A problem in optics has lead to a US patent for a car side mirror which “eliminates the dangerous ‘blind spot’” and “dramatically increases the field of view with minimal distortion” by finding approximate solutions for “the problem of controlling a single ray bundle with a single reflector”.
The press release explains about the blind spot problem:
Traditional flat mirrors on the driver’s side of a vehicle give drivers an accurate sense of the distance of cars behind them but have a very narrow field of view. As a result, there is a region of space behind the car, known as the blind spot, that drivers can’t see via either the side or rear-view mirror. It’s not hard to make a curved mirror that gives a wider field of view – no blind spot – but at the cost of visual distortion and making objects appear smaller and farther away.
On his website, author Andrew Hicks explains his research:
For many years now I’ve been looking at the problem of designing a mirror that would give a prescribed distortion to the viewer. In other words you tell me what you want to see when you look in the mirror and how it should be distorted, and I have an algorithm that spits out a mirror shape that achieves this. (Well not quite. The problem is not always solvable with one mirror, so the method does the best it can.)
If you ask then for a driver-side mirror that has, say a 45 degree field of view (thus annihilating the blind-spot) and no distortion (the view is perspective: straight lines look straight), you’ve got exactly the kind of problem I’ve got a way to solve.
In the press release he is quoted explaining the algorithm in general terms:
Imagine that the mirror’s surface is made of many smaller mirrors turned to different angles… The algorithm is a set of calculations to manipulate the direction of each face… so that each ray of light bouncing off the mirror shows the driver a wide, but not-too-distorted, picture of the scene behind him.
The press release notes that US regulations governing car manufacturing will not allow this mirror to be installed on new cars:
Cars coming off of the assembly line must have a flat mirror on the driver’s side. Curved mirrors are allowed for cars’ passenger-side mirrors only if they include the phrase “Objects in mirror are closer than they appear.”
However, “the mirror may be manufactured and sold as an aftermarket product” and “some countries in Europe and Asia do allow slightly curved mirrors on new cars”.
Press release: Driving without a Blind Spot May Be Closer Than It Appears.
Paper: Controlling a ray bundle with a free-form reflector (Hicks, 2008; Optics Letters; DOI: 10.1364/OL.33.001672).
Patent: Wide angle substantially non-distorting mirror (United States Patent 8180606).