Reliable inspection of nanosurfaces is essential to ensure the quality of nanostructure manufacturing. Angle-resolved scatterometry provides a non-invasive inspection method that can be used in-line but often suffers from long acquisition times due to dense angular sampling. This paper addresses the data acquisition challenge by proposing an end-to-end compressed learning framework for 5-level vacancy deficiency detection in zinc oxide nanograss using ARS images. The proposed framework integrates a learnable latitude-based sampling layer with a convolutional neural network, allowing sampling and classification to be jointly optimized during training. The sampling layer exploits the physical structure of ARS patterns and learns informative latitudinal regions, which reduces the sampling search space and improves convergence. Evaluation results show that the proposed approach achieves high and stable deficiency-level classification performance under different noise conditions. Using full ARS images, the model achieves 94.2% accuracy for five-level deficiency classification and 98.6% accuracy for separating deficient from non-deficient nanosurfaces. The proposed sampling model matches full-image performance while using up to 90% fewer angular sampling points. Even when sampling points are reduced by 99.7%, the classification accuracy decreases by less than 10 percentage points. To further improve training with limited data, we also studied a GAN-based augmentation approach and used GAN-generated data for model pretraining. Augmented data resulted in fast convergence within only a few fine-tuning epochs.