How to remove fundamental-frequency phase errors from phase-shifting results

Jan Burke

doi:10.1117/12.928687

13 September 2012 How to remove fundamental-frequency phase errors from phase-shifting results

Jan Burke

Proceedings Volume 8493, Interferometry XVI: Techniques and Analysis; 84930I (2012) https://doi.org/10.1117/12.928687
Event: SPIE Optical Engineering + Applications, 2012, San Diego, California, United States

Abstract

The phase shifting technique, used almost universally across those disciplines in metrology that use fringe analysis, is a powerful method to reconstruct the phase of a periodic signal from very few irradiance samples of a moving fringe pattern. Its known weaknesses, such as susceptibility to incorrect slope or shape of the phase-shift function, or harmonics in the periodic signal, have been treated quite comprehensively by signal-analysis techniques, in particular the characteristic polynomial (CP) theory (Surrel, Appl. Opt 35, 51-60, 1996). I show how to deal with one of the few problems for which the CP theory does not give a direct solution: how do we remove a fundamental-frequency phase error from the result? A straightforward way is found by a variation on standard averaging techniques. The improvement of phase maps is clearly evident in experimental results with 90° nominal phase shift per step, and suggests that the original signal does not always need to be known in detail: it is sufficient to observe the error fringes and tweak the phase-shift formula according to the rules given here. Application of the CP theory to the findings leads to some general conclusions: (i) the averaging can be generalised for any desired behaviour and any phase shift; (ii) to remove a certain harmonic from the phase result, it must be bracketed by CP zeroes at the harmonics above and below it.

Citation Download Citation

Jan Burke "How to remove fundamental-frequency phase errors from phase-shifting results", Proc. SPIE 8493, Interferometry XVI: Techniques and Analysis, 84930I (13 September 2012); https://doi.org/10.1117/12.928687

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