With the continuous development of intelligent manufacturing, laser measurement technology increasingly garners widespread attention and application. As an advanced measurement technique, it gradually becomes an essential tool in various domains, including earth science, environmental monitoring, and engineering measurement, providing efficient and precise data support across diverse application scenarios. Current laser measurement methods mainly encompass interferometry, phase method, time-of-flight method, and triangulation method. As a non-contact measurement method, laser triangulation has the advantages of high accuracy, good stability, fast response speed, and low cost. However, at present, laser triangulation is predominantly applied to small-scale and short-range working scenarios, with low measurement accuracy for long-distance measurements. Extending the measurement range of traditional laser triangulation will reduce measurement sensitivity. By using beam folding technology to increase the image distance, it is possible to improve the measurement sensitivity for long-distance measurements without significantly increasing the size of the sensor. Due to the introduction of new mirror units by beam folding technology, the imaging spot noise increases, which restricts the accuracy of subsequent spot positioning. Therefore, denoising processing is essential before spot positioning.

At present, traditional filtering denoising methods such as Gaussian filtering, median filtering, and Lee filtering are characterized by simple logic and high computational efficiency. However, these methods often blur the edges and details in the image while filtering noise and smoothing the image, which can compromise the accuracy of spot positioning. Additionally, these methods require manual adjustment of filtering parameters and exhibit variable effectiveness against complex and unknown types of noise. In recent years, with the rapid development of deep learning, self-supervised denoising networks have been widely studied and applied. These networks do not require noise-free images for training samples and better preserve image details and edges. Therefore, we propose a spot denoising method tailored for long-distance laser triangulation displacement sensors. We first construct a mathematical model of the dual-reflection long-distance laser triangulation method, establish expressions for object displacement and image displacement, and verify the rationality of the dual-reflection path structure through sensitivity analysis. Then, we construct an experimental platform to collect and produce a spot data set and use the Zero-Shot Noise2Noise (ZS-N2N) self-supervised denoising network to denoise the spot image. We assess the algorithm's denoising performance and its impact on spot positioning accuracy under varying noise levels. Finally, we verify the measurement repeatability of the system under different working distances and surface roughness conditions.

We develop a mathematical model for the dual-reflectors long-distance laser triangulation method (Fig. 1), establish a relationship expression for object and image azimuth shifts, and confirm through sensitivity simulation analysis that increasing the image distance via beam folding technology effectively improves system measurement sensitivity (Fig. 2). Based on these simulation results, we confirm the optical component parameters, construct an experimental platform, and create different noise levels of spot image datasets to validate the ZS-N2N denoising method proposed in our study. The results show that in terms of denoising performance, combining peak signal-to-noise ratio (PSNR) and root mean square error (RMSE) indicators, the ZS-N2N method has better comprehensive ability in noise removal and image feature preservation than Gaussian filtering and is superior to median filtering (Fig. 6). In terms of improving positioning accuracy, the ZS-N2N method significantly enhances positioning accuracy under different noise levels, with stable performance compared to the unstable performance of median filtering and Gaussian filtering under different noise levels (Figs. 7?8). In terms of execution efficiency, the ZS-N2N method has a lower execution time than median filtering and Gaussian filtering (Fig. 9). At the same time, in the full-scale experiment of the system, the repeatability of the system is controlled within 2.64 μm using the ZS-N2N method, which is better than median filtering and Gaussian filtering, and compared to median filtering, it can more stably control the repeatability of the system (Figs. 10?11). Finally, in the experiment of surface adaptability, the ZS-N2N method still shows good performance when facing objects with different surface roughness, controlling the repeatability of the system within 4.86 μm, effectively improving the system’s adaptability to different surfaces.

We address the issue of high spot imaging noise in the dual-reflection long-distance laser triangulation displacement measurement system and propose a self-supervised denoising network ZS-N2N for spot image denoising. The feasibility of the dual-reflection light path structure is verified through simulation, and a light path construction spot dataset is created. The denoising performance of the ZS-N2N method is analyzed. The experimental results show that under different noise levels, the ZS-N2N denoising method can effectively improve the peak signal-to-noise ratio of the spot image and the accuracy of subsequent centroid positioning. Moreover, in terms of measurement efficiency, it is superior to traditional image denoising methods such as median filtering and Gaussian filtering. In addition, within the system range, the repeatability accuracy of the system reaches the μm level after using this method. When facing objects with different surface roughness, this method still has excellent denoising performance, effectively improving the system’s adaptability to different surfaces.