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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 42, Iss. 5 — May. 1, 1952
  • pp: 321–327

Diffraction of Spherical Scalar Waves by an Infinite Half-Plane

KEITH LEON McDONALD and FRANKLIN S. HARRIS,JR.  »View Author Affiliations

JOSA, Vol. 42, Issue 5, pp. 321-327 (1952)

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A theoretical discussion of the problem of diffraction of spherical scalar waves incident upon a thin black infinite half-plane, which makes use of Maggi’s transformation, has previously appeared in the literature. However, previous treatments have been limited solely to the diffracted component. From the results of previous investigators a simple expression for the total energy distribution, which is suitable for computational purposes, is derived. The results are shown to reduce to Kirchhoff’s formulation of the same problem, for field points not far removed from the shadow-boundary-plane. A rapid approximation method, applicable to the cases of plane and cylindrical waves, is also given. Experimental results were obtained from a photometer employing a refrigerated multiplier phototube. It is shown that the theoretical and experimental intensity distributions agree only when the radius of the point source aperture becomes indefinitely small. Tests with metallic and nonmetallic screens indicate that the nature of the edge of the diffracting screen (for points far removed from the screen) is of minor importance. Possibly of somewhat greater significance, but yet minor, is the nature of the body of the diffracting screen, a metallic screen tending to displace the fringes toward the shadow-boundary-plane.

KEITH LEON McDONALD and FRANKLIN S. HARRIS,JR., "Diffraction of Spherical Scalar Waves by an Infinite Half-Plane," J. Opt. Soc. Am. 42, 321-327 (1952)

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  1. F. Kottler, Ann. Physik 70, 405 (1923).
  2. B. B. Baker and E. T. Copson, The Mathematical Theory of Huygen's Principle (Oxford University Press, New York, 1950), second edition, p. 95.
  3. A. Rubinowicz, Ann. Physik 53, 257 (1917). In particular, see Eq. 13, p. 273. Rubinowicz derived this equation from Kirchhoff's formula solely through geometric considerations.
  4. See, for example, Max Born, Optik (Julius Springer Verlag, Berlin, 1933) (reprint Edwards Brothers, Inc., Ann Arbor, Michigan, 1943), pp. 190–195.
  5. The table of Fresnel integrals used is that ofC. M. Sparrow, Table of Fresnel Integrals (Edwards Brothers, Inc., Ann Arbor, Michigan, 1934). These have been extended by Professor R. T. Birge.
  6. F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill Book Company, Inc., New York, 1950), second edition, p. 365.
  7. See Sommerfeld's electromagnetic solution in Born's Optik (reference 4, p. 209).
  8. Hause, Woodward, and McClellan, J. Opt. Soc. Am. 29, 147 (1939). Corrections had to be made to their theoretical curve because of the effects of finite slit width.
  9. E. F. Coleman, Electronics 19, 220 (June, 1946).
  10. R. W. Engstrom, J. Opt. Soc. Am. 37, 420 (1947).

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