## 5 Conclusions  
This paper proposes a novel method of calibrating system parameters for the PMD technique. The method uses a reference mirror with a matrix of hollow ring markers to determine the orientations of two LCD screens in the same camera coordinate system, by displaying orthogonal sinusoidal fringe patterns on the screens using phase data. This allows the two system parameters \(d_{1}\) and \(d_{2}\) to be calibrated in the camera coordinate system. The calibrated DPMD system was tested with an artificial specular mirror with known distances between steps, and a standard concave mirror of known radius. The experimental results validated the effectiveness and reliability of the proposed calibration method for the system parameters.  
The proposed calibration method has the following advantages: (1) The parameters of the DPMD system are calibrated using phase information calculated from sinusoidal fringe patterns. The digital phase calibration board has been designed to calibrate the position of LCD screens instead of geometric feature points. Because the plane and screen are different distances from the imaging device, they cannot be clearly captured, given the limited DOF of the lens. Using the phase target can solve this problem efficiently; (2) The calibrated DPMD system can measure specular objects that have discontinuous and/or isolated surfaces; (3) The mirror surface is selected as the reference plane, making it unnecessary to replace components, and ensuring an accurate reference position. Also, the proposed calibration method can obtain the two parameters in the same way, so that it does not need to remove the board in the measuring system after calibration, which is more convenient.  
Figure 12: Measurements on the artificial specular step: (**a**) one captured fringe pattern reflected by the step; (**b**) one absolute phase map from the reflected fringe patterns; (**c**) measured 3D shape of the step and (**d**) profile map of the step.  
Of course, this paper also considered several factors which would affect the accuracy of whole calibration process. Firstly, [PERSON]'s method was used instead of the traditional ellipse fitting method to calculate the real projection center to reduce the error as much as possible, as it has been proven to have a higher accuracy. Secondly, gamma correction by encoding the initial fringes was applied to reduce the influence of nonlinear distortion. However, the influence of a finite width of the beam splitter, the accuracy evaluation of phase matching principle and other error sources for calibration also need to be studied in further experiments.  
Conceptualization, Z.Z., N.G. and X.D.; methodology, Z.Z.; software, X.D.; validation, X.D.; formal analysis, Z.Z., N.G. and X.D.; investigation, X.D.; resources, Z.Z. and N.G.; data curation, Z.Z., N.G. and X.D.; writing--original draft preparation, X.D.; writing--review and editing, Z.Z., N.G. and X.D.; visualization, X.D.; supervision, Z.Z.and N.G.; project administration, Z.Z.; funding acquisition, Z.Z.  
This research was funded by the National Key R&D Program of China (under Grant No. 2017 YFF0106404), the National Natural Science Foundation of China (under Grant No. 51675160), and the Talents Project Training Funds in Hebei Province (under Grant No. A201500503).  
The authors declare no conflict of interest.