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The copula: a tool for simulating speckle dynamics.

Donald D Duncan1, Sean J Kirkpatrick

  • 1Department of Biomedical Engineering, Oregon Health and Science University, 3303 SW Bond Avenue, Portland, Oregon 97239, USA. donald.duncan@bme.ogi.edu

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|December 25, 2007
PubMed
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A new algorithm uses a copula to generate sequences of correlated speckle patterns with specified temporal evolution. This method easily creates realistic, time-varying speckle patterns for various scientific modeling applications.

Area of Science:

  • Optics and Photonics
  • Statistical Physics
  • Computational Science

Background:

  • Speckle patterns are crucial in optics and used to model dynamic phenomena.
  • Generating realistic, time-varying speckle patterns with controlled correlations is challenging.
  • Existing methods may lack flexibility in specifying temporal correlation evolution.

Purpose of the Study:

  • Introduce a novel copula-based algorithm for generating correlated speckle pattern sequences.
  • Enable the creation of physically realistic, temporally evolving speckle patterns.
  • Provide a flexible method for modeling dynamic light scattering and coherence propagation.

Main Methods:

  • Utilize a copula function to link random variables for generating correlated sequences.

Related Experiment Videos

  • Employ only two arrays of random numbers for computational efficiency.
  • Implement the algorithm to generate sequences with prescribed Gaussian, exponential, and equal-interval correlations.

    • Main Results:

    • Successfully generated continuous speckle sequences with specified correlation evolution.
    • Demonstrated independent control over correlation times.
    • Achieved proper first- and second-order statistics for realistic pattern generation.

    Conclusions:

    • The copula-based algorithm offers an effective and straightforward method for generating correlated speckle patterns.
    • This approach facilitates accurate modeling of dynamic light scatter, laser speckle contrast, and spatial coherence propagation.
    • The technique provides a valuable tool for researchers in optics, physics, and computational modeling.