Abstract
We propose using the Abbe transform to design binary computer-generated hologram (CGH). We consider the edges of the apertures as the basic diffraction elements and the diffraction pattern of the entire CGH as a coherent summation of all the light diffracted from all the edges. The Abbe transform computes the diffraction of polygonal apertures by the analytical formula with computation time independent of the size of the apertures. We globally optimized the apertures in the CGH using the Genetic Algorithm with local search, followed by an optimization of floating co-vertices of the elementary apertures and obtained high performance CGHs.
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