Super-resolution imaging based on auto-correlation and frequency ptychography

<sec>The second-order auto-correlation technology based on Hanbury Brown-Twiss (HBT) can obtain the Fourier spectrum information of a target even under the conditions of incoherent source illumination and near-field detection, which has better advantages in the fields of moving-target imaging, imaging in scattering medium, and X-ray imaging. However, a great number of measurements are required and the imaging resolution is also restricted by the pixel scale of the detector for high-quality Fourier spectrum image for HBT. At present, many relevant data processing methods and reconstruction algorithms can reduce the number of measurements required for the acquisition of high-quality spectral information, but the time of image reconstruction required by these methods is usually long and cannot improve the imaging resolution of the system. In recent years, Fourier ptychography based on real-space image detection has proven that higher-resolution imaging can be obtained through spectral ptychography and frequency extension. In this paper, by combining the idea of Fourier ptychography with HBT, a processing method based on multi-point parallel correlation reconstruction and spectral ptychography is proposed, which attempts to obtain high-quality spectral information of the target and achieve super-resolution imaging with few measurements. The proof-of-principle schematic of super-resolution imaging method based on autocorrelation and spectral ptychography is obtained. The corresponding super-resolution reconstruction framework is displayed, which mainly consists of three steps: multi-point parallel correlation reconstruction, spectral ptychography, and real-space image reconstruction based on phase-retrieval algorithm. Firstly, based on the physical mechanism, Fourier spectrum images of the target at different detection points are obtained through multi-point parallel correlation reconstruction. Secondly, according to the idea of spectrum ptychography, the frequency shifted spectrum obtained by multi-point parallel correlation reconstruction is aligned to form an extended spectrum. Finally, the target’s real-space image is reconstructed by phase-retrieval algorithm.</sec><sec>The super-resolution imaging method based on auto-correlation and spectral ptychography is experimentally verified by using the setup. At the number of measurements <i>N</i> = 500, the experimental results are obtained on different pixel scales of the detector. The results indicate that the imaging resolution increases with the pixel scale of the detector increasing. However, when the number of measurements is small, both the Fourier spectrum and the real-space image obtained by single point detection are poor. When the multi-point parallel correlation reconstruction and spectral ptychography are adopted, the signal-to-noise ratio of the reconstructed Fourier spectrum can be significantly improved, and its spectral bandwidth can be expanded to twice that of the original spectrum at the same parameters. In addition, the experiments also show that for a 50×50 spectral image, even with 200 measurements (i.e. a sampling rate of 8%), high-quality super-resolution imaging can still be obtained.</sec><sec>All in all, the proposed method provides important insights into super-resolution microscopy imaging and high-resolution imaging of moving target.</sec>