Error-corrected fringe discrimination using nonary-encoded patterns for phase-shifting projected fringe profilometry

Most 3D profile measurements based on phase-shifting techniques require additional projected patterns to identify fringe orders for the task of phase unwrapping. The total number of projections is usually more than that used for phase extraction. For surfaces with low signal-to-noise ratios, these approaches might further encounter challenges in phase unwrapping. In this study, an error-corrected scheme for fringe discrimination using nonary-encoded patterns is presented. There is no need to take additional projections for phase unwrapping. The fringe patterns used for phase extraction can be analyzed to obtain the absolute phase directly. Any two adjacent fringes on the inspected surface can be discerned. To identify fringes for surfaces which are projected by only two fringes is available. Even though one of the projected fringes is decoded incorrectly, the error-corrected scheme can detect such a mistake and recover the fringe order.