Scaling analyses based on wavelet transforms for the Talbot effect

The fractal properties of the transverse Talbot images are analyzed with two well-known scaling methods, the wavelet transform modulus maxima (WTMM) and the wavelet transform multifractal detrended fluctuation analysis (WT-MFDFA). We use the widths of the singularity spectra, Δ α = α H − α min , as a characteristic feature of these Talbot images. The τ scaling exponents of the q moments are linear in q within the two methods, which proves the monofractality of the transverse diffractive paraxial field in the case of these images.