Fig. 1. (a) Schematic diagram of the SAXS measurement, (b) scattering patterns of multiple AOIs, and (c) scattering map of the sample.

Fig. 2. (a) Top and side views of a complex profile grating sample. The profile is demonstrated by a structural parameter set t = {CD_n, CP_n}_n^N. (b) Various types of phenomena, including tilting, twisting, bowing, tapering, and potential combinations thereof. (c) Kendall τ correlation coefficients for the CDs and CPs. (d),(e) Correlation ellipses for the CDs and CPs, which demonstrate that the parameters of two adjacent layers are more correlated than those of the distant layers.

Fig. 3. Framework architecture of the correlation learning-based method. The framework, namely, as CLNet, consists of a residual module and a correlation learning module. The residual module is a modified ResNet34, which has an adaptive average pooling layer at the beginning and another one at the end. The correlation learning module is a Bi-LSTM structure, which can directly reconstruct the profile parameters.

Fig. 4. Reconstructed results and corresponding fitting scattering data of a randomly selected sample. (a)–(c) Reconstructed results for profiles CD and CP, respectively. (d) Measured q_x-q_z scattering map obtained from the scattering patterns at 100 AOIs, uniformly spanning from −20° to 20°. (e)–(j) Measured data, fitting data, and the corresponding residuals at the q-slices, which are indicated by the dashed green lines in (d). In the high q regions, the residual increases due to the low signal-to-noise ratio of the measured data.

Fig. 5. Reconstructed results of three randomly selected samples in the test set. Each grating consists of 40 layers. (a), (b) Corresponding reconstructed CDs and CPs, respectively. Besides our method, the plots also include results from five other models, namely, ResNet34, ResNet50, AlexNet, EffNet-b2, and TinyVit-5m. These are used for ablation and comparative experiments.

Fig. 6. (a), (c) Per-layer MAE for CD and CP in the test set, respectively. (b), (d) Cumulative error distributions of per-sample MAE for CD and CP, respectively. Per-layer MAE represents the mean absolute errors for each layer of all samples, and per-sample MAE represents the mean absolute errors for individual samples.

Fig. 7. (a), (b) Reconstructed CP and the corresponding per-layer MAE, respectively, under the ideal situation where the ground truth CPs of each layer are equal to zero.

Fig. 8. (a), (b) Model uncertainty quantification for CD and CP, respectively, based on six types of methods, including CLNet (our method), ResNet34, ResNet50, AlexNet, EffNet-b2, and TinyVit-5m. Our method performs best in terms of reconstruction accuracy and repeatability.