De Rerum Natura

Howard Schultz and I have just filed our patent application “SYSTEM AND METHOD FOR IMAGING THROUGH AN IRREGULAR WATER SURFACE” for a fully submerged periscope. The etymology of periscope means “seeing around”. In this case we are able to reconstruct the scene above a choppy water surface by measuring the polarization of the light as it refracts through the air-water interface. The figure on the right shows how a choppy air-water interface scrambles the above water scenery. Refracting through a water interface induces a polarization change, so if you can measure the full polarization state of the light, you can make a slope map of the surface. This then allows you to unscramble all the rays and magically reconstruct the scene above. Doing so is not easy. The camera has to measure the full Stokes ‘vector’ of the light rays $(I,Q,U,V)$. A typical camera just measures the light intensity $I$. The linear polarization of the light is specified by the $Q$ and $U$ terms. And the circular polarization is specified by $V$.

But one can see that this camera will never be real-time in the sense that a statistical computation will always be required. The choppy water will black out certain parts of the scene and even double up the same object on different pixel locations. We are currently working on figuring this all out. Our underwater periscope is a great combination of physics, computer vision, and statistical techniques.