Comparison of Fast Fourier Transform and Convolution in Wavelength Scanning Interferometry

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

The assessment of surface finish has become increasingly important in the field of precision engineering. Optical interferometry has been widely used for surface measurement due to the advantages of non-contact and high accuracy interrogation. In spite of the 2π phase ambiguity that can limit the measurement scale in monochromatic interferometry, other optical interferomtry have succeeded to overcome this problem and to measure both rough and smooth surfaces such as white light interferometry and wavelength scanning interferometry (WSI). The WSI can be used to measure large discontinuous surface profiles by producing phase shifts without any mechanical scanning process. Where the WSI produces the phase shifts by altering the wavelength of a broadband light source and capturing the produced interferograms by a CCD. This paper introduces an optical setup and operation principle of a WSI that used a halogen white light as a broadband illumination source and an acousto-optic tunable filter (AOTF) as a wavelength scanning device. This setup can provide a wide scan range in the visible region. The scanned range is being operated from 682.8 nm to 552.8nm and the number of captured frames is 128. Furthermore, the obtained interferograms from a Linnik interferometer have been analyzed by two methods, Fast Fourier Transform and Convolution. A mathematical description of both methods is presented then a comparison in results accuracy is made between them. The Areal measurement of a standard 4.707μm step height sample shows that FFT and convolution methods could provide a nanometer measurement resolution for the surface finish inspection.

LanguageEnglish
Title of host publicationOptical Measurement Systems for Industrial Inspection VII
EditorsPeter H. Lehmann, Wolfgang Osten, Kay Gastinger
PublisherSPIE
Number of pages8
Volume8082
ISBN (Print)9780819486783
DOIs
Publication statusPublished - 26 May 2011
EventInternational Society for Optics and Photonics Optical Meteorology: Optical Measurement Systems for Industrial Inspection VII - Munich, Germany
Duration: 23 May 201126 May 2011
https://www.spiedigitallibrary.org/conference-proceedings-of-spie/8082.toc#FrontMatter (Link to Conference Information)

Conference

ConferenceInternational Society for Optics and Photonics Optical Meteorology
CountryGermany
CityMunich
Period23/05/1126/05/11
Internet address

Fingerprint

Interferometry
Fast Fourier transform
Convolution
convolution integrals
Fast Fourier transforms
Scanning
interferometry
Wavelength
scanning
wavelengths
Interferogram
Phase Shift
Broadband
Phase shift
Light sources
White Light Interferometry
Optical Interferometry
Tunable Filter
Acousto-optics
Surface Profile

Cite this

Muhamedsalih, H., Jiang, X., & Gao, F. (2011). Comparison of Fast Fourier Transform and Convolution in Wavelength Scanning Interferometry. In P. H. Lehmann, W. Osten, & K. Gastinger (Eds.), Optical Measurement Systems for Industrial Inspection VII (Vol. 8082). [80820Q] SPIE. https://doi.org/10.1117/12.889357
Muhamedsalih, Hussam ; Jiang, Xiangqian ; Gao, Feng. / Comparison of Fast Fourier Transform and Convolution in Wavelength Scanning Interferometry. Optical Measurement Systems for Industrial Inspection VII. editor / Peter H. Lehmann ; Wolfgang Osten ; Kay Gastinger. Vol. 8082 SPIE, 2011.
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abstract = "The assessment of surface finish has become increasingly important in the field of precision engineering. Optical interferometry has been widely used for surface measurement due to the advantages of non-contact and high accuracy interrogation. In spite of the 2π phase ambiguity that can limit the measurement scale in monochromatic interferometry, other optical interferomtry have succeeded to overcome this problem and to measure both rough and smooth surfaces such as white light interferometry and wavelength scanning interferometry (WSI). The WSI can be used to measure large discontinuous surface profiles by producing phase shifts without any mechanical scanning process. Where the WSI produces the phase shifts by altering the wavelength of a broadband light source and capturing the produced interferograms by a CCD. This paper introduces an optical setup and operation principle of a WSI that used a halogen white light as a broadband illumination source and an acousto-optic tunable filter (AOTF) as a wavelength scanning device. This setup can provide a wide scan range in the visible region. The scanned range is being operated from 682.8 nm to 552.8nm and the number of captured frames is 128. Furthermore, the obtained interferograms from a Linnik interferometer have been analyzed by two methods, Fast Fourier Transform and Convolution. A mathematical description of both methods is presented then a comparison in results accuracy is made between them. The Areal measurement of a standard 4.707μm step height sample shows that FFT and convolution methods could provide a nanometer measurement resolution for the surface finish inspection.",
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Muhamedsalih, H, Jiang, X & Gao, F 2011, Comparison of Fast Fourier Transform and Convolution in Wavelength Scanning Interferometry. in PH Lehmann, W Osten & K Gastinger (eds), Optical Measurement Systems for Industrial Inspection VII. vol. 8082, 80820Q, SPIE, International Society for Optics and Photonics Optical Meteorology, Munich, Germany, 23/05/11. https://doi.org/10.1117/12.889357

