Grinding process for beveling and lapping operations in lens manufacturing

Teng

et al. 2003

Commun. Theor. Phys.

We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces. We use the mathematical decay function to approximate the duple negative exponent function in the rigorous theory of scattering, by letting them have the same maximum value and half-width, and the expression for the half-widths of the intensity profiles in the whole range of the perpendicular wave vector component is obtained. The previous results in the two extreme cases are included in the results of this paper. In the simulational verification, we propose a method for the generation of self-affine fractal random surfaces, using the square-root of Fourier transform of the correlation function of the surface height. The simulated results conform well with the theory.

Section: Introductionmentioning

confidence: 99%

Study on Properties of Intensity Profiles Scattered from the Self-Affine Fractal Random Surfaces: an Approximate Theory and Simulations

Teng

et al. 2003

Commun. Theor. Phys.

“…The statistical properties of rough surfaces is a long-standing problem that has attracted great interest in various fields of physics such as the dynamics of growth fronts [1,2], the dynamic fractures by large impact [3], the engineering of optical elements [4], etc. In random surface characterizations, scattering technique is one of the most powerful tools and has been applied to the surfaces ranging from atomic to macroscopic scales by using electromagnetic radiations of different bands of wavelengths.…”

mentioning

confidence: 99%

Speckle intensity correlation in the diffraction region near rough surfaces and simulational experiments for extraction of surface parameters

Zhang³

et al. 2004

Europhys. Lett.

Based on the light scattering theory of Kirchoff approximation, the correlation function of the speckle intensities relating to that of the random surfaces is quantitatively formulated in correspondence with the principles of Van Cittert-Zernike theorem. We then propose the method for the extraction of surfaces parameters from the correlation functions of speckles intensity produced by light scattering in the region near the random surfaces. The experiments of light scattering in the region near random self-affine fractal surfaces are simulated, and the 3 parameters, i.e., the roughness w, the lateral correlation length ξ and the roughness exponent α, are extracted by fitting the correlation function data of the speckle intensities to the formulated expression. The extracted values of the surface parameters conform well with the set values.

“…The study of random surfaces has been paid great attention in many scientific and technological fields such as the growth fronts of thin films, 1,2 surfaces of fabricated optical devices, 3,4 and the fractured cross section of materials, 5,6 etc. In modeling and describing random surfaces, we use both statistical parameters such as root-mean-square deviation roughness w and lateral correlation length , and statistical functions such as the height probability density function, the characteristic function, and the correlation functions.…”

mentioning

confidence: 99%

Extraction of height–height correlation function of random surfaces from the average intensity of image speckles

Teng

Applied Physics Letters

et al. 2002

We present a method for the extraction of the height–height correlation function of random surfaces from the average intensity of image speckles. The setup of a Fourier transforming and imaging system with a variable aperture is used for both the theoretical analysis and experimental performances. Based on the analytical expression of the image intensity, an algorithm is developed to formulate numerically the intensity data versus the aperture radius into the pair of Bessel–Fourier transform and the inversion, from which the height–height correlation function is reconstructed. Three samples of Gaussian correlation are used for the experimental demonstration. The extracted height–height correlation function and the random surface parameters obtained thereby conform with those obtained by atomic force microscopy.