During the summer I had the opportunity to attend a talk by Professor Yaron Silberberg, an Israeli physicist at the Weizmann Institute. He’s made considerable contributions in nonlinear optics, integrated optics, optical solitons integrated optics and much more. That particular talk was on his recent work on speckle correlation and scattered wavefront correction imaging. I thought I’d dissect some of the science/tools used in the latter, which allowed his group to image live objects by using walls as mirrors.
To better grasp how this can be achieved, we must first understand what genetic algorithms and spatial light modulators are.
Genetic algorithms are optimization methods that evolve and adapt to a set of constraints over multiple iterations. For each successive “generation”, random parameter modifications are applied the best performing object based the predetermined optimization function. In cases where the end goal is well defined, this evolutionary process can easily outperform humans at determining optimal parameters. The field of genetic algorithms is great on its own, but its details have been discussed here in the past, so I’ll just leave you with a short list of captivating examples where they were successfully used:
Spatial light modulators, or SLM’s, are, as their name describes, computer controlled objects that modulate the spatial distribution of light. They're used both for transmission and reflection applications. They usually consist of an array of cells or pixels (similar to a checkerboard with controllable white/black square locations) that can individually induce a phase delay and/or change the reflection or transmission intensity of the incoming light. For those less familiar with phase, consider the following animation:
In that example, we can see the wave-front gets distorted as it passes through the SLM (cross-sectional view). The grey cells in this diagram have a higher index of refraction, effectively slowing down the wave-front locally. Specifically, this shows that if the shape of the wave-front is known in advance, one can use an SLM to tune it to a desired shape. In diagram above, a flat wave-front can be recovered from using the right pixel combination (check mark), but not otherwise (red cross).
In the case of intensity modulating SLMs, the grey pixels are made in a way that partially or totally blocks the light, instead of simply slowing it down.
Uses of spatial light modulators range from the creation of incredibly complex laser beam polarization profiles to holography to wave front correction. The latter will come in handy later.
We've quickly overviewed two essential tools for controlling light. Combine them in the right order, and you just gained a super power: one that allows you to use walls as mirrors and see through thin scatterers like egg shells. Let’s take a look at a possible setup in the transmission case:
As described, a) represents a simple imaging system. In b), the scattering medium is added. As you can see, it distorts the original wave-front in such a way that the perceived image is indistinguishable from noise. Just like most surfaces around you, this scattering glass is covered in microstructures that diffuse light and appears to be of a single color instead of making it being perfectly transparent or reflective. In c), an SLM is added to allow for wave-front shaping correction. That element is added to attempt to “cancel” the effect of the of the scatterer by precisely choosing how each cell interacts with light. Since this correction can only be valid for a small bandwidth, a bandpass filter is added. [1]
So how exactly do we know what pixel distribution we need to correct for a scatterer? This is where the genetic algorithm comes in. It's used to “learn” the best pixel configuration for the SLM by evolving over multiple iteration and building on its past experience. First, we start with a point source at a distance R from the SLM. This looks like subimage a) in the following picture. Quite messy as you can see:
From this, a single speckle in the output image is selected. The task given to the genetic algorithm is then to simply try to maximize the intensity around at the chosen point. It first starts with a random pattern, but after a few generations, the speckle intensity ends up being enhanced 800 times, as shown in image b). The contrast of the image turns out to be proportional to the number of pixels in the SLM. [1]
Once that’s done, any object in the vicinity of the optimized point source will be imaged live. The end result of can be seen in d) for the object shown in the insert of c) (letter A).
In the same way, the process can be applied to walls or paper to recover an image lost due to scattering. Here it is with paper
In a) is displayed the experimental setup, b) a picture of the paper used (scatterer) and c) the image seen with the naked eye and the recovered image of the letter G in picture d). [1]
The beauty of this relatively simple technique is that it doesn’t require the use of coherent light (lasers). It could be in a variety of applications that necessitate imaging or microscopy through turbid tissue or inhomogeneous media.
What if we could one day see the inside of an egg and observe a chick grow live, in high resolution, thanks to the ability to completely cancel out the effects of shell scattering? We’re not quite at that point yet, but this sure brings the possibility closer than ever before.
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