This paper presents a comprehensive review of mechanical design and synthesis methods for piezo-actuated compliant micro-positioning stages, which play an important role in areas where high precision motion is required, including bio-robotics, precision manufacturing, automation, and aerospace. Unlike conventional rigid-link mechanisms, the motion of compliant mechanisms is realized by using flexible elements, whereby deformation requires no lubrication while achieving high movement accuracy without friction. As compliant mechanisms differ significantly from traditional rigid mechanisms, recent research has focused on investigating various technologies and approaches to address challenges in the flexure-based micro-positioning stage in the aspects of synthesis, analysis, material, fabrication, and actuation. In this paper, we reviewed the main concepts and key advances in the mechanical design of compliant piezo-actuated micro-positioning stages, with a particular focus on flexure design, kineto-static modeling, actuators, material selection, and functional mechanisms including amplification and self-guiding ones. We also identified the key issues and directions for the development trends of compliant micro-positioning stages.

We present a new two-snapshot structured light illumination (SLI) reconstruction algorithm for fast image acquisition. The new algorithm, which only requires two mutually π phase-shifted raw structured images, is implemented on a custom-built temporal focusing fluorescence microscope (TFFM) to enhance its axial resolution via a digital micromirror device (DMD). First, the orientation of the modulated sinusoidal fringe patterns is automatically identified via spatial frequency vector detection. Subsequently, the modulated in-focal-plane images are obtained via rotation and subtraction. Lastly, a parallel amplitude demodulation method, derived based on Hilbert transform, is applied to complete the decoding processes. To demonstrate the new SLI algorithm, a TFFM is custom-constructed, where a DMD replaces the generic blazed grating in the system and simultaneously functions as a diffraction grating and a programmable binary mask, generating arbitrary fringe patterns. The experimental results show promising depth-discrimination capability with an axial resolution enhancement factor of 1.25, which matches well with the theoretical estimation, i.e, 1.27. Imaging experiments on pollen grain and mouse kidney samples have been performed. The results indicate that the two-snapshot algorithm presents comparable contrast reconstruction and optical cross-sectioning capability than those adopting the conventional root-mean-square (RMS) reconstruction method. The two-snapshot method can be readily applied to any sinusoidally modulated illumination systems to realize high-speed 3D imaging as less frames are required for each in-focal-plane image restoration, i.e., the image acquisition speed is improved by 2.5 times for any two-photon systems.