Abstract
Phase reconstruction from intensity measurements in interferometry is classically solved by phase-shifting or phase-stepping techniques. At each pixel a sequence (set) of intensity measurements is taken, and between those measurements the bias phase is changed in a most precise manner (i.e. "phase-stepping"). High accuracy of the computed phases in each pixel is achieved by knowing the individual intensities but especially also the global bias-phase of every interferogram in the set. The obvious problem, that the bias-phase is a delicate quantity, highly error prone due to vibrations, air-turbulence and wavelength-instability of the laser has conventionally been tried to address by special phase-shifting formulas [1-6]. These enable correct phase reconstruction even with linear or quadratic phase-stepping errors as well as with non-linearity of the characteristic detector curve and also mitigate the effect of multiple reflections within the Fizeau-cavity.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kuchel, M.: Method and apparatus for phase evaluation of pattern images used in optical measurement. US patent 5,361,312 (1994)
De Groot, P.: Phase shifting interferometer and method for surface topography measurement. US patent 5,473,434 (1995)
Surrel, Y.: Design of algorithms for phase measurements by the use of phase stepping. Appl. Opt. 35, 51–60 (1996)
Küchel, M.: Some Progress in Phase Measurement Techniques. In: Jüptner, W., Osten, W. (eds.) Fringe 1997, Automatic Processing of Fringe Patterns, pp. 27–44. Akademie Verlag (1997)
Hibino, K., Oreb, B., Farrant, D., Larkin, K.: Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts. J. Opt. Soc. Am. 14, 918–930 (1997)
Zhu, Y., Gemma, T.: Method for designing error-compensating phase-calculation algorithms for phase-shifting interferometry. Appl. Opt. 40, 4540–4546 (2001)
Rathjen, C.: Statistical properties of phase-shift algorithms. J. Opt. Soc. Am. A 12, 1997–2008 (1995)
Hibino, K.: Susceptibility of systematic error-compensating algorithms to random noise in phase-shifting interferometry. Appl. Opt. 36, 2084–2093 erratum 5362 (1997)
Koliopoulos, C.: Simultaneous phase-shift interferometer. In: Proc. SPIE, vol. 1531, pp. 119–127 (1992)
Novak, M., Millerd, J., Brock, N., North-Morris, M., Hayes, J., Wyant, J.: Analysis of a micro-polarizer array based simultaneous phase-shifting interferometer. Appl. Opt. 44, 6861–6868 (2005)
Takeda, M., Hideki, I., Kobayashi, S.: Fourier-transform method of fringe-pattern analysis for computer based topography and interferometry. J. Opt. Soc. Am. 72, 156–160 (1982)
Kuechel, M.: The new Zeiss interferometer. In: Proc. SPIE, vol. 1332, pp. 655–663 (1990)
Sykora, D., Holmes, M.: Dynamic measurements using a Fizeau interferometer. In: Proc. SPIE 8082, article id. 80821R (2011)
Freischlad, K., Küchel, M., Schuster, K.-H., Wegmann, U., Kaiser, W.: Real-time wavefront measurement with lambda/10 fringe spacing for the optical shop. In: Proc. SPIE, vol. 1332, pp. 18–24 (1990)
Sykora, D., Kuechel, M.: In situ calibration of interferometers. Patent application US 20130063730 A1 (2013)
Lai, G., Yatagai, T.: Generalized phase-shifting interferometry. J. Opt. Soc. Am. A 8, 822–827 (1991)
Broistedt, H., Dolca, N., Strube, S., Tutsch, R.: Random-phase-shift Fizeau interferometer. Appl. Opt. 50, 6564–6575 (2011)
Küchel, M., Hof, A.: Method for analyzing periodic brightness patterns. US patent, 5,343,294 (1994)
Küchel, M., Wiedmann, W.: In-process metrology for large astronomical mirrors. In: Proc. SPIE, vol. 1333, pp. 280–294 (1990)
Farrell, C.T., Player, M.A.: Phase step measurement and variable step algorithms in phase-shifting interferometry. Meas. Sci. Techol. 3, 953–958 (1992)
Farrell, C.T., Player, M.A.: Phase-step insensitive algorithms for phase-shifting interferometry. Meas. Sci. Technol. 5, 648–652 (1994)
Han, G.-S., Kim, S.-W.: Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting. Appl. Opt. 33, 7321–7325 (1994)
Gao, P., Yao, B., Lindlein, N., Mantel, K., Harder, I., Geist, E.: Phase-shift extraction for generalized phase-shifting interferometry. Opt. Lett. 34, 3553–3555 (2009)
Xu, J., Xu, Q., Chai, L.: Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts. Appl. Opt. 47, 480–485 (2008)
Xu, J., Xu, Q., Chai, L., Wang, H.: Direct phase extraction from interferograms with random phase shifts. Opt. Exp. 18, 20620–20627 (2010)
Schmit, J., Munteanu, F.: Limitations of iterative least squares methods in phase shifting interferometry in the presence of vibrations. In: Proc. SPIE, vol. 5965 (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Küchel, M.F. (2014). Quasi Ellipse Method Enabling High Accuracy Phase Reconstruction with Random Phase Steps in Fizeau-Interferometers. In: Osten, W. (eds) Fringe 2013. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36359-7_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-36359-7_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36358-0
Online ISBN: 978-3-642-36359-7
eBook Packages: EngineeringEngineering (R0)