### Related Works  
#### 1.2.1 Eccentric Photorefraction  
Figure 2 illustrates the principle of eccentric photorefraction for a myopic eye relative to the camera focus. This geometric relationship leads to Equation (1), which expresses refractive error, where the crescent width \(s\), pupil diameter \(2r\), eccentric distance of the flash source \(e\), distance from the camera to the subject \(d\), and the eye's focusing distance \(x\) all contribute to the calculation of diopter \(A=\frac{1}{x}\), \(\triangle=-A-\frac{1}{d}\). As shown in Equation (1) and Figure 2, as the defocus distance of the eye relative to the camera increases, the crescent width also increases. For hyperopia, the crescent appears on the opposite side of the light source; for myopia, it appears on the same side. \[s=2r-\frac{e}{d\triangle} \tag{1}\]  
Figure 2: Eccentric photorefraction schematic [10]. Unlike traditional eye exams, which require subjective verbal responses, eccentric photorefraction is a noninvasive method that objectively measures the refractive error of both eyes simultaneously [11] without the need for eye drops or other invasive techniques. [PERSON] et al. [12] explored the feasibility of using a microcomputer to implement a low-cost eccentric photorefraction method and showed the potential of this method in the field of vision screening. The accuracy of refractive error measurement using eccentric photorefraction depends heavily on detecting changes in pupil brightness. This accuracy is influenced by two main factors: the precision of pupil localization and the accuracy of the brightness gradient curve extraction. Due to individual differences in pupils, low contrast in the bright and dark regions, and interference from eyelashes, eyelids, and Purkinje images, it is challenging to distinguish between different refractive states. Most existing methods use a two-stage process, where the pupil is first localized and segmented, and pixel values are extracted based on the brightness gradient along the segmented image. These data are then used to draw the grayscale change curve. After calculating the first and second derivatives of the gray value curve, the position of the abrupt change in the gray value of the pupil along the direction of brightness change is identified. The actual height of the dark area in the pupil is then obtained by conversion and substituted into Equation (1) to calculate the refractive errors of the human eye. In a single-stage related study, these data are used to train neural networks. [PERSON] et al. [13] developed an automated deep learning-based system that predicts refractive error ranges using eccentric photorefraction images captured by smartphones, assisting in early amblyopia screening. They categorized refractive errors into seven classes, achieving an overall accuracy of 81.6%. [PERSON] et al. [14] proposed a refractive error detection framework that combines pretrained CNN features with active learning, reducing reliance on handcrafted features and large-scale annotations. Their method achieved an accuracy of 81.98% in a binary classification task and an MAE of 0.653 in a regression task. [PERSON] et al. [15] introduced pupil images under different levels of eccentric LED illumination into a deep neural network, avoiding the complexity of traditional slope calculations. Their model achieved a mean squared error of \(\pm\)0.9 D in predicting refractive errors, demonstrating feasibility even with a small dataset. To improve the efficiency and accuracy of refractive error detection, [PERSON] et al. [16] proposed a deep learning model, REDNet, which integrates CNNs and RNNs to predict refractive errors from multi-directional eccentric photorefraction images. Their model achieved an accuracy of 89.50% and an MAE of 0.174 D on their self-constructed dataset. [PERSON] et al. [17] extracted infrared and color images of the pupil crescent from eccentric photorefraction images and trained different convolutional neural networks to predict refractive errors.