Results of the summarizing process for the arXiv paper: 1801.07479v1

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.

• 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.

Double Freeform Illumination Design for Prescribed Wavefronts and Irradiances

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 (PDEs) to calculate double freeform surfaces for irradiance and phase control with predefined input and output wavefronts. This new approach offers an efficient method for designing complex optical systems with specific irradiance and phase requirements that is more flexible than existing models.

Background

The PDE model introduced in this paper 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. While this approach was successful in providing solutions to paraxial problems, it did not offer a solution when nonplanar input or output wavefronts were assumed. As such, current design models often reduce to a Monge-Amp\`ere type equation for unknown freeform surfaces when nonplanar input/output wavefronts are assumed, as is often the case in real-world applications.

The Model

To overcome these restrictions, the authors developed a PDE system that does not reduce to a Monge-Amp\`ere type equation when nonplanar input/output wavefronts are assumed. This system allows designers to calculate double freeform surfaces from predefined inputs and outputs without resorting to approximation techniques or reducing the problem into simpler components. Furthermore, this PDE system can be used to solve both irradiance control problems as well as phase control problems simultaneously using only one set of equations.

Numerical Solving Strategy

To demonstrate how their model works in practice, the authors present a numerical solving strategy based on finite element methods (FEM). They show how their FEM implementation can be used to efficiently solve their PDE system by applying it to two examples: a double freeform mirror system and double freeform lens system. These examples illustrate how designers can use this new approach to create optical systems with specific irradiance or phase requirements without having to resort to approximation techniques or simplifying assumptions about either the inputs or outputs of the system.

Conclusion

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 using partial differential equations (PDEs). By demonstrating its application through two example designs—a double freeform mirror system and double freeform lens system—the authors provide evidence that this new method is both effective at producing desired results as well as being more efficient than existing models due its ability handle both irradiance control problems as well as phase control problems simultaneously using only one set of equations.