A spectral reduction algorithm for an échelle spectrometer with spherical mirrors that builds a one-to-one correspondence between the wavelength and pixel position is proposed. The algorithm accuracy is improved by calculating the offset distance of the principal ray from the center of the image plane in the two-dimensional vertical direction and compensating the spectral line bending from the reflecting prism. The simulation and experimental results verify that the maximum deviation of the entire image plane is less than one pixel. This algorithm ensures that the wavelengths calculated from spectrograms have a high spectral resolution, meaning the precision from the spectral analysis reaches engineering standards of practice.

In an echelle spectrometer equipped with a prism cross-dispersion element, wavelength calibration is very difficult because of the complex, nonlinear interaction between the prism and the echelle grating. From the spectrometer geometry and the dispersion equations for the prism and the grating, a detailed mathematical model for wavelength calibration is derived that fits the refractive index of the prism in real time. An expression relating the refractive index, wavelength, and image coordinates is constructed, and standard wavelength sources and image positions are adopted to timely calculate the refractive index, which is affected by ambient factors such as temperature and air pressure. Experimental results indicate that the fitting accuracy of the refractive index in real time approaches ${10}^{-4}$, while the wavelength accuracy approaches ${10}^{-3}\mathrm{nm}$ for the entire spectral range.

This work presents a method that can automatically estimate and remove varying continuous background emission for low-cost laser-induced breakdown spectroscopy (LIBS) without intensified CCD. The algorithm finds all third-order minima points in spectra and uses these points to partition the spectra into multiple subintervals. The mean value is then used as a threshold to select the effective points for the second-order minima in each subinterval. Finally, a linear interpolation method is used to realize extension of these effective points and complete fitting of the background using polynomials. Using simulated and real LIBS spectra with different complexities examine the validity of proposed algorithm. Additionally, five elements of five standard cast iron alloy samples are calibrated and improved very well after background removal. The results successfully prove the validity of the background correction algorithm.

Spatial heterodyne Raman spectrometry (SHRS) is a spectral analysis technique used to study material structures and compositions. We propose a multi-grating SHRS system that uses a multi-grating module rather than the single grating used to terminate each arm in traditional spatial heterodyne spectrometry (SHS). The proposed system not only retains the advantages of traditional SHS but also resolves the mutual limitation between system spectral range and resolution. The increased spectral range and resolution that can be achieved in detection are dependent on the number of sub-gratings used in the module. A verification system was built using 130 gr/mm and 150 gr/mm sub-gratings and calibrated. Under different experimental conditions (including laser power, integration time, container material and thickness, pure and mixed samples, and standoff experiments), the backscattered Raman spectra of different types of targets (including organic solutions, inorganic powders, and minerals) were tested. The multi-grating SHRS shows good performance for broad spectral range and high-resolution Raman detection.

The interference fringe period is an important phase-locking parameter in the scanning beam interference lithography (SBIL) system. To measure the interference fringe period accurately, a heterodyne period measurement method is proposed. Compared with traditional methods, the requirements for the stage motion characteristics are greatly reduced. In this paper, the theoretical error of the period measurement method is analyzed and relevant experiments are performed. The results show that the average period measurement value is 555.539 nm and the standard deviation of measurement repeatability is 2.5 pm. This method is significant for holographic grating fabrication using the SBIL system.

A profile of an X-axis stage mirror results in a phase error of gratings in Scanning Beam Interference Lithography. Traditional methods of measuring the profile require extra probes and another large stage mirror on Y-axis, or requires other operations such as rotating measured object to adjust the zero-adjustment errors. This paper introduces a three-probe system removing the need for Y-axis optical path structure and proposes a bidirectional integration model to solve the problem of zero-adjustment error, simplifying the optical path structure and the measurement process. This method is confirmed by theoretical analysis and experimental results, which is better than traditional methods and can also be used in other application fields of three-point method.