Performance of the RadonEye Monitor

Abstract

In addition to cheap track-etch and expensive research-grade radon monitors, for several years, a new generation of affordable consumer-grade active monitors has been available. Their performance raises the question of whether they could also be used for certain objectives in a scientific context. This requires particular QA/QC as well as understanding their behavior and their limitations. This paper reports experiences with the RadonEye acquired over approximately two years, mainly for recording time series of radon concentration indoors and outdoors. Specific topics include calibration uncertainty, assessed by recording parallel time series; response to thoron by exposing the monitor to thorium-bearing material; and some unresolved questions related to measurement statistics to date. The main results are that factory calibration is quite uncertain and that sensitivity to thoron has to be considered in practical usage. Some identified statistical issues regarding the occurrence of anomalies and possible non-Poisson uncertainty remain unresolved.

1. Introduction

Because of its ubiquity and the possible risk that high concentrations of radon (Rn, in most cases dealing with ²²²Rn from the ²³⁸U decay chain) pose to human health (e.g., [1]), many studies have been, and continue to be, performed worldwide concerning its distribution and transport in the environment. A central element of radon studies is measuring its concentration in various environmental media and compartments.

The objectives of measuring radon concentrations are radioprotection and scientific applications, mainly related to radon as an environmental tracer. For radon screening and surveying, usually relatively simple monitors are used such as track-etch or SSNTD (solid-state nuclear track) detectors, while for scientific research, mostly more sophisticated and expensive equipment is employed. For several years, a new generation of instruments has been available that were conceived as consumer-grade monitors; however, their performance is such that their scientific usage also appeared interesting for certain purposes. This requires particular QA/QC (quality assurance and control), including understanding their behavior and knowing their limitations. One instrument in this hybrid consumer- and science-grade segment is the RadonEye, an ionization chamber with relatively high sensitivity. It has already been subjected to studies of its performance, which suggest that it can also be used in certain scientific applications. Due to its fair price and easy usage, it also seems appropriate for citizen science (e.g., [2]) applications. However, a good understanding of the behavior of an instrument is essential for its QAed usage.

The objective of this paper is to discuss some features of the behaviors of the RadonEye that have been observed during its use for about two years. This paper is a sequel of a previous paper [3]. Its topics are calibration uncertainty, response to thoron, and issues related to measurement statistics; specifically, this paper focuses on the occurrence of anomalies and the correlation of records from monitors operating in parallel under identical ambient conditions.

2. Materials and Methods

2.1. The RadonEye Monitor

This device manufactured by the South Korean company FTLab [4] has become increasingly popular for some years due to its fair price and relatively good performance, as documented in a number of QA studies reported in the literature. Basic properties are shown in company documents [5,6]. For references on QA, see Sections 1.1 and 2.1 in [3]. It should be emphasized that QA tests in the references investigate the instruments under more or less standard conditions in terms of Rn concentration and environmental condition, mostly in controlled laboratory settings; this is different for the experiments reported here and previously in [3], with conditions in some cases different from the ones specified by the manufacturers. This concerns very low (outdoor) Rn concentration and high humidity (although well protected from direct rain), low and high temperatures (although protected against direct sunlight), and possible vibrations induced by wind. This is to say that the QA tests performed here are more severe and demanding than ones performed under laboratory conditions. One reviewer has asked for whether air reaches the detector only by diffusion or by forced suction and whether there are diffusion barriers. The documentation says nothing about this, but the absence of noise and low power consumption suggest that it works only by diffusion. The high sensitivity to thoron (see below) suggests the absence of barriers.

Calibration

The calibration procedure of the RadonEye is not really transparent. In the operation manual, a sensitivity 13.5 cpm/(1000 Bq/m³) is given. Apparently this is the default calibration factor. On the other hand, ([5]) says on p.1, “individually calibrated by equipments which are already calibrated to traceable international standards”. This indicates that RadonEye is individually calibrated using secondary standards. In this case, each device should have its particular calibration factor, but this number is not communicated. Again on the other side, [6] (Getting started, 1) says, “The device calibrates automatically and then starts measuring Radon”, which indicates some re-calibration when the RadonEye is started. Again [5] says, that “accuracy: <10% (min. error < 0.5 pCi/l (±15 Bq/m³))”. However, it is not clear whether this relates to deviations from nominal concentrations during the calibration procedure or to deviations during the operation of the device.

