Refractive Index Estimation for Michelson Interferometric Fringes Based on FAdaResNet-18

To overcome the limitations of traditional Michelson interferometry fringe analysis methods, which rely on manual counting and ring counting, we propose a Frequency-Fusion Adaptive Residual Network (FAdaResNet-18) for refractive index estimation. Traditional methods are not only labor-intensive but also prone to human errors, especially when the number of fringes is large or the fringe quality is poor, making it difficult to ensure accuracy and consistency in manual counting. Additionally, the process of manual ring counting is often affected by factors such as visual fatigue and missed details, leading to errors. Furthermore, these methods are time-consuming and inefficient, making them unsuitable for large-scale, high-throughput experiments. To address these issues, we introduce an automated deep learning-based approach that leverages frequency domain features, making the refractive index estimation process more accurate and efficient. Unlike traditional methods, FAdaResNet-18 utilizes deep learning and frequency-domain priors to automatically extract key information from interference fringe images and directly estimate the refractive index of the test sample. The network adopts an adaptive residual design, with AdaResNet-18 as the backbone, incorporating a frequency-domain branch into the deep features. By applying two-dimensional real-valued fast Fourier transform (rFFT) to extract frequency-domain features, the model captures the global periodicity and frequency characteristics of the fringes, which are then concatenated with the spatial branch features. The refractive index is finally estimated through linear regression. Due to the difficulties in acquiring interference fringe images in practical applications, we further introduce data augmentation techniques to expand the training set. Initially, we simulated 1,000 interference fringe images, and through data augmentation, we expanded the sample size to 25,000 images. The experimental results show that, compared to the lightweight AdaResNet-18 network, FAdaResNet-18 achieves a 1% increase in GFLOPs (Giga Floating-Point Operations), with a 57.14% reduction in MSE (Mean Squared Error), a 34.56% reduction in MAE (Mean Absolute Error), and a 0.01 increase in R² (Coefficient of Determination). These results demonstrate that FAdaResNet-18, through data augmentation and network design optimization, achieves an excellent balance between computational efficiency and refractive index estimation accuracy. Furthermore, we verified the feasibility and anti-interference capability of this method through practical experiments, further confirming its potential for real-world applications.