In this report a semi-analytic solution to the Laplacian magic window is proposed. The Laplacian magic window is a term recently introduced in 2017[2]. When a uniform wavefront hits a refractive surface, it creates an illumination distribution behind the surface. When the curvatu
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In this report a semi-analytic solution to the Laplacian magic window is proposed. The Laplacian magic window is a term recently introduced in 2017[2]. When a uniform wavefront hits a refractive surface, it creates an illumination distribution behind the surface. When the curvature of the surface is sufficiently small, it can be related linearly to the target illumination, and thus creates a ‘magic window’. The main idea of the semi-analytic solution is that a target illumination or a surface given in terms of Zernike polynomials can be solved analytically and expressed again in Zernike polynomials. The Zernike polynomials are set of complete and orthogonal polynomials that are already used in the field of optics to describe wavefronts of optical surfaces. The results of the semi-analytic solution agree qualitatively with the numeric results and work for complex and diverse inputs. The implementation is done in 2D, but the method is general enough so it can be extended to 3D.