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Article
Scaling analyses based on wavelet transforms for the Talbot effect
Physica A (2013)
  • Andrei Ludu, Embry Riddle Aeronautical University
Abstract
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.
Keywords
  • Multi-fractal,
  • fractals,
  • wavelet,
  • Talbot effect,
  • difraction
Publication Date
Spring 2013
Citation Information
Andrei Ludu. "Scaling analyses based on wavelet transforms for the Talbot effect" Physica A Vol. 392 (2013)
Available at: http://works.bepress.com/andrei_ludu/5/