A practical guide to Digital Micro-mirror Devices (DMDs) for wavefront shaping

TL;DR

The paper addresses enabling DMDs for coherent wavefront shaping in complex media, where diffraction, aberrations, and stability pose practical challenges. It develops practical tools including 1D and 2D diffraction models and a mu-based guide for pitch/angle selection, plus experimental validation of optimal incident angles. It introduces an in-situ aberration characterization and correction workflow using a lens–camera Fourier-plane setup and Zernike polynomials, achieving high Strehl after about 10 terms. It also documents simple mechanical and thermal stabilization strategies to limit performance drift, and provides Python code and an online calculator to support implementation. Together, these contributions enable reliable, high-speed wavefront shaping with DMDs in complex media.

Abstract

Digital micromirror devices have gained popularity in wavefront shaping, offering a high frame rate alternative to liquid crystal spatial light modulators. They are relatively inexpensive, offer high resolution, are easy to operate, and a single device can be used in a broad optical bandwidth. However, some technical drawbacks must be considered to achieve optimal performance. These issues, often undocumented by manufacturers, mostly stem from the device's original design for video projection applications. Herein, we present a guide to characterize and mitigate these effects. Our focus is on providing simple and practical solutions that can be easily incorporated into a typical wavefront shaping setup.

Figures (20)

• Figure 1: Principle of operation of a DMD in a digital projector. Left, incident light can be reflected towards the projection lens (state on), or onto a beam dump (state off). Right, zoom on the pixels. Image adapted from JacksonDMD.
• Figure 2: 1D grating geometry. Schematic representation of the geometry of two types of modulators: (a) the liquid crystal modulator, equivalent to a flat grating, and (b) the DMD geometry, equivalent to a blazed grating. $\alpha$ denotes the incident angle relative to the normal of the array plane, $\theta_0$ refers to the angle of the zeroth diffraction order, and $\theta_B$ is the tilt angle of the mirrors.
• Figure 3: Flat grating vs blazed grating. Far field diffraction patterns for a 1D flat grating (left) and a 1D blazed grating (right) for an input angle of $\alpha = -20^\circ$, a filling fraction of 95% (corresponding to a 2D filling fraction of $\approx 90$%), a pixel tilt angle of $\theta_B = 5^\circ$, and a wavelength to pixel pitch ratio $\lambda/d=0.05$. Vertical lines represent the angles of the diffraction orders, peaked at $\theta_p$ which satisfy $\sin(\theta_p)+\sin(\alpha)=p\lambda/d$, and the black dashed curve represents the amplitude of the field which peaks at $\theta_0=2\theta_B-\alpha$.
• Figure 4: 2D grating geometry. (a) Schematic representation of the geometry of the DMD. The incident angle $\alpha$ and the reflection angle $\theta_0$ (defined by the peak of the diffraction envelope) are situated within the horizontally plane, illustrated in yellow. (b) Photograph of the DMD chip oriented so that the rotation axis of the pixels is aligned vertically.
• Figure 5: Blazed number and far-field diffraction patterns. Blazing number $\mu$ (Eq.(\ref{['eq:blazed_number']})) as a function of the incident angle $\alpha$ (top) for a pixel pitch of $d=7.6$µ m (a.) and $d=10.8$µ m (b.). Corresponding far-field diffraction patterns (bottom) for two incident angles $\alpha = -15^\circ$ and $\alpha = 0^\circ$. The red cross indicates the maximum of the envelope $\theta_\text{max} = 2\theta_B - \alpha$.