1. Introduction

Neutron imaging is a powerful analysis technique that complements the more widely spread photon- or electron-based imaging techniques in applications that are out of reach for those. The complementary characteristics of neutron imaging are based on the particular interaction of neutrons with matter, which combines the ability to transmit through large thicknesses of dense materials while providing a high sensitivity to some light elements such as hydrogen, lithium and boron. This combination makes neutron imaging an excellent method in applications with demanding and bulky sample environments such as the imaging of water in fuel cells [1–5], of hydrocarbons at high pressures [6] and even of water at supercritical conditions involving pressures of more than 200 bar and temperatures above 300 °C [7]. Further applications are found in a wide field of research areas. This includes for example engineering and construction materials and processes such as the study of residual stresses in additively manufactured samples [8], of water uptake in cementitious materials [9], or of hydrogen embrittlement of nuclear materials [10,11]. Other fields include life science with the study of water uptake in plant roots [12], and magnetism with the study of magnetic domains in metal sheets for transformer cores [13].

Digital detection systems replaced early analog detection systems based on films at the end of the last century. Although some detection systems use amorphous silicon flat panels directly placed in the beam, the most common detector configuration uses a camera with an optical coupling system [14]. In all cases, the neutrons cannot be detected directly and a neutron-sensitive converter material needs to be used. For camera-based systems, the neutron converter material captures neutrons to produce charged particles, which are themselves converted into visible light by a scintillation material. Both materials are combined together in a so-called scintillator screen. The available neutron flux is usually the most limiting factor in neutron imaging experiments. Therefore, this flux must be used as efficiently as possible. However, the systematic assessment of scintillator screen characteristics towards maximum efficiency is a practice yet to be established. An important focus has been placed on the light output produced by scintillator screens, and this parameter is regularly used as a metric to tell how “efficient” a scintillator is [15–18]. The neutron capture efficiency is also occasionally reported [15]. This parameter is sometimes called “detection efficiency”, but this is incorrect because it only represents one aspect of the whole detection process. While it seems obvious that improving each of these two characteristics is desirable, the much less obvious question is how to weigh their importance, as increasing one of them usually comes at the cost of decreasing the other. To date, this question has not been answered systematically.

Here, we present a systematic approach for assessing the characteristics of scintillator screens for neutron imaging applications. While the presented work is focused on cold and thermal neutrons, the concept could also be extended to fast neutrons. We also focus on the classical “integrating” imaging configuration where the total intensity for each pixel is integrated over a given period, though we shortly discuss how the assessment would differ for event-based imaging. Using the theory of noise propagation through a cascade of linear steps proposed by Cunningham and Shaw [19], we propose a framework for assessing the sources of noise in neutron imaging detectors, taking into account all aspects of the detection system. The theoretically calculated noise and detection efficiency values are compared to experimentally measured values for different scintillator screens and for different configurations of the detection system. Finally, we discuss under which conditions the noise is dominated by the limited number of captured neutrons, or by the limited number of collected photons. We use this knowledge to provide a basis for rational scintillator selection and optimization, based on detection efficiency maximization.

2. Theoretical background

2.1 Theory of noise generation in a cascade of linear steps

The simplest way to describe the fluctuations of a quantized value around its average is the Poisson distribution. However, using this distribution independently on each pixel of a digital imaging system fails to acknowledge the fact that some physical processes result in a correlation between the noise measured in pixels in the vicinity of each other. The question of correlated noise was addressed extensively by Cunningham and co-authors [19,20] for optimizing digital X-ray imaging systems, and the present paper essentially uses the bases they introduced. The so-called detective quantum efficiency (DQE) is central to their work. The DQE must not be confused with the capture efficiency. The latter only is the characteristic of one particular detection step: the capture of the incoming radiation. On the contrary, the DQE takes into account all steps of the detection process, and relates the obtained noise to the minimal amount of noise which would be obtained with an ideal detection system, as determined by Poisson statistics. As elaborated by Cunningham and Shaw [19], the DQE depends on the spatial frequency and is related to the modulation transfer function (MTF) and the noise power spectrum (NPS) as follows:

