Spatial and axial resolution limits for mask-based lensless cameras

One of the open challenges in lensless imaging is understanding how well they resolve scenes in three dimensions. The measurement model underlying prior lensless imagers lacks special structures that facilitate deeper analysis; thus, a theoretical study of the achievable spatio-axial resolution has been lacking. This paper provides such a theoretical framework by analyzing a generalization of a mask-based lensless camera, where the sensor captures z-stacked measurements acquired by moving the sensor relative to an attenuating mask. We show that the z-stacked measurements are related to the scene's volumetric albedo function via a three-dimensional convolutional operator. The specifics of this convolution, and its Fourier transform, allow us to fully characterize the spatial and axial resolving power of the camera, including its dependence on the mask. Since z-stacked measurements are a superset of those made by previously-studied lensless systems, these results provide an upper bound for their performance. We numerically evaluate the theory and its implications using simulations. (c) 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Automated summary

One of the challenges in lensless imaging is understanding their resolution capabilities in three dimensional scenes. This paper provides a theoretical framework for analyzing the achievable spatio-axial resolution by studying a generalized mask-based lensless camera. The analysis shows that the z-stacked measurements obtained from moving the sensor relative to an attenuating mask are related to the scene's volumetric albedo function through a three-dimensional convolutional operator. The results provide an upper bound for the performance of previously-studied lensless systems.