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.

The setup is described in Figure 1.a. It is based on the photoacoustic effect; when laser pulse hits an absorber, the local and brief increase of temperature generates an acoustic pulse. The amplitude of the photoacoustic signal is proportional to the optical intensity. For a given wavefront synthesized using a phase-only SLM, the ultrasonic signal is measured by a transducer. Because the sound wave propagates in the medium with negligible scattering, the time at which is measured a signal is proportional to the depth at which the source that generated the signal is located (Figure 1.b.). For each element of a basis of illumination patterns, the optical field at each depth is measured using a phase-shifting interferometry method. The aspect of a photo-acoustic transmission matrix measured is shown in Figure 1.c.

Figure 1. Principle of the experiment. (a.) setup of the experiment. (b.) the temporal signal received by the acoustic transducer for one illumination pattern. (c.) the aspect of the transmission matrix. Image from T. Chaigne et al., arXiv, 1305.6246, (2013).

The authors first demonstrate selective focusing on targets using the transmission matrix. A column of the transmission matrix gives the effect of each pixel of the SLM at a given point inside the medium. The phase conjugation of this column gives the wavefront to sent to get all the contributions in phase at the point chosen. This results in an enhancement of the optical intensity at the targeted spot proportional to the number of pixels used on the SLM. The technique and the experimental results are shown in Figure 2. The authors demonstrate selective focusing in a solid diffusing sample and in a 0.5 mm-thick chicken breast slab.

Figure 2. Selective focusing inside a scattering medium. The wavefronts (b.) extracted from the transmission matrix (a.) are used to selectively focus on different absorbing regions. (c.) the two wavefronts selected focus light at different depths in the medium (red and green lines). The signal measured for a plane wave excitation (blue line) is shown as a reference. Image from T. Chaigne et al., arXiv, 1305.6246, (2013).

The transmission matrix carries a lot of information on the transmission properties of the medium. In this study, the authors probe the so-called memory effect using the transmission matrix. They finally show how to detect and localize targets inside the medium using the singular value decomposition of the transmission matrix.