Direct retrieval of Zernike-based pupil functions using integrated diffractive deep neural networks

Retrieving the pupil phase of a beam path is a central problem for optical systems across scales, from telescopes, where thephase informationallows for aberration correction, to the imaging of near-transparent biological samples in phase contrast microscopy. Current phase retrieval schemes rely on complex digital algorithms that process data acquired from precise wavefront sensors, reconstructing the optical phase information at great expense of computational resources. Here, we present a compact optical-electronicmodule based on multi-layered diffractive neural networks printed on imaging sensors, capable of directly retrieving Zernike-based pupil phase distributions from an incident point spread function. We demonstrate this concept numerically and experimentally, showing the direct pupil phase retrieval of superpositions of the first 14 Zernike polynomials. The integrability of the diffractive elements with CMOS sensors shows the potential for the direct extraction of the pupil phase information from a detector module without additional digital postprocessing.

Automated summary

This article presents a compact optical-electronic module based on multi-layered diffractive neural networks that can directly retrieve pupil phase information from an imaging sensor. Compared to current phase retrieval schemes, this module has a smaller size and higher practical value.