In this equation, q represents the number of incoming quanta – in our case, the number of neutrons – per pixel and u represents the spatial frequency. Note that Eq. (1) slightly differs from the relation presented by Cunningham and Shaw, as we refer to the particular case where the output signal has been normalized so that the average value is 1.0. The theoretical DQE for a cascade of N linear steps (corresponding in our case to the 5 steps described later) can be obtained by the following relation:

Each step is defined by either an amplification gain (g_i) or a modulation transfer function MTF_i, but not both. The value ε_g, called the gain Poisson excess, describes the deviation of the noise introduced in a particular step from the value expected from Poisson statistics. Its value for each of the neutron detection steps will be discussed in the following paragraph.

2.2 Detection steps in a scintillator-based neutron imaging detector

As illustrated in Fig. 1, the image formation by a standard scintillator/camera-based neutron imaging detector can be approximated by the following five steps:

 

Fig. 1. Illustration of the cascade of steps involved in a scintillator-based neutron imaging detector. Reprinted from [21], © 2023 with permission from Elsevier.

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The third step includes both amplification and blurring, as the photons are generated along the trajectory of the secondary particles. However, for simplification, we use an approximate representation where all photons are first generated at the location of the neutron capture, and subsequently spread. As such, the blurring due to this secondary particle process can be included in step 4, together with the blurring due to photon scattering in the scintillator (and to the limits of the optical collection system). The values of g, MTF and ε corresponding to these different steps are summarized in Table 1:

Table 1. Parameter values for the different detection steps

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Steps 1 and 5 correspond to a random selection process with only two possible outcomes. The standard deviation of the corresponding binomial distribution is lower than for a Poisson distribution with the same average. In consequence, the Poisson excess value is negative and can be calculated to be equal to –g [20]. The Poisson excess value of -1 for step 4 corresponds to a deterministic gain. The values corresponding to steps 2 and 3 are explained in the next paragraph. With these values, Eq. (2) reduces to:

The neutron-to-photon gain (g_np) is the product of the gains of steps 2 to 5, and the detective quantum efficiency of conversion (DQE_conv) is a function of p_conv, g_sc and ε_sc as explained in the next paragraph.

2.3 Noise introduced by the conversion and scintillation process

The process of conversion to secondary particles requires particular considerations. In the case of scintillator screens based on ⁶Li, the conversion process is fully deterministic. Each ⁶Li capture event results in the emission of one pair of secondary particles (³H and alpha) with a defined kinetic energy. In consequence, the conversion probability is 100% and step 2 degenerates to a deterministic gain of 1.0. For a fixed kinetic energy of the secondary particles, we consider that the statistical fluctuations in the number of generated photons follow a Poisson distribution. Therefore, the Poisson excess value is in a first approximation set to 0 for step 3 for the ⁶Li based scintillators. However, an implicit assumption is that the particles deposit all their energy in the scintillation process. In reality, for a mixed powder scintillator, the amount of energy deposited in the scintillating particles depends on the local structure near the neutron capture location. This is further discussed in the analysis of the experimental results.

The case of Gd-based scintillator screens is different. The secondary particles generating the scintillation process are so-called internal conversion electrons. On average, a neutron capture by a ¹⁵⁷Gd nuclei results in the production of 0.65 conversion electron [22]. Therefore, a first approach could be to use a p_conv value of 0.65 in this case. However, unlike the case of ⁶Li based scintillators where the energy of the secondary particles is the same for all events, conversion electrons have a broad spectrum of energies. Moreover, several electrons (in particular when including the Auger electrons) can be produced from a single capture event. In consequence, we consider that each neutron capture results in some release of energy in the form of electrons (therfore setting p_conv = 1) and take into account the noise induced by the uncertainty of released energy within step 3. In these conditions, the computation of the DQE of conversion can be expressed as follows:

2.4 Neutron and photon statistics contributions to the noise power spectrum

The noise power spectrum (NPS) can be expressed as follows by combining Eq. (1) and Eq. (3) and by introducing N_n = q · p_nc and N_p = q · p_nc · g_np as the number of captured neutrons and the number of collected photons, respectively:

