Deep Learning Enabled Spatially Polarization Modulated Mueller Matrix Ellipsometer

This study proposes a deep learning-based Mueller matrix ellipsometer (MME) that uses two vortex retarders to encode the Mueller matrix of a sample into a radial pattern intensity image, which is decoded by a vision transformer (ViT) model. A modified ViT model is constructed and extensively trained based on simulated images. An MME setup has been built to obtain experimental images and validate the effectiveness and accuracy of the ViT model, and a quarter-wave plate (QWP) and a liquid crystal variable retarder (LCVR) are chosen as test samples. The results demonstrate that our ViT-based MME achieves high accuracy in measuring the complete Mueller matrix. We have generated simulated ideal and noisy images to evaluate the noise immunity of the ViT model. Comparative analysis with traditional radial projection (RP) algorithms and CNN models reveals that the ViT model exhibits significant noise tolerance. In addition, we have investigated the impact of training dataset scale and network structure. For our optimized training model, the measured MaxAE and RMSE errors for the QWP’s Mueller matrix elements were 0.0184 and 0.0075, respectively, while the errors for the LCVR’s retardances were
$0.0084\lambda $
(3.024°) and
$0.0042\lambda $
(1.512°). Our ViT model’s noise immunity and its ability to handle large amounts of data make it an ideal tool for industrial applications. Furthermore, this study provides insights into applying deep learning methods to target images with sophisticated spatial structures. Our work exemplifies the great potential for incorporating deep learning techniques for optical measurements.