# Double freeform illumination design for prescribed wavefronts and irradiances

**Authors:** Christoph Bösel, Herbert Gross  
**arXiv:** [1801.07479](https://arxiv.org/abs/1801.07479)  
**Date:** 2018-01-23  
**Summary page:** https://www.summarizepaper.com/en/paper/1801.07479v1/

## Key points

- The paper presents a mathematical model for calculating double freeform surfaces for irradiance and phase control with predefined input and output wavefronts.
- The model extends the approach of Bösel and Gross in 2017 to double freeform lenses and mirrors, overcoming restrictions found in current design models.
- The PDE system does not reduce to a Monge-Amp\`ere type equation for unknown freeform surfaces when nonplanar input and output wavefronts are assumed.
- The authors present a numerical solving strategy for the PDE model, demonstrated through its application to the design of a double freeform mirror system and double freeform lens system.
- This offers an efficient method for designing complex optical systems with specific irradiance and phase requirements that is more flexible than existing models.

## Summary

In their paper "Double freeform illumination design for prescribed wavefronts and irradiances," authors Christoph Bösel and Herbert Gross present a mathematical model that uses partial differential equations (PDE) to calculate double freeform surfaces for irradiance and phase control with predefined input and output wavefronts. This model builds on the work of Bösel and Gross in 2017, which focused on the illumination design of single freeform surfaces for zero-'etendue light sources. The new PDE model extends this approach to double freeform lenses and mirrors, overcoming the restriction to paraxiality or the requirement of at least one planar wavefront found in current design models. One key advantage of this PDE system is that it does not reduce to a Monge-Amp\`ere type equation for unknown freeform surfaces when nonplanar input and output wavefronts are assumed, as is often the case in real-world applications. The authors also present a numerical solving strategy for the PDE model, which they demonstrate through its application to the design of a double freeform mirror system and double freeform lens system. This offers an efficient method for designing complex optical systems with specific irradiance and phase requirements that is more flexible than existing models. Overall, this paper provides an important contribution to the field of optics by introducing a novel approach for designing optical systems with nonplanar input/output wavefronts.