Initial experiments to verify the reproducibility (hence the validity of the calibration) are described in Section 2.2. The RadonEye devices used for the experiments have serial numbers RE22207111958, HK01RE000496, HG04RE000641, and GJ17RE000076. All four monitors have never been exposed to high Rn concentrations before the parallel measurements (only outdoors and indoors for days for some initial trial runs, but also with low concentrations), so negligible internal background can be anticipated.

2.2. Parallel Exposure

The reproducibility of Rn concentration results was checked using parallel measurements with pairs of RadonEye devices. The locations of the measurements were Berlin (Par-1 and Par-2) and Vienna (Par-3), as described in [3]. The setup of experiments Par-1 and Par-3 is shown in Figure 1. If calibration is correct, the statistics of the time series recorded under identical ambient conditions, in particular the mean over the measurement period, should be the same up to random statistical fluctuation. The results of the Rn concentrations given here always refer to factory calibration.

2.3. Response to Thoron Exposure

Ionization chambers are sensitive against thoron (²²⁰Rn, Tn) and radon (²²²Rn). Since the internal construction of the device is not known to the user, we cannot say whether a diffusion barrier is installed to mitigate a possible Tn effect. To verify Tn sensitivity, in two experiments, namely, Tn-1 and Tn-2, a monazite concentrate layer (up to about 150 Bq/g ²³²Th) was placed on the bottom of a plastic container, and the RadonEye was placed on top and separated from the monazite using space holders (Figure 2). The devices were exposed for a few hours and then removed (which means exposure “switched off”), and the decay was recorded. Exposure was higher in experiment Tn-2 than in Tn-1.

In experiment Tn-3, a RadonEye was placed in an improvised exhalation box (a plastic ice cream container) oriented against a wall, as shown Figure 2c. The objective was to see whether there is a significant difference compared to the exposure to that of the free room atmosphere about 1 m away (Figure 1a).

Theoretically, the activity of ²¹²Pb (member of the ²³²Th decay series), called A₂(t), is expressed as follows (Figure 3a):

A2(t) = (λ2/(λ2 − λ1)) A1 (exp(−λ1 t) − exp(−λ2 t))

where λ₁ = 0.0125 s⁻¹ and λ₂ = 1.810 × 10⁻⁵ s⁻¹ are the decay constants of Tn and ²¹²Pb, respectively, and A₁ = 1 is the Tn concentration inside the chamber at the beginning of the experiment, t = 0. ²¹²Bi and ²⁰⁸Tl are in approximate equilibrium with ²¹²Pb after a few hours (for a graph showing the full evaluation of the Bateman equation, see [7]; a convenient tool to evaluate decay chains is [8]). An analogous graph is shown in Figure 3b for the decay of ²¹⁴Pb and ²¹⁴Bi from the ²³⁸U series, with ²¹⁴Pb=1 at t = 0.

2.4. Anomalies

Anomalous Rn concentration values were observed. The fact was previously reported in [3]. The device concerned is #1958, which was operated outdoors. Later, the phenomenon disappeared; no physical explanation could be found. Closer examination showed no visible external humidity. The anomalies were also not related to vibrations due to wind gusts, particularly low temperatures or similar possible causes.

Since only 1-h means are stored, we cannot say whether the phenomenon occurred, or to which extent, also in the 10 min-values, or if so, only during one isolated 10-min period or in several subsequent ones.

Two time series were investigated for anomalies: (1) the outdoor series #1958, as mentioned above and serving as motivation, and (2) the indoor series #0076, for which environmental effects can be excluded. With this monitor, the anomalous behavior started in December 2024 after 10 months of continuous operation. The anomalies are less pronounced than the ones of the former monitor. The phenomenon ceased in early February 2025, and no similar anomalies have been observed since (measurement is ongoing). The position remained the same, and the ambient conditions of the monitor varied in the range of normal indoor temperature and humidity throughout the measurement period.

