## Calculation of diffraction effects on the average phase of an optical field

JOSA A, Vol. 17, Issue 10, pp. 1763-1772 (2000)

http://dx.doi.org/10.1364/JOSAA.17.001763

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### Abstract

We report on algorithms for the computation of the average phase of a beam over a detector in the near field. The basic idea is to reconstruct the optical field numerically and then use a quadrature algorithm to evaluate the quantity of interest. The various algorithms that employ discrete Fourier transform techniques for the computation of the field are described, and numerical tests that assess the accuracy of these algorithms are presented. No particular algorithm delivers the desired accuracy over the entire range of Fresnel numbers of interest, but each can produce satisfactory results within a particular range. Finally, new methods to evaluate the average phase are introduced, and their efficiency is assessed.

© 2000 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(050.1960) Diffraction and gratings : Diffraction theory

(070.2580) Fourier optics and signal processing : Paraxial wave optics

(070.2590) Fourier optics and signal processing : ABCD transforms

**Citation**

Miltiadis V. Papalexandris and David C. Redding, "Calculation of diffraction effects on the average phase of an optical field," J. Opt. Soc. Am. A **17**, 1763-1772 (2000)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-10-1763

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### References

- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
- H. H. Hopkins, “The numerical evaluation of frequency response of optical systems,” Proc. Phys. Soc. London Sect. B 70, 1002–1005 (1957).
- A. C. Ludwig, “Computation of radiation patterns involving numerical double integration,” IEEE Trans. Antennas Propag. AP-16, 767–769 (1968).
- J. J. Stamnes, B. Spjelkavic, and H. M. Pedersen, “Evaluation of diffraction integrals using local phase and amplitude approximations,” Opt. Acta 30, 207–222 (1983).
- L. A. D’Arcio, J. J. M. Braat, and H. J. Frankena, “Numerical evaluation of diffraction integrals for apertures of complicated shape,” J. Opt. Soc. Am. A 11, 2664–2674 (1994).
- W. H. Southwell, “Validity of the Fresnel approximation in the near field,” J. Opt. Soc. Am. 71, 7–14 (1981).
- H. G. Kraus, “Finite element area and line integral transforms for generalization of aperture functions and geometry in Kirchhoff scalar diffraction theory,” Opt. Eng. 32, 368–383 (1993).
- P. Horwitz, “Modes in misaligned unstable resonators,” Appl. Opt. 15, 167–178 (1976).
- E. Carcole, S. Bosch, and J. Campos, “Analytical and numerical approximations in Fresnel diffraction. Procedures based on the geometry of the Cornu Spiral,” J. Mod. Opt. 40, 1091–1106 (1993).
- E. Sziclas and A. E. Siegman, “Mode calculations in unstable resonators with flowing saturable gain. 2: Fast Fourier transform method,” Appl. Opt. 14, 1874–1889 (1975).
- M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989).
- D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).
- D. Mas, J. Garcia, C. Ferreira, L. M. Bernado, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculations,” Opt. Commun. 164, 233–245 (1999).
- J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, New York, 1980).
- J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986).
- C. W. Clenshaw and A. R. Curtis, “A method for numericalintegration on an automatic computer,” Numer. Math. 2, 197–205 (1960).
- R. K. Littlewood and V. Zakian, “Numerical evaluation of Fourier integrals,” J. Inst. Math. Appl. 18, 331–339 (1976).
- D. Levin, “Procedures for computing one- and two-dimensional integrals of functions with rapid irregular oscillations,” Math. Comput. 38, 531–538 (1982).
- I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, San Diego, Calif., 1992).
- R. Kress, Linear Integral Equations (Springer-Verlag, New York, 1989).
- A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1977).
- A. E. Siegman, “Quasi-fast Hankel transform,” Opt. Lett. 1, 13–15 (1977).
- M. Vaez-Iravani and H. K. Wickramasinghe, “Scattering matrix approach of thermal wave propagation in layered structures,” J. Appl. Phys. 58, 122–132 (1983).

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