Decomposing the images of the Jones matrix microscope for quantitative analysis

The polarization of light is a fundamental property, and its measurement is desired for extracting the optical response of the interacting matter. The Jones matrix description directly assesses a sample's response to the light-matter interactions. The Jones matrix approach uses a coherent basis and is suitable for expressing the interaction of coherent light with non-depolarizing samples, such as biological cells and thin samples. Usually, polarization measurement requires multiple measurements, which is unsuitable for dynamic samples. Here, we present a polarization digital holographic microscope to image the Jones matrix elements of biological cells from a single measurement. Using angular multiplexing, the proposed system employs a modified Mach-Zehnder interferometer with two Sagnac interferometer geometries to image the complete Jones matrix elements from a single hologram. With this approach, we retrieve the complete Jones matrix for each pixel and perform a Jones matrix decomposition to extract key polarization parameters, including inhomogeneity, diattenuation, and retardance of the cervical cancer HeLa cells. This comprehensive set of quantitative parameters characterizes cellular anisotropy and offers a meaningful interpretation of light-matter interaction in complex biological media.