As evident from Eq. (5), the noise power spectrum is composed of two additive contributions. The first is related to the captured neutron statistics and to the conversion process and depends on the MTF of the detection system (including all blurring processes). The second is related to the collected photon statistics and is independent of the spatial frequency. Because the MTF tends towards zero at high spatial frequencies, the relative contributions of neutron and photon statistics to the noise can easily be evaluated from an experimentally measured NPS. In the present work, we will refer to the neutron to photon noise power ratio (NPR) as the ratio of these two contributions at a spatial frequency of zero (where the MTF is 1):

An NPR value of 10 or higher means that the noise is dominated by neutron statistics. Even an infinitely high number of photons would reduce the noise by only 5% at best (considering the power of 2 relation between noise amplitude and noise power). Inversely, an NPR value of 0.1 or lower means that the photon collection statistics dominate the noise.

3. Experimental

3.1 Imaging setups

The open beam, sample and resolution measurements presented here were conducted at the NEUTRA [23] and ICON [14] neutron imaging instruments of the Paul Scherrer Institute (PSI). At the used measurement position (no. 2), NEUTRA has a thermal spectrum with a mean energy of 25 meV and a flux of 9.14·10⁶ n·cm^-2·s^-1 for a proton current of 1.3 mA of the driving proton accelerator (which was the current recorded during the experiments). ICON was also used at its measurement position 2, where the cold spectrum with a mean energy of 8.53 meV has a flux of 1.25·10⁷ n·cm^-2·s^-1 (likewise, for a proton current of 1.3 mA). The neutron fluxes stated here were measured using the standard procedure described in the Supplement 1, with a modification: instead of measuring the flux at the beam exit and extrapolating the flux to the measurement position, the gold foils were placed directly at the measurement position. The neutron imaging measurements were conducted using the PSI medium-size neutron imaging detector [14] which allows the installation of a scintillator screen of 160 × 160 mm. A Peltier cooled CCD camera (Andor Ikon-L, 2048 × 2048 pixels, pixel size of 13.5 µm) was used with a CCD sensor temperature of -60°C. The optical lens had a focal length of 100 mm (Zeiss Makro-Planar T*2/100) and was used at its maximal possible aperture of f/2. For the measurements specifically conducted in the frame of this study, two different sizes of the field of view (FOV) of 67 mm and 144 mm were obtained by changing the distance setting of the optical lens and correspondingly setting the distance to the scintillator screen. The corresponding effective pixel sizes were 33 µm for the small FOV and 70 µm for the large FOV, corresponding to the sensor:image ratios of 1:2.4 and 1:5.2 respectively. To minimize the impact of gamma radiation emitted by the scintillator, a lead shielding block with a thickness of 65 mm was placed inside the detector box, covering the direct path between the scintillator screen and the camera CCD sensor (see Supplement 1 and Figure S2).

In addition to the main measurement setups described above, data from a few additional setups were obtained from previous measurements realized in the frame of different projects. The configurations for the nine main measurement setups and four additional setups are summarized in Table 2:

Table 2. List of tested measurement setups

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3.2 Scintillator screens

Four different scintillator screens were used for the main measurements presented here, three of them based on ⁶Li and the fourth based on ^natGd for the capture of neutrons. Two additional scintillators based on ^natGd and isotopically enriched ¹⁵⁷Gd were used for the additional measurement points with different detector setups. The characteristics of all six scintillators are summarized in Table 3:

Table 3. List of used scintillator screens

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Scintillator materials 1-5 were applied on 1 mm Aluminum substrates using silk-screen printing, and subsequently cut to the detector dimensions of 160 mm x 160 mm for screens 1-4 and 30 mm x 30 mm for screen 5. Scintillator material 6 was applied on aSilicon wafer [26] coated with 200 nm of iridium cut to a dimension of 10 × 10 mm.

3.3 Acquired images

The standard measurement protocol applied for the main measurements included the acquisition of the images summarized in Table 4.

