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Scaling Analyses Based on Wavelet Transforms for the Talbot Effect
Physica A: Statistical Mechanics and its Applications (2013)
  • Haret C. Rosu
  • Jose S. Murguia
  • Andrei Ludu, Embry Riddle Aeronautical University
Berry and Klein studied the fractal properties of the paraxial diffracted field behind a Ronchi grating. In particular, they studied the transverse Talbot images formed at fractional distances in units of the Talbot distance chosen from the Fibonacci convergents to the complement of the inverse golden mean. Here, we analyze these Talbot images with two well-known scaling methods, the wavelet transform modulus maxima and the wavelet transform multifractal detrended fluctuation analysis. We use the widths of the singularity spectra as a characteristic feature of the Talbot images. The scaling exponents of the moments are linear within the two methods, which is a strong argument in favor of the monofractality of the transverse diffractive paraxial field.
  • Multi-fractal,
  • fractals,
  • wavelet,
  • Talbot effect,
  • difraction
Publication Date
September, 2013
Citation Information
Haret C. Rosu, Jose S. Murguia and Andrei Ludu. "Scaling Analyses Based on Wavelet Transforms for the Talbot Effect" Physica A: Statistical Mechanics and its Applications Vol. 392 Iss. 17 (2013) p. 3780 - 3788 ISSN: Imaging based techniques provide for a way for reconstructing surfaces using Shape from shading algorithms. Adding the convenient approximation of target wave fields by superposition of simple plane waves a new greedy algorithm for reconstruction of water surface is introduced. The algorithm developed optimizes each wave-front for several parameters until the least squares error is minimum. The methodology is illustrated by application to synthetic and real data obtained from the experiments performed in Linear wave lab at Embry Riddle Aeronautical University (ERAU). Generalization of approach to non-linear problem of reconstructing water waves from reflectance data modeled by Lambertian reflectance model is demonstrated. Possible improvements including use of Specular reflection model and better optimization techniques are discussed. The approach is observed to be an effective way for reconstructing any kind of water wave field.
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