Holographic optical elements that perform one-to-one coordinate transformations can be designed by using the stationary phase approximation. All coordinate transformations that are sufficiently differentiable can be decomposed into two transformations in series and therefore performed by using two holographic elements. Although the method presented here for designing the two required holographic elements is not explicit for the general case, a useful necessary condition for the decomposition is given. A simple explicit solution is given for an example for which the necessary equations for the first of the two serial transformations are separable.

© 1990 Optical Society of America

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