Coded-aperture imaging systems: Past, present and future development-A review

Scintillator based coded-aperture imaging has proven to be effective when applied for Xand gamma-ray detection. Adaptation of the same method for neutron imaging has resulted in a number of propitious systems, which could be potentially employed for neutron detection in security and nuclear decommissioning applications. Recently developed scintillator based coded-aperture imagers reveal that localisation of neutron sources using this technique may be feasible, since pulse shape discrimination algorithms implemented in the digital domain can reliably separate gamma-rays from fast neutron interactions occurring within an organic scintillator. Moreover, recent advancements in the development of solid organic scintillators make them a viable solution for nuclear decommissioning applications as they present less hazardous characteristics than currently dominating liquid scintillation detectors. In this paper existing applications of coded-apertures for radiation detection are critically reviewed, highlighting potential improvements for coded-aperture based neutron source localisation. Further, the suitability of coded-apertures for neutron imaging in nuclear decommissioning is also assessed using Monte-


Introduction
Accurate localisation of radioactive materials is crucial for nuclear safety and security. The growing threat of attacks using radioactive substances, as well as an increasing number of nuclear plants requiring characterisation to support decommissioning, necessitate development of a portable system capable of detecting radiation sources in real-time.
Radioactive substances are used in medicine, non-destructive testing, and power generation. For example, nuclear fuel used in power generation produces nuclear waste that needs to be carefully disposed of as it remains radioactive for a time period. If the source of radiation is not accurately identified and localised, radiation emitted by these materials can pose a health risk for personnel in close proximity to these materials. Localisation is particularly important during nuclear decommissioning and decontamination, since the actual location of the radioactive source within nuclear waste is often unknown.
Highly-penetrating radiation may be released in a form of X-or gamma-ray photons or free neutrons, emitted as a result of nuclear processes occurring within the atomic structure of radioisotopes. All three types of radiation mentioned can be detected using different gas filled tubes, which are sensitive to a specific type (Jahoda et al., 2006;Vanier, 2004); examples are ionisation chambers, proportional counters and Geiger-Mueller counters. Scintillators can also be used in the same way as primary detectors to detect each type of radiation (Tous et al., 2011;Woodring et al., 2003;Nakamura et al., 2009). They transform energy detected into light pulses that can be counted by photosensitive electronic components e.g. photodiodes and photomultiplier tubes (PMTs).
Although the detectors mentioned above generally provide good radiation sensitivity, by themselves, they offer no specific information about the location of the radioactive source. Preliminary results of a recent study by Schuster and Brubaker (Schuster and Brubaker, 2015) suggest that the anisotropic response of crystalline scintillation materials to neutron interactions may reveal some directional information about the source location. This type of information is of vital importance for nuclear decommissioning applications.
Substances used in the types of detectors mentioned can be difficult to source. 3 He, for instance, is mainly obtained as a byproduct from the radioactive decay of tritium; BF 3 , on the other hand, is a hazardous gas and as such not desirable (Kouzes et al., 2010). Radiographic film represents a safe implementation of radiation detector. For example, it has been employed in medical devices to perform skeletal body scanning with X-rays, successfully identifying fracture location (Lilley, 2001). A modification to the film detector, in the form of an imaging plate, allows detection of radioactive sources, where it is particularly useful for nuclear decommissioning applications (Hirota et al., 2011;Masumoto et al., 2002).
Radiation imaging methods do not only detect an occurrence of a radioactive event but also provide the location of the incident. As such their potential has led to the development of radiation cameras e based on the operation principle of a general pinhole camera (Mortimer et al., 1954). Pinhole cameras, capable of identifying radioactive substances from a distance, are frequently used in nuclear decommissioning. CARTOGAM is an example of such gammaray pinhole imager (Gal et al., 2000(Gal et al., , 2001Cattle et al., 2004). The size of the pinhole determines the angular resolution and signal-tonoise ratio (SNR) of a specific camera; the former increases in a camera with a small opening, whereas the latter decreases when the diameter of a pinhole is decreased.
It follows that an ideal single pinhole camera, would require an infinitely small pinhole to obtain the highest angular resolution. Conversely, the highest SNR would be achieved in a camera with an infinitely long diameter of the opening. Hence, in practical applications, a compromise must always be found between SNR and the angular resolution for the single pinhole cameras. In order to address this problem scatter-hole cameras were developed, where multiple holes of small diameter were distributed randomly on the aperture offering significant improvements in SNR, while maintaining good angular resolution (Dicke, 1968). However, reconstruction of the original image was difficult due to the random distribution of the pinholes. The issue was addressed by codedaperture imaging, which was introduced with 'encoding' and 'decoding' arrays to simplify the process of image reconstruction (Fenimore and Cannon, 1978).
The scintillator based coded-aperture neutron imaging systems mentioned target fast neutron localisation. In each case pulse shape discrimination (PSD) methods are exploited to separate gammarays from neutron events. Multiple channel real-time PSD has been successfully implemented laying the foundations for high resolution (high number of pixels) organic scintillator based codedaperture imagers (Joyce et al., 2014). However, identified neutron interactions must be localised within the scintillator so that the decoding process can be performed. The decoding process, which may contribute to the timing overhead of the localisation procedure, is required to infer the actual location of the radioactive substances.
In this paper existing coded-aperture imaging systems are critically reviewed with relevance to radiation detection and localisation. The advantages of the coded-aperture technique over other methods are recognised, when used for X-and gamma-ray detection, as well as its potential for neutron imaging. Additionally, the coded-mask itself, as well as sensitive neutron detectors for such an application are also highlighted. The potential of employing coded-aperture based techniques for neutron imaging in nuclear decommissioning is evidenced by a simple model generated in Monte Carlo N-Particle eXtended (MCNPX) simulation software package.

