Study of a Compton backscattering wall defects detection device using the Monte Carlo method

As shown in Fig. 1, we take the concrete wall with the same cross section and different thickness as the scatterer, fix the distance between the radiation source and the scatterer, distribute the detector on a quarter circle close to the direction of the source container, and calculate the area of the backscattering peaks under different detection angles; and the obtained results are shown in Fig. 2. It can be seen from Fig. 2 that the area of backscattering peak increases with the increase of concrete thickness, but it does not increase infinitely. When the thickness of concrete reaches 8 cm, the backscattered rays are absorbed in a large amount, and the area of backscattering peak changes slowly and gradually tends to saturate. At this time, the thickness is called the saturated thickness of the concrete. When the wall defect is outside the saturated thickness of the concrete, the change in the number of particles received by the detector is easily submerged by the noise caused by various uncertain factors in the actual detection, and the effect of detecting and imaging the wall defects cannot be achieved. Therefore, the detection range of the wall defect of the device is limited to 8 cm from the lower surface of the defects to the detection surface of the concrete.

Fig. 2.

The selection of receiving backscattered particles’ angle is the key part of the detection system design. The trend of the backscattering peak area with the angle is variously simulated in steps of 15° for the range of backscattering angle of 105–180°, and it can be seen from Fig. 2 that the number of backscattered particles increases with the increase of angle, except for 180°, which is completely opposite to the direction of incident particles. After calculation, in this model, the angle at which the backscattered rays avoid the shielding of the source container should be <160°.

In this paper, the volume element cut from the intersection of the front collimation of the radioactive source container and the rear collimation of the detector system is called the scattering element. The model shows that the volume of the scattering element is different at different detection angles, which has an impact on the defect detection efficiency of the device. Also varying with the detection angle is the backscattered peak area received by the detector. In order to consider the effects of the two variations simultaneously, this paper normalizes the two variations of scattering angle-scattering element volume and scattering angle-backscattering peak area curves in the range of backscattering angle <160° in steps of 10°. The normalized curves are multiplied together, and the results are shown in Fig. 3.

Fig. 3.

In Fig. 3, the horizontal axis is the backscattering angle, and the vertical axis is the product of the scattering element volume and the backscattering peak area, which is expressed by Q. It is dimensionless, and the significance is to measure the effect of the backscattering angle on the scattering element volume as well as the backscattering peak area at the same time. As can be seen in Fig. 3, the Q value increases and then decreases with the increase of the backscattering angle within the detection range that meets the requirements of this model, and the turning point is located in the interval around 150°. Therefore, in order to ensure the detection efficiency and maximize the utilization of source particles, the detection crystal is placed at a scattering angle of 150°.

In order to improve the detection intensity of backscattered rays and reduce the interference of backscattered rays between different measurement units, the changing relationship of energy spectrum is simulated and studied when Pb, Fe, W, Cu, and other materials are used as the rear collimating materials of the detector. The results are shown in Fig. 4. It can be seen from Fig. 4 that when other materials except Cu are used as rear collimator, there are fluorescent X-ray peaks around 70 keV in the energy spectrum, which have an impact on the counting of backscattering peak areas. Because the Compton backscattering signal is weak, the existence of fluorescence X-ray peaks will cause great error in the results, and when Cu is used as the rear collimating material, the backscattering peak counts are the highest and the peak area counts are the largest, and so Cu is selected as the rear collimating material of the detector.

Fig. 4.

It is not easy to determine the defects in a concrete wall using merely the naked eyes; coupled with the existence of quantum noise, it is necessary to ensure the single detection time in order to accurately distinguish the wall defects. If the defects can be roughly located and the detection range can be reasonably planned during the inspection process, the overall detection speed can be improved.

