White-light Phase-stepping Interferometry for Surface Profiling

Hariharan, P.; Roy, Maitreyee

doi:10.1080/09500349414552041

Cited by 67 publications

(30 citation statements)

References 12 publications

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“…We note that if Pancharatnam's phase is stepped (rather than the path di erence as is considered in this paper) the white-light phase can, in principle, be recovered exactly [7]. This is because Pancharatnam's phase is a geometric phase, which has the property of achromaticity, that is each wavelength component is shifted by the same phase.…”

Section: Introductionmentioning

confidence: 92%

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Path difference measurement using phase stepping with white light

Barron

Somervell

Haskell³

et al. 2002

Journal of Modern Optics

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Phase stepping algorithms are commonly used with narrow bandwidth sources for fast accurate measurement of interferometer phase di erences. We show that path di erence can also be measured using phase stepping with a wide bandwidth source. The errors resulting from the spectral characteristics of the source are discussed and shown to be relatively small, allowing measurement of path di erence to typically 0.1 mm or better. White-light phase stepping is demonstrated experimentally with results which closely match those predicted theoretically.

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Section: Introductionmentioning

confidence: 92%

“…The short coherence length of such sources is utilized in coherence interferometers [6,7], where the maximum of the interferogram locates zero path di erence. Another technique is to measure the exact position on the envelope of the coherence function [8] by stepping the phase.…”

Section: Introductionmentioning

confidence: 99%

Path difference measurement using phase stepping with white light

Barron

Somervell

Haskell³

et al. 2002

Journal of Modern Optics

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“…15 Nearly achromatic phase shifting with polarization components is possible, but is difficult to implement. 16,17 In this paper, we present the results of profile measurement of a stepped structure with SRWLI technique using a PZT phase shifter.…”

Section: Introductionmentioning

confidence: 99%

Optical profiler based on spectrally resolved white light interferometry

Debnath

Kothiyal

2005

Opt. Eng

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A white light interferogram can be decomposed into its constituent monochromatic interferograms using a spectrograph. By imaging the white light interferogram on the entrance slit of the spectrograph, the intensities of the monochromatic components can be accessed at its output plane by the pixels of a CCD detector along the direction of dispersion. For a given optical path difference (OPD) in the interferometer, the phases of these constituents are different and linearly related to the wave number of the constituent spectral component. If the phases of all the constituents are determined, the OPD can be obtained as the slope of the phase versus wave number linear fit. Since the OPD is related to the height of the test object at a point, a line profile of the object can be determined if the OPD is measured along the pixels of the CCD parallel to the entrance slit of the spectrograph. To get at the line profile, we must therefore determine the optical phase at all the pixels of the CCD detector. The phase-shifting technique is an obvious choice for this. A piezoelectric transducer (PZT) phase shifter is most common in the application of the phase-shifting technique to monochromatic interferometry. We present the experimental result based on our recent proposal that the conventional PZT phase shifting, although nonachromatic, can be used for this application as well with success. © 2005 Society of Photo-Optical Instrumentation Engineers.

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“…Let us now consider possible ways for the introduction of a phase shift. ¿ 0 is constant and cannot be easily modulated (even if the modulation of the geometric phase has been proposed for white light interferometry applications [14]). The phase shift has therefore to be applied through the ®rst term of equation (2).…”

Section: Two Ways For Phase Shift Introductionmentioning

confidence: 99%

Potential of a wavelength sampling approach for profilometry by phase shifting interferometry

Sandoz

Calatroni

Tribillon

1999

Journal of Modern Optics

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In this paper, we investigate how the ®eld of application of phase shifting interferometry could be extended to the reconstruction of bidimensional phase maps of vibrating samples or of static samples located in a mechanically unstable environment. The possibility to perform instantaneous recording of the necessary phase shifted interferograms is discussed and a wavelength sampling approach is proposed. In that technique, the phase shift is introduced through a variation of the optical wavelength. The implications of that choice on the range of optical path di erences that can be analysed are discussed. Since the necessary wavelengths can illuminate simultaneously the inspected sample, instantaneous acquisition procedures can be considered, providing that we dispose of a multi-spectral band image sensor for the parallel recording of the set of phase shifted interferograms. The choice of the phase computation algorithm is discussed and four of them are compared. An experimental set-up was built for the sequential recording of the necessary set of phase shifted interferograms and the proposed algorithms are evaluated experimentally. Results show that sub-nanometre accuracy can be obtained over a measurement range of a few microns. Therefore, the successful application of phase shifting methods to vibrating samples can be imagined through the development of an adapted image sensor.

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White-light Phase-stepping Interferometry for Surface Profiling

Cited by 67 publications

References 12 publications

Path difference measurement using phase stepping with white light

Path difference measurement using phase stepping with white light

Optical profiler based on spectrally resolved white light interferometry

Potential of a wavelength sampling approach for profilometry by phase shifting interferometry

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