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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 8 — Apr. 18, 2005
  • pp: 2892–2905

Frequency responses and resolving power of numerical integration of sampled data

L. P. Yaroslavsky, A. Moreno, and J. Campos  »View Author Affiliations

Optics Express, Vol. 13, Issue 8, pp. 2892-2905 (2005)

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Methods of numerical integration of sampled data are compared in terms of their frequency responses and resolving power. Compared, theoretically and by numerical experiments, are trapezoidal, Simpson, Simpson-3/8 methods, method based on cubic spline data interpolation and Discrete Fourier Transform (DFT) based method. Boundary effects associated with DFT- based and spline-based methods are investigated and an improved Discrete Cosine Transform based method is suggested and shown to be superior to all other methods both in terms of approximation to the ideal continuous integrator and of the level of the boundary effects.

© 2005 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(200.3050) Optics in computing : Information processing
(240.6700) Optics at surfaces : Surfaces

ToC Category:
Research Papers

Original Manuscript: January 19, 2005
Revised Manuscript: March 30, 2005
Published: April 18, 2005

L. Yaroslavsky, A. Moreno, and J. Campos, "Frequency responses and resolving power of numerical integration of sampled data," Opt. Express 13, 2892-2905 (2005)

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