Universal Clarity Evaluation Function for Autofocus Based on Amplitude Differences of Fractional Fourier Transform

In coherent diffraction imaging systems, autofocusing technology is used to precisely detect the distance from the detector plane to the sample plane, which is a critical factor affecting imaging resolution and quality. We propose a new clarity evaluation function (CEF) based on amplitude differences of fractional Fourier transform (ADFrFT), which focuses on issues of commonly used CEFs such as poor adaptability to the environment and samples, poor noise robustness, and significant oscillations. ADFrFT is based on the fractional-domain features of the sample as the autofocusing criterion and adds a new parameter for adjusting the ratio of fusion between the spatial and frequency domains. This parameter can take the sample type and detection scenario as prior knowledge and can be flexibly selected according to actual situations. Compared with various qualitative and quantitative CEFs, it relaxes the requirements of sample and scenario types, while guaranteeing accuracy, and the features of the autofocus curves can switch between spatial and frequency domain types. We also propose an autofocus strategy that first searches for the initial range of the focal length and then subdivides the search to optimize in the right direction, which can be achieved only using ADFrFT to obtain autofocus curves of two different characteristics. We demonstrate the effectiveness, flexibility, and versatility of ADFrFT through autofocus simulations and experiments. In the coaxial multi-distance coherent diffraction imaging experiment, we achieved a higher imaging quality compared to physical ranging by accurately correcting the diffraction distance through ADFrFT autofocus.