## 3 Experimental Setup and Results  
The experimental setup to study the evolution of the CNR with the pixel intensity distribution is shown in Figure 1. A helium-neon laser (632.8 nm) and a rotating diffuser in the focal plane of a lens constituted a nonuniform pseudothermal light source. Adding further elements into the beam path, we fully controlled the pixel distribution. With an adjustable neutral density filter, we increased or decreased the brightness of speckles' pixel intensity distributions to change the peak displacement. Inserting a second ground glass located before the diffuser allowed us to adjust the FWHM of speckles' pixel intensity distributions. Finally, by opening the aperture to change the beam waist and focal length of the lens, we ensured the same average speckle size in all experiments [21; 22]. To exclude the influence of variation in speckle size on the CNR, we kept the scatter size to 30 \(\upmu\)m in the experiment. The generated speckle field was divided by a beam splitter into two spatially correlated beams, namely the reference beam path and the object beam path. The object beam hit the object (letter \"\(\upmu\)\"), and this was followed by the integration of the transmitted light by a single-pixel detector, resulting in the so-called bucket signal. It is worth noting that the reference beam never interacted with the object, and its speckle pattern was recorded with a CCD camera having 1200 \(\times\) 1600 pixels and an effective pixel size of 5.86 \(\times\) 5.86 \(\upmu\)m\({}^{2}\). Ghost imaging with randomly distributed fields works only for the same propagation lengths of the beam path from the beam splitter to the object and the beam path from the beam splitter to the CCD camera to conserve correlations. The propagation lengths' error between the beam paths was within a few millimeters. To avoid errors when measuring the CNR, we kept the position of the pseudothermal source and the measured target constant during the whole experiment and measured the same image area retrieved. The \(\upmu\)-shaped transmitting object was laser-cut in black-coated 100-\(\upmu\)m-thick aluminum foil to ensure stability and to fully block light in the outer areas. Figure 1 also shows the designed object and the measured laser-cut result. The light transmitted the letter \"\(\upmu\)\". The width of the vertical bar of the letter \"\(\upmu\)\" in the object was 60 \(\upmu\)m. Correspondingly, the transmitted area of the object was calculated to be \(\sim\)77 \(\times\) 10\({}^{3}\)\(\upmu\)m\({}^{2}\). The CNR of the ghost image relied on the speckles' pixel intensity distribution from the nonuniform pseudothermal light, which was detected by the CCD camera. The speckles' pixel intensity distribution was manipulated by different parameters in the experiment, as described above. To better understand and generalize the role of the speckles' pixel intensity distribution on the CNR of the retrieved ghost images for an object with a given size, we first evaluated the CNR as a function of the FWHM of the Gaussian-like speckles' pixel intensity distribution from the nonuniform pseudothermal light. Our camera had a dynamic range of 8 bits, so the maximum pixel count was 256. To generalize our findings, we normalized all pixel counts to the maximum count rate. In our experiment, the FWHM of the speckles' pixel intensity distribution was increased from 92 to 146 pixel intensity values in six steps with a fixed speckle size of 30 \(\upmu\)m by reconstruction with 10,000 iterations under the same conditions. We can see from Figure 2d that the mean CNR of the object \"u\" increased rapidly from 0.51 to 1.13 with an increase in the FWHM of the speckles' pixel intensity distribution. By contrast, after being modulated by corresponding optical elements, the FWHM of the speckles' pixel intensity distribution became wider, as we can see in Figure 2a. To compare the influence of the FWHM on the speckles' pixel intensity distribution, we normalized the pixel count to the maximum.