Abstract

Most authors include a paraxial (small-angle) limitation in their discussion of diffracted wave fields. This paraxial limitation severely limits the conditions under which diffraction behavior is adequately described. A linear systems approach to modeling nonparaxial scalar diffraction theory is developed by normalization of the spatial variables by the wavelength of light and by recognition that the reciprocal variables in Fourier transform space are the direction cosines of the propagation vectors of the resulting angular spectrum of plane waves. It is then shown that wide-angle scalar diffraction phenomena are shift invariant with respect to changes in the incident angle only in direction cosine space. Furthermore, it is the diffracted radiance (not the intensity or the irradiance) that is shift invariant in direction cosine space. This realization greatly extends the range of parameters over which simple Fourier techniques can be used to make accurate calculations concerning wide-angle diffraction phenomena. Diffraction-grating behavior and surface-scattering effects are two diffraction phenomena that are not limited to the paraxial region and benefit greatly from this new development.

© 1999 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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1998 (1)

1993 (1)

1992 (1)

1990 (1)

J. E. Harvey, W. P. Zmek, C. Ftaclas, “Imaging capabilities of normal-incidence x-ray telescopes,” Opt. Eng. 29, 603–608 (1990).
[CrossRef]

1988 (1)

1987 (1)

1979 (2)

R. J. Noll, “Effect of mid and high spatial frequencies on optical performance,” Opt. Eng. 18, 137–142 (1979).
[CrossRef]

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
[CrossRef]

1978 (1)

1971 (1)

1951 (1)

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

1902 (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–410 (1902).
[CrossRef]

Beckman, P.

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Boreman, G. D.

E. L. Dereniak, G. D. Boreman, Infrared Detectors and Systems (Wiley, New York, 1996).

Boyd, R. W.

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983).

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Dereniak, E. L.

E. L. Dereniak, G. D. Boreman, Infrared Detectors and Systems (Wiley, New York, 1996).

Ftaclas, C.

J. E. Harvey, W. P. Zmek, C. Ftaclas, “Imaging capabilities of normal-incidence x-ray telescopes,” Opt. Eng. 29, 603–608 (1990).
[CrossRef]

Gallager, N. C.

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), p. 72.

Gremaux, D. A.

Harvey, J. E.

J. E. Harvey, C. L. Vernold, “Description of diffraction grating behavior in direction cosine space,” Appl. Opt. 37, 8158–8160 (1998).
[CrossRef]

J. E. Harvey, E. A. Nevis, “Angular grating anomalies: effects of finite beam size upon wide-angle diffraction phenomena,” Appl. Opt. 31, 6783–6788 (1992).
[CrossRef] [PubMed]

J. E. Harvey, W. P. Zmek, C. Ftaclas, “Imaging capabilities of normal-incidence x-ray telescopes,” Opt. Eng. 29, 603–608 (1990).
[CrossRef]

J. E. Harvey, E. C. Moran, W. P. Zmek, “Transfer function characterization of grazing incidence optical systems,” Appl. Opt. 27, 1527–1533 (1988).
[CrossRef] [PubMed]

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
[CrossRef]

J. E. Harvey, R. V. Shack, “Aberrations of diffracted wave fields,” Appl. Opt. 17, 3003–3009 (1978).
[CrossRef] [PubMed]

J. E. Harvey, “Light-scattering characteristics of optical surfaces,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1976).

J. E. Harvey, “Surface scatter phenomena: a linear, shift-invariant process,” in Scatter from Optical Components, J. C. Stover, ed., Proc. SPIE1165, 87–99 (1989).

C. L. Vernold, J. E. Harvey, “A modified Beckmann–Kirchoff scattering theory,” in Scattering and Surface Roughness II, Z. Gu, A. A. Maradudin, eds., Proc. SPIE3426, 51–56 (1998).

Mendez, E. R.

Moran, E. C.

Muray, J. J.

Nevis, E. A.

Nicodemus, F. E.

Noll, R. J.

R. J. Noll, “Effect of mid and high spatial frequencies on optical performance,” Opt. Eng. 18, 137–142 (1979).
[CrossRef]

O’Donnell, K. A.

Ratcliff, J. A.

J. A. Ratcliff, “Some aspects of diffraction theory and their application to the ionosphere,” in Reports of Progress in Physics, A. C. Strickland, ed. (The Physical Society, London, 1956), Vol. XIX.

Rice, S. O.

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

Shack, R. V.

Spizzichino, A.

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Stover, J. C.

J. C. Stover, Optical Scattering, Measurement and Analysis (McGraw-Hill, New York, 1990).

Vernold, C. L.

J. E. Harvey, C. L. Vernold, “Description of diffraction grating behavior in direction cosine space,” Appl. Opt. 37, 8158–8160 (1998).
[CrossRef]

C. L. Vernold, J. E. Harvey, “A modified Beckmann–Kirchoff scattering theory,” in Scattering and Surface Roughness II, Z. Gu, A. A. Maradudin, eds., Proc. SPIE3426, 51–56 (1998).

Wood, R. W.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–410 (1902).
[CrossRef]

Wunderman, I.

Zmek, W. P.

J. E. Harvey, W. P. Zmek, C. Ftaclas, “Imaging capabilities of normal-incidence x-ray telescopes,” Opt. Eng. 29, 603–608 (1990).
[CrossRef]

J. E. Harvey, E. C. Moran, W. P. Zmek, “Transfer function characterization of grazing incidence optical systems,” Appl. Opt. 27, 1527–1533 (1988).
[CrossRef] [PubMed]

Am. J. Phys. (1)

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
[CrossRef]

Appl. Opt. (6)

Commun. Pure Appl. Math. (1)

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

J. E. Harvey, W. P. Zmek, C. Ftaclas, “Imaging capabilities of normal-incidence x-ray telescopes,” Opt. Eng. 29, 603–608 (1990).
[CrossRef]

R. J. Noll, “Effect of mid and high spatial frequencies on optical performance,” Opt. Eng. 18, 137–142 (1979).
[CrossRef]

Philos. Mag. (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–410 (1902).
[CrossRef]

Other (14)

C. L. Vernold, J. E. Harvey, “A modified Beckmann–Kirchoff scattering theory,” in Scattering and Surface Roughness II, Z. Gu, A. A. Maradudin, eds., Proc. SPIE3426, 51–56 (1998).

J. C. Stover, Optical Scattering, Measurement and Analysis (McGraw-Hill, New York, 1990).

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

J. E. Harvey, “Light-scattering characteristics of optical surfaces,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1976).

J. E. Harvey, “Surface scatter phenomena: a linear, shift-invariant process,” in Scatter from Optical Components, J. C. Stover, ed., Proc. SPIE1165, 87–99 (1989).

Users Manual for APART/PADE, Version 7 (Breault Research Organization, 4601 East First Street, Tucson, Ariz., 1985) p. 5-2.

ASAP Reference Manual (Breault Research Organization, 4601 East First Street, Tucson, Ariz., 1990).

TracePro User’s Manual, Version 1.3 (Lambda Research Corporation, 80 Taylor Street, Littleton, Mass., 1998), p. 107.

E. L. Dereniak, G. D. Boreman, Infrared Detectors and Systems (Wiley, New York, 1996).

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983).

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

J. A. Ratcliff, “Some aspects of diffraction theory and their application to the ionosphere,” in Reports of Progress in Physics, A. C. Strickland, ed. (The Physical Society, London, 1956), Vol. XIX.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), p. 72.

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