Limits of realizing irradiance distributions with shift-invariant illumination systems and finite étendue sources

Abstract

When redistributing the light emitted by a source into a prescribed irradiance distribution, it is not guaranteed that, given the source and optical constraints, the desired irradiance distribution can be achieved. We analyze the problem by assuming an optical black box that is shift-invariant, meaning that a change in source position does not change the shape of the irradiance distribution, only its position. The irradiance distribution we can obtain is then governed by deconvolution. Using positive definite functions and Bochner's theorem, we provide conditions such that the irradiance distribution can be realized for finite étendue sources. We also analyze the problem using optimization, showing that the result heavily depends on the chosen source distribution.

Spherical-freeform lens design for uniform illumination based on differentiable ray tracing with uv polynomials

“…3 For a compact design, the size of the light source cannot be ignored. Some methods have been proposed for tailoring the irradiance distributions of extended sources, including the over compensation methods, [4][5][6][7] the simultaneous multiple surface (SMS)-based methods, 8,9 the deconvolution methods, [10][11][12][13][14] the parametric optimization methods, [15][16][17][18][19] the edge ray mapping method, 20 the expectation maximization algorithm applied for pinhole image arrangement 21 and the energy accumulating optimization method. 22 Among these methods, the parametric optimization methods are easy to implement and have strong universality.…”