Frequency response of five integration methods to obtain the profile from its slope

Alfonso Moreno; Juan Campos; L. R. Yaroslavsky

doi:10.1117/1.1872896

Frequency response of five integration methods to obtain the profile from its slope

Alfonso Moreno^*, Juan Campos, L. R. Yaroslavsky

^*Corresponding author for this work

Interdisciplinary Engineering

Autonomous University of Barcelona

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

The objective of profilometry is to obtain the topography of a surface. Some methods are based on the measurement of the slope of the test surface. Then, by integration the profile of a surface can be determined. The slope is measured in a given set of points and from these data it is necessary to obtain the profile with the highest possible accuracy. Most frequently, the integration is carried out by numerical integration methods that assume different kinds of polynomial approximation of data between sampling points. We propose the integration of the function by means of processing in the Fourier domain. The analysis of the different integration methods in the Fourier domain enables us to easily study and compare their performance.

Original language	English
Pages (from-to)	1-8
Number of pages	8
Journal	Optical Engineering
Volume	44
Issue number	3
DOIs	https://doi.org/10.1117/1.1872896
State	Published - Mar 2005

Keywords

Deflectometry
Fourier transform
Integration methods

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10.1117/1.1872896

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title = "Frequency response of five integration methods to obtain the profile from its slope",

abstract = "The objective of profilometry is to obtain the topography of a surface. Some methods are based on the measurement of the slope of the test surface. Then, by integration the profile of a surface can be determined. The slope is measured in a given set of points and from these data it is necessary to obtain the profile with the highest possible accuracy. Most frequently, the integration is carried out by numerical integration methods that assume different kinds of polynomial approximation of data between sampling points. We propose the integration of the function by means of processing in the Fourier domain. The analysis of the different integration methods in the Fourier domain enables us to easily study and compare their performance.",

keywords = "Deflectometry, Fourier transform, Integration methods",

author = "Alfonso Moreno and Juan Campos and Yaroslavsky, {L. R.}",

note = "Funding Information: The authors would like to thank M. J. Yzuel for useful discussions. This work has been partially financed by Min-isterio de Ciencia y Tecnolog{\'i}a, under Project No. BFM2003-006273-C02-01, and by the European Community Project No. CTB556-01-4175. A. M. acknowledges the grant received by this European project.",

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AU - Moreno, Alfonso

AU - Campos, Juan

AU - Yaroslavsky, L. R.

N1 - Funding Information: The authors would like to thank M. J. Yzuel for useful discussions. This work has been partially financed by Min-isterio de Ciencia y Tecnología, under Project No. BFM2003-006273-C02-01, and by the European Community Project No. CTB556-01-4175. A. M. acknowledges the grant received by this European project.

PY - 2005/3

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N2 - The objective of profilometry is to obtain the topography of a surface. Some methods are based on the measurement of the slope of the test surface. Then, by integration the profile of a surface can be determined. The slope is measured in a given set of points and from these data it is necessary to obtain the profile with the highest possible accuracy. Most frequently, the integration is carried out by numerical integration methods that assume different kinds of polynomial approximation of data between sampling points. We propose the integration of the function by means of processing in the Fourier domain. The analysis of the different integration methods in the Fourier domain enables us to easily study and compare their performance.

AB - The objective of profilometry is to obtain the topography of a surface. Some methods are based on the measurement of the slope of the test surface. Then, by integration the profile of a surface can be determined. The slope is measured in a given set of points and from these data it is necessary to obtain the profile with the highest possible accuracy. Most frequently, the integration is carried out by numerical integration methods that assume different kinds of polynomial approximation of data between sampling points. We propose the integration of the function by means of processing in the Fourier domain. The analysis of the different integration methods in the Fourier domain enables us to easily study and compare their performance.

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KW - Fourier transform

KW - Integration methods

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Frequency response of five integration methods to obtain the profile from its slope

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Keywords

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