Objective The second-order auto-correlation technique based on Hanbury Brown-Twiss (HBT) can obtain the Fourier spectrum information of a target even in the conditions of incoherent source illumination and near-field detection, which has better advantages in the field of moving-target imaging, imaging in scattering media, and X-ray imaging. However, a mass of measurements is required and the imaging resolution is also restricted by the pixel scale of the detector for high-quality Fourier spectrum images for HBT. At present, many related 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 such methods is usually long and cannot improve the system’s imaging resolution. 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 at lower measurement times.
Methods The proof-of-principle schematic of super-resolution imaging method based on autocorrelation and spectral ptychography is shown in Fig. 1. The corresponding super-resolution reconstruction framework is displayed in Fig. 2, 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 described by Eq. (5), Fourier spectrum images of the target in 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.
Results and Discussions The validity of the super-resolution imaging method based on auto-correlation and spectral ptychography is experimentally demonstrated by using the setup in Fig.1. When the number of measurements N=500, Fig. 4 gives the experimental results in different pixel scales of the detector. The results indicate that the imaging resolution increases with the pixel scale of the detector. However, when the number of measurements is small, both the Fourier spectrum and the real-space image obtained by single point detection are poor (Fig. 4 (c)). When the method of multi-point parallel correlation reconstruction and spectral ptychography is 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 in the same parameters (Fig. 4(c) and Fig. 4(f)). In addition, the experiments also show that for a 50×50 spectral image, high-quality super-resolution imaging can still be obtained even if the measurement times are 200 (namely the sampling rate is 8%) (Fig. 5).
Conclusions In summary, we propose a method based on multi-point parallel correlation reconstruction and spectral ptychography processing to improve the signal-to-noise ratio and spatial resolution of HBT system. Both theoretical and experimental results demonstrate that the proposed method can not only reduce the measurement number required for high-quality Fourier spectrum images of the target (with a sampling rate of 8%), but also achieve super-resolution imaging with two times ability capacity. This method provides important insights for super-resolution microscopy imaging and high-resolution imaging of moving target.