K. N. LaFortune, R. L. Hurd, S. N. Fochs, M. D. Rotter, P. H. Pax, R. L. Combs, S. S. Olivier, J. M. Brase, and R. M. Yamamoto, "Technical challenges for the future of high energy lasers," Proc. SPIE 6454, 1-11 (2007).

G.-m. Dai and V. N. Mahajan, "Nonrecursive orthonormal polynomials with matrix formulation," Opt. Lett. 32, 74-76 (2007).

M. Bray, "Orthogonal polynomials: a set for square areas," Proc. SPIE 5252, 314-320 (2004).

V. N. Mahajan, "Zernike polynomials and aberration balancing," Proc. SPIE 5173, 1-17 (2003).

V. N. Mahajan, "Zernike annular polynomials for imaging systems with annular pupils," J. Opt. Soc. Am. 1, 685 (1984).

H. Sumita, "Orthogonal expansion of the aberration difference function and its application to image evaluation," Jpn. J. Appl. Phys. 8, 1027-1036 (1969).

F. Zernike, "Diffraction theory of knife-edge test and its improved form, the phase contrast method," Mon. Not. R. Astron. Soc. 94, 377-384 (1934).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Oxford, 1999).

K. N. LaFortune, R. L. Hurd, S. N. Fochs, M. D. Rotter, P. H. Pax, R. L. Combs, S. S. Olivier, J. M. Brase, and R. M. Yamamoto, "Technical challenges for the future of high energy lasers," Proc. SPIE 6454, 1-11 (2007).

M. Bray, "Orthogonal polynomials: a set for square areas," Proc. SPIE 5252, 314-320 (2004).

K. N. LaFortune, R. L. Hurd, S. N. Fochs, M. D. Rotter, P. H. Pax, R. L. Combs, S. S. Olivier, J. M. Brase, and R. M. Yamamoto, "Technical challenges for the future of high energy lasers," Proc. SPIE 6454, 1-11 (2007).

K. N. LaFortune, R. L. Hurd, S. N. Fochs, M. D. Rotter, P. H. Pax, R. L. Combs, S. S. Olivier, J. M. Brase, and R. M. Yamamoto, "Technical challenges for the future of high energy lasers," Proc. SPIE 6454, 1-11 (2007).

K. N. LaFortune, R. L. Hurd, S. N. Fochs, M. D. Rotter, P. H. Pax, R. L. Combs, S. S. Olivier, J. M. Brase, and R. M. Yamamoto, "Technical challenges for the future of high energy lasers," Proc. SPIE 6454, 1-11 (2007).

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1968).

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1968).

K. N. LaFortune, R. L. Hurd, S. N. Fochs, M. D. Rotter, P. H. Pax, R. L. Combs, S. S. Olivier, J. M. Brase, and R. M. Yamamoto, "Technical challenges for the future of high energy lasers," Proc. SPIE 6454, 1-11 (2007).

G.-m. Dai and V. N. Mahajan, "Nonrecursive orthonormal polynomials with matrix formulation," Opt. Lett. 32, 74-76 (2007).

V. N. Mahajan and G.-m. Dai, "Orthonormal polynomials for hexagonal pupils," Opt. Lett. 31, 2462-2465 (2006).

[CrossRef]

V. N. Mahajan, "Zernike polynomials and aberration balancing," Proc. SPIE 5173, 1-17 (2003).

V. N. Mahajan, "Zernike-Gauss polynomials and optical aberrations of systems with Gaussian pupils," Appl. Opt. 34, 8057-8059 (1995).

V. N. Mahajan, "Zernike annular polynomials and optical aberrations of systems with annular pupils," Appl. Opt. 33, 8125-8127 (1994).

V. N. Mahajan, "Uniform versus Gaussian beams: a comparison of the effects of diffraction, obscuration, and aberrations," J. Opt. Soc. Am. A 3, 470-485 (1986).

V. N. Mahajan, "Zernike annular polynomials for imaging systems with annular pupils," J. Opt. Soc. Am. 1, 685 (1984).

V. N. Mahajan, "Zernike annular polynomials for imaging systems with annular pupils," J. Opt. Soc. Am. 71, 75-85 (1981).

V. N. Mahajan, "Zernike annular polynomials for imaging systems with annular pupils: errata," J. Opt. Soc. Am. 71, 1408 (1981).

V. N. Mahajan, "Zernike polynomials and wavefront fitting," in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007) pp. 498-546.

