# Studies on the retrospective thoron measurements by CDs/DVDs: A posteriori calibration and influence of environmental factors

Strahil Georgiev, Ivelina Dimitrova, D. Pressyanov, Benoit Sabot, Nathalie Michielsen, Krasimir Mitev, Sylvain Bondiguel

► To cite this version:

Strahil Georgiev, Ivelina Dimitrova, D. Pressyanov, Benoit Sabot, Nathalie Michielsen, et al. Studies on the retrospective thoron measurements by CDs/DVDs: A posteriori calibration and influence of environmental factors. Radiation Measurements, 2024, 175, pp.107147. 10.1016/j.radmeas.2024.107147. cea-04799489v2

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# Studies on the retrospective thoron measurements by CDs/DVDs: A posteriori calibration and influence of environmental factors

S. Georgiev<sup>a, *</sup>, I. Dimitrova<sup>a</sup>, D. Pressyanov<sup>a</sup>, B. Sabot<sup>b</sup>, N. Michielsen<sup>c</sup>, S. Bondiguel<sup>b, c</sup>, K. Mitev<sup>a</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

**Keywords:**

Thoron

Retrospective measurements

A posteriori calibration

Environmental factors influence

## ABSTRACT

Past exposure to indoor thoron poses a significant risk for lung cancer. A method based on home-stored CDs/DVDs allows the estimation of past exposure through retrospective thoron measurements. However, these measurements are significantly affected by the geometry of the CD-case. In this paper, an improved a posteriori calibration procedure is proposed that mitigates the CD-case effect, enabling the estimation of the disk's calibration factor with uncertainty of about 20%. The influence of the temperature, pressure and humidity on the thoron measurements is also studied and no effect is observed. The CD method overcomes a major source of error in evaluating the past thoron exposure related to the yearly changes in indoor thoron that could even reach an order of magnitude.

## 1. Introduction

Rn-222 (shortly radon or "Rn") and $^{220}$Rn (shortly thoron or "Tn") are natural isotopes of the noble gas Rn. They are part of the natural radioactive series of $^{238}$U (Rn) and $^{232}$Th (Tn), widely distributed in soil and building materials. As noble gases, Rn and Tn can escape from their place of origin and accumulate in closed spaces like buildings. Due to the difference in their half-lives (3.82 days for Rn, 56 s for Tn), Rn can travel much farther than Tn. High Rn concentrations often result from soil gas, while elevated Tn levels indoors are associated with high $^{232}$Th content in the building walls and floor (Cinelli et al., 2015; Jónás et al., 2016; WHO, 2009).

Currently, Rn is recognized as a major contributor to the radiation exposure of the population (Darby et al., 2005; Groves-Kirkby et al., 2016; WHO, 2009). Indoor Rn exposure is the second leading cause of lung cancer after smoking (Darby et al., 2005; WHO, 2009). National and international health protection authorities are actively working to reduce the Rn risk. Until recently, it was assumed that buildings with high Tn concentration were very rare (Cinelli et al., 2015; Tokonami, 2005, 2020), and Tn was primarily regarded as a potential source of error in measuring Rn concentration (Tokonami, 2005, 2020). However, recent research indicates that high Tn concentrations are common in

certain regions, and in these areas, the lung cancer risk associated with Tn surpasses that of Rn (Jónás et al., 2016; McLaughlin, 2010; Meisenberg et al., 2017).

The latency period of lung cancer is of the order of decades. Epidemiological studies on Rn-related lung cancer risk indicate that year-to-year variations in Rn concentrations significantly affect the exposure and risk estimation (Onishchenko and Zhukovsky, 2019). In the case of Rn, substantial changes in indoor concentrations can result from major reconstructions of the building, such as alterations in ventilation or energy-efficient modifications. In the case of Tn, even minor reconstructions like changing wallpapers or wall paint can alter Tn concentrations up to ten times (Cinelli et al., 2015; de With et al., 2016; Smetsers and Tomas, 2019). Therefore, retrospective estimation of the exposure (i.e., Rn/Tn concentration) is recommended for accurate risk assessment. Unfortunately, there is generally no information on the Rn and Tn history of buildings. For Rn, there are a few methods for retrospective measurements based on home-stored objects (e.g. CDs or DVDs (Pressyanov et al., 2012), matrices (Oberstedt and Vanmarcke, 1996), picture-frame glasses (Samuelsson, 1988), eye-glasses lens (Fleischer, 1987)), providing adequate estimates of past Rn exposure.

To the best of our knowledge, there is only one method for retrospective Tn measurements. The method relies on the track-etched

<footnote><sup>a</sup> Faculty of Physics, Sofia University "St Kliment Ohridski", 5 James Bourchier Blvd, 1164, Sofia, Bulgaria</footnote>

<footnote><sup>b</sup> Université Paris-Saclay, CEA, LIST, Laboratoire National Henri Becquerel (LNE-LNHB), F-91120, Palaiseau, France</footnote>

<footnote><sup>c</sup> Institut de Radioprotection et de Sûreté Nucléaire (IRSN), 31 avenue de la Division Leclerc, 92262, Fontenay-aux-Roses, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: strahilg@phys.uni-sofia.bg (S. Georgiev).</footnote>
properties of common CDs/DVDs stored in the building under study (Pressyanov et al., 2012, 2013). It has already been demonstrated that this method is suitable for retrospective Tn measurements (Pressyanov et al., 2012, 2013; Dimitrova et al., 2016; Georgiev et al., 2016); however, further comprehensive studies are still required. This paper addresses two key aspects of the metrological assurance of the method – the a-posteriori calibration of the disks for Tn measurements and the influence of environmental factors (such as temperature, pressure, humidity).

