## Abstract

Scattering of light by random media limits many optical imaging and sensing applications, either by scrambling waves that carry images or by generating glare—background noise that hinders detection. In recent years, it was shown that the shaping of the wavefront of light before it enters the scattering environment allows an unexpected degree of control over the scattered fields and enables various imaging techniques that are being applied in microscopy and other demanding imaging tasks. Here, we show that similar ideas can be applied to reduce glare and enable imaging under tough conditions.

© 2016 Optical Society of America

The technique of wavefront shaping has attracted a lot of attention since Vellekoop and Mosk demonstrated that a surprising degree of control over the scattered coherent field is possible even when the number of degrees of freedom that could be controlled is much smaller than the complexity of the scattering object [1,2]. In essence, they have shown that an adaptive optics approach could be useful even when the scattering completely scrambles the input field. In their pioneering work, they sent light through a spatial light modulator, and by controlling the spatial phases of the input field, they were able to enhance one of the speckles of the scattered field by a factor of $\sim N$, the number of control phases. Such an enhanced speckle can serve as an effective focal spot, thereby enabling imaging through scattering layers and various forms of microscopies [2–6].

Here, we show that wavefront shaping could also be useful to *reduce* the scattered intensity in certain directions. This could be valuable in particular for decreasing glare and enabling imaging and sensing that would be otherwise overwhelmed by background noise. Figure 1 illustrates an experiment that demonstrates the main concept: a camera attempts to image an object in the presence of a strong background from a scattered coherent field. The object is illuminated by a separate source, here just an incoherent white light source, yet later, we discuss other scenarios that may benefit from this technique. The input field illuminating the random medium is controlled by a two-dimensional spatial light modulator (SLM). Initially, the background is strong, and the object is hardly discernable. Using an iterative algorithm [7,8], the spatial phase pattern applied by the SLM is optimized for reducing the power of the total speckle field that reaches the camera. As the optimization process proceeds, the background is significantly decreased and the image of the target, which is illuminated by a separate, incoherent source, comes through very clearly [Fig. 1(b)]. Reduction of the speckle background at one point in the target area was recently demonstrated in the microwave range [9]. The reduction of speckles over a region in the target plane is encountered in the recent effort to directly image exoplanets, where speckles generated by light from the main star obscure the much fainter planet, and indeed, adaptive optics techniques are being used to engineer an optimized wavefront to reduce them [10].

In contrast with the more common application of wavefront shaping, where the goal is to enhance certain field components, the reduction of glare poses a different set of challenges. Obviously, one would like to reduce the power, not just in one speckle grain, but over an extended region in space. In the experiment shown on Fig. 1, the optimization target was to reduce all background light entering the camera. Figure 2 shows the result of an adaptive optimization experiment reducing the scattered intensity in a specific area covering $453\times 453$ pixels on the camera, an area initially containing approximately 36 speckles. The optimization reduced the integrated intensity to about 17% of its original value.

An important question is, then, how large an area can be darkened, and how effectively? We have set out to answer these questions by performing experiments and computer simulations. The speckle pattern was simulated by applying a two-dimensional Fourier transform to a random phase matrix of size $256\times 256$. The resulting random matrix representing the speckle field (as would be formed by a thin scattering layer) was used to calculate the feedback signal for the optimization algorithm. The control was affected by a square $\sqrt{N}\times \sqrt{N}$ matrix of phases, namely, $N$ degrees of freedom, representing the SLM. The optimization target was to reduce the power in a square-shaped area of varying sizes. The resulting optimal fields for a $32\times 32$ control matrix are shown in Fig. 3(a).

We found that as long as the target region size is small enough, the power can be almost completely attenuated. Figure 3(b) shows the remaining power fraction against the size of the target area for several control matrix sizes. The size of the region that can be effectively darkened grows with the number of available controls. Applying 16, 64, 256, and 1024 controls, we were able to almost completely darken $\sim 4$, $\sim 16$, $\sim 64$ and $\sim 200$ speckles, respectively. It seems it is possible to effectively darken $\sim N/4$ speckles, and we attribute the deviation from linearity for a large number of controls to the increasing difficulty of obtaining these optimal solutions in a large parameter space. Repeating these simulations by modeling a thick scattering medium produced similar results.

