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13 September 2012 Towards a general theory for MxN pixelated carrier interferometry
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Pixelated phase-mask (PPM) interferometers have become an industry standard for instantaneous phase-shifting interferometry. In commercially available PPM interferometers, an array with 2x2 unit-cells is used, which codify up-to 4 phase-steps within a single PPM interferogram. Recently we have shown that such 2x2 unit-cell arrays allows a harmonic rejection as good as the 4-step leastsquares phase-shifting algorithm (LS-PSA); this harmonics rejection is relatively-low and may not be enough to correctly demodulate some severely intensity distorted fringe patterns. In previous works we have proposed a new PPM with a 3x3 unit-cell to improve the harmonics rejection of the 2x2 array. With this new 3x3 unit-cell one is able to reject as many harmonics as with a 9-step LS-PSA10. In this paper we are extending the analysis of MxN unit-cell synchronous demodulation of PPM. The new results allow us to answer some important open questions about the method: for a given configuration, which harmonics cannot be rejected and why? Why, prior to low-pass filtering, we observe multiple copies of the interferogram’s spectrum and what does this imply? We believe these preliminary results are important contributions towards a formulation of a general theory MxN unit-cell pixelated carrier interferometry.
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J. M. Padilla, M. Servin, J. C. Estrada, and C. A. Gonzalez "Towards a general theory for MxN pixelated carrier interferometry", Proc. SPIE 8493, Interferometry XVI: Techniques and Analysis, 849315 (13 September 2012);

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