Fine Structure

Andrew Hicks' Non-Reversing Mirrors

I've read a number of pretty interesting articles recently (even mentioned one of them) about Drexel University's Andrew Hicks and the mirrors he creates. Typical mirrors distort straight lines and reverse images leading to difficulty doing computations on those images. Andy has a number of mirror shapes that solve these problems, either individually or a number of problems with the same mirror. As you'd expect, they make for some nice photo ops for the pop science magazines but these same magazines contain very little useful information about how these mirrors work. I had a number of questions about how these mirrors work so I contacted Andy to find out the details.

The Mirrors

I'll reference these different mirror effects from different articles so take a look at all of them to get a good idea of what I'm taking about:

The Effect

The image that the mirrors produce are solely produced by the curvature of the mirror surface. Other than the shape, no other tricks are used to get the desired image. For some mirrors, like the non-distorting panoramic mirror, this means that the distortion-free image is only available from a certain perspective, while other mirrors, like the non-distorting wide-angle mirror (touted as a driver's side mirror with no blind spot) provides a lot of leeway in terms of viewable angles.

The Creation

These mirrors start their life as some pen-and-paper mathematical model (this is where being a mathematics professor comes into play), eventually make their way into a computer where Andy solves them using Matlab or a similar modeling tool. The reflection shapes are tested in simulations using POV-ray, easily the most popular (and free) ray tracing software. Once the shape is tested, it's finally cut to the desired dimentions at what is essentially an ultra-high tech machine shop.

The Uses

Andy started designing these mirrors in robotic control systems for UPenn's GRASP lab. Robots that have vision-based spatial orientation systems have a difficult time using patterns or markings on the ground due to distortion of straight lines. Hicks has his own very informative page on rectifying mirrors that fix these types of problems (unfortunately not many other pages on Hicks' catadioptric sensor design page are anything more than "coming soon!"). In this sense, rectifying mirrors have almost unlimited use in vision-based robotics or any other automated camera-based industry. Additionally, Hicks is looking into getting his wide-angle mirrors into the American auto industry where there are some current restrictions on curved mirrors (probably due to the distortion that most normal curved mirrors produce).

The Point

So what's the big deal? All of these things can usually be corrected with some very light image processing software. And that's the problem. The price and complexity of a device that requires even the lightest image processing capability is significantly more than a device that can rely on simple mirror optics. Mirrors are also many times more reliable than electronics and don't require any source of electricity. By using a mirror instead of a processor, you've saved space and power for that nifty little gadget of yours.

Comments

This is gnarly. I'd love to see these implemented all over the place.

March 24, 2009
10:40 AM

From Alex