To enhance the robustness of film thickness measurements from low signal-to-noise ratio （SNR） spectral data， a measurement approach based on a self-attention neural network （SANN） is developed. While the conventional Fourier transform method effectively measures thickness on high SNR data， its accuracy deteriorates as noise obscures the principal interference frequency under low SNR conditions， hindering precise thickness extraction. This study introduces a self-attention neural network model that takes spectral data as input and outputs film thickness， employing an adaptive attention mechanism to dynamically weight spectral points across different wavelengths， thereby improving analysis of low SNR spectral data. Experimental data were obtained using a spectral interference film thickness measurement system and subsequently augmented through wavelength drift and adaptive intensity normalization strategies to expand the dataset and enhance the model's generalization. Model optimization identified an architecture comprising eight encoder layers and 128 hidden nodes per layer.Using wafer measurements as a case study， evaluation on spectral data containing outliers demonstrated a maximum relative thickness measurement error of 3.62% on the low SNR validation set. These results indicate that the proposed method effectively suppresses noise influence， mitigates outlier deviations common in Fourier transform approaches， and substantially improves measurement stability. the applicability of the proposed method is validated to a broader range of thin film measurement scenarios.