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In this paper we present several algorithms to find pupil functions which give focal fields with different desirable properties, such as a laterally elongated spot, a focal sheet, a spot with increased axial resolution, a lateral array of closely packed spots, and a lateral array of widely spaced diffraction-limited spots. All the algorithms work by writing the pupil function as a linear combination of appropriate basis functions, for which the coefficients are optimized. The focal field can be calculated repeatedly efficiently, since focal fields of each of the basis functions are precalculated. For each of the desired focal fields, the specific details of the algorithm are explained, simulation results are presented, and the results are compared to those in other publications

Pupil engineering to create sheets, lines, and multiple spots at the focal region