A. Yoshida and T. Asakura, "Diffraction patterns of off-axis Gaussian beams in the optical system with astigmatism and coma," Opt. Commun. 25, 133–136 (1978).

cal mirror under oblique illumination: An integral representation of the fieldA. Boivin, N. Brousseau, and S. C. Biswas, "Electromagnetic diffraction in the focal region of a wide-angle spherical mirror under oblique illumination: An integral representation of the field," Opt. Acta 25, 415–444 (1978).

B. Chen, E. Marom, and R. J. Morrison, "Diffraction-limited geodesic lens for integrated optics circuits," Appl. Phys. Lett. 33, 511–513 (1978).

S. K. Yao and D. E. Thompson, "Chirp-grating lens for guided-wave optics," Appl. Phys. Lett. 33, 635–637 (1978).

P. R. Ashley and W. S. C. Chang, "Fresnel lens in a thin-film waveguide," Appl. Phys. Lett. 33, 490–492 (1978).

M. A. Gusinov, M. E. Riley, and M. A. Palmer, "Focusing in a large F-number optical system," Opt. Quart. Electron. 9, 465–471 (1977).

J. J. Stamnes and G. C. Sherman, "Reflection and refraction of an arbitrary wave at a plane interface separating two uniaxial crystals," J. Opt. Soc. Am. 67, 683–695 (1977).

W. H. Southwell, "Index profiles for generalized Luneburg lenses and their use in planar optical waveguides," J. Opt. Soc. Am. 67, 1010–1014 (1977).

J. Gasper, G. C. Sherman, and J. J. Stamnes, "Reflection and refraction of an arbitrary electromagnetic wave at a plane interface," J. Opt. Soc. Am. 66, 955–961 (1976).

G. C. Sherman, J. J. Stamnes, and É. Lalor, "Asymtotic approximations to angular-spectrum representations," J. Math. Phys. (N.Y.) 17, 760–776 (1976).

19. For an account of angular-spectrum representations of three-dimensional waves, see, for example, A. J. Devaney and G. C. Sherman, "Plane-wave representations for scalar wave fields," SIAM Rev. 15, 765–786 (1973).

J. C. Dainty, "The image of a point for an aberration free lens with a circular pupil," Opt. Commun. 1, 176–178 (1969).

G. C. Sherman, "Generalization of the angular spectrum of plane waves and the diffraction transform," J. Opt. Soc. Am. 59, 146–156 (1969).

A. Walther, "Lenses, wave optics and eikonal functions," J. Opt. Soc. Am. 59, 1325–1333 (1969).

A. Boivin, J. Dow, and E. Wolf, "Energy flow in the neighborhood of the focus of a coherent beam," J. Opt. Soc. Am. 57, 1171–1175 (1967).

26. For a three-dimensional example, see, for example, G. C. Sherman, "Application of the convolution theorem to Rayleigh’s integral formulas," J. Opt. Soc. Am. 57, 546–547 (1967).

A. Boivin and E. Wolf, "Electromagnetic field in the neighborhood of the focus of a coherent beam," Phys. Rev. B 138, 1561–1565 (1965).

E. Wolf, "Electromagnetic diffraction in optical systems. I. An integral representation of the image field," Proc. R. Soc. London Ser. A 253, 349–357 (1959).

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358–379 (1959).

H. H. Hopkins, "The numerical evaluation of the frequency response of optical systems," Proc. Phys. Soc. B 70, 1002 (1957).

J. Focke, "Wellenoptische Untersuchungen zum Öffnungsfehler," Opt. Acta 3, 110–126 (1956).

E. Wolf, "The diffraction theory of aberrations," Rep. Prog. Phys. 14, 95–120 (1951).

J. Picht, "Über den Schwingungsvorgang der einem beliebigen (astigmatischen) Strahlenbündel," Ann. Phys. Leipzig 77, 685–782 (1925).

P. Debye, "Das Verhalten von Lichtwellen in der Nähe eines Brennpunktes oder einer Brennlinie," Ann. Phys. Leipzig 30, 755–776 (1909).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 5th ed. (Dover, New York, 1968).

