Hyperuniform scalar random fields for lensless, multispectral imaging systems

TL;DR

This paper introduces a new class of hyperuniform random field-based point-spread-functions for lensless, multispectral imaging, improving image quality and system performance through novel PSF design and phase retrieval algorithms.

Contribution

It presents a systematic framework for designing hyperuniform random field PSFs and phase plates, enhancing lensless imaging performance over existing methods.

Findings

Hyperuniform PSFs outperform Perlin noise-based PSFs in isotropy and sparsity.

Engineered hyperuniform phase plates improve high-fidelity object reconstruction.

The framework is effective across the visible spectrum for on-chip microscopy.

Abstract

We propose a novel framework for the systematic design of lensless imaging systems based on the hyperuniform random field solutions of nonlinear reaction-diffusion equations from pattern formation theory. Specifically, we introduce a new class of imaging point-spread-functions (PSFs) with enhanced isotropic behavior and controllable sparsity. We investigate the PSFs and the modulated transfer functions (MTFs) for a number of nonlinear models and demonstrate that two-phase isotropic random fields with hyperuniform disorder are ideally suited to construct imaging PSFs with improved performances compared to PSFs based on the Perlin noise. Additionally, we introduce a phase retrieval algorithm based on the non-paraxial Rayleigh-Sommerfeld diffraction theory and introduce diffractive phase plates with PSFs designed from hyperuniform random fields, called hyperuniform phase plates (HPPs). Finally, using high-fidelity object reconstruction, we demonstrate improved image quality using engineered HPPs across the visible range. The proposed framework is suitable for high-performance lensless imaging systems for on-chip microscopy and spectroscopy applications.