Physical parameters estimation for Michelson interferometric fringes based on FFARNet-18

Michelson interferometry, as a common high-precision, non-contact measurement method, is used to measure physical parameters through processing interferogram. Recently, utilizing convolutional neural networks (CNNs) for the automated inversion of physical parameters from interference images has demonstrated significant research value. However, existing networks are predominantly confined to spatial-domain feature extraction, struggling to effectively exploit the inherent linear frequency modulation (chirp) characteristics of the fringes, which results in limited estimation accuracy under complex noise environments. To address this issue, this paper proposes a method based on the fractional Fourier adaptive residual network (FFARNet-18). By innovatively incorporating multi-channel fractional Fourier transform (FRFT) branches within the deep feature space, the network extracts deep fractional-domain features from interferograms, thereby achieving a joint spatial-fractional domain parameter estimation. Furthermore, to overcome the challenges associated with limited data acquisition, a geometric transformation-based data augmentation strategy is employed to expand the dataset, significantly enhancing the model's generalization capability. Numerical simulations and experimental results demonstrate that FFARNet-18 achieves a substantial improvement in the estimation accuracy of refractive index and thickness, with only a marginal increase of approximately 3.8% in Giga floating-point operations (GFLOPs).