Freeform Optical Surface Representation for Aberration Correction
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Solution Overview
Problem
Current representations for freeform optical surfaces in optical design fail to provide stability during optimization, manufacturability, and the necessary degrees of freedom to correct aberrations, particularly in systems without rotational symmetry.
Innovation Solution
The approach involves representing a freeform surface as a base surface plus a departure, where the departure is applied in a direction substantially normal to the surface at or near the center, using an off-axis conic as the base surface and specifying the surface in an off-axis coordinate system aligned with the surface normal, allowing for independent variation of surface figures to correct aberrations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional spherical surfaces are used, then manufacturing and testing are easier, but image quality and system performance are limited
Solution Approach 1:
The optical surface is segmented into a base surface (spherical or conic) and a departure component. The base surface provides the easy-to-manufacture foundation, while the departure component adds the necessary complexity for high image quality. This segmentation allows the surface to be manufactured using conventional techniques for the base portion while achieving advanced optical performance through the added departure terms.
Solution Approach 2:
The optical surface uses a composite representation combining a simple base surface with a mathematical departure function. This composite approach allows the surface to possess both the manufacturability of simple spherical surfaces and the optical performance of complex freeform surfaces, effectively combining the advantages of both simple and complex surface types.
2Ease of manufacture
If rotationally symmetric surfaces are used, then manufacturing is simpler, but degrees of freedom for aberration correction are reduced
Solution Approach 1:
The surface representation is segmented into a rotationally symmetric base surface and an asymmetric departure component. The base surface maintains rotational symmetry for manufacturing simplicity, while the departure component introduces asymmetric terms that provide additional degrees of freedom for correcting aberrations in tilted and decentered optical systems.
Solution Approach 2:
The departure component incorporates asymmetric mathematical terms that break the rotational symmetry of the base surface. This controlled asymmetry provides the necessary degrees of freedom to correct aberrations in modern optical systems that utilize tilted and decentered elements, while the underlying symmetric base surface maintains manufacturing simplicity.
3Device complexity
If polynomial departure is applied in coordinate system aligned with conic axis, then mathematical representation is simpler, but the departure cannot extend beyond the point where surface becomes parallel to the axis
Solution Approach 1:
The solution transforms the coordinate system from one aligned with the conic axis to a local coordinate system aligned with the surface normal at a specific point. This dimensional transformation allows the polynomial departure to be defined in a local tangent plane, enabling the representation to extend beyond the limitations of the axis-aligned coordinate system and cover the entire surface including regions where the surface becomes parallel to the axis.
Solution Approach 2:
The coordinate system parameters are changed from global (axis-aligned) to local (surface-normal-aligned). This parameter transformation allows the mathematical representation to adapt to the local geometry of the surface, enabling the polynomial departure to be properly defined and applied across the entire surface area without the limitations imposed by the conic axis alignment.
4Manufacturing precision
If freeform surfaces with no rotational symmetry are used, then aberration correction is improved, but manufacturing and testing become more difficult
Solution Approach 1:
The freeform surface is segmented into a simple base surface that is easy to manufacture and a departure component that provides the complex aberration correction. The base surface can be manufactured using conventional techniques, while the departure component, though mathematically complex, represents only the necessary deviation from the simple surface, making the overall manufacturing process more feasible than creating the entire complex surface from scratch.
5Manufacturing precision
If current freeform surface representations are used, then some aberrations can be corrected, but optimization stability and manufacturability are compromised
Solution Approach 1:
The surface representation is segmented into a base surface with well-defined manufacturing parameters and a departure component with controlled mathematical terms. This segmentation provides a stable foundation for optimization algorithms while maintaining clear manufacturability criteria, as the base surface parameters remain well-behaved during optimization and the departure component provides the necessary flexibility for aberration correction without compromising overall stability.
Data Source
AI summary
A freeform optical surface includes, in part, an off-axis optical surface and a departure optical module. The off-axis optical surface may be an off-axis conic optical surface. The departure optical module may be substantially perpendicular to the off-axis conic optical surface.