Limitations of the ray mapping approach in freeform optics design

Abstract

It was previously demonstrated by Bäuerle et al. [Opt. Express20, 14477 (2012)] that the computation of ray paths through the optical system (ray mapping) can be used to design multisurface freeform optical elements creating a prescribed irradiance pattern for a zero-étendue source. The procedure outlined there uses the heuristic step of reducing the ray mapping's curl to improve adherence to surface integrability criteria. This Letter formally derives a quantitative estimate for the limitations of this approach in the collimated case and shows the key factors influencing the quality of the final optics.

Freeform lens collimating spectrum-folded Hadamard transform near-infrared spectrometer

“…According to the vector form of Snell's law [13], the following two partial differential equations [14] can be derived: where n is the refractive index of the freeform lens, ρ θ and ρ ϕ are the first-order partial derivatives of ρ with respect to θ and ϕ.…”

Light shaping for illumination

“…Although currently there is no hard mathematical proof, it is plausible to assume that the smaller the violation of the normal field integrability condition, the smaller will be the irradiance distribution deviation. The relationship between the rotation of the mapping and the value of Eqn (4) has been examined in [29].…”

Design of Freeform Illumination Optics

“…This is an inverse problem, the number of freeform surfaces which should be used depends on the design requirements. The design methods of freeform illumination optics can be broken into two groups according to the influence of the spatial or angular extent of an actual light source on the design: zero‐étendue algorithms based on ideal source assumption (point light sources or parallel light beams) and algorithms for extended light sources . When the influence of the spatial or angular extent of a light source can be ignored, the light source can be considered as an ideal source (a point source or a parallel beam) and the inverse problem can be converted into a well‐defined mathematical problem.…”