Theoretical analysis, simulated mathematical model and testing experiments have been performed and some outcomes have been achieved.
1)Direct phase measuring deflectometry (DPMD) based on color fringe pattern technique. A new technique of DPMD and its performance have been studied. A) The relevant techniques regarding classical PMD and the improved PMD technique have been reviewed. Some influential factors on the measured results are presented. The challenges and future research directions are discussed to further advance PMD techniques. Finally, the application fields of PMD are briefly introduced. B) A new DPMD method has been developed to measure the full-field 3D shape of complicated specular objects. A mathematical model is derived to directly relate an absolute phase map to depth data. A full-field 3D measuring system is developed. Sinusoidal fringe patterns having the optimum fringe numbers are generated by software and synchronously displayed on two screens. A color CCD camera captures the two sets of deformed color fringe pattern images. Experimental results show that the proposed DPMD method measures the full-field 3D shape of specular objects having isolated and/or discontinuous surfaces accurately and effectively. C) A new virtual measurement system has been developed to optimize the system parameters and evaluate the system’s performance in DPMD applications. Four system parameters have been analyzed to obtain accurate measurement results. Experiments are performed using simulated and actual data and the results confirm the effects of these four parameters on the measurement results.
2)Simple, flexible and automatic 3D system calibration for DPMD. For calibrating the relationship between absolute phase map and 3D shape data, the internal parameters of the CCD camera and the system parameters need to be determined. A) A novel camera calibration method has been developed by using an iterative distortion compensation algorithm. First, the initial parameters of the camera are calibrated by full-field camera pixels and the corresponding points on a phase target. Then, an iterative algorithm is proposed to compensate for the distortion. Finally, a 2D fitting and interpolation method is developed to enhance the accuracy of the phase target. B) A new distance calibration method has been studied. The direction of a mobile stage in the camera coordinate system is determined by the mirror’s pattern at several positions in the camera’s depth of field (DOF). The screen’s position can also be calibrated by displaying patterns at a known scale. The experimental results on an artificial stepped mirror and a reflected diamond distribution surface demonstrate the accuracy and practicality of the proposed method.
3)Error sources analysis and their compensation to obtain high accurate 3D shape data. For the proposed DPMD, the main error sources of chromatic aberration (CA) between color channels and non-linear response of the system have been studied. A) A full-field calibration method based on absolute phase maps has been studied. Red, green, and blue closed sinusoidal fringe patterns are generated, consecutively displayed on an LCD, and captured by a color camera from the front viewpoint. The phase information of each color fringe is obtained using a four-step phase-shifting algorithm and optimum fringe number selection method. These pixel deviations can be computed by comparing the unwrapped phase data of the red, blue, and green channels in polar coordinates. CA calibration is accomplished in Cartesian coordinates. The systematic errors introduced by the LCD are analyzed and corrected. Simulated results show the validity of the proposed method and experimental results demonstrate that the proposed full-field calibration method based on absolute phase maps would be useful for practical software-based CA calibration. B) A generic exponential fringe model has been proposed to express as an exponential function of the generated fringe patterns. Based on this model, a straightforward non-linear correction method is presented to alleviate phase error without the need for any estimation of non-linear coefficients or complex calibration. An exponential fringe projection method is also proposed based on principal component analysis (PCA) to alleviate phase error without requiring any complicated prior and post data. Experimental results demonstrate that the proposed method improves the quality of measurements by suppressing phase error and needs low computational cost by compared with the existing state of the art methods.
