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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 34 — Dec. 1, 1998
  • pp: 7933–7939

Linear systems approach to simulation of optical diffraction

Andrew J. Lambert and Donald Fraser  »View Author Affiliations


Applied Optics, Vol. 37, Issue 34, pp. 7933-7939 (1998)
http://dx.doi.org/10.1364/AO.37.007933


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Abstract

The diffractive processes within an optical system can be simulated by computer to compute the diffraction-altered electric-field distribution at the output of the system from the electric-field distribution at the input. In the paraxial approximation the system can be described by an ABCD ray matrix whose elements in turn can be used to simplify the computation such that only a single computational step is required. We describe two rearrangements of such computations that allow the simulation to be expressed in a linear systems formulation, in particular using the fast-Fourier-transform algorithm. We investigate the sampling requirements for the kernel-modifying function or chirp that arises. We also use the special properties of the chirp to determine the spreading imposed by the diffraction. This knowledge can be used to reduce the computation if only a limited region of either the input or the output is of interest.

© 1998 Optical Society of America

OCIS Codes
(050.1590) Diffraction and gratings : Chirping
(050.1940) Diffraction and gratings : Diffraction
(050.1960) Diffraction and gratings : Diffraction theory
(080.2720) Geometric optics : Mathematical methods (general)
(100.2000) Image processing : Digital image processing

History
Original Manuscript: April 13, 1998
Revised Manuscript: August 6, 1998
Published: December 1, 1998

Citation
Andrew J. Lambert and Donald Fraser, "Linear systems approach to simulation of optical diffraction," Appl. Opt. 37, 7933-7939 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-34-7933


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References

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  2. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
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  12. I. W. Selesnick, C. S. Burrus, “Fast convolution and filterings,” in The Digital Signal Processing Handbook, V. K. Madisetti, D. B. Williams, eds. (IEEE/CRC Press, Boca Raton, Fla., 1998), Chap. 8.
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  14. A. J. Lambert, D. Fraser, “An implementation of the fast Fresnel transform,” in IVCNZ’95 Image and Vision Computing New Zealand (Industrial Research Ltd., Christchurch, New Zealand, 1995), pp. 143–148.

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