Table 4. List of acquired images

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The samples, used for testing the contrast-to-noise ratio, were aluminum backed adhesive tapes with a thickness of approximately 50 µm. One of the samples was pristine from the roll and was cut into a distinctive shape. The other sample was previously used and removed, resulting in a heterogeneous adhesive distribution as well as wriggles. The same exposure time was used for all types of images, and was set to 10 s for the measurements at NEUTRA, and to 5 s for the measurements at ICON.

The 4 additional measurements were obtained from different experiment series and therefore did not follow the same measurement protocol. For these, only OB and DC images were used. The image count was at least 5 for OB images and at least 5 for DC images.

4. Data processing

4.1 Image correction

The following steps were applied for the image correction:

4.2 MTF measurement and setup resolution

The measurement of the MTF based on the averaged resolution image was performed the following way. First, a series of regions of interest containing a single edge in the resolution image were selected. The edge pixels were identified using the Canny edge detection algorithm [29] and the position and direction of the edge was computed by analyzing the main peak position in a Hough transform of the image containing the edge pixels. The edge spread function (ESF) was computed by averaging the values of all pixels contained in one pixel wide bands parallel to the edge, and the line spread function (LSF) was obtained as the first derivative of the ESF. Finally, the LSF was fitted by a Voigt function, which corresponds to the convolution of a Gaussian function defined by its parameter σ and a Lorentzian function defined by its parameter γ. The MTF is defined by the Fourier transform of the Voigt function, which is expressed as follows:

The value of u at which the MTF is 0.1 is defined as the setup resolution, and can be simply computed by inverting Eq. (7).

4.3 NPS and DQE measurement

For the NPS measurements, single OB images divided by the average OB were used. Two different pathways were used to compute the two-dimensional NPS:

For both methods, the one-dimensional NPS was obtained by radial averaging, and the noise was reduced by computing the average of the NPS obtained for all individual images. Both methods were shown to give nearly the same results, but the DFT based method resulted in noisier spectra in the low frequency range. In consequence, the results presented in this work were based on the auto-correlation method.

After the NPS was computed from the images, the DQE was simply calculated from the MTF and the known number of neutrons per pixel (q) using Eq. (1).

5. Results and discussion

5.1 Characteristics of the tested scintillators

The measured wavelength dependent transmission values for the 4 measured scintillators are presented in supplementary Figure S01. As described above, the capture efficiency was computed for the NEUTRA and ICON spectrum and are reported in Table 5 and Table 6, respectively. The light output is computed using the measured count of photons reaching each pixel of the camera, and based on the solid angle of the input lens as seen from the scintillator. It is normalized to the number of incoming neutrons. The scintillation gain is normalized to the number of captured neutrons and is computed assuming a homogenous emission of photon in all directions. It does not consider the fact that not all photons effectively escape the scintillator, so it is to be understood as an “effective scintillation gain” rather than as a fundamental parameter of the scintillation process.

Table 5. List of measured scintillator parameters at NEUTRA

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Table 6. List of measured scintillator parameters at ICON

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The light output, scintillator gain and resolution values reported in Table 5 and Table 6 were obtained using the 67 mm FOV setup described previously.

The reported effective thicknesses are the scintillator thickness obtained from the fitting of the wavelength dependent values, based on the assumption that the composition and volume fractions summarized in Table 3 are exact. Therefore, it must be kept in mind that the deviation to the nominal thickness also include the effect of deviations from these volume fractions.

5.2 Noise power spectra (NPS) and the contributions of neutron and photon statistics

The noise power spectra of all measured scintillators feature similar characteristics: the noise power spectral density is highest at low spatial frequencies and is reduced as the spatial frequency approaches the system resolution limit (see Fig. 2(a)), to finally flatten out to a new value at high spatial frequencies.

 

Fig. 2. Analysis of the neutron and photon statistics contribution to the noise. (a) Measured and calculated noise power spectra of two example scintillators (ICON, f/2 lens, 65 mm FOV). (b) Measured and calculated ratio between the noise power (at low spatial frequencies) related to photon and to neutron statistics. The symbols represent measurements, and the lines represent calculations with ideal optical lenses.

