2.1 The CR-39 and its exposure

The CR-39 detector material was manufactured by Fukuvi Chemical Industry Co., Ltd, Japan. Samples in 1 cm×1 cm size were cut from the material for experiments. A total of 128 sample detectors were randomly divided into two groups. Group A was used for investigating artifact tracks without any radon exposure. Group B were set in the passive integrated radon monitor (PIRM) we developed^[14] to study the alpha tracks after exposed to 2.02 kBq·m⁻³ of ²²²Rn in a chamber for 168 h (about 340 kBq·m⁻³·h of integrated radon exposure).

2.2 Chemical etching

All of the detectors were chemically etched in 6.25 N water solution of NaOH at 90±0.1°C. In order to investigate the artifact and alpha tracks in different etching periods, the etching was performed in eight stages, with one hour for each stage. The etched samples were taken out and cleaned for track analysis.

2.3 Track analysis

Figure 1 shows the automatic track counting system we developed. It is built on an optical microscope with a ×4 objective lens and a CCD camera. A computer controlled three-dimensional mobile object stage is implemented for autofocus and the detector movements. The software in Visual C++ development environment (Fig. 1b) is responsible for the motion control, image processing, auto-focusing and track counting. In routine application, the alpha tracks can be identified automatically from the artifact tracks based on the settings of binary threshold, size threshold and circularity threshold for the images. In this study, in order to obtain more information on the size and size-distribution of artifact and alpha tracks, the settings of size threshold and circularity threshold were banned.

Fig. 1Full-screen View

The automatic track counting system.

2.4 Overlap correction and its uncertainty

A Monte Carlo code was developed based on Matlab^® to investigate track overlap for different track densities. Fig. 2 shows an example of the simulation regions and overlapped tracks. In the simulation, the code randomly placed tracks in the 1 mm ×1 mm simulation region and counted the tracks. To avoid the boundary effects, the simulation region was surrounded by a buffer region. As shown in Fig. 1(b), most of the track images in the radon system are quasi circular or circular, for the sake of simplicity, circular tracks were assumed in simulation. Track diameters were chosen from measured size distributions. When the center-to-center distance of two tracks (D) was less than the sum of their radii (R₁ and R₂), i.e. D≤R₁ +R₂, the two tracks were regarded as overlapped tracks and counted as one track^[15].

Fig. 2Full-screen View

Simulation region and overlapped tracks.

For a specific track density of m (tracks/mm²) generated by the code, the simulations were repeated for 20000 times. The relative standard uncertainty for counting due to overlap effect can be estimated by ^[16]:

where n_i is the track density counted in each simulation (tracks/mm²); N is the repeat times of the simulations; n_mean is the arithmetic mean of n_i. The overlap correction factor K is defined as^[17]:

2.5 Verification of overlap correction

In order to verify the simulation results, five groups of PIRM monitors, 10 pieces each, were exposed to 10 kBq·m⁻³ of radon concentration in the standard radon chamber at Shanghai Institute of Measurements Technology (SIMT). The five groups were exposed to integrated radon exposures of 500–2500 kBq·m⁻³·h. The exposed CR-39 detectors were etched in a 6.25 N water solution of NaOH at 90±0.1°C for the optimized etching period, and counted by the auto-counting system.

3.1 Size distribution of artifact tracks

Figure 3 shows the size distributions of artifact tracks on the CR-39 detectors without any radon exposure after etching 1–8 hours. The background tracks from radon and its progeny were distinguished from artifact tracks manually. Although the number and size distribution of artifact tracks increase slightly with the etching time, most of the artifact tracks are less than 12 μm in diameter.

Fig. 3Full-screen View

Size distribution of artifact tracks for different etching hours.

3.2 Size distribution of alpha tracks

Figure 4 illustrates the track images of the radon-exposed CR-39 detectors within an area of 0.5 mm ×0.5 mm after etching for 1–8 h. Some inclined tracks occur for the samples of T≤ 5 h, while most of the tracks become quasi circular or circular for the samples of T >5 h. This indicates that the tracks might be over-etched at T > 5 h^[10]. Meanwhile most of the tracks enlarge with increasing etching time, hence the increase of possibility of overlapping tracks.

Fig. 4Full-screen View

Track images of the detectors etched for different hours.

