Synchronous phase-demodulation and harmonic rejection of 9-step pixelated dynamic interferograms

We propose a novel synchronous phase-demodulation of pixelated interferograms using squared 3x3 phase-shifted unit-cells. This 3x3 unit-cell is tiled over the CCD image sensor to create a two-dimensional (2D) pixelated carrier. Our synchronous phase-demodulation uses this 2D carrier to demodulate the pixelated interferogram as in the standard 2x2 unit-cell case. The main motivation behind the use of a 3x3 pixelated carrier (instead of the usual 2x2) is its higher harmonic robustness, allowing one to demodulate intensity-distorted fringe patterns. The harmonic rejection robustness of our spatial 3x3 configuration equals the robustness of the temporal least-squares 9-step phase-shifting algorithm (PSA). In other words, extending from the usual 2x2 phase-shifting unit-cell to 3x3 unit-cells, one extends the harmonic rejection of the demodulation algorithm. Finally we also prove that our proposed 9-step, 3x3 pixelated carrier uses the 2D available spectral space more efficiently than using these 9-steps in a linear spatial-carrier configuration.