This work has significance in the research of optical on-chip nano-tweezers.Dual-comb spectroscopy (DCS) is an emerging and promising spectrometric technique with high resolution, high sensitivity, broad spectral range, and fast acquisition speed. For the recovery of the information encoded on comb modes without resolution loss, two continuous wave lasers are commonly utilized as optical intermedia to track the real-time jitter of dual-comb interferograms. This paper presents a simplified error correction method based on single optical intermedium for quasi-free-running fiber DCS. This method combines the strengths of conventional optical referencing and self-referencing error correction. We acquired whole P branch H13C14N transmittance spectra in the near infrared as a demonstration. In contrast to that of conventional dual intermedium error correction, the standard deviation of our method was merely 0.01 over the 4 THz spectral range. Our method provides a balanced and practical postprocessing routine for high-performance mode-resolved DCS applications.The Huygens' principle is thoroughly investigated under scalar theory. The rigorous expressions of Huygens' principle must be independent of ∂u/∂n, and their boundaries can only be taken as either spherical or flat; thus, three cases can be concluded. An extended version of Huygens' principle is proposed to cover these cases, whose rigorous expressions are shown in this paper. Specifically, when the radius of the spherical boundary approaches infinity, the corresponding expressions become the form corresponding to the flat boundary. Expressions with spherical boundary can change the area and average intensity of small angle diffraction pattern proportionally, thus providing a promising mathematical tool for the design of curved imaging systems.The dual-frequency laser interferometer is an indispensable instrument to measure length, position, deformation and other parameters with high precision and long measurement distance in the advanced manufacturing industry and scientific research. In general, the light source of interferometer is the dual-frequency He-Ne laser. The disadvantages of He-Ne laser include generally large size, more heat radiation to the environment, and limited service life, which limits its application. In this paper, we study a microchip NdYAG dual-frequency laser interferometer with a 17.4 MHz frequency difference, which is formed by the stress-induced birefringence in the microchip itself. The down-conversion mixer is designed to decrease the beat frequency to about 5 MHz in heterodyne signal preprocessing modular to meet the bandwidth of phase meter. The experimental results show that the microchip NdYAG dual-frequency laser interferometer has a displacement resolution of 10 nm and a measuring range of 500 mm. Due to the advantages of the microchip dual-frequency laser, such as small size (40×40×35 mm), good portability, less power consumption and almost infinite service life, the microchip NdYAG dual-frequency laser interferometer has broad application prospects.In this paper, a modification method based on a U-Net convolutional neural network is proposed for the precise fabrication of three-dimensional microstructures using laser direct writing lithography (LDWL). In order to build the correspondence between the exposure intensity distribution data imported to the laser direct writing system and the surface profile data of the actual fabricated microstructure, these two kinds of data are used as training tensors of the U-Net convolutional neural network, which is proved to be capable of generating their accurate mapping relations. By employing such mapping relations to modify the initial designed exposure intensity data of the parabolic and saddle concave micro-lens with an aperture of 24µm×24µm, it is demonstrated that their fabrication precision, characterized by the mean squared error (MSE) and the peak signal-to-noise ratio (PSNR) between the fabricated and the designed microstructure, can be improved significantly. Specifically, the MSE of the parabolic and saddle concave micro-lens decreased from 100 to 17 and 151 to 50, respectively, and the PSNR increased from 22dB to 29dB and 20dB to 25dB, respectively. Furthermore, the effect of laser beam shaping using these two kinds of micro-lens has also been improved considerably. This study provides a new solution for the fabrication of high-precision three-dimensional microstructures by LDWL.Highly stable, low phase noise microwave oscillators are essential for various applications. An optoelectronic oscillator (OEO) can overcome the short-term phase noise limitation of pure electronic oscillators at high oscillation frequency. Nonetheless, the long-term frequency stability should be addressed. To stabilize the frequency of OEO, a phase-locked loop (PLL) is widely used to synchronize the OEO to a stable reference. However, due to the narrow free-spectral-range (FSR) of the oscillation cavity of the OEO, the pull-in range of the PLL is limited. It is challenging to acquire phase-locking at startup and phase-relocking when mode-hopping of OEO occurs. Here, by using an automatic frequency calibration (AFC) assisted PLL, we attain a highly stable 10 GHz phase-locked OEO with robust phase-locking at startup and phase-relocking when mode-hopping of OEO occurs, for the first time. With the use of a fast digitally-controlled frequency shifter and a real-time frequency error detection unit in the AFC loop, the phase-locking and phase-relocking time are below 120 ms.  https://www.selleckchem.com/products/FK-506-(Tacrolimus).html  Furthermore, it shows the phase noise of -135 dBc/Hz at 10 kHz offset, side-mode suppression ratio (SMSR) of 128 dBc, and Allan deviation of 4.8×10-11 at 5000 s for the phase-locked OEO. We thoroughly investigate the dynamics of the automatic frequency calibration, the phase-locking process, the phase-relocking after OEO mode-hopping, the system under vibration, and the frequency switching. Our approach is promising to generate a highly stable, low phase noise, and determinate frequency microwave signal, which can be used as a low phase noise reference for a microwave frequency synthesizer and high performance sampling clock for a data conversion system.