How to use a binary amplitude Deformable Miror Device (DMD) as a phase modulator: The "superpixel" method

I previously presented a technique based on the Lee hologram that allows to use a binary amplitude modulator (like a DLP chip you find in standard projectors) to perform a phase modulation (or amplitude and phase modulation). Recently, a new technique was introduced in [S.A. Goorden et al., Opt. Express (2014)] that allows an accurate complex modulation with less loss in term of spatial resolution. This post is more a highlight on this paper than a proper tutorial. In a nutshell, while the Lee hologram only takes advantage of one dimension to encode the amplitude and phase in fringes, this technique exploits both dimensions of the pixel array using superpixels.

Off-axis holography

Sébastien M Popoff¹

Off-axis holography is a popular technique to reconstruct a hologram. It allows retrieving the amplitude and the phase of a field pattern by measuring only one image with a digital camera. It relies on an intereferometric setup with a non-zero angle between the reference beam and the signal beam and requires to numerically filter the spatial frequencies. I provida Matlab and Python example codes.

How to use a binary amplitude Deformable Mirror Device (DMD) as a phase modulator: The Lee hologram method

The optical field measured at the output of a complex medium (multimode waveguide, multimode cavity, scattering medium...) is the result of the interference of the many paths taken by the light. Most of the applications of wavefront shaping techniques in these media rely on taking advantage of these interference effects to force the medium to perform a desired function. For this reason, the phases of the controlled segments of the input wavefront are usually the most important degrees of freedom to control. Common phase-only Spatial Light Modulators (SLMs) have a limited refresh rate (~100 Hz) due to the liquid crystal technology. This limits the applications in media with a low decorrelation time (like biological tissues) or for experiments for which a long optimization process is needed. Although a new class of phase-only SLMs based on deformable mirrors allows high-speed modulations (>30 kHz), these devices are currently very expensive compared to liquid crystal technology and have a limited resolution (~1000 pixels maximum). On the other hand, fast binary-amplitude modulators with high resolutions are widespread and affordable since the technology is the same one as used in commercial digital projectors. In a recent publication, [D.B. Conkey et al., Opt. Express (2012)] introduced a method to use such a binary-amplitude Deformable Mirror Device (DMD) for phase modulation. This technique allows a fast phase modulation (up to 23 kHz) at the cost of a loss of resolution.

Phase Measurement: Introduction

Most exciting phenomenons that occur in complex media arises from interference effects. Controlling the phase of an incident field with a spatial light modulator is what made the field of wavefront shaping possible. Nevertheless, the measurement of the phase is a crucial step for many applications. In particular, recording both the amplitude and the phase for a set of input wavefront is necessary to record the transmission matrix of a linear medium. The knowledge of the transmission matrix of a scattering medium allows, for example, to use it as a lens [1], a controllable phase plate [2,3] or polarizer [4,5].

In such experiments, the phase of the output optical field for different input illuminations has to be recorded with the same phase reference. For this reason, one uses interferometric methods to measure the complex field; Phase Shifting Digital Holography (tutorial to come) or Off-Axis Holography (tutorial to come). In both cases, the unknown optical field interferes with a reference wavefront. The intensity of the interference is measured using a CCD to reconstruct the phase image. Phase Shifting Digital Holography requires 4 different measurements to obtain one phase image, leading to longer acquisition times and making the method more sensitive to interferometric instabilities. Off-Axis Holography allows us to measure the complex field in one shot but at the cost of a loss of resolution.