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1. M. Born, and E. Wolf, Principles of Optics (Cambridge, 1999), see Sec. 9.2 and Appendix VII.
2. A. E. Siegman, Lasers (University Science Books, 1986), Chaps. 16–17.
3. M. Abramowitz, and I. Stegun, Handbook of Mathematical Functions (Dover, 1978), Chap. 22.
4. A. B. Bhatia, E. Wolf, and M. Born, “On the circle polynomials of Zernike and related orthogonal sets,” Proc. Camb. Philos. Soc. 50(01), 40–48 (1954). [CrossRef]
5. D. R. Myrick, “A generalization of the radial polynomials of F. Zernike,” J. Soc. Ind. Appl. Math. 14(3), 476–492 (1966). [CrossRef]
6. E. C. Kintner, “On the mathematical properties of the Zernike polynomials,” Opt. Acta (Lond.) 23, 679–680 (1976). [CrossRef]
7. R. Barakat, “Optimum balanced wave-front aberrations for radially symmetric amplitude distributions: generalizations of Zernike polynomials,” J. Opt. Soc. Am. 70(6), 739–742 (1980). [CrossRef]
8. C.-W. Chong, P. Raveendran, and R. Mukundan, “A comparative analysis of algorithms for fast computation of Zernike moments,” Pattern Recognit. 36(3), 731–742 (2003). [CrossRef]
9. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, 1992) Section 5.5.
10. 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 .
11. F. J. Smith, “An Algorithm for Summing Orthogonal Polynomial Series and their Derivatives with Applications to Curve-Fitting and Interpolation,” Math. Comput. 19(89), 33–36 (1965). [CrossRef]
12. H. E. Salzer, “A Recurrence Scheme for Converting from One Orthogonal Expansion into Another,” Commun. ACM 16(11), 705–707 (1973). [CrossRef]
13. E. H. Doha, “On the coefficients of differentiated expansions and derivatives of Jacobi polynomials,” J. Phys. Math. Gen. 35(15), 3467–3478 (2002). [CrossRef]
14. R. Barrio and J. M. Peña, “Numerical evaluation of the p’th derivative of Jacobi series,” Appl. Numer. Math. 43(4), 335–357 (2002). [CrossRef]
15. B. Y. Ting and Y. L. Luke, “Conversion of Polynomials between Different Polynomial Bases,” IMA J. Numer. Anal. 1(2), 229–234 (1981). [CrossRef]
16. K. A. Goldberg and K. Geary, “Wave-front measurement errors from restricted concentric subdomains,” J. Opt. Soc. Am. A 18(9), 2146–2152 (2001). [CrossRef]
17. J. Schwiegerling, “Scaling Zernike expansion coefficients to different pupil sizes,” J. Opt. Soc. Am. A 19(10), 1937–1945 (2002). [CrossRef]
18. C. E. Campbell, “Matrix method to find a new set of Zernike coefficients from an original set when the aperture radius is changed,” J. Opt. Soc. Am. A 20(2), 209–217 (2003). [CrossRef]
19. G. M. Dai, “Scaling Zernike expansion coefficients to smaller pupil sizes: a simpler formula,” J. Opt. Soc. Am. A 23(3), 539–543 (2006). [CrossRef]
20. H. Shu, L. Luo, G. Han, and J.-L. Coatrieux, “General method to derive the relationship between two sets of Zernike coefficients corresponding to different aperture sizes,” J. Opt. Soc. Am. A 23(8), 1960–1966 (2006). [CrossRef]
21. A. J. E. M. Janssen and P. Dirksen, “Concise formula for the Zernike coefficients of scaled pupils,” J. Microlith. Microfab Microsyst. 5(3), 030501–3 (2006). [CrossRef]
22. G. W. Forbes, “Shape specification for axially symmetric optical surfaces,” Opt. Express 15(8), 5218–5226 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-8-5218 . [CrossRef] [PubMed]

Appl. Numer. Math.