## 2. Materials and methods

### 2.1. Retrospective Tn measurements by home-stored CDs/DVDs

Initially, the method for retrospective measurements based on home-stored CDs/DVDs (referred to as the CD-method) was proposed and developed over the last two decades for retrospective Rn measurements (Pressyanov et al., 2012). This method relies on the ability of the polycarbonate material of the CDs/DVDs (made from a Bisphenol-A-based polymer) to absorb noble gases, particularly Rn, and the track-etched properties of this material. Subsequently, it was demonstrated that home-stored CDs/DVDs could also offer retrospective information for Tn (Pressyanov et al., 2012, 2013), again owing to their track-etched properties.

When a CD/DVD is stored indoors, its CD case acts as a diffusion barrier. Rn, Tn and their progenies, present in the ambient air, enter the case through openings and gaps in the case parts (see Fig. 1). Due to the extreme disequilibrium between Tn and its progeny (the average equilibrium factor indoors is 0.02 (UNSCEAR, 2008)), the contribution of the Tn progeny in the ambient air to the progeny inside the CD-case is negligible. Within the case, the decay of Rn and Tn generates progenies that plate-out on the CD/DVD and the case walls (see Fig. 1). Additionally, Rn and Tn are absorbed inside the disk volume (Pressyanov et al., 2012). Due to differences in their half-lives, Rn diffuses inside the disk, while Tn remains within the first 1–2 µm beneath the disk’s surface (Pressyanov et al., 2012, 2013). In a previous study (Georgiev et al., 2016), it was revealed that the dye layer on the labeled backside of the CDs prevents absorption. Therefore, Rn is only absorbed in the first few

hundred microns of the “front” side of the disk (the side facing the CD-reader’s laser and not in the backside (see Fig. 2).

As Rn, Tn, and some of their decay products are alpha-emitters (Table 1), two sources of alpha-particles are defined: an “inner” source due to Rn absorbed in the disk and its progeny generated inside the disk, and an “outer” source due to Rn, Tn, and some progeny in the air inside the case, progeny plated out on the disk and inner case walls, and Tn absorbed in a thin surface layer of the disk. Alpha-particles emitted from these sources form tracks in the disk material.

Due to the short range of alpha-particles, those emitted from the outer source reach a certain depth beneath the disk surface determined by the initial energy of the alpha-particles (see Table 1). The air gap between the disk and the CD-case is only a few millimeters, equivalent to a few microns of polycarbonate. Therefore, the outer source can be considered a flat surface source with a thickness of 3–4 µm. Conversely, the inner source, due only to absorbed Rn, forms tracks deep beneath the disk surface. The two sources create several layers in the disk volume, as illustrated in Fig. 2: Layer 1 with tracks due to all alpha-particles from both sources, Layer 1' with tracks due to all alpha-particles from the outer source, Layer 2 with tracks due to alpha-particles of $^{212}$Po and the inner source, Layer 2' with tracks only due to alpha-particles of $^{212}$Po, and Layer 3 with tracks only due to alpha-particles from the inner source. To estimate the thickness of the different layers, the ASTAR program (Berger et al., 2005) was used to calculate the specific energy loss of the alpha-particles in the polycarbonate material of the CD, combined with the polycarbonate track properties data provided by Vancraeynest et al. (1997). Due to these properties the alpha-particles maximum track length (depth) is shorter than its range in the polycarbonate (see Table 1).

To estimate the average Rn concertation, the tracks in layer 3 are analyzed (Pressyanov et al., 2012). A piece of the CD/DVD is cut and processed using a standard procedure (Pressyanov et al., 2012): A surface layer *d*, thicker than 76 µm (usually *d* = 80 µm) is removed by chemical pre-etching for about 80 min at 30 °C with chemical solution of $H_2O:KOH:CH_3OH = 1:0.937:0.702$ (mass proportion). Subsequently, the tracks are revealed via electro-chemical etching for 3.5 h at 25 °C with chemical solution of $H_2O:KOH:C_2H_5OH = 1:2.205:0.0505$ (mass proportion). During the first 0.5 h of the process the disks are treated only with the chemical solution and then AC high voltage with strength of 3 kV mm$^{-1}$ and frequency of 6 kHz is applied for the rest 3 h. The etched

