Huygens-Fresnel-Kirchhoff wave-front diffraction formulation: spherical waves

The Huygens–Fresnel diffraction integral has been formulated for incident spherical waves with use of the Kirchhoff obliquity factor and the wave front as the surface of integration instead of the aperture plane. Accurate numerical integration calculations were used to investigate very-near-field (a few aperture diameters or less) diffraction for the well-established case of a circular aperture. It is shown that the classical aperture-plane formulation degenerates when the wave front, as truncated at the aperture, has any degree of curvature to it, whereas the wave-front formulation produces accurate results from ∞ up to one aperture diameter behind the aperture plane. It is also shown that the Huygens–Fresnel–Kirchhoff incident-plane-wave-aperture-plane-integration and incident-spherical-wave-wave-front-integration formulations produce equally accurate results for apertures with exit f-numbers as small as 1.

[1]  L. B. Felsen,et al.  Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers. II. Circular cylindrical layer , 1990 .

[2]  L. Felsen.  Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation; Geometrical representation of the fundamental mode of a Gaussian beam in oblate spheroidal coordinates: comment , 1989 .

[3]  L. B. Felsen,et al.  Systematic study of fields due to extended apertures by Gaussian beam discretization , 1989 .

[4]  Ehud Heyman,et al.  Complex-source pulsed-beam fields , 1989 .

[5]  Harrison H. Barrett,et al.  New family of Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation , 1988, Annual Meeting Optical Society of America.

[6]  A. F. Behof,et al.  Optical diffraction pattern measurements using a self-scanning photodiode array interfaced to a microcomputer , 1987 .

[7]  L. Felsen,et al.  Complex rays for radiation from discretized aperture distributions , 1987 .

[8]  L. Felsen,et al.  Propagating pulsed beam solutions by complex source parameter substitution , 1986 .

[9]  L. Felsen,et al.  Reflection and transmission of beams at a curved interface , 1986 .

[10]  Leopold B. Felsen,et al.  Real spectra, complex spectra, compact spectra , 1986 .

[11]  L. Felsen,et al.  Evaluation of beam fields reflected at a plane interface , 1985 .

[12]  L. Felsen,et al.  Complex ray analysis of beam transmission through two-dimensional radomes , 1985 .

[13]  Y. Kathuria.  Fresnel and far-field diffraction due to an elliptical aperture , 1985 .

[14]  L. Felsen.  Novel ways for tracking rays , 1985 .

[15]  D. Burch.  Fresnel diffraction by a circular aperture , 1985 .

[16]  L. Felsen.  Geometrical theory of diffraction, evanescent waves, complex rays and Gaussian beams , 1984 .

[17]  J. Hudson.  Fresnel-Kirchhoff diffraction in optical systems: an approximate computational algorithm. , 1984, Applied optics.

[18]  L. Felsen,et al.  Complex ray analysis of radiation from large apertures with tapered illumination , 1984 .

[19]  L. Felsen,et al.  Evanescent waves and complex rays , 1982 .

[20]  F. Hasselmann,et al.  Asymptotic analysis of parabolic reflector antennas , 1982 .

[21]  A. Papoulis.  Linear systems, Fourier transforms, and optics , 1981, Proceedings of the IEEE.

[22]  James E. Harvey,et al.  Fourier treatment of near‐field scalar diffraction theory , 1979 .

[23]  L. Felsen,et al.  Multiply Reflected Gaussian Beams in a Circular Cross Section , 1978 .

[24]  F. Feiock,et al.  Wave propagation in optical systems with large apertures , 1978 .

[25]  A. Erteza,et al.  Contemporary optics for scientists and engineers , 1977, Proceedings of the IEEE.

[26]  Sang-Yung Shin,et al.  LATERAL SHIFTS OF TOTALLY REFLECTED GAUSSIAN BEAMS , 1977 .

[27]  L. Felsen,et al.  Gaussian beam modes by multipoles with complex source points , 1977 .

[28]  James S. Marsh,et al.  Diffraction patterns of simple apertures , 1974 .

[29]  A. J. Campillo,et al.  Fresnel diffraction effects in the design of high‐power laser systems , 1973 .

[30]  J. Goodman.  Introduction to Fourier optics , 1969 .

[31]  F. Harris.  Light Diffraction Patterns , 1964 .

[32]  E. W. Marchand,et al.  Comparison of the Kirchhoff and the Rayleigh–Sommerfeld Theories of Diffraction at an Aperture , 1964 .

[33]  H. Kraus,et al.  Huygens–Fresnel–Kirchhoff wave-front diffraction formulation: paraxial and exact Gaussian laser beams , 1990 .

[34]  Barbara T. Landesman,et al.  Geometrical representation of the fundamental mode of a Gaussian beam in oblate spheroidal coordinates , 1989 .

[35]  William H. Southwell,et al.  Validity of the Fresnel approximation in the near field , 1981 .

[36]  L. B. Felsen,et al.  Evanescent Waves , 1976 .

[37]  E. T. Copson,et al.  The mathematical theory of Huygens' principle , 1939 .