Optimized holographic optical elements

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Abstract
This paper presents a method for designing optimal holographic optical elements. The method is based on the minimization of the mean-squared difference between the desired and the actual output waves. The minimization yields an integral equation for the grating function of the designed optical element. The integral equation is converted into a set of linear equations that can be easily solved. The resulting coefficients form the final solution as a sum of polynomials. This procedure yields a well-behaved grating function that defines a holographic optical element that can be realized with the help of computer-generated holograms. The method is illustrated with a design of an imaging lens. The performance of this lens is then compared, both theoretically and experimentally, with that of a spherical holographic lens. The results show that the newly designed lens is clearly superior to the spherical lens.

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