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This is consistent with the theory (see section 2) describing the NPS as the sum of a contribution related to neutron statistics, which is multiplied by the MTF and tends towards zero at high frequencies, and a contribution related to the photon statistics, which is constant for all spatial frequencies. Importantly, the ratio between the noise power spectral densities at low and high spatial frequencies are very different for lithium- and gadolinium-based scintillators. This is directly related to the much higher scintillator gain (g_sc) of the lithium-based scintillators. The calculated noise power spectra based on Eq. (5) offers a good representation of the real measured power spectra. On this basis, we can state that the noise power spectral density measured at high spatial frequencies is directly representative of the photon statistics contribution to the noise level. As this contribution is the same at all frequencies, the neutron statistics contribution to the noise level at low frequency is obtained by subtracting the photon contribution. The ratio between these two contributions – the NPR value defined by Eq. (6) – indicates whether the noise at low spatial frequencies is determined essentially by the neutron statistics or by the photon statistics, or by a mixture of both.

As seen in Fig. 2(b), there are virtually no practical situations where this noise is purely dominated by photon statistics. Besides the measurements with 65 mm and 145 mm FOVs corresponding to the dedicated experiment reported here, also the four additional setups were included in the graphs to obtain a more complete picture. The analysis indicates that, for the lithium-based scintillators, the low frequency noise is in all cases dominated by the neutron statistics. Theoretically, a setup with the same f/2 lens as used in the present experiments and a very large FOV would bring the photon/neutron noise ratio into the mixed range, but there is no reason to use such setup as f/1.4 and even f/0.95 commercial lenses are available for the corresponding large sensor:image size ratios. For medium size FOVs (e.g. 100 mm), the neutron statistics are so dominating that even reducing the light output by one order of magnitude would have a minimal impact on the low frequency noise.

For gadolinium-based scintillators, the neutron statistics also dominate for small FOVs, e.g. for the neutron microscope [24] and the micro-setup [25]. In the middle range, neutron statistics are still the most important factor, but photon statistics become an additional limitation. At very large FOVs (e.g. 400 mm), photon statistics would become the most important limitation, with f/2 and f/1.4 optics. However, if a large aperture (f/0.95) optics is used, the contributions from photon and neutron statistics would be approximately equal.

In summary, the noise is usually dominated by the neutron capture efficiency, rather than by the photon collection efficiency. Therefore, while increasing the light output is useful in some cases, it is only effective when this increase does not come at the cost of a reduced neutron capture efficiency.

5.3 Detective quantum efficiency (DQE)

In the previous section, the noise contributions at low spatial frequencies were analyzed. This obviously does not give the full picture and, for a meaningful comparison between setups, the noise at all spatial frequencies has to be considered. However, the direct comparison of noise power spectra is of limited insight, when using them to compare systems having different spatial resolutions. A better indicator for comparison is the detective quantum efficiency (DQE), which can be computed from the noise power spectrum and from the system MTF as explained in section 2.

The DQE measured and calculated for the different tested setups are presented in Fig. 3. It must be noted that the calculated value are not fully theoretical values. They are obtained using Eq. (3) but uses the experimentally measured MTF, as well as the experimentally measured photon yield. A first important observation is that for a relatively large region of frequencies, the DQE value is similar to the limit value at zero frequency. This indicates that the considerations for the “low frequency noise” discussed in the previous paragraph are also valid for a wide range of spatial frequencies. As the frequency approaches the system resolution limit, the DQE sharply decreases. This behavior is explained as follows: the noise at low frequency is mostly determined by neutron statistics, which means that this noise is filtered by the system MTF similarly to the spatial filtering of the useful signal. Therefore, the signal-to-noise ratio – and hence the DQE – first remains constant. As the spatial frequency reaches and exceeds the system resolution limit, the noise power spectral density saturates to the level corresponding to photon statistics, while the useful signal decreases to zero.

 

Fig. 3. Measured and calculated detective quantum efficiency (DQE) for different scintillators and setups.

