Connecting tolerancing of freeform surface deformation in illumination optics with the Laplacian magic mirror

This paper presents a methodology for illumination optics tolerancing. Specifically, we investigate tolerancing deformation of a single freeform surface under a point source illumination. Through investigation, we recognized and report here three surface-deformation characteristics that build tolerancing intuitions. First, we show that positive and negative irradiance changes occur together as a consequence of flux conservation. Then, we demonstrate a linear relationship between the steepness of the surface perturbation and the magnitude of the irradiance change. Lastly, we show that the Laplacian magic mirror concept (M. V. Berry [Eur. J. Phys.27, 109 (2006)10.1088/0143-0807/27/1/012]) can be expanded to surface deformation tolerancing. Utilizing these surface deformation characteristics, we propose a fast and predictable tolerancing method for a sequential illumination optic.