ABSTRACT
Risley prism scanners are increasingly used for laser beam steering due to their wide angular scanning range and high resolution. However, the inverse problem, which focuses on obtaining the required prisms' orientations for a given target position, has not been perfectly solved so far. The existing inverse solutions are not accurate or efficient enough for high-accuracy and real-time tracking. An iterative method that combines an approximate inverse solution with an iterative refinement by the forward solution is set forth in this paper. Two case studies indicate that the rotation motions of Risley prism pairs controlled by iterative solutions can slew the beam to create the desired tracking pattern quickly and accurately. Based on this method, a Risley prism scanner developed as a standard trajectory generator is implemented for the error measurement of a robotic manipulator in our experiments. The simulation and experimental results show that the inverse solution for one target point can be obtained within nine iterations for a prescribed tracking error threshold.
ABSTRACT
An analytical reverse solution and actual examples are given to show how to direct a laser beam from a pair of orthogonal prisms to given targets in free space. Considering the influences of double-prism structural parameters, a lookup table method to seek the numerical reverse solution of each prism's tilting angle is also proposed for steering the double-prism orientation to track a target position located in the near field. Some case studies, as well as a specified elliptical target trajectory scanned by the cam-based driving double prisms, exhibit the significant application values of the theoretical derivation. The analytic reverse and numerical solutions can be generalized to investigate the synthesis of scanning patterns and the controlling strategy of double-prism tilting motion, the potentials of which can be explored to perform the orientation and position tracking functions in applications of precision engineering fields.
ABSTRACT
Support elements as key components in performing the opto-mechanical function have been an important topic for optical system development. Focusing on a rotation prism with a large aperture and asymmetric loading, a radial multi-segment support is developed to solve the dynamic mounting issue. In order to explore the actual surface deformations over the full rotation, a novel dynamic analysis method to extract the transient load spectrum is established to access the surface deformations, including dynamic load extraction to connect varying loads with corresponding rotation positions, typical position analysis to obtain maximum deformation values, and vibration analysis. The results show that a maximum peak-to-valley value on the plane side reaches 103.16 nm when the prism rotates to 159.84°, and that of the wedge side is 74.38 nm when the prism rotates to 213.84°, both of which are less than λ/4 (λ=632.8 nm). However, when excited by the external loads with response frequency, the surface deformations become more serious. Because the dynamic characteristics obtained can reflect the actual usage situation, the proposed method is preferable for system development.
