Estimation of Zernike polynomials for a highly focused electromagnetic field using polarimetric mapping images and neural networks

In this communication, we present a method to estimate the aberrated wavefront at the focal plane of a vectorial diffraction system. In contrast to the phase, the polarization state of optical fields is simply measurable. In this regard, we introduce an alternative approach for determining the aberration of the wavefront using polarimetric information. The method is based on training a convolutional neural network using a large set of polarimetric mapping images obtained by simulating the propagation of aberrated wavefronts through a high-NA microscope objective; then, the coefficients of the Zernike polynomials could be recovered after interrogating the trained network. On the one hand, our approach aims to eliminate the necessity of phase retrieval for wavefront sensing applications, provided the beam used is known. On the other hand, the approach might be applied for calibrating the complex optical system suffering from aberrations. As proof of concept, we use a radially polarized Gaussian-like beam multiplied by a phase term that describes the wavefront aberration. The training dataset is produced by using Zernike polynomials with random coefficients. Two thousand random combinations of polynomial coefficients are simulated. For each one, the Stokes parameters are calculated to introduce a polarimetric mapping image as the input of a neural network model designed and trained for predicting the polynomial coefficients. The accuracy of the neural network model is tested by predicting an unseen dataset (test dataset) with a high success rate.