# Improvements of Computational Ghost Imaging by Using Sequenced Speckle
## 3 Experiments and Simulation Results  
In order to assess the effectiveness of speckle fields in three groups (DS, DD, DG) for image reconstruction, we conducted experiments and simulations using a window-shaped object. We evaluated the image quality based on the contrast-to-noise ratio (CNR) and resolution, which are significant measures for assessing image reconstruction. Initially, we compared our novel approach to the traditional TGI method, which relied on fixed  
Figure 4: Ordering principle of sequenced random speckle patterns with different speckle composition groups (rule three). Each group is denoted by DG followed by the group number and the pattern indices within the group. For example, DG-1-1 to \(-\)12 represents Group 1 with patterns 1 to 12. DG-2-1 to \(-\)6 represents Group 2 with patterns 1 to 6, and so on. DG represents a combination of speckle sequences with multiple speckle sizes. Figure 3: Ordering principle of sequenced random speckle patterns with different speckle size steps and directions. (**a**) Ordering with different speckle size steps (first rule, DS: Different Step. DS represents speckle sequences with different increases in speckle size). (**b**) Comparison of different speckle sorting directions with fixed speckle size steps (second rule, DD: Different Directions. DD represents two sets of speckle sequences in which speckle size increases and decreases, respectively). speckle sizes ranging from 27 \(\upmu\)m to 516 \(\upmu\)m. Our results confirmed that increasing the speckle size up to the maximum value resulted in an increase in CNR, with a maximum CNR of 1.8634 obtained at a speckle size of 164.5 \(\upmu\)m in Figure 5. However, we observed a drop in visibility in the retrieved ghost images when the speckle size exceeded 297.5 \(\upmu\)m, even though the CNR remained constant. This phenomenon was evident from the blurred object boundaries in the retrieved ghost images, which was attributed to higher noise levels between intensity peaks compared to the background noise. To assess imaging quality in such cases, we employed resolution as a tool, and the best resolution of 1.16 was obtained with the smallest speckle size of 27 \(\upmu\)m in Figure 5. While the TGI demonstrated good CNR, the corresponding resolution was lower (R = 1.10). Overall, our experimental results were consistent with existing theories [18; 19], enabling subsequent comparisons with the SGI method. According to the first rule of the SGI with different steps, we present the results for the five DS groups (DS-1 to DS-5) in the experiments shown in Figure 6. As the mean step size for speckles increased from 26.68 \(\upmu\)m to 513 \(\upmu\)m from DS-1 to DS-5, respectively, the imaging quality significantly decreased. The resolution of the retrieved ghost image for DS-1 and DS-2 was higher compared to the other groups. The imaging performance of the SGI in groups DS-1 to DS-3 also surpassed the best CNR obtained in the TGI. This indicates the superiority of SGI in reconstructing objects of unknown sizes. Notably, the SGI for DS-1 with a mean speckle size step of 26.68 \(\upmu\)m could reconstruct the object with a higher CNR than the TGI, while maintaining a similar resolution. To validate our findings, we simulated the observed behavior of the SGI using the same model employed for TGI, as shown in Figure 6. The simulation results closely matched the experimental results, demonstrating that the SGI with different steps yields better images with a reduced number of iterations. We apply the second rule of SGI, which involves speckle sorting directions, to select two speckle size ranges with a mean speckle step size of 26.68 \(\upmu\)m. This allows us to compare the SGI in opposite sequence directions.