DeepPD: Joint Phase and Object Estimation from Phase Diversity with Neural Calibration of a Deformable Mirror

Sample-induced aberrations and optical imperfections limit the resolution of fluorescence microscopy. Phase diversity is a powerful technique that leverages complementary phase information in sequentially acquired images with deliberately introduced aberrations--the phase diversities--to enable phase and object reconstruction and restore diffraction-limited resolution. These phase diversities are typically introduced into the optical path via a deformable mirror. Existing phase-diversity-based methods are limited to Zernike modes, require large numbers of diversity images, or depend on accurate mirror calibration--which are all suboptimal. We present DeepPD, a deep learning-based framework that combines neural representations of the object and wavefront with a learned model of the deformable mirror to jointly estimate both object and phase from only five images. DeepPD improves robustness and reconstruction quality over previous approaches, even under severe aberrations. We demonstrate its performance on calibration targets and biological samples, including immunolabeled myosin in fixed PtK2 cells. Keywords: phase diversity, deformable mirror, adaptive optics, fluorescence microscopy, neural networks, supervised learning, neural representations, deep learning 1 Introduction The potential of light microscopy is often unrealized due to aberrations introduced either by imperfections in the optical system or by the sample itself, yielding blurry and distorted images that fail to achieve diffraction-limited resolution. The goal of adaptive optics is to estimate the aberrations present in an image and counter them during acquisition via a deformable mirror (DM) or spatial light modulator [1], or, in computational settings, to estimate and correct them post-acquisition. Aberrations are caused by variations in the phase of the optical field. Yet the phase cannot be measured directly, as conventional imaging systems only capture light intensity. Estimating the phase is a challenging problem, and various wavefront estimation 1 arXiv:2504.14157v1 These methods can be broadly classified into two categories: guidestar-based and guidestar-free methods [1]. Guidestar-based methods rely on the presence of a point source in the sample, and the phase aberration can be retrieved, for example, by a Shack-Hartmann (SH) wavefront sensor [1] that measures the phase aberration based on displacements of the point source's images on a microlens array.