Seeing in the Blind Spot

Every driver knows—or should know—about the “blind spot,” that part of the road that you just can’t see in any of your car’s rear-view mirrors, the spot that all too often hides a semi-tractor trailer full of hazardous wastes passing you at 70 miles an hour on a crowded turnpike.

R. Andrew Hicks, an associate professor of mathematics at Drexel University, has a better solution than a quick turn of the head and a yelp of surprise. He has created a slightly and elegantly curved mirror that provides drivers with a 45 degree field of view on the driver’s side. A flat mirror provides less than 20 degrees. The difference is dramatic.

Flat mirrors do not provide a wide enough field of view. Trucks and buses make use of spherical mirrors, which broaden the field, but increase the distortion of the image. The passenger-side mirror on a car, the one with the worrisome note that “objects in the mirror may be closer than they appear,” also trades a wider field for a distorted view.

Hicks has been working on creating very wide fields of view, in the new field of “omnidirectional vision,” sometimes also called panoramic vision, which has been developed to help robots to “see.” A mobile robot might use a camera with an extremely wide-angle “fish-eye” lens or with curved mirrors mounted in front of a standard lens. Omnidirectional vision provides a very large field of view.

Curved mirrors can provide the same kind of panoramic views—such as often seen in CCTV security cameras. Hicks was designing such mirrors for robots as a postdoctoral fellow at the General Robotics, Automation, Sensing, and Perception Laboratory at the University of Pennsylvania, where he received a Ph.D. in mathematics in 1995. He also was learning a lot about the problems of building them. The theoretical design of a curved mirror that has a wide and undistorted view is a “problem of classical optics,” Hicks says. That elegantly drawn curve, however, was until recently impossible to translate into a physical mirror. “The tricky part is that the machines that could actually build a practical design didn’t exist before 2000. So nobody really explored making such a mirror.”

Hicks can now make and demonstrate such a mirror, but he can’t sell it: U.S. law prohibits a curved mirror on the driver’s side. (It is allowed in Europe and Japan and as an add-on in the U.S.) Until that can be changed, he still advocates, as your driver-ed teacher did, an occasional quick glance over the shoulder.

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