• R. Barrio and J. M. Peña, “Numerical evaluation of the p’th derivative of Jacobi series,” Appl. Numer. Math. 43(4), 335–357 (2002). [CrossRef]

Commun. ACM

• H. E. Salzer, “A Recurrence Scheme for Converting from One Orthogonal Expansion into Another,” Commun. ACM 16(11), 705–707 (1973). [CrossRef]

IMA J. Numer. Anal.

• B. Y. Ting and Y. L. Luke, “Conversion of Polynomials between Different Polynomial Bases,” IMA J. Numer. Anal. 1(2), 229–234 (1981). [CrossRef]

J. Microlith. Microfab Microsyst.

• A. J. E. M. Janssen and P. Dirksen, “Concise formula for the Zernike coefficients of scaled pupils,” J. Microlith. Microfab Microsyst. 5(3), 030501–3 (2006). [CrossRef]

J. Opt. Soc. Am.

• R. Barakat, “Optimum balanced wave-front aberrations for radially symmetric amplitude distributions: generalizations of Zernike polynomials,” J. Opt. Soc. Am. 70(6), 739–742 (1980). [CrossRef]

J. Opt. Soc. Am. A

• K. A. Goldberg and K. Geary, “Wave-front measurement errors from restricted concentric subdomains,” J. Opt. Soc. Am. A 18(9), 2146–2152 (2001). [CrossRef]
• J. Schwiegerling, “Scaling Zernike expansion coefficients to different pupil sizes,” J. Opt. Soc. Am. A 19(10), 1937–1945 (2002). [CrossRef]
• C. E. Campbell, “Matrix method to find a new set of Zernike coefficients from an original set when the aperture radius is changed,” J. Opt. Soc. Am. A 20(2), 209–217 (2003). [CrossRef]
• G. M. Dai, “Scaling Zernike expansion coefficients to smaller pupil sizes: a simpler formula,” J. Opt. Soc. Am. A 23(3), 539–543 (2006). [CrossRef]
• H. Shu, L. Luo, G. Han, and J.-L. Coatrieux, “General method to derive the relationship between two sets of Zernike coefficients corresponding to different aperture sizes,” J. Opt. Soc. Am. A 23(8), 1960–1966 (2006). [CrossRef]

J. Phys. Math. Gen.

• E. H. Doha, “On the coefficients of differentiated expansions and derivatives of Jacobi polynomials,” J. Phys. Math. Gen. 35(15), 3467–3478 (2002). [CrossRef]

J. Soc. Ind. Appl. Math.

• D. R. Myrick, “A generalization of the radial polynomials of F. Zernike,” J. Soc. Ind. Appl. Math. 14(3), 476–492 (1966). [CrossRef]

Math. Comput.

• F. J. Smith, “An Algorithm for Summing Orthogonal Polynomial Series and their Derivatives with Applications to Curve-Fitting and Interpolation,” Math. Comput. 19(89), 33–36 (1965). [CrossRef]

Math. Tables Other Aids Comput.

• 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 .

Opt. Acta (Lond.)

• E. C. Kintner, “On the mathematical properties of the Zernike polynomials,” Opt. Acta (Lond.) 23, 679–680 (1976). [CrossRef]

Opt. Express

• G. W. Forbes, “Shape specification for axially symmetric optical surfaces,” Opt. Express 15(8), 5218–5226 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-8-5218 . [CrossRef] [PubMed]

Pattern Recognit.

• C.-W. Chong, P. Raveendran, and R. Mukundan, “A comparative analysis of algorithms for fast computation of Zernike moments,” Pattern Recognit. 36(3), 731–742 (2003). [CrossRef]

Proc. Camb. Philos. Soc.

• A. B. Bhatia, E. Wolf, and M. Born, “On the circle polynomials of Zernike and related orthogonal sets,” Proc. Camb. Philos. Soc. 50(01), 40–48 (1954). [CrossRef]

Other

• W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, 1992) Section 5.5.
• M. Born, and E. Wolf, Principles of Optics (Cambridge, 1999), see Sec. 9.2 and Appendix VII.
• A. E. Siegman, Lasers (University Science Books, 1986), Chaps. 16–17.
• M. Abramowitz, and I. Stegun, Handbook of Mathematical Functions (Dover, 1978), Chap. 22.

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