Anomalous values in a time series are defined here (a) as isolated peaks and (b) peaks with an empirical occurrence frequency that is much higher than the expected one. For series (1), this was visually obvious. However, for (2), the presence of anomalies appeared visually likely in some instances, but further statistical reasoning was applied to confirm it. If in an interval, the expected number of instances with a certain count number is smaller than 1 but the observed number is greater than 1, it can be considered as anomaly. Specifically, the analysis is performed following [9]. In an interval of n hours in which the Rn concentration appears approximately stationary, defined as background, the mean count number m was calculated and defined as the expectation of a Poisson process. For each count value k in the interval, the Poisson prob(k’ ≥ k) was computed as follows:

prob(k’ ≥ k) = 1 – CumPoiss (k, m),

Here, CumPoiss—the cumulative Poisson distribution, and m—the mean within a window with an approximately stationary background, excluding the instance for which the probability is evaluated, that is, the location of the suspected anomaly. The expected number of events is therefore n·prob(k’ ≥ k), and n—the number of instances in the window. Additionally, also following [9], the χ² value for observed versus expected counts within a window, in which the background is approximately visually stationary, is calculated under the Poisson hypothesis. Reported Rn concentrations are converted into count numbers as shown in Section 2.5.

2.5. Correlation Between Parallel Time Series

Two RadonEye devices were placed next to each other for the “parallel” experiments. The devices operated synchronously with an offset of maximum 2 min. This appears to be tolerable given that the typical time constant of the natural Rn dynamic is not much less than one hour due to the physical inertia of atmospheric systems (starting them exactly synchronously is not easy).

Because of measurement uncertainty that blurs the natural dynamic, the recorded series cannot be perfectly correlated (r = 1). However, the lower the dynamic is, the lower the Pearson correlation is.

As a first step, we try to find out whether the observed correlation r between parallel and synchronously operating monitors can be explained by the inevitable uncertainty induced by the Poisson statistic of count numbers.

Analysis 1: Investigate whether the Poisson uncertainty is sufficient to explain a deviation of the correlation between two parallel measurements from unity.

Let X: = x(i), i = 1 … N, and the counts represent an (unknown) true time series. The counts x exhibit a Poisson distribution. Generate two series, Y₁ and Y₂, with y_1,2(i) ~ Poiss(x(i)) independently. These are regarded as the observed series. Compute r(Y₁,Y₂). Repeat many (J) times and compute 〈r〉, 〈.〉 the arithmetical mean over J realizations. Check whether 〈r〉 is approximately equal to the observed r. This would indicate that the deviation r < 1 is indeed due to the Poisson counting statistic.

For X, an empirically observed series C (reported) is used, substituting the unknown true one. From C (reported), we build an approximate expected series EC = C+1 (see Section 4.4 in [3]). The counts are estimated as x = cint (EC cal), where EC—expected Rn concentration, cal—calibration factor, and cint—the rounding function. Next, X is subjected to Poisson sampling, resulting in a “Poissonized” series Z, which is converted into series Y that represents the observed Rn concentrations, where y = cint (z/cal). To generate Poisson deviates, the algorithm on p. 505 of [10] was used (also cited as the Knuth algorithm on the Wikipedia page “Poisson distribution”).

The correlation between Y₁ and Y₂ derived from X by Poisson sampling depends on the magnitude of X. This is because the relative differences between x_i and the derived y₁ and y₂ decrease with x_i given that the Poisson standard deviation equals √x_i, or relative 1/√x_i. Therefore, the higher the average value of X is, the more similar Y₁ and Y₂ are to X and hence to each other. Thus, the correlation between them increases →1. If one wants to test whether a correlation exists between two observed series X⁽¹⁾ and X⁽²⁾, given empirical r < 1, which can be explained by Poisson uncertainty, the simulated Poisson series Y⁽¹⁾₁ and Y⁽²⁾₂ must be derived from X⁽¹⁾ and X⁽²⁾ of equal average magnitude. This is achieved by rescaling one of the X⁽¹⁾ or X⁽²⁾ to the other, by multiplying with the ratio of their arithmetical means.

Analysis 2: If Poisson uncertainty is not sufficient to explain the deviation of the theoretical 〈r〉 from the empirically observed r (which is the case as will be shown), add noise according to a given model. The noise is quantified by the parameter σ, which is modified until 〈r(σ)〉 equals the empirically observed r. However, no physical error model underlies this reasoning. Formally, σ_opt: = argmin |〈r(σ)〉-r| is defined as the σ that explains best the deviation of the observed r from 〈r(Poisson only)〉.

