14 August 2006 Analysis of spectrally resolved white light interferometry by Hilbert transform method
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Scanning White Light Interferometry (SWLI) is a tool for measuring discontinuous surface profile. A short coherence length white light source is used in the interferometer so that the fringes are localized in the vicinity of zero Optical Path Difference (OPD). The object surface is scanned along the height axis to get the height variation over the object field. Another technique using white light is Spectrally Resolved White Light Interferometry (SRWLI) in which the white light interferogram is spectrally decomposed by a spectrometer. The interferogram displayed at the exit plane of the spectrometer has a continuous variation of wavelength along the chromaticity axis. This interferogram encodes the phase as a function of wave number. For a given OPD, the phase is different for different spectral component of the source. The OPD can be determined as the slope of the phase versus wave number linear fit. To determine the phase of the different spectral components, temporal phase shifting technique which typically uses five frames has been proposed. Since the OPD is related to the height of the test object at a point, a line profile of the object can be determined. In this paper we discuss the Hilbert Transform method for determination of phase in SRWLI. This procedure requires only one spectrally resolved white light interferogram.
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Sanjit K. Debnath, Sanjit K. Debnath, Mahendra P. Kothiyal, Mahendra P. Kothiyal, "Analysis of spectrally resolved white light interferometry by Hilbert transform method", Proc. SPIE 6292, Interferometry XIII: Techniques and Analysis, 62920P (14 August 2006); doi: 10.1117/12.680179; https://doi.org/10.1117/12.680179

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