Displacement measurement is a crucial application, with laser-based methods offering high precision and being well established in commercial settings. However, these methods often come with the drawbacks of significant size and exorbitant costs. We introduce a novel displacement measurement method that utilizes the missing-order Talbot effect. This approach circumvents the need to measure contrast in the Talbot diffraction field, opting instead to leverage the displacement within the missing-order Talbot diffraction pattern. Our method only requires parallel light, an amplitude grating, and a detector to achieve displacement measurement. The measurement dynamic range can be adjusted by altering the grating period and the wavelength of the incident light. Through careful simulation and experimental validation, our method exhibits a correlation coefficient R surpassing $0.999$ across a 30 mm dynamic range and achieves a precision superior to 3 $\mathsf{\mu }$m.

Based on the application requirements of high spectral resolutions, high spatial resolutions and wide swatches, a new-generation, high-performance, spaceborne, hyperspectral imaging spectrometer (NGHSI) with a spatial resolution of 15 m and a swatch of 90 km is proposed. The optical system of the NGHSI has a focal length of 1128 mm, an F-number of three, a field of view (FOV) of 7.32° and a slit length of 144 mm. A new off-axis, multi-mirror telescope structure with intermediate images is put forward, which solves the design problem that realizes secondary imaging and good telecentricity at the same time. And a new off-axis lens-compensation Offner configuration is adopted to address the challenge of the high-fidelity design of spectral imaging systems with long slit lengths. The relationship between X-Y polynomials and aberration coefficients is analyzed, and the X-Y polynomial freeform surfaces are used to correct the off-axis aberrations. The design results show that the image quality of the telescope system is close to the diffraction limit. The smile, known as the spectral distortion along the line, and keystone, which is the magnification difference for different wavelengths, of the spectral imaging system are less than 1/10 pixel size. The complete optical system of the NGHSI, including the telescope system and the spectral imaging system, has excellent imaging quality and the layout is compact and reasonable, which realizes the miniaturization design.

The precision of two-dimensional angular sensing is crucial for applications such as navigation, robotics, and optical alignment. Conventional methods often struggle to balance precision, dynamic range, and affordability. We introduce a novel method leveraging the Talbot effect, enhanced by 3D printing technology, to fabricate a grating prototype for high-precision angular measurements. The method detects amplitude grating displacement at the self-imaging position and employs a frequency filtering algorithm for improved accuracy. Rigorous validation through simulations and physical experiments demonstrates that our method achieves a detection resolution of 0.4 arcseconds and a dynamic range exceeding 1400 arcseconds. This research presents a cost-effective, high-precision angular detection solution with potential for broad application in precision mechanical assembly, optical alignment, and other relevant domains.

Image fusion is an effective and efficient way to express the feature information of an infrared image and abundant detailed information of a visible image in a single fused image. However, obtaining a fused result with good visual effect, while preserving and inheriting those characteristic details, seems a challenging problem. In this paper, by combining a multi-level smoothing filter and regional weight analysis, a dual-band image fusion approach is proposed. Firstly, a series of dual-band image layers with different details are obtained using smoothing results. With different parameters in a bilateral filter, different smoothed results are achieved at different levels. Secondly, regional weight maps are generated for each image layer, and then we fuse the dual-band image layers with their corresponding regional weight map. Finally, by imposing proper weights, those fused image layers are synthetized. Through comparison with seven excellent fusion methods, both subjective and objective evaluations for the experimental results indicate that the proposed approach can produce the best fused image, which has the best visual effect with good contrast, and those small details are preserved and highlighted, too. In particular, for the image pairs with a size of 640 × 480, the algorithm could provide a good visual effect result within 2.86 s, and the result has almost the best objective metrics.