In absence of knowing the physical functioning of the detector in detail, the following noise models were considered:

“LN”—lognormal noise model: Gaussian-distributed independent errors ε(σ)~N(0,σ), Z → W: = Z exp(ε) rounded to integers W_1,2.

“ADD”—additive model: simply Z → W: = Z + ε, constrained to W > 0. As modification, the model ε(σ)~U([-σ,σ]) was tried.

“MULT”—multiplicative model, Z → W: = Z·(1 + ε), constrained to W > 0.

“SQR^±”—a super-/sub-additive model, Z → W: = Z + (1 ± b/√(Z + 1))ε. The denominator is chosen as Z + 1 to avoid eventual division by zero. For b, 0.2, 0.5, 1, and 2 were tried.

These models were chosen in a free-handed manner to cover a variety of “error behaviors”. Of course many more models can be conceived. The LN and MULT models are motivated by the idea that the error grows with Z, while it remains independent of Z for the ADD model. For the SQR^± model, the error increases/decreases with lower Z.

2.6. Software

Standard statistics were performed with Excel and Past 4.17 [11]. Non-standard statistics, such as the simulations in Section 2.5, were performed with home-made programs in QB64.

3. Results and Discussion

3.1. Deviation from Nominal Calibration

Three pairs of RadonEye monitors formed from four devices were operated in parallel next to each other, that is, under identical external conditions. The objective was to check whether individual calibration factors were equal up to statistical fluctuation. The three experiments are labelled Par-1 to Par-3 in the following sections.

Table 1. Results of the experiments Par-1 to Par-3. n—number of data (=hours); AM, SD, SE—arithmetic mean, standard deviation, and error, respectively; p-values for t—t-test; M-W—Mann–Whitney; F—F-test; K-S and A-D—Kolmogorov–Smirnov and Andersen–Darling tests for equal distribution, respectively. Red text indicates the ratio between the first and second AM ± SE. Device# is the last four digits of the serial numbers, see Section 2.1.

Experiment	Par-1		Par-2		Par-3
Device#	#1958	#0641	#1958	#0496	#1958	#0076
Date	17 May–2 June 2024		24 October–3 November 2024		13 December 2024–5 January 2025
n	379		893		538
AM (Bq/m3)	3.8	2.4	5.8	3.5	22.1	15.4
SD (Bq/m3)	4.0	2.6	6.2	4.1	11.8	9.1
SE (Bq/m3)	0.20	0.13	0.21	0.14	0.51	0.39
AM1/AM2 ± SE	1.58 ± 0.12		1.66 ± 0.09		1.44 ± 0.05
Paired test
t	9.2 × 10−11		6.7 × 10−36		2.3 × 10−54
Sign	2.0 × 10−7		1.7 × 10−21		8.0 × 10−43
Wilcoxon	6.0 × 10−10		2.1 × 10−34		8.5 × 10−49
Unpaired
t (uneq var)	3.7 × 10−9		7.1 × 10−21		3.5 × 10−24
M-W	9.6 × 10−7		2.2 × 10−16		1.2 × 10−21
F eq var	6.9× 10−18		1.9 × 10−33		5.2 × 10−9
K-S	1.2 × 10−8		4.0 × 10−22		1.7 × 10−16
A-D	0		0		0
Correlation
Pearson r	0.22		0.51		0.67
Spearman ρ	0.20		0.48		0.68

shows which devices were combined into each pair. The respective parallel time series are shown in Figure 4.

It is shown that the mean Rn concentrations between the members of the pairs were not equal. The result is statistically significant, p < 1 × 10⁻³ (see Table 1).

The relative biases were (58 ± 12)%, (66 ± 0.09)%, and (44 ± 0.05)% between monitor #1958, which served as a reference, relative to monitors #0641, #0496, and #0076, respectively (see Table 1) (the selection of #1958 as a reference resulted from the use of the monitors in other measurements at the time of the study and was based on no particular reason).

This means that deviations between the latter three devices are at most 15% (1.66/1.44 = 1.15), which is higher than the declared accuracy bias <10% (Section 2.1).

