Non-Gaussian surface generation

Wu, S.C.; Chen, M.F.; Fung, A.K.

doi:10.1109/36.7721

Cited by 28 publications

(10 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This article assumes a Gaussian distribution of the standard deviation of the height on the rough surface σz, which is the basis of the theoretical approach. In order to extend the method, other distributions can also be assumed as the foundation for theoretical considerations, such as a Laplace distribution or a K-distribution [45,46].…”

Section: Discussionmentioning

confidence: 99%

Non-Contact Roughness Measurement in Sub-Micron Range by Considering Depolarization Effects

Pöller

Bloise

Jakobi

et al. 2019

Sensors

View full text Add to dashboard Cite

The characteristics of a surface, particularly the roughness, play an important role in different fields of the industry and have to be considered to ensure quality standards. Currently, there are numerous sophisticated methods for measuring surface roughness but plenty of them cause long-term damage because they are in contact with the sample. This article presents a non-contact method to accurately determine small surface roughnesses resulting from the consideration of the depolarization effects caused by the rough surface. This technique can be applied as an extension in various roughness measurements and improves the approach of Chandley’s technique, which does not take into account the depolarization of the light scattered by the sample. The experimental setup and the measurements are easy to perform. The essential component is a quarter wave plate, which is incorporated into a Michelson interferometer. With the resulting two different contrasts and the recorded intensities of the sample and the reference mirror, the surface roughness can be estimated straightforwardly. This article details the theoretical approach, followed by the experimental results and the corresponding uncertainties. The experimental results are compared with Chandley’s method. In order to have reference roughness values of the samples, measurements with a stylus profilometer and with a confocal microscope are performed and compared.

show abstract

Section: Discussionmentioning

confidence: 99%

Non-Contact Roughness Measurement in Sub-Micron Range by Considering Depolarization Effects

Pöller

Bloise

Jakobi

et al. 2019

Sensors

View full text Add to dashboard Cite

show abstract

“…He pointed out that the probability density function (pdf) of a natural surface can also be described by a Gaussian model, but the pdf could be noncritical for its scattering properties. In 1988, Wu et al [8] agreed that non-Gaussian processes would be necessary for natural surface description. The introduction of the fractal geometry provided a powerful instrument for comprehending and quantitatively describing the irregular shapes of nature.…”

Section: Measurement Of the Electromagnetic Field Backscattered By A mentioning

confidence: 99%

Measurement of the Electromagnetic Field Backscattered by a Fractal Surface for the Verification of Electromagnetic Scattering Models

Ruello

Blanco-Sanchez

Iodice

et al. 2010

IEEE Trans. Geosci. Remote Sensing

View full text Add to dashboard Cite

Abstract-Fractal geometry is widely accepted as an efficient theory for the characterization of natural surfaces; the opportunity of describing irregularity of natural surfaces in terms of few fractal parameters makes its use in direct and inverse electromagnetic (EM) scattering theories highly desirable. In this paper, we present an innovative procedure for manufacturing fractal surfaces and for measuring their scattering properties. A cardboard-aluminum fractal surface was built as a representation of a Weiestrass-Mandelbrot fractal process; the EM field scattered from it was measured in an anechoic chamber. A monostatic radarlike configuration was employed. Measurement results were compared to Kirchhoff approximation and small perturbation method closed-form results that were analytically obtained by employing the fractional Brownian motion to model the surface shape. Matching and discrepancies between theories and measurements are then discussed. Finally, fractal and classical surface models are compared as far as their use in the EM scattering is concerned.

show abstract

“…Therefore, the WM is a superposition of sinusoidal tones spaced by the irrational parameter , hence it is an almost periodic function [11].…”

Section: Fractal Surfaces: Concepts and Synthesismentioning

confidence: 99%

Synthesis, construction, and validation of a fractal surface

Ruello

Blanco-Sanchez

Iodice³

et al. 2006

IEEE Trans. Geosci. Remote Sensing

View full text Add to dashboard Cite

Abstract-Fractal geometry provides reliable models to describe geometrical properties of natural surfaces. Therefore, their use in the electromagnetic scattering methods deserves careful research. In order to have complete insight into the phenomenon, a measurement campaign on a fractal surface in a controlled environment is a key step. In this paper, we propose a technique for building a fractal surface that can be used for electromagnetic scattering evaluation purposes. The surface characteristics are imposed by computer synthesizing a bandlimited Weierstrass-Mandelbrot function, whose actual shape is constructed by means of a cheap innovative technique: the synthesized surface is made from cardboard covered with aluminum foil, which gives a conducting surface and creates the micro-scale conditions, useful to represent manufacturing errors. Statistics of the overall surface shape are then measured, analyzed and compared with the imposed ones, providing and verifying the rationale for a fully controlled surface to be applied in any kind of experiment on natural surfaces.

show abstract

Non-Gaussian surface generation

Cited by 28 publications

References 5 publications

Non-Contact Roughness Measurement in Sub-Micron Range by Considering Depolarization Effects

Non-Contact Roughness Measurement in Sub-Micron Range by Considering Depolarization Effects

Measurement of the Electromagnetic Field Backscattered by a Fractal Surface for the Verification of Electromagnetic Scattering Models

Synthesis, construction, and validation of a fractal surface

Contact Info

Product

Resources

About