High speed fringe projection for dynamic shape measurement using binary phase mask. Part 1: theory and simulation

Projection rates of up to 30,000 greyscale fringe patterns per second have been achieved recently by defocusing binary fringe patterns from a digital micromirror device (DMD) based projector. Part 1 of this two-part paper describes the design of a binary phase mask, based on a virtual scatter plate, for the purpose of enhancing the performance of a binary fringe projector. The phase mask's anisotropic point spread function (PSF) produces a well-defined blur of the fringes parallel to the fringe direction, thereby minimising degradation of fringe contrast. The shape of the PSF is also shown, by means of a polychromatic Fourier optics model, to be insensitive to projection distance over a range of ±10% of the standoff distance. Two new binary fringe design methods are proposed, including extensions to optimize the system performance in the case of a mismatch between camera and projector framing rates. Expressions for the phase noise are derived as a function of the phase mask design parameters, which demonstrate that fringe quality comparable to traditional 8-bit greyscale fringes is achievable at projection rates over two orders of magnitude higher.