Second-order supporting quadric method for designing freeform refracting surfaces generating prescribed irradiance
Optics Express
|August 14, 2026
Summary
This study introduces a second-order supporting quadric method (SQM) to design optical surfaces. The novel approach efficiently calculates surfaces for precise light distribution, advancing optical engineering.
Area of Science:
- Optics
- Computational Mathematics
- Optical Engineering
Background:
- Designing optical surfaces to control light distribution is a complex inverse problem.
- Existing methods may lack efficiency for complex irradiance patterns.
- Mass transportation problems (MTP) offer a mathematical framework for this design challenge.
Purpose of the Study:
- To develop an efficient computational method for designing optical surfaces.
- To solve the inverse problem of generating prescribed far-field irradiance distributions.
- To adapt the supporting quadric method (SQM) for enhanced optical design.
Main Methods:
- Formulating the optical design problem as a mass transportation problem (MTP) with a quadratic cost function.
- Developing a second-order supporting quadric method (SQM) by minimizing a convex function.
- Deriving analytical expressions for second derivatives to enable second-order optimization.
Main Results:
- The proposed second-order SQM efficiently calculates optical surface parameters.
- Demonstrated the design of optical surfaces generating complex irradiance distributions.
- Successfully applied the method to nonimaging optics problems with non-quadratic cost functions.
Conclusions:
- The second-order SQM is a highly efficient and effective method for optical surface design.
- This approach advances the capability to precisely control light distribution using custom optical surfaces.
- The method shows promise for both imaging and nonimaging optical applications.
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