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Applied Optics

Applied Optics


  • Vol. 33, Iss. 24 — Aug. 20, 1994
  • pp: 5820–5829

Exact spread function for a pulsed collimated beam in a medium with small-angle scattering

H. C. van de Hulst and George W. Kattawar  »View Author Affiliations

Applied Optics, Vol. 33, Issue 24, pp. 5820-5829 (1994)

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A solution has been obtained for the spatial and temporal distribution function for a pulsed fully collimated beam propagating through a homogeneous medium with Gaussian small-angle scattering. The solution was obtained first by separation of the general problem into two plane problems, which results in a partial differential equation in three variables. A Fourier transform on two projected variables (one angular and one spatial) and a Laplace transform on the projected temporal variable yielded a set of nonlinear differential equations, which were solved. A recursion relation for the moments of the distribution function was also obtained, and the software mathematica was used to evaluate these moments to high orders. The contractions on certain variables are also presented; they correspond to the solutions of less-general problems contained in the main problem. A change in the definition of the time-delay produces a remarkable change in the structure of the equations. These solutions should be quite useful for lidar studies in atmospheric and oceanic optics, x-ray and radio-wave scattering in the atmosphere and interstellar medium, and in medical physics.

© 1994 Optical Society of America

Original Manuscript: August 2, 1993
Revised Manuscript: February 15, 1994
Published: August 20, 1994

H. C. van de Hulst and George W. Kattawar, "Exact spread function for a pulsed collimated beam in a medium with small-angle scattering," Appl. Opt. 33, 5820-5829 (1994)

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