Increasing the range of unambiguity in step-height measurement with multiple-wavelength interferometry—application to absolute long gauge block measurement

Decker, J E; Miles, John; Madej, A.A.; Siemsen, Ralph F.; Siemsen, K.J.; Bonth, Sebastian de; Bustraan, Krijn; Temple, Sara; Pekelsky, James R.

doi:10.1364/ao.42.005670

Cited by 56 publications

(26 citation statements)

References 13 publications

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“…Especially when a multiplewavelength technique is utilized, the measurement can be performed point by point without any spatial phase unwrapping; therefore, the step-height is not a problem at all. Over the years, extensive research has been conducted on two-or multiple-wavelength phase-shifting techniques [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and temporal phase unwrapping. 15,16 All these efforts were intending to measure the step-height object or alleviate the limitations of phase unwrapping.…”

Section: Introductionmentioning

confidence: 99%

Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm

Zhang

2009

Opt. Eng

108

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We address a framework to reduce the unwrapping errors of the measurement system using a digital multiplewavelength phase-shifting algorithm. In particular, the following framework is proposed: (1) smooth the raw phase by smoothing the sine and cosine images of the phase computation of the inverse tangent function; (2) locate and remove the incorrectly unwrapped points by the monotonicity condition of the phase map; (3) obtain the unwrapped phase map for the shortest wavelength without smoothing; (4) detect holes and fill them to preserve as much useful information as possible. Experiments demonstrated that the proposed framework significantly alleviated the measurement errors caused by the phase noise. KeywordsVirtual Reality Applications Center, Human Computer Interaction, structured light, phase shifting, phase unwrapping, multiple wavelength, phase error RightsCopyright 2009 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic electronic or print reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. Abstract. We address a framework to reduce the unwrapping errors of the measurement system using a digital multiple-wavelength phaseshifting algorithm. In particular, the following framework is proposed: ͑1͒ smooth the raw phase by smoothing the sine and cosine images of the phase computation of the inverse tangent function; ͑2͒ locate and remove the incorrectly unwrapped points by the monotonicity condition of the phase map; ͑3͒ obtain the unwrapped phase map for the shortest wavelength without smoothing; ͑4͒ detect holes and fill them to preserve as much useful information as possible. Experiments demonstrated that the proposed framework significantly alleviated the measurement errors caused by the phase noise.

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Section: Introductionmentioning

confidence: 99%

Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm

Zhang

2009

Opt. Eng

108

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“…They were used widely to measure larger step height. [8][9][10][11] Huntley et al proposed a technique called temporal phase unwrapping algorithm 12 and apply it to measure discontinuous objects. 13 The fundamental concept of this technique is that the phase is unwrapped in time axis rather than in x − y plane spatially.…”

Section: Introductionmentioning

confidence: 99%

Digital multiple wavelength phase shifting algorithm

Zhang

2009

SPIE Proceedings

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This paper presents a digital multiple-wavelength phase-shifting technique for three-dimensional shape measurement. The projected phase-shifted fringe images have wavelengths of λ κ = W/2 κ-1 (k = 1,2,3...). The phase unwrapping is not needed for the longest wavelength because a single fringe covers the whole area. The shorter wavelength phase, φκ(x,y), is unwrapped by referring to the previously unwrapped longer wavelength phase, Φ k-1 (x,y), pixel by pixel without accessing its neighborhood pixels. Experiments demonstrate that this technique has low noise and less sensitivity to motion. It can be used to measure arbitrary step height and multiple objects simultaneously. 1, 2, 3...). The phase unwrapping is not needed for the longest wavelength because a single fringe covers the whole area. The shorter wavelength phase, φ k (x, y), is unwrapped by referring to the previously unwrapped longer wavelength phase, Φ k−1 (x, y), pixel by pixel without accessing its neighborhood pixels. Experiments demonstrate that this technique has low noise and less sensitivity to motion. It can be used to measure arbitrary step height and multiple objects simultaneously.

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“…This is achieved without the need for closely separated measurement wavelengths. The results of this work have numerous applications in absolute distance metrology [20,21,[27][28][29], discrete wavemeters [30,31], and full-field MWI and profilometry techniques [7-9, 22, 24,32], or multi-wavelength digital holography [33][34][35]. Fig.…”

Section: Discussionmentioning

confidence: 99%

Algebraic solution for phase unwrapping problems in multiwavelength interferometry

Falaggis

Towers

2014

Appl. Opt.

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Received Month X, XXXX; revised Month X, XXXX; accepted Month X, XXXX; posted Month X, XXXX (Doc. ID XXXXX); published Month X, XXXX Recent advances in multi-wavelength interferometry techniques (Falaggis et. al. Appl. Opt. 52, 5758-65 (2013)) give new insights to phase unwrapping problems and allow the fringe order information contained in the measured phase to be extracted with low computational effort. This work introduces an algebraic solution to the phase unwrapping problem that allows the direct calculation of the unknown integer fringe order. The procedure resembles beat-wavelength approaches, but provides greater flexibility in choosing the measurement wavelengths, a larger measurement range, and a higher robustness against noise, due to the ability to correct for errors during the calculation.

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Increasing the range of unambiguity in step-height measurement with multiple-wavelength interferometry—application to absolute long gauge block measurement

Cited by 56 publications

References 13 publications

Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm

Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm

Digital multiple wavelength phase shifting algorithm

Algebraic solution for phase unwrapping problems in multiwavelength interferometry

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