None of the detectors were previously exposed to high Rn concentrations. Therefore, different internal backgrounds are unlikely to be the reason for the discrepancy.

Hence, the only possible explanation is that actual calibration factors are significantly different. The Rn concentrations shown here result from the generic (default) calibration factor 1.35 cpm/(100 Bq/m³) = 0.81 cph/(Bq/m³) as given in the instruction sheet.

This means that the calibration factors of individual devices deviate from the nominal one rather substantially.

The Rn variability is essentially synchronous, as can be seen in the graphs of experiments Par-2 and Par-3 with Pearson r = 0.51 and 0.67, respectively. In experiment Par-1, the overall (natural) variability, which reflects weather episodes, was too small to allow an accurate assessment (r = 0.22 only). The deviation of r from unity is further evaluated and discussed in Section 3.5.

3.2. Effect of Thoron on the RadonEye

3.2.1. Experiments Tn-1 and Tn-2

The recorded nominal concentrations (not calibrated, because the RadonEye is not calibrated for Tn) are shown in Figure 5. The curves look different from the theoretical curve (Figure 3) probably because the 1-h recording period does not properly resolve the build-up phase controlled by the short half-life of Tn (55.6 s).

LS (least square) fit of the decay tails for experiments Tn-1 and Tn-2 yielded the estimated half-lives of 11.7 ± 1.6 h and 10.5 ± 0.2 h, respectively, which are in agreement with the true 10.64 h half-life of ²¹²Pb.

3.2.2. Experiment Tn-3

Together with the 1-hour means that are stored by the RadonEye #1958, 10-min means were also read from the display intermittently. The values are plotted in Figure 6. The subtracted background BG was estimated from the parallel operating device #0076, about half a meter away in the position shown in Figure 1b, considering the bias between the two devices (Section 3.1, Table 1: AM ratio).

The picture is less clear than in experiments Tn-1 and Tn-2. The very fast decrease after the end of exposure—poorly resolved by the 10-min and 1-h measurement intervals—indicates that the main contribution came from the progeny of ²²²Rn exhaled from the wall and perhaps some contribution of Tn. While an exhalation effect was clearly present, it was not strong enough for reliable quantification.

Perhaps a better made exhalation box and more careful BG control would allow better quantification. However, no substantial exhalation was expected in the building made of brick (probably made from local clay, as typically used in Vienna at the time of construction about 120 years ago). Additionally, the white lime coating acts as light barrier against Tn exhalation. In any case, the experiment showed the presence of the contribution of exhalation from building material to indoor Rn concentration.

3.3. Anomalies

3.3.1. Series #1958

A fraction of the time series that includes the anomalies is shown as Figure 7. Two clusters of anomalies can be recognized, but no correlation appears between the anomalous peaks. In addition, they have no heads or tails, that is, they are isolated phenomena at least for the 1-h resolution data. After 28 October 2024, no further anomalies were observed. In subsequent time series analysis, the peaks were removed and replaced by the mean of the values left and right of the peaks. It should be noted that outdoor operation is not recommended by the manufacturer; however, apart from these anomalies, the values appeared reasonable ([3]). So far, no similar large anomalies were observed for RadonEye devices when operated indoors.

3.3.2. Series #0076

As can be observed in Figure 8, suspected anomalies in this indoor time series are much less pronounced than the ones shown in the previous section. Some of these events, denoted by numbers in the figure, were investigated in more detail. The results are shown

Table 2. Characteristics of the suspected anomalies shown in Figure 8. Rn—reported radon concentration; cts k—estimated number of counts; BG—background. Red text indicates data that are probably not anomalous.

