Analytic measurement of mirror surfaces by a single shot with united modeling of incident rays

In this study, an analytic measurement system is developed to reconstruct the 3D shapes of mirror surfaces. Its principle is to compute the interception points of the incident rays and the corresponding emergent rays reflected by the mirror surface. The laser rays are produced by projecting a dot pattern using a pico laser projector and each bright dot corresponds to one single laser ray. To obtain more laser rays and a more detailed reconstruction, the distance between adjacent dots needs to be as small as possible. During the practical implementation, it is found that its sensitivity to noise increases abruptly when the adjacent distances between rays are relatively small. To reduce the noise and improve the reconstruction accuracy, a united modeling method is proposed properly. After each laser ray has been modeled separately and their equations are known, they are modeled as a whole based on the working scheme of the laser projector. The united modeling restricts the freedom of the ray distribution as a whole and thus reduces the noise greatly. In addition, the proposed united modeling method can rectify the optical distortion introduced by the projector and thus the additional projector calibration is avoided. Experimental results verified both the effectiveness of the proposed united modeling method and the effectiveness of the developed analytic measurement system.