Scaling analyses based on wavelet transforms for the Talbot effect

TL;DR

This paper investigates the fractal characteristics of Talbot images using wavelet-based scaling methods, revealing their monofractal nature through analysis of singularity spectra and scaling exponents.

Contribution

It applies wavelet transform methods to analyze the fractal properties of Talbot images, demonstrating their monofractality and providing a new quantitative characterization.

Findings

Wavelet methods confirm monofractality of Talbot images.

Singularity spectrum widths characterize fractal features.

Scaling exponents are linear in q, indicating monofractality.

Abstract

The fractal properties of the transverse Talbot images are analysed 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, Delta alpha=alpha_H-alpha_min, as a characteristic feature of these Talbot images. The tau 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