# Parallel Ghost Imaging with Extra Large Field of View and High Pixel Resolution
## 3 Discussion on Speckle Patterns, Sampling Rate, and Reconstruction of Extra-Large Speckle Space  
Speckle patterns play a decisive role in the reconstruction quality of ghost imaging, as the resolution of the reconstructed image cannot be finer than the smallest effective feature of the speckle patterns. In general, smaller pixels in the reference arm allow the detector to capture higher-density mask information, which leads to better image quality. Larger pixels in the object arm enable the detector to capture encoded object information more quickly, which results in a lower radiation dose. The effective aperture of 200-mesh sandpaper is approximately 75 \(\upmu\)m, which cannot describe the smallest feature of the mask. Irregular particle edges, sharp density gradients within the particles, and the stacking of seven layers of sandpaper all contribute to making the minimum effective feature far smaller than the particle width. The large fluctuations in the X-ray absorption ability are referred to as the X-ray modulation ability, and such fluctuations are crucial for the realization of ghost imaging. The mask's modulation capability for X-rays is shown in Figure 4d. The point spread function (PSF), as the autocovariance of the mask pattern, sets the soft upper limit for the resolution of the final ghost imaging results. However, at high sampling rates, the PSF may be surpassed. The full width at half maximum (FWHM) of the PSF in both the horizontal and vertical directions is shown in Figure 4a,b. The Fourier ring correlation (FRC), another spatial resolution criterion generated by the speckle pattern, serves as the hard upper limit for GI resolution. The FRC of PGI is 1.73 \(\upmu\)m, smaller than the 3.25 \(\upmu\)m pixel size of the object arm detector, thus satisfying the super-resolution condition of ghost imaging, as shown in Figure 4e. These three characteristic length scales are interrelated but distinct. The reconstruction quality is also influenced by the degree of correlation between speckle patterns. If one speckle used for image reconstruction is a linear combination of other recorded speckles, it represents ineffective sampling. The statistical histogram of the correlation levels between any two speckles (combination of \(C_{400}^{2}\)) is shown in Figure 4c, which implies that random speckles can be approximated as mutually orthogonal. Figure 3: Extra-large field of view and high-resolution parallel ghost imaging reconstruction result: 400 measurements, 400% sampling rate, 0.325 \(\upmu\)m/px pixel resolution, 14,000 \(\times\) 10,000 image size. As mentioned earlier, ghost imaging, when combined with compressed sensing, can significantly reduce the number of measurements required to achieve high-quality reconstructions. A lower sampling rate means higher experimental efficiency and lower radiation dose. The reconstruction results at different sampling rates, from low to high, are shown in Figure 4f-m. With low sampling rates and few measurements, parallel ghost imaging with extra-large field-of-view and high-pixel resolution still performs well. In the experiment, various factors such as X-ray energy, reconstruction block size, registration between the reference and object arms, lens distortion, experimental errors, and sample complexity all affected the final image quality. Among these, the registration issue was the most critical. Parallel ghost imaging still has considerable room for improvement in terms of resolution in the reconstruction results. If these issues can be addressed, the reconstruction could reveal many fundamental details of the sample that are currently invisible, transforming the \"ghost\" images into more informative representations. Based on this, there is still a long road ahead for further development. Figure 4: Analysis of randomly modulated speckle patterns: (**a**) Point spread function (PSF) of the speckle in the horizontal direction. (**b**) Point spread function of the speckle in the vertical direction.