A photoacoustic transmission matrix for deep optical imaging

When light propagates in a turbid medium such as biological tissue, scattering rapidly limits the possibility of recovering an image for use in biomedical applications. Thus, conventional imaging is restricted to superficial investigations. Fortunately, because scattering is an elastic—i.e., linear and deterministic—process, it conserves the phase and coherence of the waves, and the light interference can be exploited. In recent years, wavefront shaping has emerged as a powerful technique for coherent light manipulation in scattering media,¹ thanks to the emergence of digital spatial light modulators (SLMs). Wavefront shaping allows light focusing and imaging through samples of thicknesses at which conventional microscopy techniques fail, and has rapidly established itself as a promising route to optical imaging at unprecedented depths, using approaches such as digital phase conjugation or iterative algorithms.^{2, 3} One previous approach—the transmission matrix⁴—suggested measuring the matrix that describes propagation through the medium, using a camera as a detector. Unfortunately, most approaches for deep focusing by wavefront shaping must, in one way or another, access local information about the light intensity at depth, which remains a challenge.

High-frequency acoustic waves, or ultrasound, which typically propagate ballistically in biological tissue, are good candidates for deep tissue imaging. These waves have been investigated for 'tagging' light at depth within a small volume, and thus achieving deep focusing, up to optical resolution.^5–7 Another approach—the photoacoustic effect—couples light and ultrasound. In essence, when a short pulse of light diffuses inside a turbid medium, the absorbing regions heat rapidly, and thermoelastic effects generate ultrasounds that propagate to the outside of the medium and can be localized by a transducer. Photoacoustic imaging has been developed in the past decade as a very powerful approach to deep imaging with optical contrast,⁸ for example, to image blood vessels⁹ and even genetically expressed fluorescent proteins.¹⁰ But deep photoacoustic imaging usually assumes that light propagation is driven by diffusion of the optical energy.

Recently, photoacoustic imaging has been proposed as a feedback mechanism for iterative wavefront shaping.¹¹ In our recent work,¹² led by Thomas Chaigne and Ori Katz, we applied the transmission matrix approach to photoacoustics to go one step beyond iterative wavefront shaping (see Figure 1). In most photoacoustic imaging setups, one obtains images (1D, 2D, or 3D) of the heat deposited inside the sample (and thus of the absorbers' distribution). These images, just like those provided by a standard camera, make it possible to measure a transmission matrix inside the medium that links the input optical wavefront to the output acoustic signal: the photoacoustic transmission matrix. Once we have measured this matrix, we can show the many ways to exploit the information it contains. First, it is possible to focus the light intensity and, in turn, the photoacoustic signal at various positions. Therefore, we can guide light and also enhance the signal of any given absorber at will. Furthermore, by analyzing the photoacoustic transmission matrix, we are able to show that its highest singular values correspond to the strongest absorbers, providing automatic ‘target detection’ at depth, and consequently the ability to selectively address any desired region.

Figure 1. Schematic of the experiment: a nanosecond light pulse impinges on the spatial light modulator (SLM), passes through the scattering medium, and excites optical absorbers inside a gel (left). The photoacoustic signal is detected by a transducer placed outside the sample, each absorber corresponding to a spike in the temporal signal. From the photoacoustic transmission matrix (not shown), one can shape the wavefront to focus on the absorber. Here we show the SLM pattern and the resulting photoacoustic trace on the first (red) and last (green) of the six absorbers that are visible on the original trace (blue) (right). (Figure adapted from Nature Photonics.¹²)

Nonetheless, there are challenges to our approach. In particular, the acoustic resolution (in the range of tens of microns for depths of a few millimeters) and the optical resolution differ by at least one or two orders of magnitude. Regaining optical resolution remains an ongoing problem. Also, the time required to measure the transmission matrix is currently tens of minutes, and needs to be shorter than the stability time of the medium. We demonstrated the photoacoustic transmission approach through a static scattering sample, and through a thin layer of chicken breast. But going in vivo will require significant improvement in speed.

More generally, in this work we exploited the coherence of light for wavefront shaping using the measurement of a photoacoustic transmission matrix. Recently, Jérôme Gâteau at the Institut Langevin further exploited the coherence properties of illumination for photoacoustic imaging, showing that unshaped random illumination patterns (optical speckles) can provide images that overcome the limitations of conventional illumination, such as limited view or limited bandwidth artifacts. With speckle illumination, the variation of light intensity at the scale of the optical wavelength provides high-frequency and isotropic components in the ultrasound field, fluctuating from one illumination pattern to another and revealing absorbers that are otherwise invisible.¹³

Our work exploits the coherence of light in photoacoustics, creating new possibilities for optical wavefront shaping and photoacoustic imaging to benefit from each other. Our approach offers a new degree of freedom for photoacoustics, enabling control of the local signal and revealing hidden features. Furthermore, it enables wavefront shaping and light delivery at depth, which benefit other optical imaging modalities. Our future work will include moving to 2D or even 3D imaging using these techniques in vivo, and breaking the ultrasound resolution barrier to reach subcellular optical resolution.

This work was funded by the European Research Council (grant 278025) and by the Fondation Pierre-Gilles de Gennes pour la Recherche (grant FPGG031).