I present a design technique for realizing given projections as catadioptric sensors. In general, these problems do not have solutions, but approximate solutions may often be found that are visually acceptable. The method described reduces the problem to solving a linear system. A given transformation from the image plane to an object surface is shown to determine a vector field that is normal to the surface in the case where the vector field is a gradient. For the case when the vector field is not a gradient, several functionals are presented that may be minimized to give approximate solutions. As an application several new designs are described, including a mirror that directly gives a full 360-deg cylindrical projection without the need for any digital processing.
© 2005 Optical Society of America
R. Andrew Hicks, "Designing a mirror to realize a given projection," J. Opt. Soc. Am. A 22, 323-330 (2005)