Comparison of Fast Fourier Transform and Convolution in Wavelength Scanning Interferometry. / Muhamedsalih, Hussam; Jiang, Xiangqian; Gao, Feng.

Optical Measurement Systems for Industrial Inspection VII. ed. / Peter H. Lehmann; Wolfgang Osten; Kay Gastinger. Vol. 8082 SPIE, 2011. 80820Q.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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T1 - Comparison of Fast Fourier Transform and Convolution in Wavelength Scanning Interferometry

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AU - Jiang, Xiangqian

AU - Gao, Feng

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N2 - The assessment of surface finish has become increasingly important in the field of precision engineering. Optical interferometry has been widely used for surface measurement due to the advantages of non-contact and high accuracy interrogation. In spite of the 2π phase ambiguity that can limit the measurement scale in monochromatic interferometry, other optical interferomtry have succeeded to overcome this problem and to measure both rough and smooth surfaces such as white light interferometry and wavelength scanning interferometry (WSI). The WSI can be used to measure large discontinuous surface profiles by producing phase shifts without any mechanical scanning process. Where the WSI produces the phase shifts by altering the wavelength of a broadband light source and capturing the produced interferograms by a CCD. This paper introduces an optical setup and operation principle of a WSI that used a halogen white light as a broadband illumination source and an acousto-optic tunable filter (AOTF) as a wavelength scanning device. This setup can provide a wide scan range in the visible region. The scanned range is being operated from 682.8 nm to 552.8nm and the number of captured frames is 128. Furthermore, the obtained interferograms from a Linnik interferometer have been analyzed by two methods, Fast Fourier Transform and Convolution. A mathematical description of both methods is presented then a comparison in results accuracy is made between them. The Areal measurement of a standard 4.707μm step height sample shows that FFT and convolution methods could provide a nanometer measurement resolution for the surface finish inspection.

AB - The assessment of surface finish has become increasingly important in the field of precision engineering. Optical interferometry has been widely used for surface measurement due to the advantages of non-contact and high accuracy interrogation. In spite of the 2π phase ambiguity that can limit the measurement scale in monochromatic interferometry, other optical interferomtry have succeeded to overcome this problem and to measure both rough and smooth surfaces such as white light interferometry and wavelength scanning interferometry (WSI). The WSI can be used to measure large discontinuous surface profiles by producing phase shifts without any mechanical scanning process. Where the WSI produces the phase shifts by altering the wavelength of a broadband light source and capturing the produced interferograms by a CCD. This paper introduces an optical setup and operation principle of a WSI that used a halogen white light as a broadband illumination source and an acousto-optic tunable filter (AOTF) as a wavelength scanning device. This setup can provide a wide scan range in the visible region. The scanned range is being operated from 682.8 nm to 552.8nm and the number of captured frames is 128. Furthermore, the obtained interferograms from a Linnik interferometer have been analyzed by two methods, Fast Fourier Transform and Convolution. A mathematical description of both methods is presented then a comparison in results accuracy is made between them. The Areal measurement of a standard 4.707μm step height sample shows that FFT and convolution methods could provide a nanometer measurement resolution for the surface finish inspection.

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M3 - Conference contribution

SN - 9780819486783

VL - 8082

BT - Optical Measurement Systems for Industrial Inspection VII

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PB - SPIE

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Muhamedsalih H, Jiang X, Gao F. Comparison of Fast Fourier Transform and Convolution in Wavelength Scanning Interferometry. In Lehmann PH, Osten W, Gastinger K, editors, Optical Measurement Systems for Industrial Inspection VII. Vol. 8082. SPIE. 2011. 80820Q https://doi.org/10.1117/12.889357