Event #	Date	Rn	cts k	BG (cts)	Prob (k’ ≥ k)	p (χ2)
1	24.12., 0:48	23	19	6.94	1.2 × 10−4	0.0024
2	29.12., 18:48	51	42	22.93	2.2 × 10−4	0.022
3	30.12., 10:48	38	32	21.00	0.015	0.15
4	31.12., 15:48	42	35	20.50	0.0022	0.12
5	2.1., 6:48	40	33	21.82	0.015	0.45
6	2.1., 16:48	40	33	21.00	0.0093	0.012
7	2.1., 21:48	31	26	16.6	0.020	0.25
8	5.1., 7:48	22	19	10.67	0.013	0.21
9	6.1., 16:47	26	22	13.85	0.026	0.59
10	8.1., 5:47	26	22	11.74	0.0047	0.017
11	9.1., 22:47	32	27	14.41	0.0020	0.20
12	11.1., 18:47	26	22	8.09	3.9 × 10−5	6.0 × 10−6
13	12.1., 2:47	22	19	7.50	3.0 × 10−4	0.0072
14	15.1., 4:47	29	24	11.33	7.0 × 10−4	0.050
15	20.1., 16:47	37	31	10.22	1.3 × 10−7	1.8 × 10−5
16	23.1., 11:47	29	24	14.87	0.018	0.75
17	24.1., 9:47	51	42	15.87	3.8 × 10−8	1.2 × 10−4
18	26.1., 15:48	32	27	14.32	0.0018	0.010

. The most relevant statistic is prob(k’ ≥ k), indicating the probability that an equal or greater number of counts would be registered at a given time under the Poisson hypothesis. Choosing p = 0.01 as a (deliberate) threshold, we declare events with p < 0.01 as anomalies. These registered counts are considered unlikely to result from a Poisson process within a window with an approximately stationary background (assessed visually). The χ² statistic denotes whether the distribution within the window approximately conforms to a Poisson distribution, exploiting the fact that mean and variance are equal in this case. Figure 9 shows that the two statistics are essentially well aligned, as could be expected. Deviations may result from deviations from the Poisson statistic or an ill-defined background region given that the assumption of stationary background was not sufficiently fulfilled.

Within a window, for the event (time) with the highest count number, the number of instances with equal or higher counts is equal to 1 by definition. An observed event is likely an anomaly if the expected number of events with a higher or equal number of counts is far lower than 1. In Figure 10b (also introduced in [9]), event 17 (Table 2) shows the situation for a very significant anomaly; an opposite example is event 9, which is shown in Figure 10a. This is well within what can be expected for a Poisson process and therefore it is not an anomaly.

In conclusion, the monitor #0076 shows some degree of anomalous behavior, although much less pronounced than that noted for #1958. The physical reason is not known.

3.4. Missing Concentration Values

In [3], the fact was reported that certain concentration values were systematically missing. As a hypothesis, this may partly be caused by the rounding algorithm implemented in the RadonEye device.

Since then, another RadonEye device was acquired (#HK01RE000496), and the respective results are included here. The lowest missing values are summarized in

Table 3. Systematically missing nominal concentration values of four RadonEye devices.

Device ID.	Missing Concentration Values (Bq/m3)
GJ17RE000076	3, 6, 9, 12, 15, 18, 21, 24, …
RE22207111958	1, 4, 5, 7, 9, 11, 13, 15, 17, 18, …
HG04RE000641	3, 6, 8, 11, 13, …
HK01RE000496	3, 6, 9, 12, 15, …

. A satisfactory explanation for the finding is still missing.

3.5. Correlation Between Parallel Time Series

As “true” time series X, the observed ones from experiments Par-1 to Par-3 were used.

3.5.1. Analysis 1

If Poisson uncertainty was sufficient to explain the deviation of the empirical r (Table 1) from unity, applying the “Poissonization” according to Section 2.4 of each series involved in the experiment should lead to 〈r〉 being approximately equal to the empirical r. For example, in experiment Par-1, if series #0641 and #1958 were observations of the same (unknown) true series and different only by Poisson uncertainty, their empirical r should be approximately equal to both 〈r〉 derived from #0641 and #1958, which should be approximately equal between them. Theoretical 〈r〉 values are based on J = 1000 realizations. The results are shown in

Table 4. Theoretical correlations 〈r〉 ± standard deviation between parallel time series. The series represent the X⁽¹⁾ and X⁽²⁾ (Section 2.4), and 〈r〉 denoted the correlations between Y⁽¹⁾₁ and Y⁽¹⁾₂ as well as Y⁽²⁾₁ and Y⁽²⁾₂, respectively. Empirical r is obtained from Table 1.

