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Optimization Strategy for Designing Computer-Generated Holograms and Diffractive Optical Elements

A computer-generated hologram (CGH) or diffractive optical element (DOE) is adapted in a free-space optical system to modulate the incident wavefront and then generate a diffractive pattern in a specified output plane [1]. The optical field function of the diffractive pattern is related to the modulated function of CGH/DOE through an operation based on the Fourier transform [2]. For simplicity, I assume the output function is the Fourier transform of the input function. Because of constraints (conditions) imposed on the input and the output functions, there is in general no solutions to exactly fulfill the constraints [3]. A good approximation to the solution is determined when the difference between the approximation and the solution is reduced as much as possible. To find an approximation with mini-mum difference or error, one needs to decide an optimization algorithm and a merit function of CGH performance which will be introduced in details in this presentation.