Radiation imaging and development of collimator-based detectors
Radiographic film was the original method of X-ray detection, used by Roentgen to discover X-rays, that was later adopted for gamma-radiography. Radiographic film has been successfully implemented in medical devices to perform skeletal body imaging with X-rays. It was possible due to the attenuation properties of Xrays for elements such as Ca (Lilley, 2001). A modification in a form of an imaging plate was introduced to the film detector to map 239 Pu in human lungs (Hirota et al., 2011). In medical applications, an X-ray radiation source is placed in front of an object to be imaged, whose shadow is cast on the photographic film, where the picture of the object is projected. Images generated using this method show good spatial resolution but low sensitivity. Replacing the film with a pixelated charge coupled device (CCD) offers a way of improving the low sensitivity issue. It allows an analogue to digital converter (ADC) to be connected to individual pixels on the device. The ADC can be adjusted to ignore signals below certain voltage threshold to reduce the amount of noise reconstructed, effectively increasing the sensitivity of such a device (Ott et al., 2000).
Semiconductor solid state detectors, for instance cadmium zinc telluride (CdZnTe), may also be implemented (either independently or in conjunction with gas filled tubes, scintillators) for radiation localisation. When solid state detectors are exposed to radiation sources directly, they convert the pulses -emitted as a result of the interaction between the radiating particles and the detector e into electrical current, which can be easily measured. Although semiconductor solid state detectors are more susceptible to damages caused by radiation, they are sometimes preferred in spectrometry applications due to their superior energy resolution (Knoll, 2010).
As an alternative to direct detection methods, ionising properties of specific gases prompted the development of detector tubes. The tubes filled with gas produce an electronic signal as a result of ionisation between the gas and radioactive particles (Knoll, 2010). Depending on the radiation type gases utilised include BF 3 and Xe for neutron and X-, gamma-ray detectors respectively. Alternatively, the scintillating properties of specific chemical compounds, for example CsI(Tl) and CsI(Na), offer a way of transforming X-and gamma-ray energy to light photons that can be counted using photosensitive electronic components.
Scintillator, such as CsI(Tl), can be used as a sensitive detector for a single pinhole radiation camera (Baek et al., 2013). Spatial resolution of the pinhole camera depends predominantly on the size of the single opening in the aperture and the performance of the sensitive detector used. However, it can be significantly improved if a collimator is used to narrow the path of the incoming radiation to the single opening of the aperture (Islamian et al., 2015). Replacing the single pinhole camera with a multi hole version, which was then followed by a new family of coded-aperture imaging systems, enhanced the quality of images obtained even further.

Coded-aperture based imaging
The coded-aperture approach for radiation detection has its roots in development of scatter-hole cameras for X-and gammarays. Introduction of a multi-hole mask improves the SNR while maintaining a good angular resolution of a small diameter, single hole imaging device (Dicke, 1968). In mathematical terms masks were represented as binary arrays with the ones corresponding to the pinholes, and the zeros to opaque elements in the aperture. In the early work on coded-apertures, pinholes were randomly distributed on the mask and placed in front of a source to be analysed. The source casts multiple overlapping shadows on the detector through the mask as presented in Fig. 1. Fourier convolution theorem is then used to reconstruct a single, high resolution image from the photons counted on the detector plane (Ables, 1968). Since the pinholes were randomly distributed, a construction of a unique binary array was required for each specific application.
Random patterns pose difficulties with image reconstruction due to a lack of uniformity in pinholes distribution. An inherent noise appears as a result of small terms present in Fourier transform of large size random binary arrays. This problem was addressed by the development of uniformly redundant arrays (URAs). If the distribution of the transparent and opaque elements of the aperture can be represented as a binary encoding array A and the decoding array as G, then A and G can be chosen such that the reconstructed image (correlation of A and G with addition of some noise signal N) approximates a delta function. Delta function is represented by a single impulse located at the central point in signal analysis. In radiation detectors the impulse indicates the location of the reconstructed source (Poularikas, 2006).
Calculation of possible dimensions of the arrays is based on pseudo-noise arrays and previous research documents their implementation for URA based coded-apertures. It has experimentally been shown that URAs offer significant improvements to SNR in comparison with randomly distributed arrays; the quality of reconstruction is improved if the exposure time is increased. URA based coded-apertures are constructed by 2 Â 2 arrangement of the basic design (Fenimore and Cannon, 1978;Calabro and Wolf, 1967). Thus, the size of the detector can be kept small as only the basic array is required to fully recover the source distribution.
Despite its advantages the algorithm used for the construction of URAs restricts the shape of the aperture to a rectangle as vertical and horizontal sides dimensions, p and q, must satisfy the condition p À q ¼ 2 (Fenimore and Cannon, 1978). This limitation was recognised and a modification to the original design was introduced in a form of a hexagonal URA (HURA). An algorithm, based on pseudonoise (PN) sequences (MacWilliams and Sloane, 1976), for the realisation of URA on a hexagonal lattice was first presented by Finger and Prince (Finger and Prince, 1985). It followed a previously proposed implementation of a rotating HURA for gamma-ray imaging (Cook et al., 1984). In the new form HURA was successfully adopted for X-and gamma-ray imaging in high energy astronomy (Goldwurm et al., 1990). In addition a set of characteristics to assess the performance of the aperture was also proposed (Caroli et al., 1987).
The limitation imposed on the physical dimensions of the coded-aperture designs based on URA algorithm led to the development of another class of coded-aperture arrays. Pseudo-Noise Product (PNP) arrays allowed a construction of coded-apertures in previously unavailable dimensions. PNP array can be implemented in any dimensions, provided a corresponding PN sequence exists. However the transparency of PNP arrays is halved in comparison to URAs, because a two-dimensional PNP array is constructed through a direct product of two one-dimensional PN sequences. Although the resulting transparency of the codedaperture is reduced to 25%, SNR comparison with other techniques shows that PNP arrays achieve superior results to pinhole cameras and only slightly inferior to URAs (Gottesman and Schneid, 1986).
Modified Uniformly Redundant Array (MURA), introduced with a change to URA's encoding algorithm, enabled new arrays to be created in linear, hexagonal and square configurations. The design method for URAs was modified, so that the new arrays were based on quadratic residues rather than PN sequences (Gottesman and Fenimore, 1989). Consequently, hexagonal MURA patterns differ significantly from the previously developed HURAs. The hexagonal Fig. 1. Scatter-hole camera aperture as proposed by Dicke (Dicke, 1968).
MURAs can now be formed by mapping of the linear MURAs in exactly the same way as proposed before by Finger and Prince (Finger and Prince, 1985). Linear MURA can now be built in any length L that is a prime number and satisfies the condition Similarly, linear MURAs use quadratic residue modulo L to establish locations of transparent and opaque elements in the coding array A. It was also shown that apertures can be formed in dimensions satisfying not only p À q ¼ 2, but also p À q ¼ 0 (Gottesman and Fenimore, 1989). The square option proved to be particularly popular due to a good balance between design complexity and the high resolution achieved.

