The spherical pair has an important role in the inner frame of the stabilization mechanism of the aviation optoelectronic pod. However, its two-degrees-of-freedom (2-DOF) angular displacement signal is difficult to detect, seriously restricting its application in aviation optoelectronic pods. Therefore, this study proposes a new method to measure a spherical pair’s 2-DOF angular displacement using a spherical capacitive sensor. The capacitive sensor presented by this method realizes the measurement of the 2-DOF angular displacement of the spherical pair by integrating the spherical electrode groups in the ball head and the ball socket of the spherical pair. First, based on the geometric structure of the spherical pair, the structure of the capacitive sensor is designed, and the mathematical model for the capacitive sensor is deduced. Then, the sensor’s output capacitance, in different directions, is simulated by Ansoft Maxwell software. Finally, an experiment device is built for the measurement experiments. The simulation analysis and experimental results show that the spherical capacitive sensor has an approximately linear output in different directions, and the measured output capacitance is as high as $89.7\%$ of the theoretical value. Compared with the existing sensors that measure the 2-DOF angular displacement signal of the ball pair, the sensor proposed in this study has an integrated structure, which can be integrated into the spherical pair. That makes it possible to apply the spherical pair to the inner frame of the aviation optoelectronic pod.

Conventional eddy-current sensors have the advantages of being contactless and having high bandwidth and high sensitivity. They are widely used in micro-displacement measurement, micro-angle measurement, and rotational speed measurement. However, they are based on the principle of impedance measurement, so the influence of temperature drift on sensor accuracy is difficult to overcome. A differential digital demodulation eddy current sensor system was designed to reduce the influence of temperature drift on the output accuracy of the eddy current sensor. The differential sensor probe was used to eliminate common-mode interference caused by temperature, and the differential analog carrier signal was digitized by a high-speed ADC. In the FPGA, the amplitude information is resolved using the double correlation demodulation method. The main sources of system errors were determined, and a test device was designed using a laser autocollimator. Tests were conducted to measure various aspects of sensor performance. Testing showed the following metrics for the differential digital demodulation eddy current sensor: nonlinearity 0.68% in the range of ±2.5 mm, resolution 760 nm, maximum bandwidth 25 kHz, and significant suppression in the temperature drift compared to analog demodulation methods. The tests show that the sensor has high precision, low temperature drift and great flexibility, and it can instead of conventional sensors in applications with large temperature variability.

The ball joint is a multi-degree-of-freedom transmission pair, if it can replace the inner frame in the aviation photoelectric pod to carry the optical load, which will greatly simplify the system structure of the photoelectric pod and reduce the space occupied by the inner frame. However, installation errors in ball joint siting introduce nonlinear errors that are difficult to correct and two degree of freedom angular displacement of the ball joint is difficult to detect, which limits application in the precision control of two degrees of freedom systems. Studies of spherical capacitive sensors to date have not tested sensors for use in an inner frame stabilisation mechanism nor have they analysed the influence of installation error on sensor output. A two-axis angular experimental device was designed to measure the performance of a ball joint capacitive sensor in a frame stabilisation mechanism in an aeronautical optoelectronic pod, and a mathematical model to compensate for ball joint capacitive sensor installation error was created and tested. The experimental results show that the resolution of the capacitive sensor was 0.02° in the operating range ±4°, the repeatability factor was $0.86\%$, and the pulse response time was 39 $\mathsf{\mu }$s. The designed capacitive sensor has a simple structure, high measurement accuracy, and strong robustness, and it can be integrated into ball joint applications in the frames of aeronautical photoelectric pods.

As the fields of aviation and aerospace optics continue to evolve, there is an increasing demand for enhanced detection capabilities in equipment. Nonetheless, in applications where both optical and mechanical constraints are stringent, the continuous expansion of optical aperture and focal length is impractical. Given the existing technological landscape, employing super-resolution algorithms to enhance the imaging capability of optical systems is both practical and highly relevant. This study capitalizes on using a 2D scanning galvanometer in optical systems to acquire micro-displacement information. Initially, an imaging model for optical systems equipped with a 2D scanning galvanometer was established, and the displacement vectors for both forward and sweep image motions were defined. On this foundation, we incorporated micro-displacement information that can induce high-frequency aliasing. Subsequently, the motion paths of the galvanometer were planned and modeled. To align image sequences with micro-displacement correlations, the Lucas–Kanade (L-K) optical flow method was employed with multi-layer pyramid iteration. Then, super-resolution reconstruction was performed using kernel regression techniques. Ultimately, we tested the algorithm on an aeronautical optoelectronic pod to evaluate its impact on optical resolution and imaging quality. Compared with the original images, the 16-frame image demonstrated a 39% improvement in optical resolution under laboratory conditions. Moreover, the algorithm exhibited satisfactory performance under both nighttime and daytime conditions, as well as during aerial tests.

As a core functional component of multi-degree-of-freedom precision motion mechanisms, spherical hinges are widely used in high-end equipment fields such as industrial robots, vehicle engineering, and intelligent manufacturing. Their dynamic performance directly determines the motion accuracy and the level of intelligent control of the equipment. The high-precision real-time measurement of two-degree-of-freedom (2-DOF) angles is a key prerequisite for achieving precise closed-loop control of spherical hinges. However, due to the strong coupling characteristics between the 2-DOF angle signals, it is difficult to directly and accurately measure the angular motion parameters of spherical hinges, which has become a core technical bottleneck restricting the improvement in their application efficiency. To address this challenge, this paper presents an improved study of the previously proposed spherical differential quadrature capacitance sensor for measuring the 2-DOF angle signals of spherical hinges. Firstly, the 2-DOF angle signal decoupling model is reconstructed and optimized. Secondly, a real-time decoupling circuit architecture for phase-shift detection with single-frequency signal excitation is innovatively proposed. This solution effectively addresses the incomplete decoupling of 2-DOF angle signals in previous studies, as well as the problems of considerable measurement noise, low resolution, and high calibration difficulty caused by random amplitude and phase errors in the excitation signals. Through the construction of an experimental platform for verification tests, the results show that the proposed scheme can significantly suppress the random errors caused by the parameter dispersion of the device, achieve an angle measurement resolution of 0.001°, and simultaneously considerably reduce the complexity of system calibration, laying a key technical foundation for the engineering application of spherical hinges in the fields of precision measurement and high-performance control.