Figure 5 shows the size distributions of alpha tracks on the CR-39 detectors at different etching hours. They were re-plotted by subtracting size distributions of the control group from the experimental group for corresponding etching hour. Most of the tracks enlarged with etching time in different growth rates. The track sizes for 1–8 etching hours are 9.4±3.3 μm (1.6–17.3 μm), 13.2±4.9 μm (1.6–24.6 μm), 18.5±7.2 μm (1.6–36.5 μm), 24.8±9.0 μm (1.6–48.8 μm), 33.3±10.9 μm (1.6–66.2 μm), 39.5±13.8 μm (6.2–78.4 μm), 44.6±17.3 μm (6.2–90.2 μm) and 50.1±19.7 μm (6.2–96.5 μm), respectively. The standard deviation of the track sizes expanded from 3.3 μm at 1 h to 19.7 μm at 8 h. This indicates that negative effects in track counting may occur for an automatic counting system, especially in recognition of overlapped tracks.

Fig. 5Full-screen View

Size distribution of alpha tracks for different etching time

3.3 Errors in track discrimination

Despite technique developments in automatic discrimination of tracks in the past decades^[18-20], the threshold of track size was still a fundamental parameter for the automatic counting system to eliminate most of the artifact tracks. An appropriate threshold can significantly reduce uncertainty in track discrimination. In general, two types of discrimination errors are considered. Type-I is to reject small-size alpha tracks, while Type-II is to identify artifact tracks as big as alpha tracks. Having neglected the influence of geometrical parameters other than the diameter, Table 1 lists the two types of errors for different thresholds and etching time based on the experimental data. The results show that Type-II error deceases rapidly with the threshold, while Type-I error depends on the etching time obviously. At etching time T = 5–8 h, it was reasonable to set the threshold at Φ12 μm. Therefore, taking the discrimination error, deviation in track size and time cost into account, an appropriate etching time for this system is 5h.

3.4 Overlap correction

Based on size distribution of the tracks etched for 5 h, the overlap correction curve for the simulated track densities is plotted in Fig. 6. It shows that the overlap effect may cause nearly 10% loss in track counting when the track density is 50 tracks·mm⁻², and the counting loss will exceed 70% when the track density reaches to 200 tracks·mm⁻². It indicates that the overlap correction is important for an accurate counting when the track density is greater than several tens.

Fig. 6Full-screen View

Overlap correction factor for different track densities.

3.5 Experimental verification results

Figure 7 shows the relationships between track density and radon exposure before and after overlap correction. The mean track density has a non-linear response to the radon exposure, while the corrected track density has an excellent linear response to the integrated radon exposure. After overlap correction, the range of linear response for PIRM can reach to at least 2500 kBq·m⁻³·h with a detection efficiency of 6.6×10⁻³ tracks·cm⁻²·Bq⁻¹·m³·h⁻¹. The results revealed that the simulation provides a reliable overlap correction.

Fig. 7Full-screen View

Relationships between track density and radon exposure

3.6 Uncertainty of track counting

The uncertainties of alpha track counting for an automatic system mainly result from three factors, i.e., the error of track discrimination, the uncertainty due to overlap effect and the statistical fluctuation of incident particles. The error in track discrimination is usually considered as the inherent characteristics of an automatic reading system, which is determined by the mechanical and optical properties, and the discrimination strategy as well, of the system. However, the uncertainties due to overlap effect and the statistical fluctuation of incident particles depend greatly on the track density.

Figure 8 shows the two uncertainties as a function of track density. The relative standard uncertainty due to overlap effect, U_OL, was estimated by Eq. (1) based on Monte Carlo simulation, while the relative standard uncertainty due to statistical fluctuation was calculated by U_ST=(n_meanSK)^−1/2,^[21] where n_mean is the mean track density on CR-39, in tracks·mm⁻²; K is the overlap correction factor; and S is the scanned area on each CR-39, in mm². The results indicate that the uncertainty due to overlap effect increases with the track density, while the statistical fluctuation shows the opposite trend. Based on the etching conditions (6.25 N of NaOH, 90±0.1°C, 5h) in this study, it was estimated that the relative uncertainty of the track counting system would be less than 6%, at track density of 10–160 tracks·mm⁻².

Fig. 8Full-screen View

Relative uncertainty for different track densities