Coded-aperture based X-ray imaging
Development of large scale X-ray imaging systems was mainly motivated by the space exploration missions SuperAGILE Feroci et al., 2007), SWIFT (Gehrels et al., 2004), EXIST Vadawale et al., 2005;Grindlay and Hong, 2004) and INTEGRAL (B elanger et al., 2004). As a result, there exists a number of readily available X-ray imagers, where coded-aperture imaging is the dominant technique adopted. Different types of coded-aperture X-ray cameras and telescopes were implemented. Some systems utilise CdZnTe sensors for direct detection of the signals projected through the aperture (Gehrels et al., 2004;Hong et al., 2004;Tumerl et al., 1997). Other examples make use of sensitive silicon microstrip detectors Feroci et al., 2007), where X-ray photons interact directly with the sensitive elements of the detector. Kinetic energy of photons is transformed into electrons, which can be processed by dedicated electronic circuitry.
A comprehensive account of coded-aperture applications in Xray imaging for space exploration was presented by Caroli et al. (Caroli et al., 1987). A set of experiments was conducted to compare the coded-aperture based devices with other approaches. The advantages of using URA based coded masks, as opposed to fresnel pinhole or random masks, are clear when the angular resolution of the reconstruction is considered. Decreasing the hole size results in higher angular resolution e SNR is not affected as the increased number of holes can provide up to 50% aperture transparency. As the dimensions of the aperture elements are kept small, the overall size of the aperture may also be small and reduce the field of view (FOV) of the device. However, multiple devices can be built (in e.g. 2 Â 2 configuration), which will compensate for FOV reduction at the cost of greater number of signals required to be processed on the output. This may in turn affect the detection speed as signals from the position sensitive detector require decoding to localise the source of radiation in the coded-aperture imaging systems.
A coded-aperture based X-ray camera, which utilises CCD as the position sensitive detector, was tested with a 241 Am source and the results confirmed the improvement in sensitivity when compared to a pinhole camera (Ivanov et al., 1999). In the experiment a device was built comprising a mask, CsI(Tl) scintillator, image intensifiers, CCD, lead shield and high voltage insulation. Different combinations of hole sizes and thicknesses were tested for two types of masks, namely single pinhole and coded-aperture mask based on HURA design. Sensitivity increase of up to four times was observed when images obtained by coded-aperture mask were contrasted with those generated by a single pinhole mask (Ivanov et al., 1999).
For comparison a 5 mm thick brass disk was used for both the HURA coded-aperture and the pinhole plate. Pinhole diameter was also kept the same for both tests at 2 mm. Images created using both techniques are presented in Fig. 2. The top four images shown in Fig. 2 are corresponding to the single hole plate case, and the bottom four images to the coded-aperture disk. It is clear that coded-aperture based reconstruction of the circular 241 Am source shows superior spatial resolution, when compared to the single hole plate.

Coded-aperture based gamma imaging
Since gamma-rays are released in a form of high energy photons, X-ray imaging methods can also be exploited for gamma-ray detection. Therefore, coded-apertures, as well as pinhole collimators have been implemented into scintillator based devices for gamma-ray detection and localisation. The primary application of coded-aperture based gamma-ray detectors in far-field high energy cameras for space exploration formed a basis for the study of nearfield radiation detection in medicine and nuclear decommissioning. A very thorough investigation of coded-aperture approach as compared to pinhole camera collimator, for medical applications, was presented by Accorsi (Accorsi, 2001). Results of the study are presented in Table 1. These findings highlighted the advantages of employing coded-mask in place of a pinhole aperture when resolution and sensitivity are considered.
An often quoted disadvantage of coded-aperture approach is its limited FOV . Moreover, coded-aperture imagers are claimed to perform better than pinhole collimators only when point source localisation is performed. In spite of these potential weaknesses for large scale applications, recent research suggests that large horizontal FOV can be achieved by combining multiple coded-apertures into a single hexagonal device . In this particular case a system with 360 horizontal FOV presented angular resolution of average 3.5 when tested with standard calibration source of 137 Cs with energy of 662 keV. The system was also able to detect multiple sources in 360 FOV.
Detectors of such scale may sometimes be impractical for decommissioning applications as portability plays a key role during deployment. Therefore the overall dimensions are frequently decreased and, as a result, the FOV is reduced. Scanning collimator, for example RadScan, can be used to perform the analysis of greater area alleviating the problem of the limited FOV (Santo et al., 2006;Hughes et al., 2004). Exact location of radionuclides in nuclear decommissioning and environment characterisation applications is often unknown; hence the detection efficiency is of greater significance than the extended FOV.
A recent experiment performed by Gmar et al (Gmar et al., 2011). presents a strong correlation between the thickness of the mask used and the detection efficiency of a coded-aperture imaging system. During the study two MURA based masks were used e a rank 11, 4 mm thick mask and a rank 13, 2 mm thick mask. The rank number specifies the number of elements (pixels) comprising one side of a basic square MURA pattern, and coded-apertures are conventionally built by 2 Â 2 arrangement of the basic pattern, following the cyclic permutation of rows and columns (Gottesman and Fenimore, 1989). Therefore, the total number of pixels for the rank 13 and the rank 11 aperture are 625 and 441 respectively. When both masks were tested with lower energy gamma-ray emitter ( 241 Am), the rank 13, 2 mm thick mask provided higher resolution than the rank 11, 4 mm thick aperture. However, when the system was exposed to relatively higher energy gamma sources ( 137 Cs and 60 Co), the rank 13, 2 mm thick mask performed distinctly inferior to the lower rank mask. In the latter case ( 60 Co) the configuration with rank 13, 2 mm thick aperture was found unable to detect the source (Gmar et al., 2011).

