WO2024028615A1

WO2024028615A1 - Radiation imaging robot

Info

Publication number: WO2024028615A1
Application number: PCT/GB2023/052075
Authority: WO
Inventors: Rosemary LESTER; Matthew Paul Mellor; Benjamin Jonathan BIRD
Original assignee: Createc Ltd
Priority date: 2022-08-05
Filing date: 2023-08-04
Publication date: 2024-02-08
Also published as: GB202211434D0

Abstract

A radiation imaging apparatus comprises radiation detectors configured to detect ionising radiation and a position and orientation detector configured to determine an instantaneous position and orientation of the radiation imaging apparatus in six degrees of freedom relative to real world structures as a fixed frame of reference. A method of estimating radiation source distribution within a facility is provided. A method for estimating the spatial distribution of the minimum detectable activity of radiation by taking into account one or more parameters is provided.

Description

RADIATION IMAGING ROBOT FIELD This invention relates to a radiation imaging apparatus for detecting ionising radiation, a radiation imaging method and a computer program. BACKGROUND When operating or decommissioning facilities containing radioactive nuclear materials, it is frequently necessary to understand the quantity of radioactive material within the facility being surveyed as well as the distribution of the radioactive material within the facility. When decommissioning a facility containing radioactive material it is frequently necessary to understand the activity and distribution to assess and sentence the waste for commercial landfill or nuclear waste disposal. It is often the case that the physical properties of such a facility need to be determined also. Conventional methods for determining this information typically involve taking measurements using contamination monitoring devices and manually recording the results. This is typically extremely slow and can take months. The method of recording can also be inaccurate. When carrying out detection of radiological measurements it is important to consider the minimum detectable activity which is detectable by the specific radiation imagining apparatus being used for that measurement. The minimum detectable activity of a measurement is the lowest activity level that is practically detectible by the specific system for that measurement. If the activity in a sample is below the minimum detectable activity level, the measuring system will not be able to detect it during that measurement. The minimum detectable activity depends on a number of factors, including, but not limited to, the characteristics of the radiation imaging apparatus, the sample characteristics, the method of measurements and the measurement condition. Therefore, the minimum detectable activity can vary within a single facility or within a single survey due to a non- uniform distribution of radiation sources and due to different measurement conditions and measurement methods. Using higher sensitivity equipment, longer measuring times and being in the vicinity of a highly radioactive sample generally reduces the minimum detectible activity of a radiological measurement. In situations where it can be assumed that distribution of radiation sources is confined to the surfaces within a facility, it is possible to consider the minimum detectable concentration on the surfaces of a facility, without taking into account the density of depth of activity. Considering the minimum detectable activity or the minimum detectable concentration and its distribution is particularly important in areas with low level radioactivity. EP 07823931 discloses a method of determining distribution of a radioactive material within a facility. Known methods to provide this information are time consuming and require high computational power. Furthermore conventional methods do not take into account the spatial distribution of the minimum detectable activity, meaning that in low level nuclear waste facilities it is difficult to tell apart a true measurement from random errors. SUMMARY Accordingly, the present invention provides a radiation imaging apparatus comprising: (a) two or more radiation detectors configured to detect ionising radiation, or (b) a single radiation detector configured to be moved to two or more predetermined positions with respect to a body of the radiation imaging apparatus, wherein the radiation detector is configured to detect ionising radiation at the predetermined positions; and a position and orientation detector configured to determine an instantaneous position and orientation of the radiation imaging apparatus in six degrees of freedom relative to real world structures as a fixed frame of reference. Providing a radiation imaging apparatus with two or more detectors configured to detect ionising radiation allows to improve the efficiency with which ionising radiation data is detected. Furthermore, detecting ionising radiation data with two or more detectors simultaneously as well as the position and orientation of the device allows for more efficient analysis of the spatial distribution of radiation sources. In a further optional aspect of the invention, the radiation imaging apparatus comprises an imaging device configured to image real world structures. This allows the apparatus to image real world structures as well as detecting ionising radiation and the position and orientation of the detector which allows for more data pertaining to the real world to be collected. In a further optional aspect of the invention, the radiation imaging apparatus comprises a speed detector configured to determine a speed of the radiation imaging apparatus. In a further optional aspect of the invention, the radiation imaging apparatus comprises a radiation source determination section configured to determine a distribution of radiation sources based on data of the ionising radiation detected by the radiation detector and number of detectors, combined with data of the position, orientation of the radiation imaging apparatus relative to the real world structures. In a further optional aspect of the invention, the radiation imaging apparatus comprises radiation source determination section which is further configured to determine a distribution of radiation sources based