Objective   The prism scanning system is used to achieve optical imaging with both large field of view and high resolution by adjusting the beam direction or optic axis. It is widely used in optical reconnaissance, laser communication, lidar, etc. In airborne laser imaging lidar, the prism scanning system, as a transmission scanning structure, has high optical utilization, effectively reduces the volume of the system, and has the advantages of low power consumption, high precision and good stability. In array imaging lidar, high energy efficiency, high resolution, and broad field detection are all achieved by means of array beam illumination and Risley-prism scanning. However, when sub-beams are obliquely incident on the prism, the rotational symmetry of the traces of ray propagation is broken, the beam deflection of the sub-beams through the prism is different, and the regular beam array produces shape distortion, resulting in beam pointing error and affecting the position accuracy of the point cloud. Therefore, it is necessary to analyze the rules of beam array distortion to improve the accuracy of the point cloud.

  Methods   The conical scanning mode that combines the array beam and prism is broken down into multi-beam parallel scanning with numerous incident angles, and the propagation characteristics of the array beam are thoroughly described by the propagation characteristics of all sub-beams (Fig.2). The three-dimensional vector optical approach is used to establish the laser transmission process of the array beam through a Risley-prism (Fig.3), and the relationship between the pointing variation of the sub-beam and the scanning angle of the prism is obtained (Fig.4). The association between beam pointing variability and point cloud data quality is demonstrated by the numerical simulation of imaging process with prism scanning by flight experiment of airborne lidar (Fig.6-7).

  Results and Discussions   When the array beam is orthographically and obliquely incident into the prisms with different angles, the beam steering of the prism to each sub-beam is different at various scanning angles (Fig.5(a)). The spatial shape distortion analysis of the array beam is based on the spatial angle difference between the outgoing sub-beam and the central sub-beam. When the prism rotates one cycle, the spatial shape distortion of the array beam is shown (Fig.6(b)). The quality of point cloud data affected by the array beam distortion is evaluated by using plane fitting RMS value as the quantitative index of point cloud position accuracy (Fig.7). Simulation results of ground scanning imaging process of prism in airborne lidar indicate that the plane error RMS is approximately 5 cm at a navigation height of 0.5 km (Fig.8(a)), which varies linearly with navigation height, and slopes at a rate of around 0.1 m/km in prism scanning system with beam array (3×3) (Fig.8(b)) and the accuracy of point cloud plane decreases with the increase of array beam scale (Fig.9) and sub-beam angular separation (Fig.10).

  Conclusions   The combination of array beam illumination and prism scanning improves the energy utilization, spatial resolution and detection field of view of airborne lidar system. However, the shape distortion of array beam leads to beam pointing error and affects the accuracy of point cloud position. The array beam incidence prism includes orthographic and oblique incidence. The oblique sub-beam destroys the rotational symmetry of the beam propagating in the prism, and the beam steering ability is different at different scanning positions. Furthermore, the larger the oblique angle is, the stronger the steering ability of the prism to the beam is. Given that the above two work together, the time-varying array beam is emitted when the regular array beam is incident. The relationship between beam pointing error and spatial position error is obtained by using the three-dimensional vector optics method. The increase of the incident angle of the sub-beam and the altitude will lead to the dispersion of the point cloud and the decrease of the data quality. The law of beam array distortion during prism scanning lays a foundation for the correction of subsequent airborne flight test data, especially for the improvement of position accuracy of medium and long-distance airborne lidar. In addition, it provides a reference for the design of array beam combined with multi-prism scanning system.