Neutron detection and coded-aperture imaging approach
The radioactive waste streams can contain neutron-emitting radioactive materials, hence localisation of neutron sources plays an important part in nuclear decommissioning. It is of vital importance that personnel working on a nuclear site are also not exposed to neutron radiation. For many years, neutron detection systems were largely based on techniques involving 3 He as the primary detector, for example 3 He proportional counters were used extensively by security organisations to identify potential terrorist threats (Peerani et al., 2012). Despite its popularity and efficiency, an alternative system capable of neutron detection in real-time must be considered as 3 He supply has decreased sharply in the aftermath of September 2001 attacks.
Devices based on 3 He are preferred due to higher thermal neutron capture cross-section, in comparison to detection systems based on BF 3 gas-filled detectors (Knoll, 2010). Their absolute efficiency depends greatly on the thickness of the moderation material, which is used to slow down fast neutrons. Generally, detectors with the thicker moderation layer provide better response for higher energy neutron detection. However, if the moderator layer is too thick, lower energy neutrons may be captured by the moderator before reaching the sensitive part of the detector. Also, as the higher energy neutrons lose some of their energy before hitting the detector surface, the information about the neutron origin is lost. Consequently, the detection efficiency of the system is reduced (Knoll, 2010). Moreover, moderation thickness can limit the portability of the device, since significantly thicker moderation layer may be required for higher energy neutrons (Rees and Czirr, 2012).
Four alternative methods have been tested by Kouzes et al (Kouzes et al., 2010). identifying their absolute neutron efficiency and gamma-ray sensitivity. Each option was tested according to the specification of radiation portal monitoring (RPM) systems for national security in the United States. Only a set of three BF 3 tubes and a B-lined detector met the RPM absolute neutron detection efficiency requirement, as well as intrinsic gamma-ray efficiency requirement. Although BF 3 tubes proved to be effective for detection of slow neutrons, it would not be a feasible solution for fast neutron localisation due to significant efficiency reduction for higher energy neutrons (>100 eV) and moderation requirement in the same way as 3 He (Knoll, 2010).
Collimators coupled with B-and Gd-doped microchannel plates (MCP) present an interesting option for low energy neutrons. Neutrons are absorbed by B or Gd atoms inside the glass mixture plates, and electrons are emitted as a consequence of the absorption (Tremsin et al., 2005). Each of the electrons emitted is then multiplied inside an individual microchannel. This approach offers a very high spatial resolution, due to the dimensions of individual elements in the range of micrometers. As a result, the collimator size is also small. The weakness of the system lies in the requirement of stacking multiple MCPs to detect higher energy neutrons which are otherwise limited to thermal energy neutron detection.
An analogous method to Compton scattering for gamma-rays can be employed to image high energy neutrons. The neutron scatter camera method measures the energy of the recoil proton and time of flight (TOF) of the scattered neutron (Mascarenhas et al., 2006). Experiments performed showed that these two measurements are not sufficient to undoubtedly distinguish gamma photons from neutron events in mixed-field environment. It was essential to add a PSD module, so the signals can be reliably separated (Marleau et al., 2007).
A release of a neutron, following a nuclear reaction, is often accompanied by an emission of high energy gamma photons. Therefore, an efficient technique is required to distinguish between gamma-rays and neutron events in mixed radiation fields. Undoped organic liquid scintillators, such as EJ-301 and EJ-309, are regularly used to separate fast neutrons from gamma rays in mixed radiation  (Ivanov et al., 1999). Detection time is equal to 8, 4, 2 and 1 of relative units (from left to right).

Table 1
Resolution and sensitivity comparison for collimator, pinhole and coded aperture with 99m Tc used as gamma source (Accorsi, 2001 fields, due to their excellent PSD capabilities. The light pulses triggered by the neutron interactions, within the organic scintillator, decay more slowly as compared to those triggered by gamma ray interactions. The difference in the decay time is caused by greater energy loss rate for neutron than for gamma ray interactions within the scintillator (Gamage et al., 2011). Consequently, PSD can be performed to establish the type of the event detected. Various algorithms have been considered by the researchers in the time domain, as well as in the frequency domain (Gamage et al., 2011;Liu et al., 2010). The aforementioned liquid scintillators (EJ-301 and EJ-309), were developed with capability of detecting fast neutrons, whereas they are not sensitive to thermal neutrons. They require doping with large thermal neutron capture cross-section isotopes to allow the detection of thermal neutrons. An example of such a detector is BC-523A, which is loaded with 4.4% of 10 B. As such, it presents greater detection efficiency when compared with the undoped EJ-309. In an experiment performed by Peerani et al (Peerani et al., 2012). both detectors were irradiated with 252 Cf and AmBe sources. Both detectors were 5 inch Â 5 inch cylinders with a total detection volume of approximately 1600 cm 3 . In each case detection efficiency was approximately 15% better for BC-523A than EJ-309. Moreover, PSD applied to organic liquid scintillators is insufficient to distinguish gamma photons from neutrons perfectly. A partial overlap between the gamma and neutron clouds is recorded suggesting an inevitable degree of misclassification of the events (Peerani et al., 2012). Recently developed plastic and crystal scintillators, such as EJ-299-33 (Eljen Technology, 2014) and stilbene (Inradoptics), promise a very good separation characteristics for neutrons and gamma-rays. However, the signals emitted by the plastic scintillators are faster compared to liquid scintillators making the application of PSD more challenging (Peerani et al., 2012).
Despite the challenges, PSD has been established as a standard method of separating neutron events from gamma-rays in radiation detectors based on organic scintillators. Development of fast ADCs and field programmable gate arrays (FPGAs) enabled PSD algorithms to be implemented reliably in the digital domain (Gamage et al., 2011;Hawkes et al., 2010). A well-established in the laboratory setting Charge Comparison Method (CCM) for example (Brooks, 1959), relies on the comparison of two time integrals of the detected pulse. The first integral is associated with the entire pulse, whereas the second one can be calculated as the area under the tail of the pulse. Hence, they are often described as the long and the short integral, respectively. The light pulse resulting from a gammaray photon interaction in the scintillator decays faster than the pulse corresponding to a neutron event. Consequently, the short integral is smaller for gamma-rays than for neutrons, when compared to the same magnitude long integral (Brooks, 1959;Adams and White, 1978). Alternatively, CCM can be defined as follows: the short integral as the peak of the pulse, and the long integral as the whole pulse. Regardless of the CCM definition, integration can be performed digitally by the summation of the areas under the pulse corresponding to each sample taken by the ADC.