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** (a) Picture of different CD-cases with holes pointed with arrows: 1. Standard case with 4 holes (2 at each side); 2. Standard case with 6 holes (3 at each side); 3. Thin case with 4 holes (2 at each side). (b) Scheme of CD-case with disk inside. Dashed arrows illustrate Rn and Tn entry in the CD-case. Solid arrows illustrate the plate-out of the progeny. The dashed rectangle is enlarged in Fig. 2.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Cross-section of a disk in a CD-case. The scheme illustrates the different zones (layers) of the disk in which alpha-particles from different origin can form tracks.</figcaption></figure>
<table><caption>**Table 1**
Initial energies, ranges and maximum track formation depths of Rn, Tn and their progeny in polycarbonate.</caption><thead><tr><th></th><th>Nuclide</th><th>E,keV</th><th>range, µm</th><th>max track depth, µm</th></tr></thead><tbody><tr><td rowspan="4">Rn chain</td><td>Rn-222</td><td>5489</td><td>37.0</td><td>35.2</td></tr><tr><td>Po-218</td><td>6002</td><td>42.5</td><td>40.7</td></tr><tr><td>Po-214</td><td>7687</td><td>63.2</td><td>61.4</td></tr><tr><td>Po-210</td><td>5034</td><td>32.4</td><td>30.6</td></tr><tr><td rowspan="6">Tn chain</td><td>Rn-220</td><td>6288</td><td>45.8</td><td>44.0</td></tr><tr><td>Po-216</td><td>6778</td><td>51.6</td><td>49.8</td></tr><tr><td>Bi-212</td><td>6051</td><td>43.1</td><td>41.3</td></tr><tr><td>Bi-212</td><td>6090</td><td>43.5</td><td>41.7</td></tr><tr><td><b>Po-212</b></td><td><b>8785</b></td><td><b>78.6</b></td><td><b>76.8</b></td></tr></tbody></table>

surface is then scanned using a computer scanner, and the tracks are automatically counted using dedicated software (Mitev et al., 2010). The estimated track density $n_3$ (number of tracks per unit area) is used to estimate the average Rn concertation $C_{A,Rn}$:

$$C_{A,Rn} = \frac{(n_3 - n_{3,b})f(d)}{CFR T_{exp}} \quad (1)$$

where CFR is the calibration factor for Rn, $T_{exp}$ is the exposure time of the disk, $n_{3,b}$ is the background track density and $f(d)$ is a well-known function accounting for the depth dependence of the track density due to the absorbed Rn (Pressyanov et al., 2012). The function $f(d)$ is applied when the removed surface layer has a thickness different from the depth for which CFR is determined.

To estimate the average Tn concentration, the tracks in layer 2 or 2' are analyzed (Pressyanov et al., 2013; Georgiev et al., 2016). The procedure followed is identical to that for Rn, with the exception that the removed surface layer $d$ should be in the interval from 64 µm to 76 µm. Analyzing the tracks in layer 2' is preferable because the signal is not influenced by Rn. In this case, the estimated track density $n_2$ is used to determine the average Tn concentration $C_{A,Tn}$:

$$C_{A,Tn} = \frac{(n_2' - n_{2,b})}{CFT T_{exp}} \quad (2)$$

where CFT is the calibration factor for Tn and $n_{2,b}$ is the background track density at this depth estimated for new disks. Another advantage of layer 2' over layer 2 is it has higher sensitivity to Tn (up to 1 order of magnitude, depending on the CD-case geometry) (Georgiev et al., 2016), because the air-gap in the CD case above the back side of the disk is times greater than the gap facing the front side. However, it is not always possible to use layer 2'. For instance, the dye layer of some CDs is formed by several layers of various thicknesses, resulting in variations in the layer 2' depth (Georgiev et al., 2016). The back side of DVDs is also unusable, since it is not made of polycarbonate. In such cases, layer 2 could be employed for Tn measurements:

$$C_{A,Tn} = \frac{n_2 - n_{3f}(d)}{CFT T_{exp}} \quad (3)$$

To achieve this, two sections of the disk are analyzed – one at Rn depth (layer 3) to estimate the Rn signal and one at Tn depth (layer 2). The estimated Rn signal, along with the known function $f(d)$, is used to calculate the Rn contribution $n_{3f}(d)$ to the signal in layer 2. One drawback of layer 2 is that this correction leads to increase in the uncertainty of the Tn measurement and more importantly, to restriction on the minimum measurable Tn concentrations (Pressyanov et al., 2013).

An estimate of the calibration factor CFT for Tn for a disk in a CD-case is given by (Dimitrova et al., 2016; Georgiev et al., 2016):

$$CFT = \frac{\eta \epsilon h}{2R} \quad (4)$$

where $\eta \approx 0.64$ is the branching ratio of Tn to decay to $^{212}$Po, $\epsilon \approx 0.074$

(Dimitrova et al., 2016; Georgiev et al., 2016) is the track formation efficiency, i.e. the probability for the alpha-particles of $^{212}$Po (outer source) to form tracks in the CD at certain depth beneath the surface, $h$ is the height of the gap between the CD and the CD-case and $R=C_{A,out}/C_{A,in}$ is the diffusion resistivity of the case (Dimitrova et al., 2016). The diffusion resistivity is the ratio between the Tn activity concentrations outside and inside the CD-case and $1/R$ represents the relative amount of Tn that enters the case.