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The noise model presented in section 2 gives a very good quantitative estimate of the DQE for the gadolinium-based scintillator. For the lithium-based scintillator, the DQE is about 1.8 times lower than expected from the theory. As illustrated in the rightmost column of Fig. 3, including this correction factor (corresponding to a DQE of conversion of 0.55) results in a very good quantitative estimate of the noise, regardless of the setup and scintillator thickness. A possible reason for the deviation from the assumption of a DQE of conversion of 1.0 for lithium-based scintillators is that, while the physical process of conversion to secondary particles is well known, the microstructure of the scintillator – and in particular the fact that the neutron conversion and scintillation process occurs in two different materials – may result in a different photon yield for different capture locations. The result would be a higher standard deviation of the photon count than when considering this a pure Poisson process, effectively resulting in a DQE of conversion lower than one. However, unlike the case of gadolinium-based scintillators where the DQE is limited by the physical process of conversion electrons generation, the DQE of conversion for lithium-based scintillators could theoretically reach 100%. Setting apart this discrepancy between model and observations, the experimentally measured DQE confirms an important point predicted by the model: Despite its much lower light output, the gadolinium-based scintillator equals or surpasses the lithium-based scintillator in terms of overall DQE. This is well in line with the fact that, as described in the previous paragraph, the neutron statistics are the most important contribution to the noise formation. The fact that the gadolinium-based scintillators have a significantly higher neutron capture efficiency results in a higher captured neutron count, although this advantage is partly offset by the additional noise introduced by the internal conversion process. The advantage of gadolinium-based scintillators over lithium-based ones is slightly higher for thermal neutrons than for cold neutrons, which can well be explained based on the neutron capture efficiency for the different spectra (see Table 5 and Table 6). Consistently with the expectations (see previous paragraph), the photon statistics contribution become more significant for the large FOV (145 mm), and the DQE of the Gadolinium based scintillator is reduced compared to the small FOV. The DQE of the Lithium based scintillator remains the same for the lower frequencies for both FOVs, because the photon statistics have no impact in this case. These results mean that the relevance of the Gadolinium based scintillator goes clearly beyond the fact that it has a higher resolution. Even for relatively large FOVs of 145 mm (where the resolution is not anymore limited by the scintillator), the higher capture efficiency of this scintillator is sufficient to compensate for its lower light output.

5.4 Contrast-to-noise ratio (CNR) and image examples

The previous measurements suggest that the gadolinium-based scintillator outperforms lithium-based scintillators in terms of noise, even at low spatial frequencies. To confirm this, we evaluated the contrast-to-noise ratio (CNR) – defined as the ratio between the contrast of the test object and the noise standard deviation – for aluminum backed adhesive tapes. The adhesive thickness is of about 50 µm and the contrast of approximately 2% obtained with these samples is representative of different real cases, such as the measurement of water in fuel cell porous media [2], small amounts of water [30] or of binder [31] in materials, condensation in music instruments [32] or liquid in pre-filled syringes [33,34].

As seen in Fig. 4(a), the CNR for unfiltered images is highest for the thick lithium-based scintillators, while the CNR of the gadolinium-based is only marginally better than that of the thinnest lithium-based scintillator. However, a meaningful comparison requires to consider the achieved spatial resolution. The line plots in Fig. 4(a) show the impact on the CNR of filtering the images (using a Gaussian filter). For any specific resolution, the CNR of the gadolinium-based scintillator is higher than that of all three lithium-based scintillators. One remarkable point is that the thinnest lithium-based scintillator and the gadolinium-based scintillator have similar CNR and resolution when the image is unfiltered – which may lead to conclude that they are nearly equivalent. However, filtering has a much stronger effect on the CNR of the gadolinium-based scintillator: the CNR can be doubled with a marginal loss of resolution. The reason is that a significant fraction of the noise is at high spatial frequencies, due to the limited photon statistics of this scintillator. Because there is no useful signal at these frequencies, the noise can be reduced by filtering with a minor impact on resolution. The same does not apply to the lithium-based scintillators, whose photon statistics are so high that the high spatial frequency component of the noise is negligible. After filtering, the CNR of the gadolinium-based scintillator is about twice as high as that of the thin lithium-based scintillator. Because the noise amplitude depends on the square root of the exposure time, reaching a given CNR will take approximately four times longer with this thin lithium-based scintillator than with a gadolinium-based scintillator.