Coded-aperture based approach
A large energy spectrum of neutron events complicates the employment of the coded-mask approach for neutron imaging. Therefore systems developed to date, focus on a specific energy range of neutrons. One of the implementations of the MURA based coded-aperture for thermal neutron detection was studied with a 3 He ionisation chamber (Vanier, 2004). High angular resolution obtained by coded-aperture based X-and gamma-ray imagers was maintained, when the same method was employed for thermal neutron localisation. Nevertheless the shortage of 3 He supply, as well as the limitations in portability of such a device makes the developments of 3 He based coded-aperture detection systems undesirable.
A fast neutron detector design based on the linear MURA using liquid scintillator EJ-301 revealed promising results when tested in security applications (Marleau et al., 2010). Both the mask as well as the detector plane were built using EJ-301 filled aluminium tubes (Marleau et al., 2009). This enabled the mask to scatter the fast neutrons rather than block them. As a result the neutrons detected in the mask were removed from the reconstructed image. The results showed high spatial resolution for two AmBe sources placed simultaneously in front of the aperture. The normally opaque elements of the coded-mask are replaced with neutron detectors. Consequently, neutron scattering occurs within the coded-mask, when the system is exposed to a fast neutron source. The scattered neutron will then disperse again (double scattering) when it causes another scattering event with the actual detector plane. Thus, the energy spectrum of the source can be determined by measuring the TOF between scatters. While the primary application of the system developed was fast neutron detection, it also exhibits potential for detecting gamma sources when PSD is applied. In an analogous test to the one performed for AmBe neutron source, a high energy gamma source 60 Co was placed 6.7 m away from the detector. The results presented support the claim of comparable detection efficiency for neutron and gamma-ray sources (Marleau et al., 2010).
Another implementation of a fast neutron and gamma-ray imaging system based on coded-aperture MURA pattern was developed at the U.S. Naval Research Laboratory (NRL) to support maritime security in the US (Woolf et al., 2012). The system tested comprises a square (13 Â 13), 11.2 cm thick aperture made of Pb and high density polyethylene (HDPE) and an array of 30 liquid scintillation detectors (EJ-301). Each element of the aperture, as well as the detector is a 5.1 cm Â 5.1 cm square. The detector array was placed 76 cm behind the coded-aperture. The system in this arrangement was tested with 252 Cf gamma/neutron source and 137 Cs gamma source placed 5.1 m away from the aperture plane.
Since the lower energy threshold was set to >2.5 MeV neutron energy in each detector, there was no misclassifications recorded between gamma-ray and neutron events. An angular resolution of up to 4.6 was reported for the reconstructed images.
Further research conducted by the NRL led to a development of a large-scale, coded-aperture imager for fast neutrons (Woolf et al., 2015). In comparison to the work reported in the above paragraph, a 12 Â 12 elements coded-aperture made of pure HDPE was built using pseudorandom pattern. EJ-301 scintillators were replaced with bigger EJ-309 detectors. The size of the individual detector was increased to 15 cm Â 15 cm Â 15 cm and the number of detectors to 32. The system was tested with two 252 Cf sources of different activities e 13 mCi (481 kBq) and 1.8 mCi (66.6 kBq) e located at various distances from the aperture. Similarly to the previous work, 4.5 angular resolution was reported in the reconstructed images. However, when the lower activity source was placed 26 m away from the aperture, it was not detected due to the high level of noise detected. Additional shielding around the detector array was necessary to improve the SNR and hence localise the lower activity source. Neutron and gamma PSD was implemented using digital CCM algorithm for each of 32 single channel PMTs.
MURA based coded-aperture fast neutron detection system was also tested for measurement of plutonium holdup at fuel cycle facilities (Hausladen et al.,46191). This system was a result of improvements to the previous work performed at Oak Ridge National Laboratory (ORNL), which used liquid scintillators as sensitive detectors and utilised Pb shielding to block gamma-rays Hausladen et al., 1055983). The new system utilised modulating properties of HDPE to slow down the high energy neutrons, as the rank-11 MURA based aperture was built entirely from this material. In this experiment a new PSD capable plastic scintillator (EJ-299-34) was tested as a replacement to a fragile and susceptible to leaks liquid detector (EJ-309). The detector was built as an 8 Â 8 array of individual plastic scintillator pixels with 1.35 Â 1.35 Â 5 cm 3 making the total volume of the detector to be 10.8 Â 10.8 Â 5 cm 3 . The detector was positioned behind the 53.4 Â 53.4 Â 2.54 cm 3 coded-aperture pattern machined in an 81 Â 81 Â 2.54 cm 3 piece of HDPE. Multiple apertures can be joined together to increase the thickness of the HDPE if required. Several scenarios were tested with single and multiple 252 Cf sources placed in various location with the reference to the detection system. The main focus of the study was sensitivity rather than spatial resolution. The results suggest that the location of the neutron source in three dimensions can be inferred with a high level of accuracy (Hausladen et al.,46191). Nonetheless, the large scale of the system may present difficulties when attempting to incorporate such a system in nuclear decommissioning environment.
A different implementation of coded-masks to fast neutron localisation was presented by Brennan et al. (Brennan et al., 2015). In contrast to spatial modulation of a particle flux, normally used in coded-aperture imaging, time modulation of the particle flux was introduced. Time-encoded imaging (TEI) technique adapted in this study, relies on a small number of time-sensitive detectors, as opposed to position-sensitive detectors normally used in the coded-aperture imaging systems. Two time-sensitive detectors were built of two 1 inch diameter aluminium tubes filled with EJ-309 scintillator, coupled with two 2 inch diameter cylindrical PMT. The detectors were placed in the centre of a rotating circular mask made of HDPE. The mask had a 30% open fraction and the thickness chosen such that the fission neutrons were sufficiently moderated. The complete system was moved by a stepper motor which enabled the data from the motor encoder to be synchronised with the incidents detected by the PMTs. An angular resolution of 2 was achieved for two 252 Cf point sources after 12 h exposure time (Brennan et al., 2015). Due to the rotational operation of the system a 360 horizontal FOV can be realised. However, long exposure time required may prevent the employment of such systems where real or near real-time radiation detection is desired.
More recent attempts of utilising the coded-aperture approach for neutron detection also show promising results. If the codedaperture is made of a neutron absorbing material, its thickness affects the overall performance of the detector. Recently performed Monte Carlo simulations used an 8 cm thick MURA based codedaperture model (made of 10 B, 113 Cd and 157 Gd), EJ-426 e a thermal neutron scintillator e and 241 AmBe as the neutron source. The results present high spatial resolution for the neutron source located near the central point of the aperture. However, a decrease in spatial resolution is observed when the source is placed nearer the edges of the aperture. The decrease is caused by a greater number of neutrons being absorbed by the shielding implemented around the edges of the coded-aperture. Since fewer neutrons reach the detector surface, the accuracy of the source reconstruction decreases (Hayes and Gamage, 2013).
Despite the high angular resolution achieved across the codedaperture based neutron imagers presented in this section, their adaptation for nuclear decommissioning remains to be demonstrated. None of the systems described performs neutron localisation in real-time. Moreover, the large scale systems (Hausladen et al., 46191;Marleau et al., 2007;Brennan et al., 2015) would be difficult to deploy or maneuver within a nuclear decommissioning environment. They would be impractical in the environment where portability of radiation imaging systems is crucial.

