or polarization) can be characterized at the pixel-by-pixel level. In this work, we perform Jones matrix imaging for an unknown object based on two-photon interference. By using a reference metasurface with panels of known polarization responses in pairwise coincidence measurements, the object’s polarization responses at each pixel can be retrieved from the dependence of the coincidence visibility as a function of the reference polarization. The post-selection of coincidence images with specific reference polarization in our approach eliminates the need in switching the incident polarization and thus parallelized optical measurements for Jones matrix characterization. The parallelization in preparing input states, prevalent in any quantum algorithms, is an advantage of adopting two-photon interference in Jones matrix imaging. We believe our work points to the usage of metasurfaces in biological and medical imaging in the quantum optical regime.

Characterization of a spatial light modulator using polarization-sensitive digital holography.

We show a digital holographic approach for polarimetric characterization of a twisted nematic liquid crystal spatial light modulator (TNLC-SLM). An experimental scheme is designed to perform polarization analysis of the SLM with gray levels. This is realized by simultaneous detection of the polarization states of the light from the SLM for a given gray level with the help of a specially designed spatial-frequency multiplex polarization interferometer. This provides amplitude and phase characteristics of the SLM in a single shot. In order to characterize the SLM, we perform Jones matrix imaging at its various gray values (driving voltages), and corresponding results are presented. These results are expected to be useful in designing and developing various SLM-based experiments in the scalar and vectorial domain.

Jones-matrix images corresponding to networks of biological crystals for diagnostics and classification of their optical properties

Jones-matrix images corresponding to networks of biological crystals for diagnostics and classification of their optical properties

Wavelet analysis of Jones-matrix images corresponding to polycrystalline networks of biological crystals in diagnostics of tuberculosis

Wavelet analysis of Jones-matrix images corresponding to polycrystalline networks of biological crystals in diagnostics of tuberculosis

Singular analysis of Jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period

Determined in this work are analytical interrelations between orientations of optical axes and birefringence of biological crystals and characteristic values of Jones- matrix elements corresponding to flat layers of polycrystalline networks, which set the conditions providing formation of polarization singularities in laser images. Performed is the complex statistical, correlation and fractal analysis of distributions for the amount of characteristic values inherent to Jones-matrix elements corresponding to bile layers of healthy and sick patients. Also, offered are the objective criteria for differentiation of optical properties typical to polycrystalline networks of human bile in different physiological states, and realized is the Jones-matrix diagnostics of cholelithiasis.

Polarization contrast imaging of biological tissues by polarization-sensitive Fourier-domain optical coherence tomography

Jones matrix imaging of biological samples by a polarization-sensitive Fourier-domain optical coherence tomography has been demonstrated using a two-dimensional CCD camera to obtain two spectra corresponding to the orthogonal polarization components simultaneously. The measurement results of a quarter-wave plate are compared between the two incident polarization sets, H-V linear and R-L circular polarization. Jones matrix imaging of the bovine tendon is demonstrated. Measured Jones matrix images are converted to equivalent Müller matrix images. Local polarization properties are obtained by longitudinal differentiation of Jones matrix components. The layered structure of the bovine tendon and birefringence are revealed.

Polarization-sensitive complex Fourier domain optical coherence tomography for Jones matrix imaging of biological samples

A polarization-sensitive Fourier domain optical coherence tomography (PS-FD-OCT) system is demonstrated. This OCT system is based on a spectral interferometer, does not require mechanical axial scanning, and enables phase information to be used in an OCT image. Owing to this phase information, the system requires only two measurements for determining the Jones matrix images and Müller images of biological samples. This system reveals the birefringence properties of the inner surface of a porcine esophagus.

Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography.

Two-dimensional depth-resolved Jones-matrix images of scattering biological tissues were measured with novel double-source double-detector polarization-sensitive optical coherence tomography (OCT). The Jones matrix can be determined in a single scan with this OCT system. The experimental results show that this system can be effectively applied to the measurement of soft tissues, which are less stable than hard tissues. Polarization parameters such as diattenuation, birefringence, and orientation of the fast axis can be extracted through decomposition of the measured Jones matrix. The Jones matrix of thermally treated porcine tendon showed a reduction of birefringence from thermal damage. The Jones matrices of porcine skin and bovine cartilage also revealed that the density and orientation of the collagen fibers in porcine skin and bovine cartilage are not distributed as uniformly as in porcine tendon. Birefringence is sensitive to changes in tissue because it is based on phase contrast.

Photoelastic Analysis through Jones Matrix Imaging Fourier Polarimetry.

The paper presents further development of the authors' hybrid method for the three-dimensional nondestructive photielastic analysis. The general arrangement and measurement procedure of a Jones matrix imaging Fourier polarimeter is described with emphasis in error analysis. Errors that are due to orientational misalignment of the polarization elements are considered, an analytical treatment is given and is followed by experimental examples.