Freeform construction method for illumination design by using two orthogonal tangent vectors based on ray mapping.

Area of Science:

• Optics
• Computational Geometry
• Illumination Design

Background:

• Illumination design often involves complex freeform surfaces.
• Traditional methods struggle with accuracy, especially in off-axis scenarios.
• Optimal mass transport (OMT) offers a potential framework for ray mapping.

Purpose of the Study:

• To develop an efficient numerical method for constructing freeform surfaces.
• To improve the accuracy and feasibility of illumination design using OMT.
• To minimize normal deviation and enhance pattern restoration.

Main Methods:

• Transforming illumination design into an OMT problem via ray mapping.
• Constructing normal vectors from orthogonal tangent vectors.
• Solving nonlinear equations derived from Snell's law for surface coordinates.

Main Results:

• The proposed method yields lower relative standard deviation compared to traditional approaches.
• Significant reduction in normal deviation, particularly in off-axis cases.
• Accurate restoration of complex illumination patterns with controlled normal vector errors.

Conclusions:

• The developed numerical method is a feasible and efficient solution for freeform surface design in illumination.
• The approach offers superior accuracy and performance over traditional methods.
• Effective control over illumination patterns and reduced errors are achievable.