Potential improvements to coded-aperture based neutron imaging
The currently employed techniques for neutron imaging do not offer sufficient sensitivity across the energy spectrum between thermal and fast neutrons (up to 15 MeV). Existing research suggests adding moderation materials or building apertures of greater thicknesses to solve the problem. These solutions may substantially increase the weight and limit the portability of the complete imaging system.
Portable, real-time neutron imaging will be of great benefit to nuclear decommissioning and security applications. In this paper, authors simulated a coded-aperture model considering the practicality of such a device. The shape and the dimensions of the aperture are also chosen such that a scintillator and a position sensitive photo multiplier tube (PSPMT) can be matched. Since an organic scintillating material which is sensitive to a range of neutron energies between thermal and fast (up to 15 MeV) is not available, focus was placed on developing a system suitable for the digital PSD implementation. Modern organic liquid scintillators offer discrimination between neutron and gamma incidents down to approximately 40 keVee, which corresponds to 450 keV energy neutrons (Yong-Hao et al., 2014;Balmer et al., 2015). Improvements into methods of growing single stilbene crystals led to a development of a scintillator, which claims better PSD for lower energy neutrons than previously mentioned EJ-309 liquid scintillator (Gerling et al., 2014). Hence, the prospect of utilising the stilbene scintillator will be explored. The system could then be paired with a multi-channel, FPGA based signal processing electronic circuitry, making real-time detection, localisation and discrimination of neutron and gamma sources in a mixed radiation field possible.

Design of MURA based coded aperture
The model created in this work comprises a square rank 7 coded-aperture with 169 elements, a scintillator and a neutron source. The coded-aperture was designed using original MURA algorithm (Gottesman and Fenimore, 1989). The design of the codedaperture based system involves construction of both an encoding and a decoding array. The encoding array A is placed in front of a source of radiation S resulting in an encoded image being projected on the detector surface D. Considering the practicality of the simulated system, a 13 Â 13 aperture e the encoding array A e was designed through a 2 Â 2 arrangement of the basic rank 7 pattern. Location of opaque and transparent elements in the encoding array A was determined by following equations (1) and (2) (Gottesman and Fenimore, 1989).
The quadratic residue modulo L calculation stems from the number theory and identifies which elements in each row C_i and each column C_j should be open (þ1) or closed (À1). As the case L ¼ 0 is normally excluded from the lists, quadratic residue lists typically range from 1 to LÀ1 (Hardy and Wright, 1979); from 1 to 6 for the system considered in this work.
Equation (1) is then applied to include the row and column when i and j are equal to zero. The resulting encoding array A is obtained by simply replacing þ1 terms with 1 and À1 terms with 0. In accordance with equation (1), the row with i equal to zero contains all zeros, whereas the column with j equal to zero contains all ones apart from the case when i is zero. Such an aperture can be easily rearranged into a symmetrical form by a cyclic permutation of rows and columns (Gottesman and Fenimore, 1989). The basic array in this form can be simply made into 2 Â 2 version as presented in Fig. 3.
In order to decode the image projected by the aperture, equation (3) is applied to the array A resulting in the decoding array G. In this case all 0 terms are changed to À1 and all 1 terms to þ1 except for the situation when the 0 term for i,j ¼ 0 is replaced with þ1. In the 2 Â 2 arrangement of the basic array, it is the middle element that changes its value in comparison to the encoding array A (Gottesman and Fenimore, 1989).
The reconstructed image R is obtained by applying the convolution theorem to the image projected on the detection plane D and the decoding array G as presented in equation (4). The detection plane array D was obtained by running a simulation in MCNPX (Booth et al., 2005).

