Speckle statistics from programmable modulators

2026 — Submitted. Topics: Smart microscopy, Super-resolved microscopy

Experimental and theoretical speckle and autocovariance with and without beam stop — Speckle engineering with a DMD. Pupil filtering suppresses the coherent background, increasing speckle contrast and strongly reducing long-range correlations. Theory, simulations and experiments show the same behaviour.

Speckle is usually described using Gaussian statistics, but fields generated with programmable pixelated devices such as SLMs and DMDs do not generally fall into this regime. We establish a predictive framework linking the statistics programmed on the modulator to the contrast and spatial correlations of the resulting speckle, with the classical Gaussian theory recovered as a limiting case.

The theory also provides practical design rules for generating highly contrasted speckles with controlled correlations. For examples in the case of DMDs, a coherent background strongly reduces contrast and generates long-range correlations; we show that filtering out the zero spatial frequency in a pupil plane largely suppresses these effects.

Publications

Mazzella, Murugan, Mangeat, Sentenac, LeGoff (2026). Statistics of speckles formed by a spatial light modulator. Submitted. link