 

Fig. 4. Contrast-to-noise ratio (CNR) and image examples. (a) CNR for unfiltered images (dots) and as a function of effective spatial resolution for filtered images (lines). (b) Histograms of filtered images having an effective resolution (10% MTF) of 4 cycles/mm. (c) Filtered images (4 cycles/mm resolution) of two test samples. The samples are Aluminum backed adhesive tapes with an approximate thickness of 50 µm (used tape on the left side and pristine tape on the right side). The CNR values refer to the contrast of the sample on the right.

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The image examples in Fig. 4(c) are filtered with different filter sizes for each scintillator, in order to reach the same spatial resolution of 4 cycles/mm for all of them, and the same filtering is used to obtain the histograms in Fig. 4(b). As observed in these histograms, the contrast is slightly higher for the lithium-based scintillators than for the gadolinium-based scintillator. This is attributed to the different wavelength dependence of the neutron capture efficiency for these two types of scintillators. Because the gadolinium-based scintillator reaches saturation (transmission below 5% for wavelengths above 3 Å, see Figure S01), the capture efficiency does not increase much as a function of wavelength. Oppositely, the capture efficiency of lithium-based scintillators further increases at long wavelengths where the sample contrast is highest. These contrast differences partly offset – for this sample – the advantage of the gadolinium-based scintillator in terms of DQE. However, as mentioned above, the CNR as a function of resolution is still the highest for the gadolinium-based scintillator. It must be noted that the relatively small FOV used allows an efficient light collection which mitigates the impact of the low light output of the Gd scintillators. For larger FOVs, this low light output becomes an important limitation, as discussed in the section “DQE as a function of the field of view.”

5.5 Maximizing the efficiency

The best obtained DQE – with the gadolinium-based scintillator and the smaller FOV – was measured to be 27%. This means that, if a scintillator featuring nearly 100% DQE was achievable, the necessary exposure time for a given application could be reduced by a factor of nearly four. This motivates the evaluation of the maximal achievable DQE.

As discussed in section 2, the randomness of the internal conversion process for gadolinium-based capture events introduces additional noise. Therefore, even if a capture efficiency of 100% is reached, a maximum DQE of approximately 37% is estimated for gadolinium-based scintillators. In Fig. 5, we compare the calculated achievable DQE with the effectively obtained DQE. Corrected values are also presented, which correspond to an estimation of the DQE which would be reached with an infinitely high light output. These results show that the limited light output of the 30 µm gadolinium-based scintillator can explain the difference between the ideal reachable DQE and the measured DQE. As such, there is still some potential for improvement (e.g. using high aperture custom lenses) but, as mentioned above, we don’t expect that the 37% limit can be exceeded with this type of scintillator. One point should however be considered to put this statement in perspective: the present DQE calculation assumes that the detector is only able to measure a total number of received photons over a period of time. Advanced detectors based on single neutron event detection [35] could in principle overcome this limit, as the noise induced by the variable number of photons collected from each capture event would be suppressed in this case. However, the rate capability of such detectors currently does not allow to use them for standard white beam applications with FOV sizes similar to those described in this paper.

 

Fig. 5. Measured and calculated maximal detective quantum efficiency (DQE) as a function of the scintillator screen thickness for different materials (for boron-based materials, only theoretically calculated values are given). The “corrected” values (open symbols) correspond to the estimated DQE when only limited by neutron statistics.

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Neutron capture events producing a deterministic amount of energy in the form of secondary particles, such as the splitting of ⁶Li, have the potential to reach higher DQE value. However, for lithium-based scintillators, this would require very high screen thicknesses (> 300 µm). Boron-based scintillators [15] may be able to exceed this limit at lower thicknesses, potentially leading to DQE values as high as 80% for 200 µm scintillator screens – assuming the same volume fractions for the capture material and scintillator material than for the lithium based scintillators. This requires a very high packing of the Boron atoms. The most promising candidate for this seems to be boron nitride (with the dense cubic or wurtzite structure), with ¹⁰B enrichment. While such a compound is, to our knowledge, not available commercially in its isotopically enriched form, its synthesis has already been demonstrated in the frame of thermal conductivity studies [36].

