Correction of rotational position error in Fourier space for ptychography

X-ray ptychography has an ultrahigh resolution at the nanoscale and an extended field of view, making it widely used in many cutting-edge fields. In this technique, precisely determining the scanning position is crucial for improving imaging quality and resolution. In this study, we propose and validate a novel method for correcting rotational position errors in ptychography. This method combines the Fourier-space bisection search with the ptychography reconstruction algorithm. By progressively rotating the diffraction pattern in Fourier space and continuously narrowing the predicted angular error interval based on the reconstruction errors from inner loops, the method iteratively approaches and determines the deflection angle of the detector plane relative to the sample plane (around the optical axis). This method can correct rotational angle errors efficiently in Fourier space and is highly robust against uncertainties in experimental parameters and diffraction signal quality. Both simulation and experimental reconstructions demonstrate the method's capability to precisely correct rotational errors and recover fine sample structures, thereby improving imaging resolution.