Robust, efficient computational methods for axially symmetric optical aspheres

Optics Express

Volumn 18, Issue 19, 2010, Pages 19700-19712

  Forbes, G W ^a  

^a QED TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY ORDER; ASPHERES; AUXILIARY POLYNOMIAL; AXIALLY SYMMETRIC; EFFICIENT METHOD; OPTICAL ASPHERES; ORTHOGONAL POLYNOMIAL;

POLYNOMIALS;

ALGORITHM; ARTICLE; COMPUTER AIDED DESIGN; COMPUTER ASSISTED DIAGNOSIS; EQUIPMENT; EQUIPMENT DESIGN; IMAGE ENHANCEMENT; METHODOLOGY; OPTICAL INSTRUMENTATION;

ALGORITHMS; COMPUTER-AIDED DESIGN; EQUIPMENT DESIGN; EQUIPMENT FAILURE ANALYSIS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; LENSES;

EID: 77956988046     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.18.019700     Document Type: Article

References (11)

1. G. W. Forbes, "Shape specification for axially symmetric optical surfaces," Opt. Express 15, 5218-5226, (2007) http://www.opticsinfobase. org/oe/abstract.cfm?URI=oe-15-8-5218
2. G. W. Forbes, and C. P. Brophy, "Designing cost-effective systems that incorporate high-precision aspheric optics", SPIE Optifab (2009) TD06-25 (1). Available at http://www.qedmrf.com.
3. C. du Jeu, "Criterion to appreciate difficulties of aspherical polishing," Proc. SPIE 5494, 113-121 (2004), doi:10.1117/12.551420.
4. G. W. Forbes, "Robust and fast computation for the polynomials of optics," Opt. Express 18, 13851-13862, (2010) http://www.opticsinfobase. org/oe/abstract.cfm?URI=oe-18-13-13851.
5. E. W. Weisstein, "Jacobi Polynomial" from MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/JacobiPolynomial.html, see esp. Equations (10-14).
6. M. Abramowitz, and I. Stegun, Handbook of Mathematical Functions (Dover, 1978), Chap. 22.
7. C. W. Clenshaw, "A Note on the Summation of Chebyshev Series," Math. Tables Other Aids Comput. 9, 118-120 (1955), http://www.jstor.org/stable/ 2002068.
8. F. J. Smith, "An Algorithm for Summing Orthogonal Polynomial Series and their Derivatives with Applications to Curve-Fitting and Interpolation," Math. Comput. 19, 33-36 (1965).
9. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, 1992) Section 2.9.
10. A useful overview is given at http://en.wikipedia.org/wiki/Discrete- cosine-transform.
11. G. W. Forbes, "Can you make/measure this asphere for me?", Frontiers in Optics, OSA Technical Digest (2009),http://www.opticsinfobase.org/ abstract.cfm?URI=FiO-2009-FThH1.