Spatial Behaviour of Singularities in Fractal- and Gaussian Speckle Fields

Angelsky, Oleg V.; Maksimyak, A. P.; Maksimyak, Peter P.; Hanson, Steen Grüner

doi:10.2174/1874328500903010029

Cited by 9 publications

(11 citation statements)

References 18 publications

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“…The spectral strength K ] and the spectral index ] supply an alternative fractal-surface characterization often more consistent than the correlation length (11) or the RMS roughness (12). In particular, there exists a direct correspondence with the Hearst index H (] = 2H + 1) and the fractal dimension (Hausdorff-Besicovitch dimension) D f = (5-])/2 [98,101].…”

Section: Fractal Objects and Fractal Properties Of Scattered Fieldsmentioning

confidence: 99%

“…A fruitful approach to this problem involves the optical correlation technique, and is further applied for studying the fields scattered by random and fractal rough surfaces [29,98]. In general, a rough surface is an example of a specific scattering object with a highly irregular structure.…”

Section: Statistical Characteristics Of Random Objects and Speckle Fi...mentioning

confidence: 99%

“…as well as other higher-order parameters of statistical distributions (skewness Sk, kurtosis Ku, etc. [98,101]). In Eq.…”

Section: Statistical Characteristics Of Random Objects and Speckle Fi...mentioning

confidence: 99%

“…18 differs from the common one by the second summand, for which reason it expresses, in fact, the kurtosis "excess" above 3 [101]. The next step is to study peculiar features of light fields scattered by surfaces of different types [98]. An example of the field scattered from a non-fractal rough surface observed at an off-surface distance z = 100 μm is shown in Figure 8.…”

Section: Fractal Objects and Fractal Properties Of Scattered Fieldsmentioning

confidence: 99%

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Optical phase singularities: Physical nature, manifestations and applications

Angelsky

Bekshaev²,

Vasnetsov³

et al. 2022

Front. Phys.

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Over the past 30 years, physical optics has been enriched by the appearance of singular optics as a new branch approved in scientific classifiers. This review briefly outlines the main concepts of the singular optics, their role in physical research and applications, and prospects of further development. The wave singularities are considered as a sort of structured-light elements and analyzed based on the generic example of screw wavefront dislocation (optical vortex). Their specific topological and mechanical properties associated with the transverse energy circulation are discussed. Peculiar features of the non-linear optical phenomena with singular fields are exhibited, with the special attention to generation of multidimensional entangled quantum states of photons. Optical fields with multiple singularities, especially, the stochastic speckle fields, are discussed in the context of optical diagnostics of random scattering objects. The exact and approximate correspondences between characteristic parameters of the optical-field intensity and phase distributions are analyzed with the aim of recovering phase information from the intensity measurements (“phase problem” solution). Rational singularity-based approaches to informative measurements of the scattered-field distribution are discussed, as well as their employment for the objects’ diagnostics. In particular, the practical instruments are described for the high-precision rough-surface testing. Possible enhancements of the singular-optics ideas and concepts in a wider context, including the transformation optics, near-field optics (surface waves), partially-coherent fields, and wave fields of other physical nature, are briefly exposed.

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Section: Fractal Objects and Fractal Properties Of Scattered Fieldsmentioning

confidence: 99%

Section: Statistical Characteristics Of Random Objects and Speckle Fi...mentioning

confidence: 99%

“…as well as other higher-order parameters of statistical distributions (skewness Sk, kurtosis Ku, etc. [98,101]). In Eq.…”

Section: Statistical Characteristics Of Random Objects and Speckle Fi...mentioning

confidence: 99%

Section: Fractal Objects and Fractal Properties Of Scattered Fieldsmentioning

confidence: 99%

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Optical phase singularities: Physical nature, manifestations and applications

Angelsky

Bekshaev²,

Vasnetsov³

et al. 2022

Front. Phys.

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“…Classification of the coordinate d( ) m ń distributions is fulfilled using the following criteria [1,14,[27][28][29][30][31][32][33][34][35] …”

Section: Algorithms For Statistical Correlation and Fractal Analysementioning

confidence: 99%

Phase maps of polycrystalline human biological fluids networks: statistical, correlation, and fractal analysis

Ushenko

2011

Opto-Electronics Review

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The complex statistical and fractal analysis of phase properties, inherent to birefringence networks of liquid crystals consisting of optically-thin layers, prepared from synovial fluid taken from human joints, is performed in this work. Within the framework of a statistical approach, the authors have investigated values and ranges for changes of statistical moments of the 1-st to the 4-th orders that characterize coordinate distributions for phase shifts between orthogonal components of amplitudes inherent to laser radiation, transformed by synovial fluid layers, for human joints with various pathologies. The correlation criteria for differentiation of phase maps, describing pathologically changed liquid-crystal networks, have been ascertained. In the framework of the fractal approach, dimensions of self-similar coordinate phase distributions as well as features of transformation of logarithmic dependences for power spectra of these distributions for various types of human joint pathologies are determined.

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