Transmission of a Gaussian beam through a circular aperture: comments Andres A. Taklaja

Tallinn Technical University, Ehitajate tee 5, Tallinn 200108, Estonia, U.S.S.R. Received 21 June 1987. 0003-6935/87/245202-01$02.00/0. © 1987 Optical Society of America. The problem of transmission of a Gaussian beam through a

circular aperture treated by the authors of Ref. 1 as unique was studied earlier2-4 in another context. The problem leads to the Marcum Q function,5 whose general form makes it possible to take into account not only the eccentricity of beam and aperture centers but also the ellipticity of the beam or aperture.

If there is a need for processing further results, the inte­grals and partial differentials of the Q function are presented in Refs. 6 and 7, respectively.

References 1. K. Uehara and H. Kikuchi, "Transmission of a Gaussian Beam

Through a Circular Aperture," Appl. Opt. 25, 4515 (1986). 2. R. Esposito, "Power Scintillations Due to the Wandering of the

Laser Beam," Proc. IEEE 55, 1533 (1967). 3. P. J. Titterton, "Power Reduction and Fluctuations Caused by

Narrow Laser Beam Motion in the Far Field," Appl. Opt. 12, 423 (1973).

4. M. Tamir, U. Halavee, and E. Azoulay, "Power Fluctuations Caused by Laser Beam Wandering and Shift," Appl. Opt. 20, 734 (1981).

5. J. I. Marcum, "Table of Q functions," AD 1165511. January 1950. 6. A. H. Nuttal, "Some Integrals Involving the QM Function," IEEE

Trans. Inf. Theory IT-21, 95 (1975). 7. W. K. Pratt, "Partial Differentials of Marcum's Q Function,"

Proc. IEEE 56, 1221 (1968).

5202 APPLIED OPTICS / Vol. 26, No. 2 4 / 1 5 December 1987