Exact Scan Patterns of Rotational Risley Prisms Obtained with a Graphical Method: Multi-Parameter Analysis and Design

Development of a near-infrared single-photon 3D imaging LiDAR based on 64×64 InGaAs/InP array detector and Risley-prism scanner

A near-infrared single-photon lidar system, equipped with a 64×64 resolution array and a Risley prism scanner, has been engineered for daytime long-range and high-resolution 3D imaging. The system's detector, leveraging Geiger-mode InGaAs/InP avalanche photodiode technology, attains a single-photon detection efficiency of over 15% at the lidar's 1064 nm wavelength. This efficiency, in tandem with a narrow pulsed laser that boasts a single-pulse energy of 0.5 mJ, facilitates 3D imaging capabilities for distances reaching approximately 6 kilometers. The Risley scanner, composing two counter-rotating wedge prisms, is designed to perform scanning measurements across a 6-degree circular field-of-view. Precision calibration of the scanning angle and the beam's absolute direction was achieved using a precision dual-axis turntable and a collimator, culminating in 3D imaging with an exceptional scanning resolution of 28 arcseconds. Additionally, this work has developed a novel spatial domain local statistical filtering framework, specifically designed to separate daytime background noise photons from the signal photons, enhancing the system's imaging efficacy in varied lighting conditions. This paper showcases the advantages of array-based single-photon lidar image-side scanning technology in simultaneously achieving high resolution, a wide field-of-view, and extended detection range.

An Automatic Calibration Method for the Field of View Aberration in a Risley-Prism-Based Image Sensor

Risley-prism-based image sensors can expand the imaging field of view through beam control. The larger the top angle of the prism, the higher the magnification of the field of view, but at the same time, it aggravates the problem of imaging aberrations, which also puts higher requirements on the aberration correction method for the Risley-prism-based image sensor. To improve the speed, accuracy, and stability of the aberration correction process, an automatic calibration method for the Risley-prism-based image sensor is proposed based on a two-axis turntable. The image datasets of the calibration plate with different prism rotation angles and object distances are acquired using a two-axis turntable. Then, the images of the calibration plate are pre-processed using the bicubic interpolation algorithm. The calibration parameters are finally calculated, and parameter optimization is performed. The experimental results verify the feasibility of this automated calibration method. The reprojection error of the calibration is within 0.26 pixels when the distance of the imaging sensor is 3.6 m from the object, and the fine aberration correction results are observed.

Scale-adaptive three-dimensional imaging using Risley-prism-based coherent lidar

We present a scale-adaptive three-dimensional (3D) imaging architecture for coherent light detection and ranging (lidar) that incorporates Risley-prism-based beam scanning. An inverse design paradigm from beam steering to prism rotation is developed for demand-oriented beam scan pattern generation and prism motion law formulation, which allows the lidar to perform 3D imaging with adaptive scale and configurable resolution. By combining flexible beam manipulation with simultaneous distance and velocity measurement, the proposed architecture can achieve both large-scale scene reconstruction for situational awareness and small-scale object identification against long range. The experiment results demonstrate that our architecture enables the lidar to recover a 3D scene in a ±30° field of view and also focus on distant objects at over 500 m with spatial resolution up to 1.1 cm.

Single-Camera Three-Dimensional Digital Image Correlation with Enhanced Accuracy Based on Four-View Imaging

Owing to the advantages of cost-effectiveness, compactness, and the avoidance of complicated camera synchronization, single-camera three-dimensional (3D) digital image correlation (DIC) techniques have gained increasing attention for deformation measurement of materials and structures. In the traditional single-camera 3D-DIC system, the left and right view images can be recorded by a single camera using diffraction grating, a bi-prism, or a set of planar mirrors. To further improve the measurement accuracy of single-camera 3D-DIC, this paper introduces a single-camera four-view imaging technique by installing a pyramidal prism in front of the camera. The 3D reconstruction of the measured points before and after deformation is realized with eight governing equations induced by four views, and the strong geometric constraints of four views can help to improve the measurement accuracy. A static experiment, a rigid body translation experiment, and a four-point bending experiment show that the proposed single-camera 3D-DIC method can achieve higher measurement accuracy than the dual-view single-camera 3D-DIC techniques and that the single-camera 3D-DIC method has advantages in reducing both random error and systematic error.

Demonstration of a Fizeau Directly-Imaging Sparse-Aperture Telescope with Pointing and Tracking Capabilities

At present, the majority of sparse-aperture telescopes (SATs) are unable to observe moving targets. In this paper, we describe the construction of and present the results obtained using a Fizeau directly-imaging sparse-aperture telescope (FDISAT) that permits pointing and the tracking of moving targets. The telescope comprises three sub-apertures, each of which is equipped with a Risley prism system that permits a maximum tracking range of 5° and has independent boresight adjustment capability. On targets in various positions, experiments with pointing and tracking are conducted. The maximum root-mean-square error (RMSE) of pointing in the sub-apertures was found to be 8.22 arcsec. When considering a target moving at 0.01°/s for approximately 320 s, the maximum RMSE of tracking in the sub-apertures was found to be 4.23 arcsec. The images obtained from the focal plane detector exhibit clear interference fringes while tracking. The experimental results demonstrate that the system can effectively track moving targets, providing a method for SAT observation of moving targets.

