Simultaneous phase and amplitude modulation for dual-sensitivity profilometry of discontinuous objects

Fringe projection profilometry (FPP) is a well-known technique for digitizing solids. In FPP, straight fringes are projected over a digitizing solid, and a digital camera grabs the projected fringes. The sensitivity of FPP depends on the spatial frequency of the projected fringes. The projected fringes as seen by the camera are phase modulated by the surface of the digitizing object; the demodulated phase is usually wrapped. If the digitizing object has discontinuities larger than the fringe period, the phase jumps are lost. To preserve large phase discontinuities, one must use very low spatial frequency (low-sensitivity) fringes. The drawback of low-sensitivity FPP is that the demodulated phase has low signal-to-noise ratio (SNR). Much higher SNR is obtained by projecting shorter wavelength, at the cost of obtaining wrapped phase. A way out of this problem is to use dual-wavelength FPP (DW-FPP). In DW-FPP, two sets of projected fringes are used, one with long wavelength and another with shorter wavelength. Due to harmonics and gamma distortion, in DW-FPP, one usually needs four phase-shifted fringes for each sensitivity. Here we are proposing to combine the two sensitivities simultaneously, one coded in phase (PM) and the other coded in amplitude (AM), in order to obtain phase and amplitude modulated (DW-PAM) fringes. The low-sensitivity phase is coded as AM of the DW-PAM fringes. The main advantage of DW-PAM fringes is that one reduces the number of phase-shifted fringes by half: instead of using eight phase-shifted fringes (four for low and four for high sensitivities), one would need only four DW-PAM fringes. Of course, if one wants to increase the harmonic rejection of the recovered phase, one may use a higher order phase-shifting algorithm (PSA).