on the speed of the radiation imaging apparatus. In a further optional aspect of the invention, the radiation source determination section is further configured to determine a spatial distribution of the minimum detectable activity of radiation based on data of the ionising radiation detected by the radiation detector and number of detectors, combined with data of the position, orientation of the radiation imaging apparatus relative to the real world structures. Taking into account the number of detectors used allows to determine the spatial distribution of minimum detectable activity with greater accuracy. Increasing the number of detectors used increases the accuracy of the determination of the minimum detectable activity. Determining the spatial distribution of the minimum detectable activity allows for improved radiation data analysis. The spatial distribution of minimum detectable activity indicates the distribution of the lowest activity level that is detectable within the facility. Therefore, it is possible to discern with greater accuracy areas with lower and higher radiation activity. Furthermore it is possible to determine which measurements are true and which are due to random noise with greater accuracy. In a further optional aspect of the invention, the radiation source determination section is further configured to determine a distribution of the minimum detectable activity of radiation based on the speed of the radiation imaging apparatus. Taking into account the speed of the detector allows to determine the minimum detectable activity with greater accuracy. In a further optional aspect of the invention, the radiation imaging apparatus is disposed on a motorised controllable platform. This allows the radiation imaging apparatus to be controlled by a user who is located away from the real world structures being surveyed, meaning that the user can be shielded against the sources of radiation. In a further optional aspect of the invention, the radiation imaging apparatus includes a path planning and collision avoidance system which is configured to allow semi- autonomous navigation avoiding mobile and fixed obstacles. This allows for more effective path planning which avoids obstacles. In a further optional aspect of the invention, the radiation imaging apparatus further comprises a communication unit configured to communicate with the radiation source determination section, wherein the radiation source determination section is disposed remotely from the radiation imaging apparatus. This allows for the radiation source distribution and/or minimum detectable activity determinations to be done remotely, which reduced the number of components of the radiation imaging apparatus which are sent to the facility being surveyed. In a further aspect of the invention, the one or more radiation detectors are alpha-particle detectors. In a further aspect of the invention, the alpha-particle detectors are disposed on an arm. In a further aspect of the invention, the radiation detectors are beta-particle detectors, or gamma radiation detectors, or X-ray radiation detectors. In a further aspect of the invention, the position and orientation detector is configured to determine the instantaneous position and orientation of the radiation imaging apparatus using photogrammetry, or neural rendering, or simultaneous localisation and mapping based on photographs, or LIDAR measurements, or SONAR measurements, or RADAR measurements. According to the invention there is provided a method for estimating radiation source distribution within a facility comprising the steps of obtaining a position of each radiological measurement within a 3D model of the facility by using geometrical measurements; ascribing radiological measurements to a distribution of sources restricted to defined locations within a 3D model of a facility; parameterising the source distribution over the defined source locations, where the number of parameters exceeds the number of radiological measurements; relating each parameter (si, s2,...) to a calculated observable radiation field, calculated using a physical model, at each measurement position; adjusting the parameters (si, s2,...) to optimize the correspondence between said plurality of radiological measurements and the calculated observable radiation field, to yield the distribution of radioactive material as defined by the adjusted parameters by using an iterative method wherein the step size is recalculated during the iterative method based on the difference between prediction of given iteration and actual measurement; adjusting the parameters subject to the constraint that all sources have non-negative values. Recalculating the step size during the iterative process significantly reduces the computational power required for estimating the radiation source distribution. In a further aspect, the geometrical measurements of the method of estimating radiation source distribution within a facility comprise photographs, or LIDAR measurements, or SONAR measurements, or RADAR measurements. In a further aspect, the 3D model used in the method is generated from the photographs, or the LIDAR measurements, or the SONAR measurements, or the RADAR measurements using photogrammetry, or neural rendering, or simultaneous localisation and mapping. The 3D model may be updated as the apparatus surveys the facility. In a further aspect, the radiological measurements used in the method are acquired from two or more detectors. According to the present invention there is provided a method for estimating the spatial distribution of the minimum detectable activity of radiation by taking into account one or more parameters, wherein the parameters may be any one or more of: the data collected by the two or more radiation detectors, the number of detectors, the data of the position, orientation of the radiation imaging apparatus relative to the real world structures, the speed of the radiation imaging apparatus. According to the present invention there is provided a computer program for processing radiation data configured to estimate the radiation source distribution. In a further aspect of the invention the computer program is configured to estimate the spatial distribution of the minimum detectable activity of radiation. BRIEF