Multivariable Decoupling and Nonlinear Correction Method for Image-Based Closed-Loop Tracking of the Risley Prisms System

Image-based closed-loop tracking (IBCLT) is an important part of the process of target tracking. The Risley prism system has a unique advantage in improving the target tracking ability because of its compact and lightweight structure. Compared with traditional target tracking equipment, the Risley prism system has two difficulties in the process of IBCLT. First, the Risley prism is a complex coupling system of double input and double output. Second, the Risley prism itself is a nonlinear system. These problems lead to decrease in dynamic response and inconsistent target tracking capabilities. Thus, this paper proposes a method to implement multivariable decoupling and reduce the nonlinear effect. First, the boresight error of IBCLT is decoupled to the azimuth and elevation directions by the rotation matrix error-decoupling (RMED) method. Second, the gains of IBCLT in azimuth and elevation directions are independent variables that comes from two functions of the target elevation angle. The experimental results show that the IBCLT error deviation of different static targets in the field of view is within 0.025 arcsec, which is 70% lower compared with the fixed gain method. Furthermore, the steady-state error deviation of moving targets is controlled within 2.5 arcsec. These experimental results prove the feasibility and effectiveness of the proposed method.

Low-Cost 3D-Printed Electromagnetically Driven Large-Area 1-DOF Optical Scanners

In this paper, we demonstrate 3D-printed 1-DOF (one torsional axis; 1 degree of freedom) optical scanners with large mirror areas (up to 20 × 20 mm2). Each device consists of an aluminum-coated square silicon substrate serving as the mirror, two miniature permanent magnets, an electromagnet, and a 3D-printed structure including the mirror frame, torsion springs, and base. One device can reach a static half optical scan angle of 14.8 deg., i.e., a full optical scan angle of 29.6 deg., at 12 VDC; this particular device exhibits a mechanical resonance frequency of 84 Hz. These scanners can be a potential, low-cost alternative to the expensive conventional galvanometer scanners.

Optomechanical Analysis and Design of Polygon Mirror-Based Laser Scanners

Polygon Mirror (PM)-based scanning heads are one of the fastest and most versatile optomechanical laser scanners. The aim of this work is to develop a multi-parameter opto-mechanical analysis of PMs, from which to extract rules-of-thumbs for the design of such systems. The characteristic functions and parameters of PMs scanning heads are deduced and studied, considering their constructive and functional parameters. Optical aspects related to the kinematics of emergent laser beams (and of corresponding laser spots on a scanned plane or objective lens) are investigated. The PM analysis (which implies a larger number of parameters) is confronted with the corresponding, but less complex aspects of Galvanometer Scanners (GSs). The issue of the non-linearity of the scanning functions of both PMs and GSs (and, consequently, of their variable scanning velocities) is approached, as well as characteristic angles, the angular and linear Field-of-View (FOV), and the duty cycle. A device with two supplemental mirrors is proposed and designed to increase the distance between the GS or PM and the scanned plane or lens to linearize the scanning function (and thus to achieve an approximately constant scanning velocity). These optical aspects are completed with Finite Element Analyses (FEA) of fast rotational PMs, to assess their structural integrity issues. The study is concluded with an optomechanical design scheme of PM-based scanning heads, which unites optical and mechanical aspects—to allow for a more comprehensive approach of possible issues of such scanners. Such a scheme can be applied to other types of optomechanical scanners, with mirrors or refractive elements, as well.

Multiview three-dimensional imaging using a Risley-prism-based spatially adaptive virtual camera field

We present a three-dimensional (3D) imaging system that incorporates a stationary camera and Risley prisms. By planning prism rotation to generate a spatially adaptive virtual camera field, the system allows multiple virtual cameras in the field to capture any object from different perspectives for 3D reconstruction. An automatic virtual camera calibration method based on perspective projection and geometric optics is developed to enable virtual camera field construction and characterization. Moreover, a 3D computational reconstruction framework is proposed for multiview information fusion using the virtual camera field. This framework combines nonlinear distortion correction with epipolar geometry computation to efficiently perform image rectification and stereo matching, which can further facilitate 3D object reconstruction through multiview triangulation. The experiments on synthetic and real data validate the feasibility and flexibility of our 3D imaging technique.

Analytic solution for double optical metasurface beam scanners

Optical metasurfaces are researched more and more intensively for the possible realization of lightweight and compact optical devices with novel functionalities. In this paper, a new beam-steering system based on double metasurface lenses (metalenses) is proposed and developed. The proposed system is lightweight, small volume, low cost, and easy to integrate. The exact close-form forward and numerical inverse solutions are derived respectively using the generalized Snell's law of refraction. Given the orientations of the double metalenses, the pointing position can be accurately determined. If the desired pointing position is given, the required metalenses' orientations can be obtained by applied global optimization algorithms to solve nonlinear equations related to the inverse problem. The relationships of the scan region and blind zone with the system parameters are derived. The method to eliminate the blind zone is given. Comparison with double Risley-prism systems is also conducted. This work provides a new approach to control light beams.

Inverse Solution Error Analysis and Correction of Beam Steering System Based on Risley Prisms

The pointing accuracy of the Risley prisms beam-steering system mainly depends on the accuracy of the solution method and the impact of the error on the solution. To improve pointing accuracy, the impact of systematic errors on the inverse solution precision is investigated and a correction method is proposed. First, a more accurate error model for Risley prisms is established, and the errors are obtained by the parameter identification method, which corrects the forward solution error. Second, we explain the reason for the error generated by the inverse solution and analyze the variation of the inverse solution error magnitude with the beam deflection angle. A correction method based on pointing-field transformation is proposed. Finally, simulations and experiments are performed to verify the feasibility of the method. Experimental results show that when the beam deflection angle is equal to 0.1°, the maximum and RMS values of the pointing error are reduced by 94.08% and 95.18%, respectively.