# Ghost Imaging by a Proportional Parameter to Filter Bucket Data
## 2 Experimental Setup and Principle  
The schematic diagram of the experimental system is shown in Figure 1, which consisted of the optical setup part and the data processing part. In the optical setup part, the pseudo-thermal light source was generated through a laser beam illuminating a rotating ground glass. The pseudo-thermal source was divided into the reference beam path and the object beam path by a 50:50 beam splitting mirror. After the object beam illuminated the target object with transmission function \(\mathbf{T}(x,y)\), its total light intensity was recorded by a charge coupled device (CCD1), and the nth measurement value was denoted as \(B_{n}\). At the same time, the optical intensity distribution on the surface of the object was recorded by another same model CCD(CCD2) located at the same distance in reference path with the object (L1 = L2), and the nth measurement value was denoted as \(\mathbf{I_{n}}(x,y)\). We defined the nth measurement value \(B_{n}\) and \(\mathbf{I_{n}}(x,y)\) at the same moment as a set of sampled data. Since the \(B_{n}\) and \(\mathbf{I_{n}}(x,y)\) were one-to-one corresponding, when we screened \(B_{n}\), the \(\mathbf{I_{n}}(x,y)\) was screened as well. In the data processing part, after screened all of the \(B_{n}\) and \(\mathbf{I_{n}}(x,y)\), these data that met the conditions participate in reconstructing the object. Assuming that the total measurements time were \(N\), the conventional GI algorithm can be expressed as:  
\[\mathbf{T}_{GI}(x,y)=\frac{1}{N}\sum\limits_{n=1}^{N}{(B_{n}-\langle B_{n}\rangle )\mathbf{I}_{n}(x,y)} \tag{1}\]  
where \(\langle B_{n}\rangle=\frac{1}{N}\sum\limits_{n=1}^{N}{B_{n}}\) denotes the ensemble average of \(B_{n}\). It is known from Equation (1) that the group of data had little influence on retrieving the object information when \((B_{n}-\langle B_{n}\rangle)\) approximated zero. Therefore, removing these \(\langle B_{n}\rangle\) and their corresponding \(\mathbf{I_{n}(x,y)}\) simplified the calculation and reduced reconstruction time cost. Now, the question became how to find these data. We know that the mean value approximately equals the median when the sampled data are sufficient. Fortunately, a traditional GI algorithm and most modified reconstruction algorithms require a large amount of sampled data. In other words, those \(B_{n}\) which equal or nearly equal to \(\langle B_{n}\rangle\) are in the exact middle when all \(B_{n}\) are arranged from large to small. To confirm this statistical property, 5000 sets of sampled data used in the experiment part were organized to tabulate the frequency statistics histogram, as shown in Figure 2, where the \(B_{n}\) equals to \(\langle B_{n}\rangle\) ranks 2438 th when all of \(B_{n}\) were arranged from large to small, and approximately equals to the median. According to our experiments, DTTCI was effective for NGI and DGI for a similar reason. As can be seen in Figure 1, those \(B_{n}\) meeting the condition that \((B_{n}-\langle B_{n}\rangle)\) equals or nearly equals to zero were located in the very center when all of \(B_{n}\) were arranged from large to small. Since the amount of \(B_{n}\) was rather large, so we could remove a certain number of \(B_{n}\) values distributed around \(\langle B_{n}\rangle\) along with their corresponding \(\mathbf{I_{n}(x,y)}\). To implement our method, the major obstacle was how to preselec  
Figure 1: The schematic diagram of the experimental setup and data processing. L1 is the distance between the rotating ground glass and the measured object, L2 is the distance between the rotating ground glass and the charge coupled device 2 (CCD2) (L1 = L2). f is the focal length of the lens. Figure 2: Frequency statistics histogram of \((B_{n}-\langle B_{n}\rangle)\). The red box represents the approximate range of data we deleted. threshold values that were relative to the average of \(B_{n}\) since the average of \(B_{n}\) could only be determined after all the values of \(B_{n}\) had been measured and calculated.