Experiment	Series	〈r〉 ± SD	Empir. r
Par-1	#0641	0.738 ± 0.0235	0.22
	#1958	0.735 ± 0.025
Par-2	#0496	0.851 ± 0.010	0.51
	#1958	0.821 ± 0.011
Par-3	#0076	0.860 ± 0.009	0.68
	#1958	0.829 ± 0.015
rnd-1		0.514 ± 0.030
rnd-2		0.703 ± 0.020

. Figure 11 shows an example of a “true” concentration series (in reality unknown) and one realization of two “observed” series generated by Poisson sampling, representing the measured values of two RadonEye devices. The targeted 〈r〉 is the mean over many (J) realizations of the correlation between the two “observations”. Additionally, in Table 4, the 〈r〉 values for random series (X~U([1,a])) with a = 5 and 10 for the series rnd-1 and rnd-2 are given. The finding that 〈r〉 of rnd-1 is lower than the one of rnd-2 illustrates what has been said in Section 2.4 about the need to rescale the input series before generating the Poisson-simulated Y₂ and Y₂.

While the theoretical 〈r〉 values are (1) approximately equal between the series of each pair (third column), they are (2) evidently very different from the empirically observed r. (1) It can be interpreted that the shape (representing the dynamic) of each in a pair of series is about equal and only differ based on different mean AM (Table 1). (2) It means that there must be another error or noise component that decreases the correlation from 〈r(Poisson)〉 (the correlation expected if only Poisson statistic was responsible for r < 1) to the empirical r.

3.5.2. Analysis 2

To investigate this further, independent errors are added to the series according to different models, as suggested in Section 2.5.

For illustration of the effect of such added noise, Figure 12 shows an example of a “true” (in reality unknown) concentration series EC and three noisy series generated by adding a lognormal error, that is model LN, C_noisy = EC exp(ε). Here, ε~N(0,σ) represents the measured values of two RadonEye devices disturbed by noise. Since this noise is added independently to the two series that represent the parallel operating RadonEye devices, 〈r〉 must decrease with σ increasing.

In the following, two models are presented: (1) the LN model and (2) the SQR⁺ model with b = 0.5. The latter was chosen because it performed best among the models tried.

Here, σ is modified until the resulting 〈r〉 equals the empirical correlation (Table 4, last column; Table 1, second to last row). Figure 13 shows the variation of 〈r〉 with σ increasing for two error models. Like in analysis 1, the mean results 〈r〉 are based on J = 1000 realizations.

The σ_opt values are given in

Table 5. Optimal noise parameters σ_opt for two noise models.

Experiment	Series	σopt		Empir. r
		Model LN	Model SQR+, b = 0.5
Par-1	#0641	0.92	4.76	0.22
	#1958	0.92	4.89
Par-2	#0496	0.56	4.42	0.51
	#1958	0.52	3.80
Par-3	#0076	0.26	5.54	0.67
	#1958	0.22	4.58

. (1) The LN error model: While for each experiment, the σ_opt values are similar for both series, they are not between the series. One might have expected that the devices behave similarly and therefore all σ_opt would be similar. Evidently, this is not the case. (2) However, the discrepancy can be mitigated by varying the error model. SQR⁺ (b = 0.5) yielded the lowest discrepancy, as can be seen by the σ_opt lying closer together in the right (b), than in the left (a) graph of Figure 13. However, further optimization of the models may lead to a better result. For the latter model, the mean σ_opt equals 4.7 ± 0.6. This can be assumed a reasonable estimate for the non-Poisson error of the instrument based on the SQR⁺ (b = 0.5) error model. In any case, the physical meaning of the error models is unknown.

4. Conclusions and Recommendations

An inquiry was sent to the manufacturer of the RadonEye, FTLab, asking for assistance in solving some of the problems addressed here, specifically including inconsistency of information about calibration (Section 2.1, Section 2.2 and Section 3.1) and missing values (Section 3.4). The request was rejected (e-mail 23.1.2025), citing trade secrets regarding the implemented algorithms. Regarding the anomalies (Section 3.3), the question for possible physical causes was answered in the sense that rare short instances of high Rn values may be caused by “floating particles including uranium or radium” and “interference by cosmic radiation and cases where the wavelength of a specific electromagnetic wave” generates such effect. The question for whether there exists a specific calibration factor for thoron was not answered.

The rather negative reaction is unfortunate because solving these problems would help improve the quality assurance of the RadonEye device. The lack of this information certainly affects the usability of the device in scientific applications.

