B-spline representation of optical surfaces and its accuracy in a ray trace algorithm.
Philipp Jester1, Christoph Menke, Karsten Urban
1Corporate Research and Technology, Carl Zeiss AG, Carl-Zeiss-Strasse 22, 73447 Oberkochen, Germany. p.jester@zeiss.de
Applied Optics
|February 24, 2011
Summary
A new B-spline quasi-interpolation method accurately represents aspheric surfaces for optical systems. This approach improves ray tracing accuracy and enables advanced tolerance analysis of optical designs.
Area of Science:
- Optics and Optical Engineering
- Computational Science
Background:
- Aspheric surfaces are crucial in advanced optical systems for improved performance.
- Accurate surface representation is essential for precise optical design and analysis.
- Existing methods may have limitations in handling complex surface data and local variations.
Purpose of the Study:
- To introduce a novel B-spline quasi-interpolation scheme for representing aspheric surfaces.
- To establish bounds on the approximation error for this new representation.
- To demonstrate the scheme's utility in ray tracing and tolerance analysis.
Main Methods:
- Development of a B-spline quasi-interpolation scheme for aspheric surface representation.
- Implementation of the scheme within a ray tracing algorithm.
- Establishment of mathematical bounds for approximation error.
- Application to polynomial surface descriptions and measured data.
Main Results:
- The B-spline scheme effectively reproduces aspheric surfaces with quantifiable error bounds.
- Ray tracing accuracy is demonstrated using the proposed representation.
- The method efficiently handles both local and global surface structures.
- Wavelet analysis is enabled for tolerance studies.
Conclusions:
- The B-spline quasi-interpolation offers a robust and efficient method for aspheric surface representation in optical design.
- This approach enhances the accuracy of ray tracing and provides new possibilities for tolerance analysis.
- The method is suitable for incorporating measured surface data and complex optical system designs.
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