Some additional insight could be gained by considering the problem of the controlled addition of fields in the complex plane [11,12]. The light passing through each SLM element $(k,l)$ generates its own random pattern ${a}_{k,l}(x,y)$ on the camera, with $\u27e8|{a}_{k,l}|\u27e9=\overline{\alpha}$. The total field on the camera is $A=\sum {a}_{k,l}{e}^{j{\varphi}_{k,l}}$, with ${\varphi}_{k,l}$ representing the control phases applied by the SLM. To maximize the field at one point, one has simply to align all phasors in a single direction, that is, to apply as controls ${\varphi}_{k,l}=-\mathrm{arg}({a}_{k,l})$. On average, the intensity at the selected spot increases by a factor of $\sim \pi N/4$, where $N$ is the number of control elements [1,2]. Minimizing the field at a single spot does not have a unique solution. Since the random addition of (uncontrolled) phasors yields on average a total amplitude of $\u27e8|A|\u27e9=\u27e8|\sum {a}_{k,l}|\u27e9\approx \sqrt{N}\overline{\alpha}$, it seems that $\sqrt{N}$ phasors aligned correctly would be enough to significantly reduce the amplitude at a selected spot. This suggests that at least $\sqrt{N}$ independent speckles could be darkened simultaneously. Our results show that we could effectively darken even larger areas.

Note that even if the transfer matrix is known, it is not obvious how to find the correct SLM control to achieve darkening over a large area. One approach for constructing a control matrix that works well for thin scattering layers is to align phasors in pairs in an anti-ferromagnetic-like pattern [see Fig. 4(a)] so as to minimize their contribution to a particular point at target area, that is, to apply ${\varphi}_{k,l}=-\mathrm{arg}({a}_{k,l})+{(-1)}^{k+l}\pi /2$. It can be shown that this simple approach reduces the average intensity by about 80% at the target, affecting an area that contains about $N$ speckles (more details are given in the Supplement 1). To reduce the background even more, further iterations, properly aligning a quartet of cells against the next, and so forth, would reduce the background significantly, although over a smaller area. The resulting power reduction using this approach is shown in Fig. 4. This form of control is reminiscent of techniques to engineer non-Markovian speckle patterns [13,14]. However, this procedure becomes less effective for thick media, and the darkened area shrinks with the thickness, eventually reducing to one darkened speckle (see the Supplement 1). This is an echo of the so-called “memory effect” that enables wide-field imaging through thin scattering layers but is not effective for thick ones [15,16].

In conclusion, we have demonstrated that by properly shaping the wavefront of an incident beam, we could reduce the glare light that scatters into a detector or camera and blinds it. While in this work, we generally investigated the degree of improvement that could be achieved and its dependence on the number of available controls, we would like to discuss briefly the situations where this technique could be relevant.

Of course, if the object we are attempting to observe is static and is illuminated by the same coherent source, this procedure would darken it as well. Yet, a very relevant scenario is when the target object is dynamic, for example moving, while the background is dominated by light from a static, random medium. This method will reduce the background signal, not affecting the light arriving from the object. Such situations could arise, for example, in laser flow cytometry and certain scenarios in medical imaging [17,18]. Indeed, it would be interesting to investigate the effectiveness of the darkening process and its dependence on the relative dynamics of the object, the scattering medium, and the speed of the algorithm.

Still, this method could be useful in other scenarios. In the above-mentioned application in astronomy, for example, the speckles from a main star were eliminated to expose a faint planet [10] that was illuminated actually by the same main star, yet the two sources are mutually incoherent. More speculative applications, for example, involving back reflections from fog, could be imagined, but these will require extremely fast adaptations, far beyond what is technically feasible today.

**Experimental setup**: The experimental setup is illustrated schematically in Fig. 1(a) (more details shown in Supplement 1). The light source is an 808 nm diode laser (Thorlabs, LP808-SA40, 40 mW). The beam reflects off an SLM (HAMAMATSU, LCOS-SLM X10468) with a resolution of $600\times 800$ pixels. The SLM is divided into $32\times 40$ effective segments; each block is controlled independently to apply a phase between 0 and $2\pi $. The reflected beam illuminates the diffuser (LSD, angle: 5°). Light scattered by the diffuser creates a speckle pattern on the CCD camera. Optimization of the phase pattern is performed with a genetic algorithm [7,8], with the target of reducing the total power reaching the CCD. The object (a toy figurine) is illuminated by weak white light and is imaged simultaneously on the same CCD camera.

**Simulations:** Scattering was simulated with $256\times 256$ matrices of random phase. Far-field scattering was implemented by a discrete Fourier transform. Finite size speckles could have been generated by zero padding, but this was avoided to increase the computation efficiency. A thick, multiply scattering medium was simulated by two such random scattering layers separated by a distance $L$. SLM control was implemented by applying $\sqrt{N}\times \sqrt{N}$ controls, each affecting $256/\sqrt{N}\times 256/\sqrt{N}$ elements in the scattering matrix. Optimization was implemented either through the genetic algorithm or through simulated annealing procedures.

## Funding

Israeli Centers for Research Excellence (I-CORE) of the ISF; The Crown Photonics Center at Weizmann Institute of Science; European Research Council (ERC) (ERC-AdG “QUAMI”).

## Acknowledgment

We thank Robert Fischer for his interest and help.

See Supplement 1 for supporting content.

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