It’s the dream of spooks and teenagers alike: how to take photographs through opaque objects.

That’s always been impossible because light is so badly scattered when it travels through an opaque medium that it is impossible to reconstruct the original image. Or so we had thought.

Today, Sebastian Popoff and pals at the Langevin Institute in Paris show how it can be done with the aid of some mathematical trickery.

Send a laser beam through an opaque medium and all you’ll get on the other side is speckle: the beam has been mixed in a seemingly random as it bounces around and interferes inside the material.

But Popoff and co point out that however complex this process, multiple scattering is ultimately deterministic. No information is actually lost when the light is scattered. That means that it ought to be possible to extract the information, the only question is how.

Popoff and pals’s approach is to think of the speckled pattern as an image which has been transmitted through a large number of complicated optical channels. Reconstructing the image in then a matter of processing it in a way that reverses the effect of these channels.

But how to find such an operator, the transmission matrix, as Popoff and co call it?

Simple, they say. Just send several known wavefronts through the material and record how they are distorted. The transmission matrix can then be deduced from the difference between the projected and transmittted wavefronts. This process takes just a few minutes, they say.

And that’s exactly what they’ve done using a spatial ligt modulator to create suitable wavefronts and images to send through an opaque layer of zinc oxide on a glass microscope slide.

The zinc oxide layer turns any image into seemingly random speckle. Popoff and co then reconstruct the original using the transmission matrix (or actually its inverse).

There is one other additional complexity: noise. It turns out that noise significantly changes the transmission matrix so even small amounts ruin the reconstruction process.

To get around this, Popoff and co illuminate the object to be imaged with several different wavefronts and measure the transmission matrix for each. This is equivalent to sending light through several different scattering channels and works like a kind of averaging process that cancels out the effect of noise.

That’s interesting work inspired by techniques that have been around in acoustics for some time. One member of the team is Mathias Fink, who invented time-reversed acoustic mirrors back in the 90s.

The question now is what to use this device for. It has some limitations, the most obvious being that at least some light needs to pass through the material for the technique to work. Anything that absorbs light completely will still be opaque so teenagers hoping to peak into bedrooms will be disppointed. The material must also be linear, ruling a out certain classes of rather weird materials.

Other than that anything goes. And of course, it ought to work for reflected as well as transmitted images. So it could turn an ordinary wall into a perfect mirror.

Frosted windows may never be private again.

Ref: arxiv.org/abs/1005.0532: Image Transmission Through an Opaque Material