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.

A noninvasive measure of the transmission matrix in scattering media using the photo-acoustic effect

[T. Chaigne et al., Nat. Photon., 8, (2013)]

Optical wavefront shaping allows imaging or focusing of light in strongly scattering media at a depth where usual microscopy techniques fail. However, wavefront shaping techniques usually require captors (like a CCD array) or probes (like fluorescent entities) to guide the focusing of light or to characterize the system for imaging purposes. Recently, [X. Xu, H. Liu and L.V. Wang, Nat. Photon., 5, 154, (2011)] and [X. Xu, H. Liu and L.V. Wang, Nat. Photon., 7, 300, (2013)]  (see Retrieving an optical scale resolution with light focusing guided by ultrasound) have shown how to use ultrasound to noninvasively guide light focusing in a scattering medium. This method uses an iterative optimization scheme for focusing on each target. This limits the applications for imaging due to the time requirements. In this paper, the authors use the photo-acoustic effect to measure the transmission matrix that links the optical field on the surface of a spatial light modulator (SLM) modulating the input light to the optical field on different points inside a scattering medium. This knowledge of this matrix allows selective focusing on multiple points and detection of targets buried in the medium.

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.

Subwavelength light focusing through a scattering medium

[J. H. Park et al., Nat. Photon., (2013)]

After the first experiment of light focusing through a scattering medium using wavefront shaping (see A pioneer experiment), the same group demonstrated in [I. M. Vellekoop et al., Nat. Photon., 4, 320, (2010)] that a random medium can improve the sharpness of the focus. The scattering in a medium behind a lens randomizes the direction of the light. The speckle pattern shows high spatial frequencies not allowed by the lens alone because of its finite numerical aperture. After optimization of the input wavefront, the focus spot obtained is sharper than the resolution limit of the lens. In these experiments, the intensity profile was always measured in the far field, i.e. at least several wavelengths away from the surface, where only the propagating waves contribute to the optical field. In the present paper, J. H. Park and his colleagues optimize the input wavefront impinging on turbid media to increase the intensity measured in the near field at a given position. Subwavelength focusing is achieved thanks to the contributions of the evanescent waves.