## 2.2. Transport of Tn inside the CD-case

The application of the CD-method involves processing different disks stored in various CD-cases. The diffusion coefficient of the Rn-gas in air is about $D \approx 10^{-5} \text{ m}^2 \text{ s}^{-1}$ and the half-lives of Rn and Tn are $T_{1/2,Rn} = 3.82 \text{ d}$ and $T_{1/2,Tn} = 56 \text{ s}$ respectively. This results in different diffusion lengths $L_D = \sqrt{\overline{DT_{1/2}}}/\overline{\ln 2}$ of Rn ($L_{D,Rn} \approx 2 \text{ m}$) and Tn ($L_{D,Tn} \approx 3 \text{ cm}$) in air. Thus, the $L_D$ of Rn is times greater than the CD case dimensions (about 10 cm × 10 cm), while that of Tn is times smaller. Although the transport of Rn and Tn in the CD-case is not purely by diffusion, it results in very different behaviors for Rn and Tn: Rn enters the case freely ($R = 1$) and is distributed homogeneously inside, while Tn entry could be significantly impeded ($1 < R < 46$ as shown by Dimitrova et al. (2016) and Georgiev et al. (2016)) and exhibits a non-homogeneous distribution. Additionally, the transport of Tn in the case could also be affected by environmental parameters such as temperature, pressure, and humidity.

The effect of the CD-case on the Rn measurements has been thoroughly studied, demonstrating that the case has no effect. Moreover, since the tracks from the inner source (Fig. 2) are analyzed for Rn measurements, the disks could even be stored bare. Additionally, due to the similar absorption properties of the disks’ material, the calibration factor for Rn varies within 15% (Dimitrova et al., 2009). In contrast, it has been shown that the CD-case geometry significantly affects the amount of Tn in the air gap and the homogeneity of the plate-out distribution (Dimitrova et al., 2016). This leads to variation in the sensitivity of the disk as a Tn detector. An important advantage of the CD-method is the possibility for a posteriori calibration (see Section 2.3), allowing the calibration of detectors (CDs/DVDs) after their exposure, in order to account for these differences and CD-case effects.

The influence of air pressure, temperature, and humidity on Rn measurements has been previously studied. It was shown that only temperature has an effect on Rn measurements (through the temperature dependence of the Rn absorption in the disk). This influence was studied and can be accounted for. For Tn, the influence of environmental parameters has not been previously studied, but could lead to change of the plate-out distribution and the amount of Tn that enters the case.

## 2.3. A posteriori calibration

The aim of a-posteriori calibration is to estimate the CFT of a CD/DVD in its CD-case after it had been exposed indoors. This is achieved through additional exposure in laboratory conditions. Prior to this secondary exposure, one or more pieces of the disk are cut and used for retrospective Rn/Tn measurements as described in Section 2.1. The remaining part of the disk is returned to its case and exposed to a controlled Tn concentration $C_{A,cal}$ for a certain time $T_{cal}$. Following this exposure, the disk undergoes the same standard processing described in Section 2.1. The increase in track density resulting from the supplementary exposure is used to calculate the calibration factor:

$$CFT = \frac{(n_{cal} - n_i)}{C_{A,cal} T_{cal}} \quad (5)$$

where $n_{cal}$ is the gross track density after the additional calibration exposure and $n_i$ takes the value of $n_2$ or $n_2'$, depending on the etched side of the disk. As noted, in the a-posteriori calibration, only a portion of the
disk, typically half, is used. This deviation from the original exposure geometry could impact Tn entry and its distribution within the case. In order to reproduce the original exposure geometry, a complementary piece was cut from another disk and placed in the case during the exposure (see Fig. 3).

Previous studies (Dimitrova et al., 2016) have indicated that the various sizes of Tn entry points in the CD-case (see Fig. 1) result in radial and angular non-uniformity of the activity distribution within the case. It has been demonstrated (Dimitrova et al., 2016) that angular inhomogeneity significantly affects track density estimation in disks exposed for calibration, while radial inhomogeneity has minimal or no impact. Additionally, it is suggested that during the regular use of home-stored disks over the years, they are placed randomly in the cases, potentially averaging the track distribution and significantly reducing the effect of angular inhomogeneity. Based on this suggestion, we proposed an improvement to the a-posteriori calibration procedure to reduce the influence of the angular inhomogeneity. During the calibration exposure, the disks were periodically rotated in their cases (see Fig. 3) to simulate everyday use. To rotate the disk, the exposure was temporary stopped for 10 min to let thoron decay. Then the exposure vessel was opened and the disks were rotated manually. After closing the vessel, the exposure was resumed. Considering the half-lives of Tn decay products, the rotation was optimized for the calibration exposure conducted in the present study: the disks were rotated at 90° every 12 h – three times during the 48-h exposure and four more times after the exposure. The post-exposure rotation was introduced because in short-term exposures like a-posteriori calibrations, a significant portion of the signal is formed after the exposure due to the relatively long half-life of $^{212}$Pb ($T_{1/2}$ = 10.64 h).

