Testing phase-shifting algorithms for uncertainty evaluation in interferometric gauge block calibration

This paper describes the uncertainty contribution of nine different phase-shifting algorithms (PSAs) to a gauge block calibration evaluated using a Monte Carlo method. The phase map and its standard deviation, codified in the output distribution obtained with each PSA, are used as input parameters in the exact fractions method for the final calculation of the gauge block length. Results obtained show the behaviour of each PSA versus different types of error sources. Uncertainty evaluation fits well to a Gaussian distribution for all algorithms tested with more than 104 trials and the central limit theorem is satisfied. As expected, the Symmetric 5 + 1 PSA shows the best behaviour with the lower uncertainty contribution and appears among PSAs used as the best algorithm for this technical application. As the selected PSAs are representative for the main PSA families, the protocol employed can be used for any other specifically tailored algorithm.

[1]  Jiří Novák,et al.  Multi-step phase-shifting algorithms insensitive to linear phase shift errors , 2008 .

[2]  B. Acko,et al.  Verification of the conventional measuring uncertainty evaluation model with Monte Carlo simulation , 2005 .

[3]  Qian Kemao,et al.  Determination of the best phase step of the Carré algorithm in phase shifting interferometry , 2000 .

[4]  B. Edĺen.  The Refractive Index of Air , 1966 .

[5]  Rainer Winkler,et al.  A Monte Carlo method for uncertainty evaluation implemented on a distributed computing system , 2007 .

[6]  Kieran G. Larkin,et al.  Efficient nonlinear algorithm for envelope detection in white light interferometry , 1996 .

[7]  D. Malacara,et al.  Interferogram Analysis for Optical Testing , 2018 .

[8]  Ted Doiron,et al.  The Gage block handbook , 1995 .

[9]  B. Taylor.  The international system of units (SI) , 1991 .

[10]  A. Gustavo González,et al.  Estimation of the uncertainty of indirect measurements from the propagation of distributions by using the Monte-Carlo method: An overview , 2005 .

[11]  B. Taylor,et al.  Status Report on the ISO/IEC/OIML/BIPM Guide, Expression of Uncertainty in Measurement , 1992 .

[12]  K. P. Birch,et al.  LETTER TO THE EDITOR: Correction to the Updated Edln Equation for the Refractive Index of Air , 1994 .

[13]  N. Metropolis,et al.  The Monte Carlo method. , 1949 .

[14]  B. V. Dorrio,et al.  Error‐phase compensation properties of differential phase‐shifting algorithms for Fizeau fringe patterns , 2008 .

[15]  J. Briers.  Interferometric optical testing: an inter-laboratory comparison , 1999 .

[16]  C. Tilford.  Analytical procedure for determining lengths from fractional fringes. , 1977, Applied optics.

[17]  K. P. Birch,et al.  An Updated Edln Equation for the Refractive Index of Air , 1993 .

[18]  D. Malacara.  Optical Shop Testing , 1978 .

[19]  Kieran G. Larkin,et al.  Design and assessment of symmetrical phase-shifting algorithms , 1992 .

[20]  V. Álvarez-Valado,et al.  Monte-Carlo technique for uncertainty evaluation of gauge block calibration using laser interferometry , 2008, Photonics Prague.

[21]  Alan A Madej,et al.  Increasing the range of unambiguity in step-height measurement with multiple-wavelength interferometry--application to absolute long gauge block measurement. , 2003, Applied optics.

[22]  L R Watkins,et al.  Automation of a 1960s Hilger gauge block interferometer , 2003 .

[23]  P. Carré.  Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures , 1966 .

[24]  Jennifer E. Decker,et al.  Considerations for the evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry , 2004 .

[25]  B V Dorrío,et al.  REVIEW ARTICLE: Phase-evaluation methods in whole-field optical measurement techniques , 1999 .

[26]  Jong-Ahn Kim,et al.  Optical gauge block metrology in KRISS , 2007 .

[27]  Chris L. Koliopoulos,et al.  Fourier description of digital phase-measuring interferometry , 1990 .

[28]  T. Eiju,et al.  Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm. , 1987, Applied optics.

[29]  K. Creath.  V Phase-Measurement Interferometry Techniques , 1988 .

[30]  R. Thalmann,et al.  European comparison of short gauge block measurement by interferometry , 1995 .

[31]  Daniel Malacara,et al.  Interferogram Analysis For Optical Testing, Second Edition , 2005 .

[32]  Maurice G. Cox,et al.  The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty , 2006 .

[33]  Christos E. Papadopoulos,et al.  Uncertainty estimation and Monte Carlo simulation method , 2001 .

[34]  Jérôme Molimard,et al.  Uncertainty analysis of temporal phase-stepping algorithms for interferometry , 2007 .

[35]  J. Schwider,et al.  Digital wave-front measuring interferometry: some systematic error sources. , 1983, Applied optics.

[36]  J E Decker,et al.  Uncertainty evaluation for the measurement of gauge blocks by optical interferometry , 1997 .