4.1. Calibration Issues

The parallel measurements showed that the default calibration factor is not really reliable. Accurate measurements require calibration of individual monitors, for example, using parallel measurements with science-grade instruments such as an Alphaguard or RAD-7 as secondary standards or by direct calibration in a calibration chamber. Unfortunately, for normal citizens, this is an expensive option (also noted in [12]). The preferable option would be that the manufacturer communicates the individual calibration of each device, which is apparently performed for each one according to the instructions (Section 2.1). However, the manufacturer did not comment on the inconsistent information on calibration in the publicly available documents.

4.2. Thoron

The RadonEye is sensitive to thoron. Since long-lived decay products are deposited inside the chamber, the instrument has an increased background until these radionuclides have decayed. The relevant time scale is the half-life of ²¹²Pb, 10.64 h. Thus, one must wait about 10 half-lives or about 100 h or 4 days until the background has practically disappeared. This behavior has been expected. It shows, however, that one should avoid exposure to high concentrations to Rn, whose long-lived decay products are much longer lived than those of Tn, leading to persistent instrument background due to internal contamination. Indoors, the Tn concentration is highest near walls, floors, or ceilings, that is, close to building material that exhales the gas. Therefore, it is recommended to measure Rn some distance away from surfaces because, due to its short half-life, the molecular diffusion length of Tn in the atmosphere is only 2.9 cm. However, it can be transported further by advection or turbulent diffusion.

Experiment Tn-3 aimed to detect Tn exhalation from the wall by positioning one device in an exhalation box close to the wall and one a distance away as background control. While the exhalation of Rn, together probably with Tn, could be confirmed, the result was not sufficiently reliable statistically. Future experiments with improved experimental set-ups may yield more reliable evidence. In any case; the very simple feasibility of such experiments in principle was demonstrated.

4.3. Anomalies

The physical origin of the observed anomalies remained unknown. However, the finding shows that one should check the time series if high accuracy is required and in particular for devices operated in a mode not recommended by the manufacturer (outdoors, in this case). In both investigated cases, the problem occurred after long continuous operation, but disappeared after some time. Although this cannot be proven, perhaps some kind of “vacation” should be granted to a monitor after long operation. It should be further discussed how to deal with the occurrence of anomalies. As long as anomalies are rare, they do not strongly affect the mean over some time, which is usually the main objective of measurement. However, time series must be interpreted with care.

4.4. Statistical Issues and Missing Concentration Values

The problem of missing values (Section 3.4) could not be solved because the manufacturer does not disclose necessary information about internal data processing.

The results of RadonEye devices running parallel and synchronously under the same external conditions are less correlated than one would expect if the uncertainties were only due to Poisson statistics of count numbers. Hence, there must be other sources of uncertainty that blur the correlation. In the absence of knowledge about the physical functioning of the device, several error models were tried. A reasonable model of the non-Poisson error seems to be a super-additive error Z + δZ (Z—the count number) of the kind δZ = (1 + 0.5/√(Z + 1))ε, ε~N(0,σ), σ ≈ 4.7, which was identified by trial and error.

Future detailed investigations possibly involving some kind of back-engineering may shed more light on these issues.

4.5. Citizen Science and Professional Use

The experiments show that the RadonEye monitor can also be used in citizen science. It can be used not only for surveying and monitoring, which is the usage for which the RadonEye device has been conceived, but also in an educative context. Simple experiments about responses to sudden shifts of the Rn source term and basic considerations related to measurement statistics and to time series analysis can be performed easily.

For professional use, certain precaution must be taken. If the objective is accurate Rn concentration values, re-calibration and assessment of the internal background seem inevitable. This is most easily done by secondary calibration under varying Rn concentrations (first experiments have been performed in this direction, to be communicated in a future publication). If the objective is the investigation of temporal dynamics and correlation with Rn predictors and proxies, the exact value of the Rn concentration is not so important.

If the objective is legally defensible assessment whether a room or a building conforms to a regulatory standard, either re-calibration is necessary, or considerable calibration error must be accounted for in the uncertainty budget. Methodology in this direction can be found in [13].

Ongoing research is concerned with correlation of Rn with causal or proxy-type predictors such as meteorological variables including atmospheric stability, ambient dose rate, and concentrations of air pollutants.