DESCRIPTION OF DRAWINGS Figure 1 is a schematic diagram of an embodiment of the present invention which comprises a radiation imaging apparatus disposed on a motorised controllable platform with two detectors disposed on an arm which is configured to image a floor. Figure 2 is a schematic diagram of an embodiment of the present invention which comprises a radiation imaging apparatus disposed on a motorised controllable platform with two detectors disposed on an arm which is configured to image a wall. In the drawings, like parts are identified by like references. Figure 3 shows the method steps of estimating radiation source distribution. Figure 4 is a schematic diagram of an embodiment of the present invention which comprises a radiation imaging apparatus disposed on a motorised controllable platform with two alpha detectors disposed on an arm. Figure 5A shows an example spectrum of background radiation. Figure 5B shows an example spectrum including a signal measurement. Figures 5A and 5B show the counts collected by a radiation detector as a function of radiation energy. Figure 6A is a photograph of an embodiment of the present invention, having a single detector disposed on a moveable arm. Figure 6B is a schematic diagram of this embodiment. DETAILED DESCRIPTION Various embodiments of the disclosed methods and arrangements are discussed in detail below. While specific implementations are discussed, it should be understood that this is done for illustration purposes only. A person skilled in the relevant art will recognise that other components, configurations, and steps may be used without departing from the scope of the appended claims. The apparatus 100 according to a first embodiment of the present invention comprises two or more radiation detectors 101 configured to detect ionising radiation, and a position and orientation detector configured to determine an instantaneous position and orientation of the radiation imaging apparatus 100 in six degrees of freedom relative to real world structures as a fixed frame of reference. The radiation detectors 101 remain at a fixed distance from each other during a survey of the facility. Alternatively, a single radiation detector may be provided, wherein the single radiation detector is configured to be moved between two or more predetermined positions with respect to a body of the radiation imaging apparatus. The single radiation detector may be provided on an arm, such that two or more radiation detection readings can be taken from two or more predetermined positions while the radiation imaging apparatus is stationary with respect to the facility being surveyed. This embodiment can obtain two or more readings from two or more locations, which are fixed relative to the body of the radiation imaging apparatus during a survey of the facility. A survey of the facility consists of taking the apparatus 100 to the facility to be modelled and making numerous observations where each observation comprises each radiation detector 101 taking a measurement of the level of ionising radiation, and the position and orientation detector determining the instantaneous position and orientation of the radiation imaging apparatus 100 in six degrees of freedom relative to real world structures as a fixed frame of reference. The facility could be any three dimensional environment. For example, the facility could be an operating or a decommissioned nuclear power plant. Taking measurements from two or more detectors during each observation wherein the detectors remain fixed relative to each other for each observation allows to gather information about the distribution of radiation sources with greater efficiency. These measurements can be used by the radiation source determination section to determine a distribution of radiation sources as outlined below. These measurements can also be used by the radiation source determination section to determine a spatial distribution of the minimum detectable activity of radiation as outlined below. These measurements can also be used for the method of estimating radiation source distribution within a facility as outlined below. The methods may be performed by a computer program. The apparatus 100 may further comprise a speed detector which monitors the speed of the radiation imaging apparatus 100. In this embodiment, each observation includes the speed detector taking a measurement of the speed with which the radiation imaging apparatus 100 moves. The speed of the radiation imaging apparatus 100 may be used as one of the parameters for determining a distribution of radiation sources and/or the a spatial distribution of the minimum detectable activity of radiation by the radiation source determination section as outlined below, or in the method outlines below. The apparatus 100 may be disposed on a on a motorised controllable platform 102. This allows the apparatus 100 to be controlled remotely which eliminates the risks associated with sending a human to a location with ionising radiation levels which could pose a significant health risk. The apparatus 100 disposed on a motorised controllable platform 102 may include a path planning and collision avoidance system which is configured to allow semi-autonomous navigation avoiding mobile and fixed obstacles. This limits the manual intervention needed to carry out a survey of the facility and reduces the measurement time. [ The apparatus 100 may also be handheld. This could be beneficial in situations where appropriate safety measures are available to protect the user from significant exposure to radiation, and it is undesirable to control the apparatus 100 remotely. The radiation detectors 101 may be alpha-particle detectors, beta-particle detectors, gamma radiation detectors 101 or X-ray detectors. The two or more detectors which are configured to detect ionising radiation in a given survey of the facility are one type of detector. The apparatus 100 may comprise multiple types of detector on a single apparatus 100 so that multiple surveys can be carried out in parallel, wherein each survey is aimed at studying the distribution of different types of radiation. The alpha-detectors may be disposed on an arm, such as the examples shown on Figures 1 and 2. Alpha-particles have a short range in air, therefore