A. Yoshida and T. Asakura, "Diffraction patterns of off-axis Gaussian beams in the optical system with astigmatism and coma," Opt. Commun. 25, 133–136 (1978).

P. R. Ashley and W. S. C. Chang, "Fresnel lens in a thin-film waveguide," Appl. Phys. Lett. 33, 490–492 (1978).

cal mirror under oblique illumination: An integral representation of the fieldA. Boivin, N. Brousseau, and S. C. Biswas, "Electromagnetic diffraction in the focal region of a wide-angle spherical mirror under oblique illumination: An integral representation of the field," Opt. Acta 25, 415–444 (1978).

cal mirror under oblique illumination: An integral representation of the fieldA. Boivin, N. Brousseau, and S. C. Biswas, "Electromagnetic diffraction in the focal region of a wide-angle spherical mirror under oblique illumination: An integral representation of the field," Opt. Acta 25, 415–444 (1978).

A. Boivin, J. Dow, and E. Wolf, "Energy flow in the neighborhood of the focus of a coherent beam," J. Opt. Soc. Am. 57, 1171–1175 (1967).

A. Boivin and E. Wolf, "Electromagnetic field in the neighborhood of the focus of a coherent beam," Phys. Rev. B 138, 1561–1565 (1965).

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Sec. 8.3.2.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).

cal mirror under oblique illumination: An integral representation of the fieldA. Boivin, N. Brousseau, and S. C. Biswas, "Electromagnetic diffraction in the focal region of a wide-angle spherical mirror under oblique illumination: An integral representation of the field," Opt. Acta 25, 415–444 (1978).

P. R. Ashley and W. S. C. Chang, "Fresnel lens in a thin-film waveguide," Appl. Phys. Lett. 33, 490–492 (1978).

B. Chen, E. Marom, and R. J. Morrison, "Diffraction-limited geodesic lens for integrated optics circuits," Appl. Phys. Lett. 33, 511–513 (1978).

R. Courant and D. Hilbert, Methoden der Mathematische Physik 2nd ed. (Springer-Verlag, Berlin, 1968).

J. C. Dainty, "The image of a point for an aberration free lens with a circular pupil," Opt. Commun. 1, 176–178 (1969).

P. Debye, "Das Verhalten von Lichtwellen in der Nähe eines Brennpunktes oder einer Brennlinie," Ann. Phys. Leipzig 30, 755–776 (1909).

19. For an account of angular-spectrum representations of three-dimensional waves, see, for example, A. J. Devaney and G. C. Sherman, "Plane-wave representations for scalar wave fields," SIAM Rev. 15, 765–786 (1973).

A. Erdélyi, Asymptotic Expansions (Dover, New York, 1956).

L. B. Felsen and N. Marcuwitz, Radiation and Scattering of Waues (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 4.

J. Focke, "Wellenoptische Untersuchungen zum Öffnungsfehler," Opt. Acta 3, 110–126 (1956).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th ed. (Academic Press, New York, 1965).

M. A. Gusinov, M. E. Riley, and M. A. Palmer, "Focusing in a large F-number optical system," Opt. Quart. Electron. 9, 465–471 (1977).

R. Courant and D. Hilbert, Methoden der Mathematische Physik 2nd ed. (Springer-Verlag, Berlin, 1968).

H. H. Hopkins, "The numerical evaluation of the frequency response of optical systems," Proc. Phys. Soc. B 70, 1002 (1957).

G. C. Sherman, J. J. Stamnes, and É. Lalor, "Asymtotic approximations to angular-spectrum representations," J. Math. Phys. (N.Y.) 17, 760–776 (1976).

L. B. Felsen and N. Marcuwitz, Radiation and Scattering of Waues (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 4.

B. Chen, E. Marom, and R. J. Morrison, "Diffraction-limited geodesic lens for integrated optics circuits," Appl. Phys. Lett. 33, 511–513 (1978).

B. Chen, E. Marom, and R. J. Morrison, "Diffraction-limited geodesic lens for integrated optics circuits," Appl. Phys. Lett. 33, 511–513 (1978).