5.6 DQE as a function of the field of view

The calculated values presented in the previous section represent the maximal reachable DQE in case of an infinite light output. The effectively reachable DQE depends on the light output, and, because the light collection efficiency strongly depends on the distance between the lens and the scintillator screen, on the size of the FOV. As shown in Fig. 6, small field of views corresponding to a high light collection efficiency result in a better DQE for the gadolinium-based scintillators, as already shown previously. This advantage fades out with increasing FOV sizes, though this effect can be partially mitigated by using lenses with higher apertures. According to our calculations, even for the largest field of view at NEUTRA (420 mm), the DQE with the gadolinium-based scintillator would only be slightly less than with the lithium-based scintillators if a f/0.95 lens is used.

 

Fig. 6. Measured and calculated low frequency detective quantum efficiency (DQE) as a function of the field of view. The calculated values are based on the experimentally observed DQE of conversion of 0.55 for Li based scintillators.

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After introducing a DQE of conversion of 0.55 for the lithium-based scintillators, calculated values match well the experimental measurements. In particular, as seen in Fig. 6(b), the DQE for a gadolinium-based scintillator decreases with an increasing FOV size, while the DQE for a lithium-based scintillator remains virtually constant.

5.7 Limits of DQE based analysis

The analysis of neutron imaging setup performance based on DQE is useful in many cases, but also has certain limitations which are discussed here. The first limitation is the presence of additive noise independent of the exposure time, for example from the camera readout electronics. Usual neutron imaging measurements with several seconds of exposure per image result in image intensities sufficient to make this contribution negligible. However, for very fast measurements [37], such a contribution cannot be neglected.

The second limitation is the presence of noise contributions other than the shot noise, such as the white spots mentioned previously. As shown in Fig. 7, these white spots have a much stronger impact on images acquired using gadolinium-based scintillators. The quantity of white spots can be significantly reduced by shielding (see Supplement 1 and Figure S2) as applied in the present work, but cannot be reduced to zero. In the example shown in this paper (Fig. 4), the white spots could be effectively filtered but the practicality of applying such filtering depends on the particular application. For example, for tomography, a possibility is to acquire several images for each projection, though this comes at the cost of an increase time lost to read-out when compared to a single exposure of the same total time. Other options include advanced spatial filtering [38], based on a priori knowledge of typical white spots shapes.

 

Fig. 7. Unfiltered image using a Gadolinium based scintillator (left) and a lithium-based scintillator (right), illustrating the higher impact of white spots on measurements with a gadolinium-based scintillator.

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While the white spots are generated by gamma radiation directly hitting the camera, the scintillator sensitivity to gamma radiation may result in a background contribution with an additional noise component. Our measurements were realized at the SINQ spallation source which has a very low gamma background. For measurements at sources with high gamma background, this may result in an additional noise component, and the different sensitivity of the scintillators to gamma radiation may have to be taken into account.

Finally, the DQE analysis should be an important element for the scintillator selection, as it conveniently combines a measurement of noise characteristics and resolution, which are two key parameters for many experiments. Nevertheless, other properties of the scintillator screen can play an important role. In particular, when precise quantification is sought, or for challenging measurements with very low transmission, scintillator burn-in and afterglow effects can play a very important role. These two effects are much less pronounced in gadolinium-based scintillators, which may be a reason to choose them even in situation when another scintillator would result in a slightly better DQE.

6. Conclusions

Based on theoretical calculations and experimental measurements, we presented a systematic methodology for selecting scintillator screens for neutron imaging experiments. The main findings obtained from the measurements on scintillators using two different neutron capture materials (lithium and gadolinium) can be summarized as follows:

The results presented here specifically apply to the types of tested scintillator and cannot be generalized to all type of scintillator based on the same capture elements. However, some fundamental limitations such as the DEQ of conversion for gadolinium-based scintillators, and the limited capture efficiency for lithium-based scintillators are intrinsically linked to the use of these capture elements and can be considered generic results. The results and theoretical framework presented here are not only expected to be useful for the selection of the best scintillator screen for a given application, but also provides a guidance for the development of future scintillator screens.