Optical imaging in scattering media
Because of multiple scattering, optical imaging techniques can be divided in two categories. The first one uses ballistic light or single-scattered photons. This was previously referred to as con-ventional optical imaging. This regime can be interpreted in terms of geometrical optics but given the transport mean free path of biological tissues (l∗ ∼ 1mm), it does not allow for deep imaging. The second category relies on multiply scattered photons. Since the trajectories of such photons are random, the information they carry is more diﬃcult to interpret. We will show here a brief overview of the diﬀerent optical imaging techniques. More detailed information can be found in reviews like .
Imaging with ballistic light
Imaging with ballistic light is the most natural form of imaging because it is the way our eyes form images. The main advantage of such techniques is that they benefit from optical resolution. However, in biological tissues, their depth of imaging is seriously limited because of multiple scattering which will rapidly degrade the image quality.
The archetypal optical imaging technique is microscopy. Conventional transmission microscopes map the transmission of ballistic light through a sample and are thus sensitive to absorption while reflection gives a contrast of scattering by recording the single-scattered photons. Consequently, they are limited in terms of depth because multiply scattered light adds a lot of parasitic noise for depths higher than the scattering mean free path.
In order to increase the depth of imaging, one solution is to spatially filter out the multiply scattered photons. This is the case of confocal microscopy  in which pinholes are used to limit the field of view to collect only the ballistic or single scattered photons. With such techniques, the imaging depth can be increased up to the transport mean free path, above which ballistic photons no longer exist. The main disadvantage of this technique is that it requires a mechanical scan of the focus to obtain images
Another approach to filter multiply scattered photons is to make use of the time of flight. Ballistic photons, single-scattered and snake-like photons travel in straight or almost straight lines whereas multiply scattered photons have complex trajectories. Consequently, it takes multiply scattered photons more time to travel through the medium. One can exploit this by sending a short pulse of light from a laser and by time gating the detection. Ballistic photons will usually go through the medium in a few hundreds of picoseconds while it takes nanoseconds for multiply scattered photons. The time gates thus need to be extremely small. This can be achieved with streak cameras, Time-Correlated single photon counting  or by activating non linear eﬀect such as Kerr eﬀect [26, 27], stimulated Raman scattering  or Optical Parametric Amplification .
Imaging with multiply scattered light
Imaging techniques working with ballistic or single-scattered photons have the great advantage of having optical resolution. Yet they are limited to a few transport mean free paths which corresponds to a few millimetres in tissues. If one wants to image deeper in biological sam-ple, several techniques using multiply scattered light exist. However, because of the nature of multiply-scattered photons, extracting the information from the outgoing light is not as straight-forward. The imaging techniques roughly fall into two categories: the techniques that use detailed model of the light propagation to reconstruct optical contrast inside a scattering medium (NIRS, DOT…) and methods that combine light with another type of wave to extract the information (Photoacoustics, Acousto-optics…).
Near Infra-Red Spectroscopy
Near Infra-Red Spectroscopy (NIRS) is a technique which can probe the optical absorption at a few centimetres depth inside multiply scattering medium. A sample is illuminated by a near infra-ref source and light is collected on the same side by a detector. The most likely trajectories form a « banana shape » between the source and the detector which probes the medium at a depth related to the distance between source and detector, as shown on 1.8(a). NIRS is not properly speaking an imaging technique since it sensitive to the average absorption on a wide area, but it is possible to probe at diﬀerent depths by changing the source-detector distance. NIRS is also used to perform spectroscopy by changing the wavelength of the input source. Since it has been proposed in 1977  is it commonly used to measure the oxygenation of blood, and a variety of modalities have been developed (e.g. NIRS-CW (continuous wave), NIRS-TD (time domain) or NIRS-FD (frequency domain)).
