# Shape specification for axially symmetric optical surfaces.

@article{Forbes2007ShapeSF, title={Shape specification for axially symmetric optical surfaces.}, author={G. W. Forbes}, journal={Optics express}, year={2007}, volume={15 8}, pages={ 5218-26 } }

Advances in fabrication and testing are allowing aspheric optics to have greater impact through their increased prevalence and complexity. The most widely used characterization of surface shape is numerically deficient, however. Furthermore, with regard to tolerancing and to constraints for manufacturability, this representation is poorly suited for design purposes. Effective alternatives are therefore presented for working with rotationally symmetric surfaces that are either (i) strongly…

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## References

SHOWING 1-6 OF 6 REFERENCES

### Optical design with rotationally symmetric NURBS

- MathematicsInternational Optical Design Conference
- 2002

The standard aspheric surface, a conic surface figured with a polynomial expansion, provides excellent correction in many optical design problems. But there are problems where this set of basis…

### Concise formula for the Zernike coefficients of scaled pupils

- Physics
- 2006

Modern steppers and scanners have a projection lens whose numerical aperture (NA) can be varied so as to optimize the image performance for certain lithographic features. Thus a variable fraction of…

### Superconic and subconic surface descriptions in optical design

- PhysicsInternational Optical Design Conference
- 2002

The superconic surface description has been around since 1986 and more recently implemented in commercial design software. A simpler version dubbed the 'subconic' is proposed and appears to work well…

### On the coefficients of differentiated expansions and derivatives of Jacobi polynomials

- Mathematics
- 2002

A formula expressing explicitly the derivatives of Jacobi polynomials of any degree and for any order in terms of the Jacobi polynomials themselves is proved. Another explicit formula, which…

### General ray-tracing procedure

- Physics
- 1962

Computing formulas are presented for tracing skew rays through optical systems containing cylindrical and toric surfaces of arbitrary orientation and position. Particular attention is given to the…