## 2.4. Experimental setups and exposure

The exposure experiments were conducted in two laboratories equipped to generate a controlled Tn atmosphere and vary different environmental parameters. The exposure setup at Sofia University (SU), Bulgaria (Pressyanov et al., 2017) was used for the exposure of disks at different temperatures in the range 2 °C–35 °C, at constant atmospheric pressure (approximately 950 hPa). It was also used for exposures at different humidity (RH = 2% or RH = 90%), at normal temperature

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** A picture of disk(s) prepared for a posteriori calibration. The lower half is the piece of the original CD and the upper is a complementary piece of new CD. The disk was periodically rotated during the calibration exposure (circling arrows).</figcaption></figure>

(20 °C) and constant pressure (about 950 hPa). The laboratory at SU is equipped with dedicated etching setups for both chemical and electro-chemical etching of disks.

The exposure experiments at different atmospheric pressures in the range 500 hPa to 1500 hPa were carried out at the Institut de Radio-protection et de Sûreté Nucléaire (IRSN), France. During these exposures a fixed temperature of approximately 29 °C was maintained. The activity concentration of Tn was controlled by the primary Tn standard (Sabot et al., 2016). In both exposure facilities fans were used to homogenize the thoron activity inside the exposure volumes. Previous studies have shown that the activity concentration of thoron at the positions where the disks were placed is homogenous withing 10 % (Mitev et al., 2020).

The exposure duration and the activity concentration in all experiments ranged from 40 h to 200 h and from 100 kBq·m⁻³ to 1.4 MBq·m⁻³, respectively. This resulted in integrated thoron activity concentrations ranging from 20 h MBq·m⁻³ to 60 h MBq·m⁻³. Two types of disks were used in the exposure experiments: 1) Newly purchased disks of a single brand to ensure low initial background and similar track properties, and 2) Old disks already exposed to Tn indoors or in laboratory conditions. To investigate the effect of the CD-case, the new CDs were placed in three types of cases as shown in Fig. 1 and described in Table 2. The old disks were exposed in their original cases, which were of the Standard type with 4 or 6 holes.

# 3. Results

## 3.1. Effects of the environmental parameters

The whole surface of the disks exposed at different values of the environmental parameters was etched. The average track density for different fields covering the whole surface was used to estimate the calibration factor. To account for the track inhomogeneity, the standard deviation of the track density in the separate fields was added to the uncertainty. This source dominated the uncertainty of the calibration factor. The results from these experiments are shown in Figs. 4–6. For comparison purposes, the average (solid lines) and its standard deviation (dashed lines) are shown for the group of disks exposed at one and the same value of the given environmental parameter and for all disks in the given figure.

The results from exposures at different temperatures are presented in Fig. 4. Although the temperature varied in extremely wide range (from 2 °C to 35 °C) compared to typical indoor temperatures, no statistically significant or systematic effect of the temperature on the calibration factor was observed. Moreover, the results in Fig. 4a show good agreement between the calibration factors obtained through independent exposures in the two laboratories. The results also reveal a significant dispersion of calibration factors for different disks exposed together. This dispersion could possibly be attributed to variations in the case geometry. It is seen from Eq. (4) and Table 2 that variations in the gap *h* between the disk and the case or the diffusion resistivity *R* of the case could lead to significant variations in the calibration factor. This highlights the major influence of the case geometry and the importance of the a-posteriori calibration.

The results from exposures at different pressures are shown in Fig. 5. Similar to the exposures at different temperatures, the pressure was varied in a range (from 0.5 atm to 1.5 atm) much wider than typical

<caption>**Table 2**</caption>

Dimensions of the CD-cases used in the present studies. Picture of the cases is given in Fig. 1.

<table><thead><tr><td>Case type</td><td>LxWxT (mm)</td><td>Front-gap (mm)</td><td>Back-gap (mm)</td></tr></thead><tbody><tr><td>Standard, 4 holes</td><td>125 × 140 × 10</td><td>1.0–1.5</td><td>3.5–4.5</td></tr><tr><td>Standard, 6 holes</td><td>125 × 140 × 10</td><td>1.0–1.5</td><td>3.5–4.5</td></tr><tr><td>Thin</td><td>125 × 140 × 5</td><td>0.3–0.6</td><td>1.0–1.5</td></tr></tbody></table>
<figure><img src="image_7.png" /><figcaption>Fig. 4. Calibration factors CFT for disks exposed at different temperature. (a) Disks in standard cases etched at the front side (Layer 2) and (b) disks in thin cases etched at the front side (Layer 2).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 5. Calibration factors CFT for disks exposed at different pressure. (a) Disks in standard cases etched at the front side (Layer 2) and (b) disks in standard cases etched at the back side (Layer 2').</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Calibration factors CFT for disks exposed at different humidity. (a) Disks in standard cases etched at the front side (Layer 2) and (b) Disks in thin cases etched at the front side (Layer 2).</figcaption></figure>

indoor fluctuations. The calibration factors agreed within the estimated uncertainties and no systematic effect of the atmospheric pressure was observed. The results also confirm significant variations (2–3 times) in individual calibration factors, even for disks in cases that were similar.

