2 November 2011 Unified theory of phase unwrapping approaches in multiwavelength interferometry
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Multi-wavelength interferometry (MWI) has a long tradition and provides a solution to a number of applications in the field of optical metrology. In MWI phase unwrapping procedures are usually based on beat wavelength approaches, Chinese Remainder Theorem (CRT) techniques, or the method of Excess Fractions (EF). Each of these unwrapping approaches has distinct advantages making it suitable for a given application. Beat wavelength and CRT based approaches offer a direct calculation of integer fringe order, however, the unambiguous measurement range (UMR) is limited by the available measurement wavelengths. On the other hand, EF offers many alternative sets of wavelengths to achieve a large UMR with high reliability; however, the calculation of the integer fringe order involves a large number of computational steps. In this work, a unified theory of beat wavelength, EF and CRT approaches is reported. It is shown that the calculation of the integer fringe order requires a low computational effort, which hitherto had only been possible for CRT and beat wavelength approaches, whilst offering flexibility in choosing the measurement wavelengths for a given UMR, which had only been the case for EF. As the model can be used in a predictive way to determine the UMR and measurement reliability it is possible to define optimization criteria that are based on parameters which are dependent on the choice of the measurement wavelengths.
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Konstantinos Falaggis, Konstantinos Falaggis, David P. Towers, David P. Towers, Catherine E. Towers, Catherine E. Towers, } "Unified theory of phase unwrapping approaches in multiwavelength interferometry", Proc. SPIE 8011, 22nd Congress of the International Commission for Optics: Light for the Development of the World, 80117H (2 November 2011); doi: 10.1117/12.902646; https://doi.org/10.1117/12.902646

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