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]

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]

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

[CrossRef]

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

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

[CrossRef]

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

[CrossRef]

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]

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 .

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]

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]

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]

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]

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]

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 .

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]

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

[CrossRef]

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]

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

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

[CrossRef]

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]

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

[CrossRef]

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]

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]

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

[CrossRef]

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]

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

[CrossRef]

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]

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]

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

[CrossRef]

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

[CrossRef]

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]

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]

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

[CrossRef]

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

[CrossRef]

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]

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 .

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

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]

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]

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.