Large scale measurement plays a pivotal role in the manufacturing and assembly process of substantial equipment such as ships and airplanes. The distributed multi-base station measurement systems, represented by workshop measurement and positioning systems (wMPSs), have been widely used in large-scale measurement due to their characteristics of real-time, multiple objectives and tasks, high precision, and high efficiency. wMPS is made up of numerous transmitters and photoelectric receivers that are spread throughout space, and each transmitter emits two fan-shaped laser beams that rotate and scan the entire space. The model parameters used to fit the spatial surface shape of the scanning light are referred to as internal parameters. The initial observation of the instrument refers to how long it takes for the scanning light to reach the photoelectric receiver. By converting the scanning time into spatial azimuth, single station scanning angle measurement can be accomplished. Furthermore, employing an internal parameter model facilitates the achievement of multi-station spatial rendezvous, enabling the calculation of three-dimensional coordinates. The accurate description of the scanning light spatial surface by the internal reference model is crucial for ensuring the measurement precision of the instrument. The scanning laser used in wMPS disperses the point light source emitted by the semiconductor laser into a linear laser through a cylindrical mirror, thereby forming a light plane in space. Previous research has shown that optical non-uniformity, geometric errors, and assembly errors of cylindrical mirrors in lasers can induce small deformations of the optical surface in various shapes and directions when deviating from the ideal plane within large spatial domains. Therefore, the spatial surface depicted by the traditional in-plane parametric model, which assumes the scanning light surface to be an ideal plane, may not fully correspond to the actual surface, leading to systematic errors in the measurement outcomes. During the laser production process, the machining quality and assembly error of cylindrical mirrors exhibit a certain degree of randomness, rendering the optical surface deformation intricate and challenging to anticipate. Hence, devising an accurate assessment method for evaluating scanning optical surfaces and establishing a more precise internal parameter model based on the evaluation outcomes hold paramount significance for enhancing the measurement accuracy of wMPS.

We propose a novel approach for evaluating the scanning light surface shape. By fixing the wMPS transmitter on a turntable and using the turntable to drive the elevation angle of the transmitter to rotate instead of the photoelectric receiver rotating around the transmitter, it achieves subdivision sampling of different positions on the scanning light surface. On this basis, a mapping relationship between surface deformation information and the scanning time of the instrument’s original observation is established, and the scanning light surface is accurately evaluated by the difference between the ideal scanning time and the measurement time. Building upon these evaluations, a partition plane parameter model is proposed, which divides the space into multiple sub-regions based on the elevation angle. The positions for region segmentation are determined using a differential evolution algorithm, which improves the fitting effect of the parameter model and reduces instrument system errors. At the same time, it overcomes the drawbacks of low computational efficiency and high model complexity of folded and curved models. Finally, the effectiveness of the proposed research method is validated by comparing the fitting performance and coordinate measurement accuracy of the new and old internal reference models on the scanning light surface, verifying the effectiveness of the research method.

We validate the proposed theory using the wMPS transmitter, which is fixed on a turntable with precision tooling (Fig. 4). The transmitter’s elevation angle is systematically altered at fixed intervals, and the scanning time of the two received scanning light surfaces by the photoelectric receiver is recorded. After normalizing the obtained data, a comparison is made with the ideal scanning time when the light surface is an ideal plane. The deformation of each scanning light surface relative to the ideal plane is obtained, and multiple experiments are repeated at different calibration distances. The experimental results reveal a consistent relationship between the deformation of the light surface and the distance (Fig. 5). Based on the evaluation results of the scanned light surface, the region segmentation angle of the partition plane model was determined using the differential evolution algorithm. Subsequently, the model parameters were calibrated using a high-precision coordinate field (Fig. 8, Table 1). By fitting the residuals, comparisons are made with the ideal plane model and the folded plane model (Fig. 9). For surface 1, the partition plane model, the residuals exhibit a 40% and 26% reduction in residuals on average compared to the ideal plane model and the folded plane model, respectively. For surface 2, these reductions are 10% and 6%, indicating a correlation between the improvement of the partition plane model’s fitting effect and the magnitude of surface deformation. Furthermore, a wMPS measurement network is constructed and the coordinate measurement accuracy of different models is compared. The results (Fig. 10) show that compared to the ideal plane model and the folded plane model, the partition plane model can reduce coordinate measurement errors by about 35% and 22% on average, respectively, thus establishing it as a parameter model with enhanced accuracy.

The inaccurate evaluation of the scanning light surface shape and poor fitting performance of the parameter model in the workshop measurement and positioning system lead to systematic measurement errors. We propose a method for evaluating the surface shape by establishing a mapping relationship between the surface deformation information and the scanning time of the instrument’s original observation. By analyzing error influencing factors, more accurate scanning of light surface shape data can be obtained. On this basis, it is proposed to use a differential evolution algorithm to calculate the optimal segmentation angle and divide the measurement space into multiple sub-regions of the partition plane parameter model, effectively improving the fitting effect of the parameter model while also considering the computational efficiency.