# Study of reflectors for illumination via conformal maps

## TL;DR

This paper introduces a conformal mapping method for designing symmetric reflectors that efficiently redirect light from point sources into specified intensity patterns, applicable to both segmented and continuous reflectors, and extendable to extended sources.

## Contribution

It presents a novel conformal map-based approach for reflector design, enabling precise control of light distribution with symmetry considerations and extending applicability to extended sources.

## Key findings

- Effective design of symmetric reflectors demonstrated
- Method simplifies analysis of reflector characteristics
- Applicable to both point and extended light sources

## Abstract

We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map that transforms the reflectors' shape into a curve that describes light's direction after reflection. Both segmented and continuous reflectors are discussed, illustrating how certain reflector characteristics become apparent under this transformation. This method can also be used to study extended sources via translations.