Analytic optimization for holographic optical elements

A method is presented for designing optimal holographic optical elements. The method is based on an analytic ray-tracing procedure that uses the minimization of the mean-squared difference of the propagation vector components, between the actual output wave fronts and the desired output wave fronts. The minimization yields integral equations for the grating vector components that can be solved analytically, in some cases without any approximation. This leads to a well-behaved grating function that defines a holographic optical element.