Error-free demodulation of pixelated carrier frequency interferograms

Recently, pixelated spatial carrier interferograms have been used in optical metrology and are an industry standard nowadays. The main feature of these interferometers is that each pixel over the video camera may be phase-modulated by any (however fixed) desired angle within [0,2pi] radians. The phase at each pixel is shifted without cross-talking from their immediate neighborhoods. This has opened new possibilities for experimental spatial wavefront modulation not dreamed before, because we are no longer constrained to introduce a spatial-carrier using a tilted plane. Any useful mathematical model to phase-modulate the testing wavefront in a pixel-wise basis can be used. However we are nowadays faced with the problem that these pixelated interferograms have not been correctly demodulated to obtain an error-free (exact) wavefront estimation. The purpose of this paper is to offer the general theory that allows one to demodulate, in an exact way, pixelated spatial-carrier interferograms modulated by any thinkable two-dimensional phase carrier.