Diﬀuse Optical Tomography
The recent advances in modelling light propagation in highly scattering media lead to the develop-ment of Diﬀuse Optical Tomography (DOT) . The basic principle is to surround the medium with a high number of near infra-red sources and detectors, as shown on figure 1.8(b), extracted from  and to detect the multiply scattered photons on the boundaries of the medium. Then the propagation of light between sources and detectors is simulated using the Radiative Transfer Equation or one of its approximations and the collected data are used with a model based inversion to reconstruct the optical properties .
DOT has been implemented in several commercial devices and can be used for breast cancer imaging  or mapping of the brain haemodynamics for functional imaging . DOT can give 3D images of the absorption or scattering coeﬃcient with a resolution which is usually of the order of 5 to 10 mm which is sometimes too large to detect early stage tumours.
Light modulation in scattering media
In a scattering medium, the interaction between light and ultrasound is diﬀerent from a case without scattering. Since the trajectories of photons are complex and random, it doesn’t make sense to talk about beam deflection any more. However, phase modulation of light still occurs and is driven by two eﬀects which both contribute to the modulation of the optical path: the modulation of the scatterers’ position and the modulation of the refractive index of the medium.
The study and modelling of the acousto-optic modulation only started in the 1990s. At first only one of the phenomena was taken into account, usually the vibration of the scatterers. The first theory was published by Leutz and Maret in 1995 . They modelled the light modulation by considering Brownian motion of the scatterers and a collective motion due to ultrasound. This model was completed by Kempe et al. in 1997  by taking into account the inhomogeneity of the ultrasound field. In 2001, Wang analytically modelled the modulation of light by considering both the scatterers movements and the modulation of the refractive index .
Table of contents :
1 Light propagation in thick scattering media
1.1 Of the interest of optical imaging
1.2 Light-matter interaction
1.2.3 Orders of magnitude in biological tissues
1.3 Light propagation in scattering media
1.3.1 Propagation regimes
1.4 Optical imaging in scattering media
1.4.1 Imaging with ballistic light
1.4.2 Imaging with multiply scattered light
2 Acousto-optic imaging
2.1 Principle of acousto-optic imaging
2.1.1 The acousto-optic effect
2.1.2 Applications of the technique
2.2 Light modulation in scattering media
2.2.1 Modulation of the scatterers positions
2.2.2 Modulation of the refractive index
2.2.3 Coherent acousto-optic modulation
2.3 Image formation and resolution
2.4 Detection of tagged photons
2.4.1 Incoherent methods
2.4.2 Coherent methods
2.5 Conclusion on acousto-optic imaging
3 Photorefractive detection of tagged photons
3.1 The photorefractive effect
3.1.2 The band-transport model
3.1.3 Characteristics of the photorefractive effect
3.2 Detection of the acousto-optic signal
3.2.1 Two-wave mixing
3.2.2 Acousto-optic signal detection
3.2.3 Experimental configuration
3.3 Choice of the crystal
3.3.1 Measurement of the crystals characteristics
3.3.2 SPS vs. ZnTe
4 Acousto-optic imaging in reflection mode
4.1 Fusion between conventional ultrasound and Acousto-Optic Imaging
4.2 Monte Carlo Simulations
4.2.1 The algorithm
4.2.2 Influence of source-detector distance
4.3 Imaging in reflection mode
4.3.1 The imaging setup
4.3.2 Influence of source-detector distance
4.3.3 Towards a handheld probe
4.3.4 A multiple detector approach
4.4 Towards In Vivo imaging
5 Inverse Problems for Quantitative Acousto Optic Imaging
5.1 Inverse problems for medical imaging
5.1.1 Definition of an inverse problem
5.1.2 Reconstruction algorithms
5.1.3 Application to imaging
5.2 Inverse problems for acousto-optic imaging
5.2.1 The inverse problem and model corrections
5.2.2 Reconstruction of the absorption coefficient
5.2.3 Limitations of the current algorithm
5.2.4 Next steps for quantitative acousto-optic imaging
Conclusions and perspectives