In order to check the effect of the humidity, two extreme values of the humidity were created. The results from this experiment (Fig. 6) show no effect of the humidity on the calibration factor.

In summary, the extreme variations in the studied parameters did not lead to observable effect in the average calibration factor. It should be noted however, that the ventilation in homes can be different than the ventilation during laboratory exposures. On the other hand, the environmental parameters indoors are expected to vary in much narrower intervals.

## 3.2. Tracks inhomogeneity and a posteriori calibration procedure

To investigate angular and radial inhomogeneity, new disks were exposed in standard CD-cases with two or three holes (see Fig. 1 and Table 2). Some of these disks (Sa-1, Sa-2, Sb-1, Sb-2, see Table 3) were rotated during calibration as proposed in Section 2.3, while others (Sa-3, Sb-3) were not. Disks “Sa” were in cases with 4 holes and “Sb” in cases with 6 holes. Subsequently, the entire front surface (Layer 2) of the disks was etched and divided into eight angular sectors, consisting of inner and outer segments, as illustrated in Fig. 7. For all disks, the average and standard deviation of track density were calculated for the inner, outer, and all segments. The statistics of the track densities is summarized in Table 3. The typical statistical uncertainty of the track density in separate segments was about 5–7%.

It is observed that, for rotated disks, the standard deviation of track
<caption>**Table 3**</caption>

Results from the calibration of new CDs: average net track densities for the inner, outer and all (inner + outer) fields and calibration factors. The uncertainties are at the level of one standard deviation.

<table><thead><tr><th rowspan="2">CD</th><th colspan="3">INNER-fields average</th><th colspan="3">OUTER-fields average</th><th colspan="3">ALL-fields average</th><th colspan="3">CFT, cm<sup>-2</sup>·h<sup>-1</sup>·kBq<sup>-1</sup>·m<sup>3</sup></th></tr><tr><th>n, cm<sup>-2</sup></th><th>σ(n)</th><th>δ(n)</th><th>n, cm<sup>-2</sup></th><th>σ(n)</th><th>δ(n)</th><th>n, cm<sup>-2</sup></th><th>σ(n)</th><th>δ(n)</th><th>CFT</th><th>σ(CFT)</th><th>δ(CFT)</th></tr></thead><tbody><tr><td>Sa-1</td><td>250</td><td>21</td><td>9%</td><td>298</td><td>21</td><td>7%</td><td>274</td><td>32</td><td>12%</td><td>0.0071</td><td>0.0008</td><td>11%</td></tr><tr><td>Sa-2</td><td>180</td><td>24</td><td>13%</td><td>216</td><td>13</td><td>6%</td><td>198</td><td>26</td><td>13%</td><td>0.0051</td><td>0.0006</td><td>13%</td></tr><tr><td>Sa-3*</td><td>230</td><td>79</td><td>35%</td><td>290</td><td>128</td><td>44%</td><td>260</td><td>107</td><td>41%</td><td>0.0067</td><td>0.0028</td><td>42%</td></tr><tr><td>Sb-1</td><td>297</td><td>27</td><td>9%</td><td>323</td><td>19</td><td>6%</td><td>310</td><td>26</td><td>8%</td><td>0.0080</td><td>0.0010</td><td>12%</td></tr><tr><td>Sb-2</td><td>199</td><td>21</td><td>10%</td><td>225</td><td>13</td><td>6%</td><td>212</td><td>21</td><td>10%</td><td>0.0054</td><td>0.0007</td><td>13%</td></tr><tr><td>Sb-3*</td><td>221</td><td>33</td><td>15%</td><td>247</td><td>51</td><td>20%</td><td>234</td><td>43</td><td>19%</td><td>0.0060</td><td>0.0012</td><td>20%</td></tr><tr><td>AVERAGE</td><td></td><td></td><td></td><td></td><td></td><td></td><td>248</td><td>42</td><td>17%</td><td>0.0064</td><td>0.0013</td><td>20%</td></tr></tbody></table>

<figure><img src="image_10.png" /><figcaption>**Fig. 7.** (a) A scheme of the segmentation of the CD used for the inhomogeneity study. (b) A scanner preview of a disk. The inner and the outer segments are marked.</figcaption></figure>

density is significantly smaller compared to non-rotated disks and is close to the statistical uncertainty. This confirms that rotation significantly reduces angular inhomogeneity. Additionally, a radial inhomogeneity is noted – track densities in the outer field are 10–25% higher than those in the inner field. However, in a standard Tn measurement procedure, this effect would be considerably reduced because typically, a relatively large field is etched, covering both inner and outer segments. Furthermore, the all-segment average values of rotated and non-rotated disks agree well, demonstrating that the rotation procedure does not interfere with the calibration factor. These calibration factors also agree with those obtained in the previous experiments for the same CD cases (see Fig. 4a, 5a, and 6a).

To study the calibration procedure, it was applied to old disks that had been previously exposed to Tn in dwellings (disks No 1–4 in Table 4) or under laboratory conditions (disks No 5 and 6 in Table 4). All disks were stored in standard-type cases. As these disks were half-pieces (they were already used in Tn studies), the original exposure geometry was restored by adding half-pieces of new disks (see Fig. 4). After the exposure, the additional pieces from the new disks were processed and compared with the old ones.

