We have developed a compact, asymmetric three-channel echelle spectrometer with remarkable high-spectral resolution capabilities. In order to achieve the desired spectral resolution, we initially establish a theoretical spectral model based on the two-dimensional coordinates of spot positions corresponding to each wavelength. Next, we present an innovative and refined method for precisely calibrating echelle spectrometers through parameter inversion. Our analysis delves into the complexities of the nonlinear two-dimensional echelle spectrogram. We employ a variety of optimization techniques, such as grid exploration, simulated annealing, genetic algorithms, and genetic simulated annealing (GSA) algorithms, to accurately invert spectrogram parameters. Our proposed GSA algorithm synergistically integrates the strengths of global and local searches, thereby enhancing calibration accuracy. Compared to the conventional grid exploration method, GSA reduces the error function by 22.8%, convergence time by 2.16 times, and calibration accuracy by 7.05 times. Experimental validation involves calibrating a low-pressure mercury lamp, resulting in an average spectral accuracy error of 0.0257 nm after performing crucial parameter inversion. Furthermore, the echelle spectrometer undergoes a laser-induced breakdown spectroscopy experiment, demonstrating exceptional spectral resolution and sub-10 ns time-resolved capability. Overall, our research offers a comprehensive and efficient solution for constructing, modeling, calibrating, and applying echelle spectrometers, significantly enhancing calibration accuracy and efficiency. This work contributes to the advancement of spectrometry and opens up new possibilities for high-resolution spectral analysis across various research and industry domains.

Fourier ptychography imaging is a powerful phase retrieval method that can be used to realize super-resolution. In this study, we establish a mathematical model of long-distance camera scanning based on reflective Fourier ptychography imaging. In order to guarantee the effective recovery of a high-resolution image in the experiment, we analyze the influence of laser coherence in different modes and the surface properties of diverse materials for diffused targets. For the analysis, we choose a single-mode fiber laser as the illumination source and metal materials with high diffused reflectivity as the experimental targets to ensure the validity of the experimental results. Based on the above, we emulate camera scanning with a single camera attached to an X-Y translation stage, and an experimental system with a working distance of 3310 mm is used as an example to image a fifty-cent coin. We also perform speckle analysis for rough targets and calculate the average speckle size using a normalized autocorrelation function in different positions. The method of calculating the average speckle size for everyday objects provides the premise for subsequent research on image quality evaluation; meanwhile, the coherence of the light field and the targets with high reflectivity under this experiment provide an application direction for the further development of the technique, such as computer vision, surveillance and remote sensing.

The echelle grating spectrometer, with a wide spectral range and high-resolution spectral analysis, is one of the best tools for fine spectral measurement. Nevertheless, it suffers from excessive residual aberrations and a large overall size. In this study, the design and implementation of a novel asymmetric Czerny–Turner ultra-wide spectral range achromatic echelle spectrometer are described. The echelle spectrometer has three channels, and it uses an off-axis parabolic mirror to obtain collimated light without aberrations. Three sets of gratings and dispersive prisms with different coatings are utilized as cross-dispersion elements to acquire two-dimensional images containing spectral information. Suitable detectors are selected according to the requirements of each channel, and three sets of coaxial focusing lenses are designed separately to minimize the aberration. The results of the simulation analysis by ZEMAX indicate that in the entire operating band (200–1100 nm), the root mean square radius of the dispersion spots is ≤ 2.2 μm, all of which are located within the limited range of the size of the detector, thus ensuring that the system’s spectral resolution reaches 0.02 nm at 200 nm, 0.04 nm at 650 nm, and 0.1 nm at 1100 nm.

Fourier ptychography (FP) is a powerful phase retrieval method that can be used to reconstruct missing high-frequency details and high-space-bandwidth products in microscopy. In this study, we further advanced the application of FP in microscopic imaging to the field of macroscopic far-field imaging, incorporating camera scanning for spatial resolution improvement. First, on the basis of the Fraunhofer diffraction mechanism and the transmission imaging model, we found the analysis of the associated theoretical fundamentals via simulations and experiments to be crucially relevant to the far-field of FP imaging. Second, we built an experimental device with long-distance imaging and experimentally demonstrated the relationship between the spectrum overlap ratio and the reconstructed high-resolution image. The simulation and experimental results showed that an overlap ratio higher than 50% had a good reconstruction effect. Third, camera scanning was used to obtain low-resolution intensity images in this study, for which the scanning range was wide and spherical wave illumination was satisfied, and therefore different positions corresponded to different aberrations of low-resolution intensity images, and even different positions of the same image had aberration differences, leading to inconsistencies in the aberrations of different images. Therefore, in the reconstruction process, we further overcame the effect of the inconsistency of aberrations of different images using the partition reconstruction method, which involves cutting the image into smaller parts for reconstruction. Finally, with the proposed partition reconstruction algorithm, we were able to resolve 40 μm line width of GBA1 resolution object and obtain a spatial resolution gain of 4× with a working distance of 2 m.

We present a differentiable, curriculum-based optimization workflow for the engineering-oriented design of large-aperture reflective optical systems. The method integrates physics-informed differentiable ray tracing with a progressive, two-stage optimization strategy that evolves from simple Ritchey–Chrétien (RC) foundations to complex four-mirror architectures. Without relying on pretrained models or large datasets, the workflow optimizes geometric and physical parameters under field-weighted RMS, focal length, and dynamic obscuration constraints while maintaining minimal perturbation to primary and secondary mirrors. Validated through Zemax-based analysis, the optimized systems achieve high imaging quality with improved RMS uniformity and stable convergence across varying aperture scales. This approach provides a practical and scalable pathway for the design and optimization of reflective optical instruments, offering strong robustness and adaptability for diverse imaging applications.