When photographing objects underwater, it is important to utilize an optical window to isolate the imaging device from the water. The properties of the entire imaging system will change, and the imaging quality will decrease due to the refraction impact of the water and the window. The theoretical calculation method for air imaging is no longer relevant in this context. To analyze the unique rule, this research derives the formulas for key parameters of underwater imaging systems under paraxial circumstances. First, the optical window is modeled, then the formula for the optical window’s focal length in the underwater environment is derived, and the change rule for the focal length of various window forms underwater is condensed. For the ideal imaging system using a domed optical window, the equivalent two-optical group model of the imaging system is established, and the formula for calculating the focal length, working distance, and depth of field of the underwater imaging system is derived through paraxial ray tracing. The accuracy of the formula is verified through the comparative analysis of the formula calculation results and the Zemax modeling simulation results. It provides an important theoretical basis for the in-depth study of underwater imaging technology.

In this paper, a depth-sensing method employing active irradiation of a semi-annular beam is proposed for observing the multi-layered reflective surfaces of transparent samples with higher resolutions and lower interference. To obtain the focusing resolution of the semi-annular aperture diaphragm system, a model for computing the diffracted optical energy distribution of an asymmetric aperture diaphragm is constructed, and mathematical formulas are deduced for determining the system resolution based on the position of the first dark ring of the amplitude distribution. Optical simulations were performed under specific conditions; the lateral resolution ${\delta }_r$ of the depth-sensing system was determined to be 0.68 μm, and the focusing accuracy ${\delta }_z$ was determined to be 0.60 μm. An experimental platform was established under the same conditions, and the results were in accord with those of the simulation results, which validated the correctness of the formula for calculating the amplitude distribution of the diffracted light from the asymmetric aperture diaphragm.

Diffraction significantly deteriorates the quality of the laser image, causing severe degradation that undermines the theoretical performance parameters of the autofocus system. In this paper, we conduct a comprehensive analysis of the non-uniform features of the images. To enhance the imaging quality of each individual image, we propose a de-diffraction algorithm based on gradient iteration. This algorithm is capable of rapidly removing the interference spots resulting from diffraction and restoring the distorted laser spots. By doing so, it effectively eliminates the inevitable reduction in the autofocus resolution and focusing accuracy caused by diffraction. Furthermore, the proposed calculation model for the intra-localisation interval significantly improves the convergence of the iterative calculation process. Through experiments, it has been verified that, under the same conditions, the interlayer resolution between the reflective surfaces of the samples processed using this algorithm is increased to a quarter of the original value. This remarkable improvement in resolution, which far exceeds the microscope’s inherent resolution, demonstrates that the algorithm successfully achieves super-resolution for the microscope.