Wavefront shaping offers the possibility to increasing microscopic imaging depth. By learning how to focus deep inside a (not too) scattering medium, we also learn how to compensate for scattering effects around this area, allowing us to retrieve an image of this area. Typically, finding the wavefront that focuses light at a given target is done using a feedback optimization procedure, or by measuring the response of the system. In this paper, the authors propose another approach. They first create a model of the system thanks to some calibration measurements. The model is then used for finding the optical input wavefront that would be utilized for imaging at different depths. They experimentally demonstrate the advantage of this technique for two-photon fluorescent imaging through a low scattering medium.
The easiest way to focus light at a given target through an inhomogeneous medium is usually to use a feedback signal. Maximizing this signal can be done by iteratively optimizing the input wavefront. Another way is to learn the response of the system, which can be done with a guide star or by measuring the transmission matrix of the system. Either way, the calibration obtained is only valid in a limited region. However, if we know all the relevant parameters of the system, we can ideally create an accurate model that could be used to focus light anywhere we want. This approach is of course only valid for systems simple enough to be characterized by a reasonable number of parameters, which is the case for single scattering samples with a rather smooth surface like it is the case here.
Figure 1. Principle of the experiment. Image from [A. Thendiyammal et al., Opt. Lett., 45 (2020)].
The sample consists of fluorescent beads buried inside a polymer that has an irregular interface with water, as shown in Fig. 1. The index of refraction of both components is known, the knowledge of the shape of the interface then fully characterizes the scattering properties of the system. In the first step, the authors acquire a 3D intensity image of the scattering surface. It is used to reconstruct the 3D refractive index model of the interface. This data is fed into a numerical model. The authors then numerically propagate light coming from a source at a given depth to the plane of the modulator. The phase conjugation of this mask corresponds to the wavefront that focuses light at the position of the virtual source. It also corresponds to the mask that compensates for the aberrations undergone by the light coming from an area around this position and can be used to reconstruct images at this depth.
These masks can also be found using a feedback-based algorithm by increasing the signal from actual fluorescent beads inside the medium. It is limited by the signal to noise ratio, that decreases with the depth, and the number of controlled pixels. Increasing the number of controlled pixels increases the accuracy of the aberration compensation, but increases the convergence time of the optimization. In Fig 2. the authors show the comparison between the direct measurements (no correction), the correction obtained using the mask optimized using the feedback approach, and their model-based approach.
Figure 2. Comparison between direct imaging (a), iterative focusing by wavefront shaping (b) and the model-based approach. Image from [A. Thendiyammal et al., Opt. Lett., 45 (2020)].
The demonstration clearly shows a strong improvement for in-depth imaging. It is efficient as after a one-shot measurement, one can find the masks to use for any depth, as long as the model is still valid. It is to be noted that this is the case because the system can be fully described by a few parameters that correspond to the shape of the surface of the interface. For multiple scattering systems, characterized by the position of numerous scatterers, such an approach would likely fail, but for simpler systems, as biological tissues with little inhomogeneities, this approach may be quite simple and effective to implement.