Absolute height measurement of specular surfaces with modified active fringe reflection photogrammetry

Deflectometric methods have been studied for more than a decade for slope measurement of specular freeform surfaces through utilization of the deformation of a sample pattern after reflection from a tested sample surface. Usually, these approaches require two-directional fringe patterns to be projected on a LCD screen or ground glass and require slope integration, which leads to some complexity for the whole measuring process. This paper proposes a new mathematical measurement model for measuring topography information of freeform specular surfaces, which integrates a virtual reference specular surface into the method of active fringe reflection photogrammetry and presents a straight-forward relation between height of the tested surface and phase signals. This method only requires one direction of horizontal or vertical sinusoidal fringe patterns to be projected from a LCD screen, resulting in a significant reduction in capture time over established methods. Assuming the whole system has been precalibrated during the measurement process, the fringe patterns are captured separately via the virtual reference and detected freeform surfaces by a CCD camera. The reference phase can be solved according to the spatial geometric relation between the LCD screen and the CCD camera. The captured phases can be unwrapped with a heterodyne technique and optimum frequency selection method. Based on this calculated unwrapped-phase and that proposed mathematical model, absolute height of the inspected surface can be computed. Simulated and experimental results show that this methodology can conveniently calculate topography information for freeform and structured specular surfaces without integration and reconstruction processes.