Scientific Method / Science & Exploration

Getting a view through the fog with scattered laser light

Peeping Toms (of science) enjoy a better show through a frosted glass window.


A clear view of an object is quite often difficult to obtain. For instance, a frosted glass window provides near-perfect privacy while still allowing light into a room. Similarly, biological tissue is almost transparent—that is, it does not absorb much light—but we are most definitely opaque. This is due to scattering, which limits our ability to create images of things below the skin.

Creating images of objects that are otherwise obscured by scattering has become a major cottage industry recently. But despite all efforts, it has proven difficult to do. Friends of mine who did some of the pioneering work in this area always talked of using the "memory effect" to image. Yet, actual images were never forthcoming... Until now, that is.

Before we get to the meat of the physics, let's describe the experiment. An object made of fluorescent dye was placed behind a frosted glass window. To obtain an image, the researchers shine light through the window from many different angles. The light, when it happens to hit a fluorescent part of the material, creates a glow that is recorded—the frosted glass makes this a diffuse glow, rather than a sharp point. At each angle, they rock the light source back and forth just a small amount and record the intensity of the fluorescence as a function of angle.

After that, you perform a few mathematical tricks, and produce an image. It all seems a little improbable, but here is how it works.

Memory effect?

To understand this latest imaging trick and its limitations, we need to take a look at how light scattering works. If you look out a glass window, you will see a faint reflection of yourself in the window. The lies-for-children explanation is that the refractive index of glass is different from air, so some light is reflected at the interface between the glass and the air. Rather, this tiny reflection that occurs at every interface between two materials is part of the key to light scattering.

The second part can be understood by remembering how badly you misjudge the distance when diving for objects in a pool. When you look into the water, the difference in refractive index causes the light to bend, making objects appear closer to you than they actually are. Every time light passes from one material to another, it is likely to have its direction changed.

So, we have two processes, both of which change the direction of light. Imagine something like a sugar cube, which is just a clump of transparent crystals. This can be thought of as a bazillion interfaces between air and sugar, with each interface bending and reflecting a portion of light. The end result is that the sugar crystal appears white.

For the purposes of this story, however, we need to consider one other thing: interference. Imagine a beam of laser light passing through our frosted glass window. The light arriving at a particular point on the other side of the window is made up from lots of little contributions that have arrived by many different paths. Each of those paths has a different length, so the phase of the light is scrambled. On one side of the glass, the phase is smooth and flat—the electric field of the light at one spatial point oscillates perfectly in time with the light at another point. On the other side, this is no longer true.

At some locations, these little oscillations add up in phase, creating a bright dot, or speckle, while at others, they don't. These sharp little points of light are the key to creating an image using light that has passed through a frosted glass window.

All this long explanation leads up to two points: when the laser light hits the glass at different angles, then you get different patterns of speckle. And, when the changes in angle are small enough, the speckle position doesn't randomly jump—instead, it shifts predictably. The researchers use both of these effects to image through the scatter.

Imaging the invisible

When one of these bright speckles hits the fluorescent material, it glows, which we see. So each speckle acts as a tiny probe. As the angle of the light is changed, the speckle scans on and off the fluorescent material. But, each speckle only scans a little way, and we never know which of them caused any particular bright spot. Each scan tells us very little.

Now, what follows is going to be a bit technical, but essentially you just need to remember one thing: the bright spots in the speckle pattern are much smaller than the features in the object we're imaging. So, the total fluorescent glow is a measure of the overlap between the bright spots of the speckle pattern and the object. The trick is to use a bunch of math to obtain the image without having to figure out the details of the speckle pattern.

To do this, the researchers make use of three facts: the object they are imaging doesn't change; for small angle changes, the speckle pattern scans; and for large angle changes, a completely different speckle pattern is obtained. The first fact—an unchanging object—means that the only thing changing is the speckle pattern, and the key to obtaining an image is to extract the unchanging part of the pattern.

The second fact—the speckle scans for small angle changes—means that one can correlate the fluorescent intensities from nearby angles to generate an autocorrelation that provides a picture that is related to real, physical distances along the object. (An autocorrelation is used to compute how similar the fluorescent intensity is at one angle to some zero angle.) The final fact—that very different speckle patterns are obtained for different input angles—means that one can average these autocorrelation pictures in a way that leaves you with only that part of the autocorrelation that relates to the one thing that is constant: the object.

After all this, you have a two-dimensional autocorrelation of the object with, essentially, itself. The researchers then use a second mathematical trick to calculate the image that would produce this autocorrelation.

Are we going to see this outside the lab?

It's hard to say if this will get far outside of research laboratories. The researchers show that this works brilliantly, providing a nice accurate image of the object. Nevertheless it has its limitations. For instance, the memory effect gets smaller for stronger scattering. So, for instance, you might be able to image quite nicely a few millimeters into the human body, but the deeper you go, the smaller the extent of the object that can be imaged.

The researchers don't say, but I expect that you need a lot of contrast. In this case, fluorescence was used to give huge contrast. Luckily, fluorescence is quite common, but I would still like to have seen how the image sharpness and accuracy changed as the contrast reduced.

No matter what, though, this is going to find itself to be of great use in many research areas.

Nature, 2012, DOI: 10.1038/nature11578

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