Shape specification for axially symmetric optical surfaces

Optics Express

Volumn 15, Issue 8, 2007, Pages 5218-5226

  Forbes, G W ^a  

^a QED TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; NUMERICAL ANALYSIS;

AXIALLY SYMMETRIC OPTICAL SURFACES; MANUFACTURABILITY; SHAPE SPECIFICATION;

ASPHERICS;

EID: 34247187459     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.15.005218     Document Type: Article

References (8)

1. See, for example, the discussion and references in H. Chase, "Optical design with rotationally symmetric NURBS", SPIE Proceedings 4832, 10-24 (2002)
2. and A. W. Greynolds, "Superconic and subconic surface descriptions in optical design," Proc. SPIE 4832, 1-9 (2002). Such matters are also treated within the manuals for commercial optical design software.
3. G. H. Spencer and M. V. R.K. Murty, "General ray-tracing procedure," J. Opt. Soc. Am. 52, 672-678 (1962), see Eq. (16).
4. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, 1978), see 22.2.1.
5. E. H. Doha, "On the coefficients of differentiated expansions and derivatives of Jacobi polynomials," J. Phys. A: Math. Gen. 35, 3467-3478 (2002).
6. E. W. Weisstein, "Jacobi Polynomial" from MathWorld - A Wolfram Web Resource. http://mathworld.wolfram.com/JacobiPolynomial.html, see esp. Eqs. (10-14).
7. B. Y. Ting and Y. L. Luke, "Conversion of polynomials between different polynomial bases," IMA J. Numer. Anal., 1, 229-234 (1981).
8. A. J. E. M. Janssen and P. Dirksen, "Concise formula for the Zernike coefficients of scaled pupils", J. Microlithogr., Microfabr., Microsyst. 5, 1-3 (2006). (Note that the Zernikes are also Jacobi polynomials.)