Solar thermal power generation is a clean and renewable energy technology that utilizes focusing mirrors to concentrate solar radiation, converting it into high-temperature thermal energy, which is then used to generate electricity. Focusing mirrors play a crucial role in solar thermal power systems and surface shape errors can lead to significant optical efficiency losses. Therefore, accurate measurement of the mirror surface shape is essential. Currently, there are three primary methods for measuring the surface shape of solar focusing mirrors: laser scanning, photogrammetry, and fringe reflection methods. Among these, laser scanning and fringe reflection can obtain the normal data of the mirror surface, while photogrammetry directly captures the three-dimensional (3D) shape data of the mirror. In practical applications, it is often necessary to measure both the normal data to assess optical performance and the 3D shape data for feedback on support point adjustments. To enable fast, batch, and online measurement of mirrors, the fringe reflection method is particularly suitable. Therefore, we explore the theoretical foundations of fringe reflection-based surface shape measurement and propose a 3D surface reconstruction method based on the L-BFGS-B optimization algorithm. The four-step phase-shifting algorithm, normal calculation method, and L-BFGS-B optimization algorithm are described in detail. A fringe reflection measurement system (FRMS) is designed and implemented, enabling the normal measurement and 3D surface reconstruction of heliostat mirrors.

In this study, we use the fringe reflection method to acquire the normal data of the mirror surface, followed by 3D surface reconstruction using the L-BFGS-B algorithm. Initially, sinusoidal patterns with varying brightness are projected onto a screen via a projector. The patterns, after reflecting off the measured mirror, form an image on the camera, and images with different periods and phases are captured. Subsequently, the four-step phase-shifting algorithm is used to process the images and determine the coordinates of point T on the screen corresponding to point P on the captured image. Through coordinate transformations, the coordinates of point M on the mirror surface, point P on the image, and point T on the screen are unified in the same coordinate system. The direction vectors of the incident light MT and the reflected light PM are calculated. According to the law of reflection, the normal vector at point M on the mirror surface is determined. From the normal data, the 3D surface profile of the mirror is reconstructed using the L-BFGS-B algorithm. Lastly, the surface height of the focusing mirror is measured using a FARO Vantage laser tracker, and the results are compared with experimental outcomes to verify the accuracy of the reconstruction.

A FRMS is designed and developed (Fig. 5) for experiments on a focusing mirror with dimensions of 2060 mm×1605 mm. By processing the captured stripe images (Fig. 6), the normal distributions of the mirror surface along the X and Y axes are obtained (Fig. 7). Using the normal data acquired through the system, a 3D reconstruction of the mirror surface is performed, producing a height distribution map [Fig. 8(a)]. To validate the accuracy of this height distribution, the surface is pre-measured with the FARO Vantage laser tracker. The point cloud data obtained from the laser tracker [Fig. 8(b)] are then interpolated to yield the height distribution [Fig. 8(c)]. A comparison between the results from the fringe reflection method and the laser tracker [Fig. 8(d)] reveal a root mean square (RMS) deviation of 0.22 mm in the height measurements between the two methods.

Solar concentrator mirrors are essential components in solar thermal power generation systems, and their surface shape accuracy significantly affects the optical efficiency of the system. In this study, we propose a method for surface shape measurement of solar concentrator mirrors based on fringe reflection, addressing the need for fast, batch, and online detection. The four-step phase-shift algorithm and the method for calculating surface normals are detailed. We also propose a surface reconstruction technique using the L-BFGS-B optimization algorithm, leading to an accurate height distribution of the mirror surface. A FRMS is designed and validated through the measurement and reconstruction of a 2060 mm×1605 mm mirror. The system’s accuracy is verified through comparison with measurements obtained from a FARO Vantage laser tracker, showing an RMS deviation of 0.22 mm between the two methods.