MCNPX modelling and simulation
As creation of complicated geometry models in MCNPX can be troublesome and error-prone, MCAM CAD-based software was used for the design of the aperture and detector plane (Wu et al., 2015). Models can be built in 3D and converted to commonly used radiation transport codes e.g. MCNP, Geant4. The model of the aperture created in MCAM is shown in Fig. 4. It was created by closely following the equations presented in the previous subsection. 113 Cd and naturally occurring W were tested as potential materials for the coded-mask considering their neutron modulating and reflecting properties (Gamage et al., 2012). 113 Cd was chosen due to its relatively high thermal neutron absorption cross-section (26,719 b). High atomic number of natural W, and its low thermal neutron absorption cross-section (23.86 b) provide marginal moderation of neutrons but adequate reflection for high energy neutrons, due to its high density (19.3 g/cm 3 ). Moreover, mean free path was calculated for each material for thermal and 15 MeV neutrons (maximum neutron energy of 252 Cf as specified in (International Organization for Standardization, 2001)). Results presented in Table 2 support the assumption that 113 Cd is a better choice for thermal neutron absorption than natural W. However, high density of the natural W is reflected in the comparison between the mean free path values for the two materials at 15 MeV. In both cases, an increase in detection sensitivity is to be expected when the aperture thickness is increased. Therefore, aperture models of two thicknesses were tested e10 mm and 25 mm. Each square element of the aperture was set to 5 mm Â 5 mm. The size of each detector element is identical to the thinner aperture in terms of area as well as thickness of a single element. Commercially available liquid scintillators, for instance EJ-301, present good PSD characteristics. But their implementation in systems targeted for nuclear decommissioning can be hindered by some of their properties: for example, EJ-301 consists of highly toxic, flammable and volatile aromatics. Recently developed plastic scintillators have proven to achieve similar results to organic liquid scintillators with regard to PSD (Zaitseva et al., 2012). As these detectors are not manufactured from dangerous substances, they present a potential for use in neutron detection application in nuclear decommissioning.
Recent research into methods of obtaining single stilbene crystals suggests that their light output can be two times higher than that of commonly used liquid scintillator (EJ-309) (Knoll, 2010;Zaitseva et al., 2015). Furthermore, a comparison performed between EJ-309 and stilbene crystal scintillators shows that stilbene has superior PSD and energy resolution (Gerling et al., 2014). These developments in stilbene manufacture made it a viable candidate for the work undertaken. Therefore a stilbene crystal scintillator (C 14 H 12 ) with density of (1.15 g/cm 3 ) was modelled in the MCNPX environment (Inradoptics). According to the technical data sheet, the crystal offers excellent neutron gamma separation, while being non-hygroscopic, non-flammable and non-hazardous (Inradoptics); features of great importance in industrial applications.
As the primary interest of this work lies in localisation of neutron sources, 252 Cf was modelled as the radiation source. It was defined in the MCNPX code based on the characteristics specified in the BS ISO 8529-1:2001standard (International Organization for Standardization, 2001. 252 Cf spontaneous fission source releases several fast neutrons as a result of each fission event (Knoll, 2010), which makes it a viable choice for the requirements of the work described in this paper.
MCNPX geometries were set up with the 252 Cf point source, represented as a red sphere in Fig. 5, located either 5 cm or 10 cm away from the aperture. The coded-aperture and the detector plane -shown in grey and yellow in Fig. 5, respectively -were arranged to be 10 cm apart. The midpoint of the aperture was located at the origin of the geometry regardless of its thickness. As a result, the coordinates of the source in space were changing, as the thickness of the aperture was altered.
A pulse height tally was recorded for each detector cell. The pulse height tally (F8) was chosen as the data recorded offers the closest representation of a physical detector cell (Booth et al., 2005). Special treatment of the pulse height tally was utilised (FT8 CAP), which transforms it to a neutron capture tally (Pelowitz, 2011).
Once MCNPX completed each simulation, number of neutrons captured within each detector cell were read through a MATLAB script and then stored as a 13 Â 13 array. The array obtained is equivalent to the detector plane array D described in section 6.1. Using MATLAB, the detector plane array D was convoluted with the decoding array G and the resultant was utilised to find the reconstructed array R.

