Linear assignment problem in the design of freeform refractive optical elements generating prescribed irradiance...

Area of Science:

• Optics and Photonics
• Computational Electromagnetics
• Optical Engineering

Background:

• Designing optical elements to achieve specific light distributions is crucial in various applications.
• Traditional methods often struggle with complex, non-paraxial irradiance patterns.
• Calculating the eikonal function is key to understanding light propagation and surface design.

Purpose of the Study:

• To develop an iterative algorithm for calculating refractive optical surfaces.
• To generate prescribed near-field irradiance distributions in non-paraxial cases.
• To demonstrate the algorithm's effectiveness for custom optical element design.

Main Methods:

• The study reduces ray mapping to a linear assignment problem (LAP).
• An iterative algorithm sequentially calculates eikonal functions on curved surfaces using the LAP-based approach.
• Ray-tracing simulations are used to validate the designed optical elements.

Main Results:

• The proposed method successfully calculates the eikonal function and corresponding ray mapping.
• The iterative algorithm effectively designs refractive optical elements for specific irradiance patterns.
• Simulations confirm the high efficiency of the algorithm in generating uniform rectangular and custom "IPSI" shaped irradiance distributions.

Conclusions:

• The LAP-based iterative algorithm is a powerful tool for designing optical surfaces.
• This method enables precise control over irradiance distributions, even in complex non-paraxial scenarios.
• The approach offers a significant advancement in the field of optical element design and light shaping.