V. N. Mahajan, Optical Imaging and Aberrations, Part II: Wave Diffraction Optics (SPIE, 2004).

K. N. LaFortune, R. L. Hurd, S. N. Fochs, M. D. Rotter, P. H. Pax, R. L. Combs, S. S. Olivier, J. M. Brase, and R. M. Yamamoto, "Technical challenges for the future of high energy lasers," Proc. SPIE 6454, 1-11 (2007).

K. N. LaFortune, R. L. Hurd, S. N. Fochs, M. D. Rotter, P. H. Pax, R. L. Combs, S. S. Olivier, J. M. Brase, and R. M. Yamamoto, "Technical challenges for the future of high energy lasers," Proc. SPIE 6454, 1-11 (2007).

K. N. LaFortune, R. L. Hurd, S. N. Fochs, M. D. Rotter, P. H. Pax, R. L. Combs, S. S. Olivier, J. M. Brase, and R. M. Yamamoto, "Technical challenges for the future of high energy lasers," Proc. SPIE 6454, 1-11 (2007).

H. Sumita, "Orthogonal expansion of the aberration difference function and its application to image evaluation," Jpn. J. Appl. Phys. 8, 1027-1036 (1969).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Oxford, 1999).

K. N. LaFortune, R. L. Hurd, S. N. Fochs, M. D. Rotter, P. H. Pax, R. L. Combs, S. S. Olivier, J. M. Brase, and R. M. Yamamoto, "Technical challenges for the future of high energy lasers," Proc. SPIE 6454, 1-11 (2007).

F. Zernike, "Diffraction theory of knife-edge test and its improved form, the phase contrast method," Mon. Not. R. Astron. Soc. 94, 377-384 (1934).

W. B. King, "The approximation of vignetted pupil shape by an ellipse," Appl. Opt. 7, 197-201 (1968).

J. L. Rayces, "Least-squares fitting of orthogonal polynomials to the wave-aberration function," Appl. Opt. 31, 2223-2228 (1992).

V. N. Mahajan, "Zernike annular polynomials and optical aberrations of systems with annular pupils," Appl. Opt. 33, 8125-8127 (1994).

V. N. Mahajan, "Zernike-Gauss polynomials and optical aberrations of systems with Gaussian pupils," Appl. Opt. 34, 8057-8059 (1995).

G. Harbers, P. J. Kunst, and G. W. R. Leibbrandt, "Analysis of lateral shearing interferograms by use of Zernike polynomials," Appl. Opt. 35, 6162-6172 (1996).

R. Barakat and L. Riseberg, "Diffraction theory of the aberrations of a slit aperture," J. Opt. Soc. Am. 55, 878-881 (1965). There is an error in their polynomial S2, which should read as x2−1/3.

R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-211 (1976).

V. N. Mahajan, "Zernike annular polynomials for imaging systems with annular pupils," J. Opt. Soc. Am. 71, 75-85 (1981).

V. N. Mahajan, "Zernike annular polynomials for imaging systems with annular pupils: errata," J. Opt. Soc. Am. 71, 1408 (1981).

S. Szapiel, "Aberration balancing techniques for radially symmetric amplitude distributions; a generalization of the Maréchal approach," J. Opt. Soc. Am. 72, 947-956 (1982).

V. N. Mahajan, "Zernike annular polynomials for imaging systems with annular pupils," J. Opt. Soc. Am. 1, 685 (1984).

H. Sumita, "Orthogonal expansion of the aberration difference function and its application to image evaluation," Jpn. J. Appl. Phys. 8, 1027-1036 (1969).

F. Zernike, "Diffraction theory of knife-edge test and its improved form, the phase contrast method," Mon. Not. R. Astron. Soc. 94, 377-384 (1934).

K. N. LaFortune, R. L. Hurd, S. N. Fochs, M. D. Rotter, P. H. Pax, R. L. Combs, S. S. Olivier, J. M. Brase, and R. M. Yamamoto, "Technical challenges for the future of high energy lasers," Proc. SPIE 6454, 1-11 (2007).

M. Bray, "Orthogonal polynomials: a set for square areas," Proc. SPIE 5252, 314-320 (2004).

V. N. Mahajan, "Zernike polynomials and aberration balancing," Proc. SPIE 5173, 1-17 (2003).

V. N. Mahajan, "Zernike polynomials and wavefront fitting," in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007) pp. 498-546.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Oxford, 1999).

V. N. Mahajan, Optical Imaging and Aberrations, Part II: Wave Diffraction Optics (SPIE, 2004).

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1968).

http://scikits.com/KFacts.html.