The results from this experiment are presented in Table 4. The average calibration factor agrees very well with the calibration factors for this case type obtained in the current study (shown in Table 3 and Fig. 4a, 5a, and 6a). This confirms the applicability of the calibration procedure for disks that were already used for Tn measurements. Additionally, five out of six couples show very good agreement between the calibration factors of the original disk and the new half within their uncertainties. This implies that, for a-posteriori calibration, the influence of the reproduction of the exposure geometry could be negligible,

<caption>**Table 4**</caption>

Results from the a-posteriori calibration of old (already exposed) disks. Disks from 1 to 4 were previously exposed in dwellings, while disks 5 and 6 are from laboratory exposure. The uncertainties of the AVERAGE are estimated as the standard deviation of the CFTs of the disks in couples 1–4 and 5–6, respectively.

<table><thead><tr><th rowspan="2">No</th><th rowspan="2">ID</th><th colspan="3">CFT, cm<sup>-2</sup>·h<sup>-1</sup>·kBq<sup>-1</sup>·m<sup>3</sup></th></tr><tr><th>CFT</th><th>σ(CFT)</th><th>δ(CFT)</th></tr></thead><tbody><tr><td rowspan="2">1</td><td>Original-Half-1</td><td>0.0105</td><td>0.0011</td><td>11%</td></tr><tr><td>New-Half-1</td><td>0.0097</td><td>0.0012</td><td>12%</td></tr><tr><td rowspan="2">2</td><td>Original-Half-2</td><td>0.0149</td><td>0.0019</td><td>13%</td></tr><tr><td>New-Half-2</td><td>0.0072</td><td>0.0011</td><td>16%</td></tr><tr><td rowspan="2">3</td><td>Original-Half-3</td><td>0.0048</td><td>0.0015</td><td>30%</td></tr><tr><td>New-Half-3</td><td>0.0047</td><td>0.0009</td><td>18%</td></tr><tr><td rowspan="2">4</td><td>Original-Half-4</td><td>0.0033</td><td>0.0020</td><td>62%</td></tr><tr><td>New-Half-4</td><td>0.0038</td><td>0.0006</td><td>15%</td></tr><tr><td rowspan="2">AVERAGE</td><td></td><td>0.0073</td><td>0.0041</td><td>55%</td></tr><tr><td>Original-Half-5</td><td>0.0057</td><td>0.0034</td><td>59%</td></tr><tr><td rowspan="2">5</td><td>Original-Half-5</td><td>0.0057</td><td>0.0010</td><td>17%</td></tr><tr><td>New-Half-5</td><td>0.0080</td><td>0.0054</td><td>68%</td></tr><tr><td rowspan="2">6</td><td>Original-Half-6</td><td>0.0053</td><td>0.0013</td><td>25%</td></tr><tr><td>New-Half-6</td><td>0.0062</td><td>0.0012</td><td>20%</td></tr></tbody></table>

provided that the geometry is accurately reproduced. Moreover, the good agreement of the calibration factors within the couples suggests that the disks do not differ significantly in their track properties.

The discrepancy in CFT of Couple No. 2 could be attributed to a failure in reproducing the exposure geometry. This is likely due to challenges in securely fixing the two halves of the disks together without interfering with the case geometry, potentially allowing them to tilt or move unnoticed, compromising the a-posteriori calibration.

The observation that different disks exhibit similar efficiency in track formation, presents a potential solution to the geometry reproduction issue. If disks do not differ in their track properties, the calibration factor would depend solely on the case geometry. Replacing loosely attached pieces of disks with a whole new disk could ensure accurate geometry reproduction and improve the uncertainty of the calibration factor, because a new disk has only a few initial tracks ($n_i$ in Eq. (5)), while the old disk has a significant initial signal due to prior indoor exposure.

To verify that disks have the same track properties, disks from eight different brands were exposed to an external $^{241}$Am alpha-source for the same duration. The disks were etched to reveal the tracks and automatically counted, similar to standard disks used for Tn measurements. The obtained track densities are shown in Fig. 8. All but one disk show excellent agreement within 5% of the average value. A 12% difference in the track density of one of the disks could be attributed to counting statistics. However, even if it represents a true difference in track properties, it introduces only a 12% bias, well below the bias potentially introduced by the geometry failure indicated by Couple No. 2 in Table 4. These results lead to the conclusion that old disks can be successfully replaced by new ones in the a-posteriori calibration.

