Coarse-to-fine golden section autofocus for ptychography using gradient and frequency metrics

Accurate knowledge of the sample-to-detector distance is essential for high-quality ptychographic reconstruction, as even minor errors in this parameter inevitably introduce phase distortions and defocus artifacts. To address this challenge, we propose a robust and efficient two-stage autofocus strategy based on the golden section search algorithm. Exploiting the approximately unimodal behavior of image sharpness under spectrally constrained conditions, the proposed method combines the Tenengrad gradient metric for rapid coarse localization with a band-limited frequency energy (BLFE) metric for high-precision refinement. This hybrid approach combines the noise robustness of gradient-based search with the sensitivity of frequency-domain analysis. Experimental results demonstrate that the method achieves superior convergence speed and focusing accuracy compared to conventional autofocus algorithms. By effectively eliminating defocus errors under a limited computational budget, the proposed strategy achieves higher spatial resolution, improved image contrast, and superior quantitative metrics, establishing a practical solution for high-quality ptychographic imaging.