Calculation of a three-dimensional (3D) diffraction field from arbitrarily distributed field samples over 3D space is an important problem in holographic 3D television systems. Straightforward superposition of diffracted fields from the samples may not provide accurate calculation of the diffraction field because of the possible mutual couplings between those samples. We define an inverse problem to overcome that deviation caused by mutual couplings. First, the diffraction field on a reference plane is estimated accurately from the known field values at the sampling points. Then, the diffraction field over the entire space can be calculated from the field on the reference plane. Sparse representation of the diffraction field on the reference plane may provide a suitable framework in terms of L-1-norm minimization. Once the diffraction field over the reference plane is obtained, the harmonics that form the diffraction field can be calculated. After that, the field over the entire 3D space can be found by using those harmonics. In this work, we proposed a method based on the SPGL1 algorithm that solves the inverse problem of accurate calculation of the diffraction field on the reference plane by using fewer samples in calculation compared to the methods based on L-2-norm minimization. Furthermore, the proposed method requires less memory allocation as well. (C) 2019 Optical Society of America
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