Wavefront sensing is essential in visual optics for evaluating the optical quality in systems, such as the human visual system, and understanding its impact on visual performance. Although traditional methods like the Hartmann-Shack wavefront sensor (HSS) are widely employed, they face limitations in precision, dynamic range, and processing speed. Emerging deep learning technologies offer promising solutions to overcome these limitations. This paper presents a novel approach using a modified ResNet convolutional neural network (CNN) to enhance HSS performance. Experimental datasets, including noise-free and speckle noise-added images, were generated using a custom-made monocular visual simulator. The proposed CNN model exhibited superior accuracy in processing HSS images, significantly reducing wavefront aberration reconstruction time by 300% to 400% and increasing the dynamic range by 315.6% compared to traditional methods. Our results indicate that this approach substantially enhances wavefront sensing capabilities, offering a practical solution for applications in visual optics.