M. A. Gusinov, M. E. Riley, and M. A. Palmer, "Focusing in a large F-number optical system," Opt. Quart. Electron. 9, 465–471 (1977).

J. Picht, "Über den Schwingungsvorgang der einem beliebigen (astigmatischen) Strahlenbündel," Ann. Phys. Leipzig 77, 685–782 (1925).

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358–379 (1959).

M. A. Gusinov, M. E. Riley, and M. A. Palmer, "Focusing in a large F-number optical system," Opt. Quart. Electron. 9, 465–471 (1977).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th ed. (Academic Press, New York, 1965).

J. J. Stamnes and G. C. Sherman, "Reflection and refraction of an arbitrary wave at a plane interface separating two uniaxial crystals," J. Opt. Soc. Am. 67, 683–695 (1977).

G. C. Sherman, J. J. Stamnes, and É. Lalor, "Asymtotic approximations to angular-spectrum representations," J. Math. Phys. (N.Y.) 17, 760–776 (1976).

J. Gasper, G. C. Sherman, and J. J. Stamnes, "Reflection and refraction of an arbitrary electromagnetic wave at a plane interface," J. Opt. Soc. Am. 66, 955–961 (1976).

19. For an account of angular-spectrum representations of three-dimensional waves, see, for example, A. J. Devaney and G. C. Sherman, "Plane-wave representations for scalar wave fields," SIAM Rev. 15, 765–786 (1973).

G. C. Sherman, "Generalization of the angular spectrum of plane waves and the diffraction transform," J. Opt. Soc. Am. 59, 146–156 (1969).

26. For a three-dimensional example, see, for example, G. C. Sherman, "Application of the convolution theorem to Rayleigh’s integral formulas," J. Opt. Soc. Am. 57, 546–547 (1967).

J. J. Stamnes and G. C. Sherman, "Reflection and refraction of an arbitrary wave at a plane interface separating two uniaxial crystals," J. Opt. Soc. Am. 67, 683–695 (1977).

G. C. Sherman, J. J. Stamnes, and É. Lalor, "Asymtotic approximations to angular-spectrum representations," J. Math. Phys. (N.Y.) 17, 760–776 (1976).

J. Gasper, G. C. Sherman, and J. J. Stamnes, "Reflection and refraction of an arbitrary electromagnetic wave at a plane interface," J. Opt. Soc. Am. 66, 955–961 (1976).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 5th ed. (Dover, New York, 1968).

S. K. Yao and D. E. Thompson, "Chirp-grating lens for guided-wave optics," Appl. Phys. Lett. 33, 635–637 (1978).

A. Boivin, J. Dow, and E. Wolf, "Energy flow in the neighborhood of the focus of a coherent beam," J. Opt. Soc. Am. 57, 1171–1175 (1967).

A. Boivin and E. Wolf, "Electromagnetic field in the neighborhood of the focus of a coherent beam," Phys. Rev. B 138, 1561–1565 (1965).

E. Wolf, "Electromagnetic diffraction in optical systems. I. An integral representation of the image field," Proc. R. Soc. London Ser. A 253, 349–357 (1959).

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358–379 (1959).

E. Wolf, "The diffraction theory of aberrations," Rep. Prog. Phys. 14, 95–120 (1951).

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Sec. 8.3.2.

S. K. Yao and D. E. Thompson, "Chirp-grating lens for guided-wave optics," Appl. Phys. Lett. 33, 635–637 (1978).

A. Yoshida and T. Asakura, "Diffraction patterns of off-axis Gaussian beams in the optical system with astigmatism and coma," Opt. Commun. 25, 133–136 (1978).

P. Debye, "Das Verhalten von Lichtwellen in der Nähe eines Brennpunktes oder einer Brennlinie," Ann. Phys. Leipzig 30, 755–776 (1909).

J. Picht, "Über den Schwingungsvorgang der einem beliebigen (astigmatischen) Strahlenbündel," Ann. Phys. Leipzig 77, 685–782 (1925).

B. Chen, E. Marom, and R. J. Morrison, "Diffraction-limited geodesic lens for integrated optics circuits," Appl. Phys. Lett. 33, 511–513 (1978).