Simulation results
For each simulation scenario cell particle activity table e table 126 in MCNPX output file -was analysed and compared for the two aperture materials modelled. Across all arrangements tested, number of neutron collisions in the aperture was on average 40% higher in the natural W than in 113 Cd. Additionally, average neutron mean free path was greater (approx. 3.78 cm) for 113 Cd than for W (approx. 2.32 cm). These results are comparable with the values presented in Table 2., given the theoretical analysis was performed for the maximum energy of the specified source rather than the average.
Detection errors were calculated based on the results obtained. The errors presented in Tables 3 and 4 took into account the difference between the actual source position and the location obtained through the reconstruction process described. The results are presented as 2D images with a scale between À3 and þ3 cm in Y and Z directions. Given the rank of the aperture and the dimensions of the detector simulated, the centre of each cell is located every 0.5 cm. Hence the maximum error (100%) in one direction is associated with the situation, when a hot-spot is detected 6 cells away from the actual location of the source. For example Fig. 6(b), presents the reconstructed source at Y ¼ 3 cm i.e. 6 cells away from the actual source in Y direction -maximum error 100%. In the Z direction the difference is only 1/6 cells (Z ¼ 0.5 cm) -approximate error 16.67%. Using trigonometry the resultant error can be calculated to be 25.32% (accounting for the fact that only one quarter of the whole graph is considered).
In the first modelled set-up, the source was located at (5.5 cm, 0.0 cm, 0.0 cm) with the front of the 10 mm thick aperture, exactly 5 cm behind. Images of the reconstructed arrays R were plotted for each simulated scenario. Fig. 6(a) and (b) present plots of the filtered neutron capture results for 113 Cd and natural W, respectively. It can be observed that both materials provide low detection sensitivity, when the source is located only 5 cm away from the aperture and neutron capture tallies are considered. The following two plots e Fig. 6(c) and (d) e represent the reconstruction of the sources for the aperture of 25 mm thickness with the neutron source located 5 cm away. Although the detection accuracy increases marginally in the case of natural W when the aperture thickness is increased, it is not sufficient to provide reliable localisation data.
Results of the simulation for the source located at the distance of 10 cm from the aperture front present a significant improvement in detection sensitivity, when compared to the previously discussed case. Regardless of the thickness 113 Cd aperture provides an ideal reconstruction of the source. The improvement for the mask made of natural W is not as prominent as in the case of 113 Cd. It should Table 2 Neutron mean free path calculation results for 113 Cd and Natural W based on ENDF/ B-VII.1 library from (Soppera and Dupont, 2012).

Material
Neutron mean free path (cm)  also be noted that a weighted error calculation was applied for all the images presented. Hence, the detection error is greater for 10 mm thick W mask, as contrasted with the 25 mm thick W mask; multiple hot-spots suggest lower confidence in the results obtained. The reason for image splitting can be associated with the neutron reflective properties of natural W. As the aperture is placed farther away from the source, a higher number of particles can be reflected through the internal surfaces of the aperture's open elements. These in turn lead to false neutron events being detected within scintillator cells.
Since the main focus of this study was to assess a workable neutron localisation solution for nuclear decommissioning an isotropic 252 Cf source was used. It was found that 113 Cd aperture absorbed lower number of neutrons than natural W, which supports the calculated and achieved neutron mean free path values for each material. In both cases the statistical uncertainty of the results did not exceed 0.01% for the neutron capture tally. The detectors response in the relevant energy ranges did not exceed the statistical uncertainty of 0.05%. This level of statistical accuracy was achieved with 10 8 particle histories simulated.
The modelled stilbene scintillator performed well in the simulated environment, despite its small thickness (1 cm), which makes it a possible solution for practical implementation of the system. Moreover, initial results suggest that even with a relatively large element size (5 mm Â 5 mm) and small thickness of 10 mm, 113 Cd coded-aperture can achieve good detection sensitivity as shown in Fig. 7(a) and (c). It should also be noted that with doubling of the distance between the aperture and the neutron source, an improvement in detection sensitivity was observed. The importance of this is that neutron localisation from a distance would be of great benefit for nuclear decommissioning applications, as access to the areas of nuclear power plants requiring characterisation is often limited.

Discussion
Existing coded-aperture imaging systems have been reviewed and potential improvements for a practical coded-aperture based neutron imaging system have been discussed and simulated. Scintillator based coded-aperture radiation imaging has been previously well documented by researchers with reference to X-and gamma-ray detection. Coded-aperture neutron imaging systems have shown encouraging results for fast neutron detection in security applications, as well as in nuclear material instrumentation. Neutron detection and localisation in nuclear decommissioning, on the other hand, relies largely on commercially available collimator Table 4 Detection error for the distance of 10 cm between the source and the aperture.

Material
Detection error (%) based pinhole detectors. Many of these systems employ liquid scintillation detectors, which are not favourable in sensitive decommissioning environment, due to their hazardous properties. In this study, an organic stilbene crystal scintillator has been identified, which claims excellent PSD, and provided promising results in the fast neutron environment modelled. In contrast to liquid scintillators, it is not hazardous, easy to transport and not susceptible to leaks. Furthermore, the results obtained from an MCNPX simulation also suggest that using high density material for the mask enables it to reliably stop fast neutrons from reaching the scintillator through the opaque elements of the mask, without increasing its thickness to impractical dimensions. The theoretical model proposed holds potential for a portable coded-aperture neutron detection system if paired with a commercially available PSPMT, such as Hamamatsu H9500. It is a square 256 channel PSPMT with pixel size of 2.8 mm Â 2.8 mm. The size of a single coded-aperture element can be matched to that of the PMT pixel increasing the overall resolution of the system. As the location of the interaction in the scintillator can be extracted via readout electronic system, the detection sensitivity could also be potentially increased. However, in order to reliably distinguish neutron from gamma interactions within organic scintillator, not only the interaction location but also the shape of the pulse must be retrieved. Hence, a bespoke readout electronic system for the PSPMT would be required. Pulses extracted from the PSPMT would necessitate digitisation using high sampling rate ADCs before being processed on a fast FPGA chip (up to 500 MHz) to perform digital PSD. With a correctly characterised scintillator, real-time mixed field characterisation could be achieved.
The modelling work completed, proposes one of the implementations of the scintillator based coded-aperture neutron imaging systems. In comparison to the coded-aperture neutron imaging systems reviewed, the model proposed in this paper is a relatively small scale system. It aims to present an adaptation of the proven advantages of the larger coded aperture imaging systems for neutron localisation in nuclear decommissioning, where portability and detection efficiency play vital roles. Hence, the system is intended to perform initial scanning of a larger area from a distance of several meters and then gradually focus on the specific location of the radioactive source. Alternatively, multiple modules can be arranged into square arrays avoiding the need for initial scanning of larger areas.
As scintillator based coded-aperture neutron imagers are continuously being explored and improved, owing to technological advancement, coded-aperture based neutron imagers can be adapted in new application fields, such as nuclear decommissioning. Hence, a careful selection of hardware elements, a novel design approach, as well as innovative digitised PSD implementation will play a key role in the performance of an imaging system suitable for this application.