Flexible and universal autofocus based on amplitude difference of fractional Fourier transform

Autofocus technology is a crucial technique in computational optical imaging. The clarity evaluation function (CEF) serves as the criterion for autofocus, making it the core of the autofocus algorithm. In this paper, we propose a CEF based on amplitude differences of fractional Fourier transform (ADFrFT). ADFrFT extracts information from the fractional domain, which corresponds to the fusion of the spatial and frequency domains. This renders ADFrFT highly accurate and robust to noise, making it suitable for various types of sample images. Additionally, ADFrFT provides an added dimension of flexibility to address different autofocus requirements for distinct sample image types and focusing scenarios. Simulations and experiments confirmed the effectiveness of ADFrFT, and we improved the imaging resolution via distance calibration in the coaxial multi-distance coherent diffraction imaging (MDCDI) experiment.