S. K. Yao and D. E. Thompson, "Chirp-grating lens for guided-wave optics," Appl. Phys. Lett. 33, 635–637 (1978).

P. R. Ashley and W. S. C. Chang, "Fresnel lens in a thin-film waveguide," Appl. Phys. Lett. 33, 490–492 (1978).

G. C. Sherman, J. J. Stamnes, and É. Lalor, "Asymtotic approximations to angular-spectrum representations," J. Math. Phys. (N.Y.) 17, 760–776 (1976).

G. C. Sherman, "Generalization of the angular spectrum of plane waves and the diffraction transform," J. Opt. Soc. Am. 59, 146–156 (1969).

A. Walther, "Lenses, wave optics and eikonal functions," J. Opt. Soc. Am. 59, 1325–1333 (1969).

J. Gasper, G. C. Sherman, and J. J. Stamnes, "Reflection and refraction of an arbitrary electromagnetic wave at a plane interface," J. Opt. Soc. Am. 66, 955–961 (1976).

J. J. Stamnes and G. C. Sherman, "Reflection and refraction of an arbitrary wave at a plane interface separating two uniaxial crystals," J. Opt. Soc. Am. 67, 683–695 (1977).

W. H. Southwell, "Index profiles for generalized Luneburg lenses and their use in planar optical waveguides," J. Opt. Soc. Am. 67, 1010–1014 (1977).

A. Boivin, J. Dow, and E. Wolf, "Energy flow in the neighborhood of the focus of a coherent beam," J. Opt. Soc. Am. 57, 1171–1175 (1967).

26. For a three-dimensional example, see, for example, G. C. Sherman, "Application of the convolution theorem to Rayleigh’s integral formulas," J. Opt. Soc. Am. 57, 546–547 (1967).

cal mirror under oblique illumination: An integral representation of the fieldA. Boivin, N. Brousseau, and S. C. Biswas, "Electromagnetic diffraction in the focal region of a wide-angle spherical mirror under oblique illumination: An integral representation of the field," Opt. Acta 25, 415–444 (1978).

J. Focke, "Wellenoptische Untersuchungen zum Öffnungsfehler," Opt. Acta 3, 110–126 (1956).

J. C. Dainty, "The image of a point for an aberration free lens with a circular pupil," Opt. Commun. 1, 176–178 (1969).

A. Yoshida and T. Asakura, "Diffraction patterns of off-axis Gaussian beams in the optical system with astigmatism and coma," Opt. Commun. 25, 133–136 (1978).

M. A. Gusinov, M. E. Riley, and M. A. Palmer, "Focusing in a large F-number optical system," Opt. Quart. Electron. 9, 465–471 (1977).

A. Boivin and E. Wolf, "Electromagnetic field in the neighborhood of the focus of a coherent beam," Phys. Rev. B 138, 1561–1565 (1965).

H. H. Hopkins, "The numerical evaluation of the frequency response of optical systems," Proc. Phys. Soc. B 70, 1002 (1957).

E. Wolf, "Electromagnetic diffraction in optical systems. I. An integral representation of the image field," Proc. R. Soc. London Ser. A 253, 349–357 (1959).

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358–379 (1959).

E. Wolf, "The diffraction theory of aberrations," Rep. Prog. Phys. 14, 95–120 (1951).

19. For an account of angular-spectrum representations of three-dimensional waves, see, for example, A. J. Devaney and G. C. Sherman, "Plane-wave representations for scalar wave fields," SIAM Rev. 15, 765–786 (1973).

A. Erdélyi, Asymptotic Expansions (Dover, New York, 1956).

L. B. Felsen and N. Marcuwitz, Radiation and Scattering of Waues (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 4.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th ed. (Academic Press, New York, 1965).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 5th ed. (Dover, New York, 1968).

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Sec. 8.3.2.

For a review of the literature up to 1951, see Ref. 2.

Ref. 18, Sec. 8.8.

Ref. 18, Sec. 9.1.

Ref. 18, Sec. 8.6.2.

R. Courant and D. Hilbert, Methoden der Mathematische Physik 2nd ed. (Springer-Verlag, Berlin, 1968).