White-light interferometry—Envelope detection by Hilbert transform and influence of noise

White-light interferometry is an established method for the measurement of the geometrical shape of objects. It can also be used for the measurement of the shape of objects with rough surfaces. Because of the rough surface, the phase of the white-light interferogram is not evaluated, the height info...

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Bibliographic Details
Published in:Optics and lasers in engineering 2012-08, Vol.50 (8), p.1063-1068
Main Authors: Pavliček, Pavel, Michálek, Václav
Format: Article
Language:English
Subjects:
Envelope detection
Hilbert transform
Measurement uncertainty
Noise
White-light interferometry
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Summary:White-light interferometry is an established method for the measurement of the geometrical shape of objects. It can also be used for the measurement of the shape of objects with rough surfaces. Because of the rough surface, the phase of the white-light interferogram is not evaluated, the height information is obtained from the interferogram envelope. Hilbert transform is a classical method to calculate the envelope. In a real measurement, the interferogram is affected by the noise. We look for the answer to following questions: how does the noise of the calculated envelope look like? How does the noise influence the measurement uncertainty? ► We calculate the autocorrelation of the noise of the calculated envelope in white-light interferometry. ► The autocorrelation function depends on the ratio between the mean wavelength of the used light and the sampling step. ► The correlation of the envelope noise causes that the measurement uncertainty of white-light interferometry. ► By factor square root of two higher than that of a sensor with a signal without modulation.
ISSN:0143-8166
1873-0302
DOI:10.1016/j.optlaseng.2012.02.008