Recent Publication in “Top Downloads from April 2023” at JOSA A

Our recent publication, Two-Dimensional Freeform Reflector Design with a Scattering Surface, was listed in the Journal of the Optical Society of America (JOSA) A as a “top download from April 2023.” The paper is available for open access, so if the summary below intrigues you, please feel free to boost the downloads further via the link above 😉

Background

Before the freeform scattering optics (FFSO) consortium was formed, a significant effort was spent improving our understanding of specular optics. In particular, at Eindhoven University of Technology (TU/e), and in close collaboration with Signify, multiple former PhDs have developed methods to compute freeform reflectors and lenses assuming no light scattering in the system.

Indeed, Dr. Romijn graduated cum laude with her thesis, Generated Jacobian Equations in Freeform Optical Design: Mathematical Theory and Numerics, as the first PhD student to finish within the FFSO consortium on this very topic. In particular, her work includes a coherent framework for computing freeform reflectors and lenses for various configurations, such as parallel to near- and far-field and point to near- and far-field. This is known as solving the “inverse problem of optical design.” While extremely elegant, her thesis still assumes no scattering in the system, which limits the kinds of optical systems the methods can develop.

Goal of This Work

Include Scattering in The Inverse Problem of Optical Design

Main Contributions

• A consistent mathematical description of the inherently stochastic process of light scattering.
• We go from a well-known microfacet bidirectional reflection distribution function (BRDF) to a convolution integral for the scattered light.
• Applying a deconvolution algorithm to the final integral equation gives an “equivalent” specular distribution.
• Using this “equivalent” specular distribution when solving the inverse problem of optical design allows us to compute reflectors with a scattering surface.
• When taking scattering into account, the reflectors achieve the original target distribution.

Assumptions

• Due to the complexity of the problem, we started in two dimensions, meaning we restricted our attention to rotationally or cylindrically symmetric reflectors with in-plane scattering.
• There are no losses in the system due to, e.g., absorption.
• The scattering is isotropic along the reflector surface, meaning each point on the surface scatters light with the same probability density function.

Outlook

• Treat three-dimensional freeform reflectors without the in-plane scattering assumptions.
• Lift the restriction of isotropic scattering, i.e., allow the probability density function to vary with position.