The defect orientation detection process is shown in Fig. 5; in this device, symmetrically distributed detectors are used to detect defects, and the present study adopts the following procedure for this purpose: the ray incident direction is taken as the boundary, and since the backscattered rays detected by the detector located in the positive half axis of the y-axis mainly come from the defects in the negative half axis of the y-axis, it is s et as a negative detector. Similarly, the detector located on the negative half axis of the y-axis is set as the positive detector. We fix the size of the defect, move the ring array detector in the y-axis direction to detect the defect, and analyze the situation when the defect is located at different depths. As the defect detection depth increases, the amount of backscattered particles received by the detector becomes less and less, the quantum noise ratio increases, and the effective signal ratio decreases [22]. To achieve the goal of detecting defects at deeper locations, the ratio method is used here to eliminate the effect of quantum noise and emphasize the change in the effective signal. Compared with the ratio calculation using the result value of the count without defects as the reference group, the ratio calculation using the result value of the count with any known defect size and position as the reference group can predict the size and position of the defects based on the change in the number of backscattered particles, which would in turn be based on the orientation judgment, and reasonably set the detection range according to the magnitude of the change combined with the presetting algorithm. In this study, the detection value of the defect located at 0.5 cm depth with a radius of 0.8 cm is used as an example of the reference group, and the defects with a radius of 1 cm and depths of 1 cm, 4 cm, and 7 cm are analyzed, the results of which are shown in Fig. 6.

Fig. 5.

Fig. 6.

It can be seen from Fig. 6 that these curves have the same trend regardless of the distance between the wall defects’ surface and the detection surface. If analyzing from left to right: at the beginning of detection, the wall defect is located below the detector. In the first period of time, the wall defect did not enter the detection range of any detector, and so the counting of the positive and negative detectors is in a relatively stable state, as shown in area I in the figure. When the detector gradually approaches the location of the defect, the wall defect first enters the detection range of the negative detector. At this time, the ratio of the negative detector will fluctuate compared with the positive detector, as shown in area II in the figure. With the movement of the detector, the volume of wall defects entering into the negative detector detection range increases and begins to enter the detection range of the positive detector, and at this time the ratio of both positive and negative detectors will have a large fluctuation, as shown in area III in the figure. When the detector gradually moves away from the location of the defect, the wall defect gradually emerges out of the detection range of the negative detector, and thereafter only exists in the detection range of the positive detector. At this time, the ratio of the positive detector will fluctuate compared with the negative detector, as shown in area IV in the figure. Finally, the wall defect will gradually move away from the detection range of any detector, and the counts of the two detectors will be in a relatively stable state again, as shown in area V in the figure. Therefore, if area II occurs in the measurement, it indicates that the defect exists only in the detection range of the negative detector. All that is needed is to move along the detection range of the negative detector to reach the location of the defect. If area III occurs in the measurement, it indicates that the defect exists in the detection range of both positive and negative detectors, whose size and position will increase the number of backscattered particles compared to the reference group, and the size and position of the defect can be predicted according to its variation and combined with the presetting algorithm to improve the overall detection speed.

The objectives of the detection of defects include the cross-sectional size of the defect, the thickness of the defect, and the depth at which the defect is located. To begin with, the cross-sectional size of the defect is judged. The effect of simulating wall defects models with different cross-sectional sizes is shown in Fig. 7. Under the same conditions, the larger the cross section of the defect, the less the number of particles received, and the more obvious the change range. The defects simulated in this model are several cylinders with a radius of 1–3 cm. Taking 0.5 cm as the detection step, the detection counts of the detector are displayed in the range of r = 2.5–4.5 cm. The simulation results have the same variation law as the set defect radius, and the difference is constant at the same depth.

Fig. 7.

When the device is used to determine the thickness and depth of defects, the two parameters are closely related. We fix the cross-sectional area of the defects, change the depth and thickness of the defects for simulation, and calculate the ratio between the simulation results and the number of backscattered particles received in the defect-free state. The effect is shown in Fig. 8.

Fig. 8.

It can be seen from the figure that the counting of backscattered particles at a certain position mainly depends on the depth of the defect at the current position and the thickness of the defect in the direction of the incident ray, and has little to do with the cross-sectional area of the defect under the current condition. When the position of the defects exceeds the saturated thickness of the concrete wall, with the deepening of the defects’ depth, the corresponding curve will tend to coincide with the curve with thinner defect thickness at the same depth, that is, when the defect thickness at a certain depth increases beyond the saturated thickness of the concrete, the contribution of the part exceeding the saturated thickness to the overall counts will gradually decrease. Therefore, only the defects located completely inside the saturated thickness of the concrete walls are analyzed and discussed here. Excluding the data other than the saturated thickness in Fig. 8, we fit the data into two cubic curves with correlation coefficients >0.99, within which the maximum error fluctuation range for the detection of defect depth as well as thickness was ±1 cm.