Adaptive optical systems are originally developed for the field of astronomy to eliminate image blurring aberrations induced by atmospheric disturbance. In some complex applications, such as the contactless thin adaptive mirror for large-aperture ground-based optical telescopes, displacement sensors are needed to measure the deformation of the deformable mirror and construct a local position control loop. In the past adaptive secondary mirrors, capacitive sensors are designed to measure the mirror deformation. However, they suffer problems of manufacturing, maintenance, and environment. In this paper, a high-performance eddy current displacement sensor is proposed for the deformation measurement of adaptive secondary mirrors. Simulation and optimization of the detecting coil and conductive target are carried out. A deliberate signal processing circuit is designed for weak signal detection. Experimental results of the prototype sensor indicate a resolution up to 5 nm and a linearity better than 0.1% within the measuring range of 50 μm and bandwidth of 3 kHz, which meet the basic technical requirements of the adaptive optical systems.
Torsional vibrations of circular tubes, rods, rings, and disks are widely used as operation modes of acoustic wave transducers in various piezoelectric devices. In this paper, a piezoelectric disk with spiral interdigitated electrodes is proposed to generate in-plane torsion in a simple and effective manner. Design and working principle of the torsional transducer are introduced. Vibration characteristics of the transducer with a constant spiral angle are studied. A simplified model is established to investigate the basic dynamic characteristics of torsional vibration accompanying with radial vibration. Electric admittance, resonant frequencies, and mode shapes with different boundary conditions are calculated. Resonant frequencies as functions of several structural parameters are discussed.