<footnote>* Disks not rotated.</footnote>
<figure><img src="image_11.png" /><figcaption>Fig. 8. Comparison of the track properties of disks of different brands.</figcaption></figure>

## 4. Discussion

The present study shows that the typical uncertainty of the calibration factor of the CD-method for retrospective Tn measurements could be estimated with uncertainty about 20%. The components of the uncertainty are shown in Table 5. This is satisfactory, if we consider the sources of uncertainty related to conducting the actual measurement in buildings. Assuming that a disk is exposed in standard case for $T_{exp} = 5$ years at an average Tn concentration $C_{A,Tn} = 100 \text{ Bq} \cdot \text{m}^{-3}$, with the back side of the disk (Layer 2') used for Tn measurements, the overall uncertainty of the net Tn signal $n_2$ - $n_{2,b}$ (see Eq. (2)), would be less than 8%. The estimation of the exposure duration $T_{exp}$ is also a source of uncertainty. Our experience shows that for $T_{exp} > 5$ the typical uncertainty is about 10%. Another source of uncertainty, that is also present in prospective measurements, is the position of the detector inside the room and more particularly its distance from the walls. This is due to the fact that the primary source of indoor Tn are building materials (McLaughlin, 2010) and Tn distribution is typically inhomogeneous because of its small diffusion length in air. This uncertainty should be estimated case by case based on interview with the building occupants. For example, an uncertainty of 5 cm in the distance at which the detector is positioned related to the wall would introduce 30% uncertainty (McLaughlin, 2010). Therefore, it is advisable to report the measured thoron concentration along with the distance to the walls of the CD/DVD detector.

Moreover, it should be noted that prospective measurements can introduce a significant bias in the estimation of the exposure, since they cannot account for the Tn variations over time. Even minor interior modifications, such as changing wallpaper or painting the walls, could lead to an order of magnitude change in the Tn concentrations (de With et al., 2016). The CD-method for retrospective thoron measurements has the potential to eliminate this source of bias.

It could also be of interest to estimate the minimum detectable activity concentration MDAC achievable with the method:

<caption>**Table 5**</caption>

Sources of uncertainty in the a-posteriori calibration of retrospective Tn measurement with the CD-method.

<table><thead><tr><td>Source of uncertainty</td><td>rel. uncertainty</td></tr></thead><tbody><tr><td>Exposure activity</td><td>10%</td></tr><tr><td>Geometry reproduction</td><td>12%</td></tr><tr><td>Different track properties</td><td>12%</td></tr><tr><td>Combined uncertainty</td><td>20%</td></tr></tbody></table>

$$MDAC = \frac{n_D}{CFT \ T_{exp}} \qquad (6)$$

Following the approach of Currie (1968), the estimated detection limit is $n_D \approx 12 \text{ cm}^{-2}$, at 95% confidence. Considering the average calibration factor $0.0175 \text{ cm}^{-2} \text{ h}^{-1} \text{ kBq}^{-1} \text{ m}^{-3}$ for Layer 2' shown in Fig. 5b and an exposure duration of 5 years, the value estimated by Eq. (6) is $MDAC \approx 20 \text{ Bq} \cdot \text{m}^{-3}$.

Up to now, there is no reference level set for thoron. Since the health risk formed by Tn is similar to that of Rn, the MDAC could be compared to the reference levels for Rn: $100 \text{ Bq} \cdot \text{m}^{-3}$ recommended by WHO (2009) and $300 \text{ Bq} \cdot \text{m}^{-3}$ recommended by the Consil of the EU, 2013 and adopted by most countries. The MDAC is well below the reference levels and allows the identification of buildings with high thoron activity concentration. However, it should be kept in mind that CFT could vary a lot due to the CD-case resistivity R (see Eq. (4)) and a-posteriori calibration should always be performed.

## 5. Conclusions

In this study, we investigated the impact of environmental factors such as temperature, air pressure, and humidity on retrospective Tn measurements using CDs/DVDs stored indoors in their cases. Even under extreme variations in these parameters, no effect on the signal in disks was observed. However, the observed dispersion in the results for identical disks exposed in seemingly identical cases, under the same conditions, implies that the primary source of bias (leading to 2–3 times differences) in such measurements stems from slight differences in the case geometry.

To address this bias, as well as other sources of uncertainties considered in this study, we developed and tested an enhanced a-posteriori calibration procedure. After the exposed disks are collected from the dwellings with their cases, new disks are exposed in the same cases and used to determine the calibration factor. The proposed procedure allows to estimate the calibration factors for disks used in retrospective Tn measurements with an uncertainty of about 20%. This is sufficiently low uncertainty comparable to the uncertainty of other sources. It should be highlighted that one of the major sources of bias in prospective Tn measurements, which arises by the possibility for significant jumps in thoron levels caused by minor interior changes, could be avoided by the retrospective CD-method.

### CRediT authorship contribution statement

S. Georgiev: Data curation, Conceptualization, Investigation, Methodology, Validation, Visualization, Writing – original draft, Writing – review & editing. I. Dimitrova: Writing – review & editing, Writing – original draft, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. D. Pressyanov: Writing – review & editing, Methodology, Investigation, Conceptualization. B. Sabot: Writing – review & editing, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. N. Michielsen: Writing – review & editing, Resources, Methodology, Investigation, Data curation, Conceptualization. S. Bondiguel: Data curation, Investigation, Writing – review & editing. K. Mitev: Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Resources, Writing – review & editing.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
## Data availability

Data will be made available on request.

## Acknowledgment

This study is financed by the European Union- NextGenerationEU, through the National Recovery and Resilience Plan of the Republic of Bulgaria, project No BG-RRP-2.004-0008-C01.

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