disposing them on an arm which extends from the apparatus 100 in a distal direction allows for measurements to be taken very close to a surface such as a wall or the floor of the facility being surveyed. All alpha- particle detectors may be disposed on one arm, or they may be distributed across multiple arms such that each arm has at least one detector disposed on it. The arm may be moveable and/or the position of detectors on the arm may be moveable, such that the position of the detectors relative to be apparatus 100 may be changed between different surveys. This can be done manually by a user or automated means may be provided to allow for the position of the arm and/or detectors to be changed remotely. The position of the detectors relative to each other and the apparatus 100 is fixed for a given survey, such that the relative position of the detectors and the apparatus 100 does not change between the observations of a given survey. The relative position may be changed between different surveys to take into account, for example, the geometry of the facility being surveyed. Beta-particle detectors, gamma radiation detectors or X-ray detectors may also be disposed on an arm, for example, to accommodate for a facility with a complex geometry. The position and orientation detector is configured to determine an instantaneous position and orientation of the radiation imaging apparatus 100 in six degrees of freedom relative to real world structures as a fixed frame of reference. However, it is not necessary for the instantaneous position and orientation detector to determine the position and orientation of the radiation imaging apparatus 100 in six degrees of freedom. The position and orientation detector is a means of determining the instantaneous position of the radiation imaging apparatus 100 in a least two dimensions relative to real world structures surrounding the radiation imaging apparatus 100. Accordingly, it may be that the position and orientation detector detects the position of the radiation imaging apparatus 100 in two degrees of freedom, three degrees of freedom, four degrees of freedom or five degrees of freedom. The position and orientation detector may determine the position and orientation of the radiation imaging apparatus 100 by means of one or more range sensors and an orientation detector. Each of the range sensors is configured to measure range data of distances from the radiation imaging apparatus 100 to real world structures in at least two dimensions. The range data is interpreted by an algorithm to determine an instantaneous position of the radiation imaging apparatus 100 in at least two dimensions relative to the real world structures as a fixed frame of reference. The range sensors combine with software running the algorithm to determine the position of the radiation imaging apparatus 100 relative to the real world structures. Accordingly, each observation (when radiation is detected) is performed at a known position. The software comprises part of the position and orientation detector. For example, the range data may provide information about the distance from the radiation imaging apparatus 100 to a series of points of a room. The position of the radiation imaging apparatus 100 can then be determined by aligning the range data to a map of the room. The map of the room is an example of known information about the layout of the real world structures. Hence, the measured range data is interpreted to provide positional information relative to the real world structures. This interpretation is performed by software that runs an algorithm configured to deduce the motion of the radiation imaging apparatus 100 by aligning the range data with reference range data (e.g. a map). The range data of distances from the radiation imaging apparatus 100 to real world structures in at least two dimensions can be used to determine the position and orientation of the device by taking into account the range data and the known position of the sensor relative to the apparatus 100. The range sensor(s) may be any appropriate sensor which can measure range data of distances from the radiation imaging apparatus 100 to real world structures. For example, Light Detection and Ranging (LIDAR), Sound Navigation and Ranging (SONAR) or Radio Detection and Ranging (RADAR) may be used. By aligning the measured range data to reference range data (e.g. a map of the real world structures), the position of the radiation imaging apparatus 100 can be determined relative to the real world structures as the fixed frame of reference. This is different from other means of detecting position such as GPS, radio beacon methods and QR code readers. GPS, radio beacon methods and QR code readers rely on measuring the distance to satellites, beacons or QR codes that have a known position in another coordinate system. The position of the reader can be determined by measuring the distance to multiple satellites, beacons or QR codes and solving equations to determine the position of the reader within that coordinate system. These methods do not involve aligning the measured distances to the satellites, beacons or QR codes to reference range data. The invention does not require any real world objects to be installed for the purpose of position determination. In particular, the invention does not require any satellite, beacon or QR code. The real world structures are not satellites, beacons or QR codes. Instead, each range sensor measures the range to objects that just happened to be there. The position of the objects in another coordinate system is not required to be known. The measured range data is aligned with the reference range data so that the real world structures themselves become the fixed frame of reference. The position and orientation detector may use photogrammetry, or neural rendering, or simultaneous localisation and mapping techniques to determine the instantaneous position and orientation of the radiation imaging apparatus 100. Using photogrammetry to determine the instantaneous position and orientation of the radiation imaging apparatus 100 involves taking one or more photos during an observation, and using the photo(s) to determine the position and orientation of the imaging device by mapping them to a 3D model of the facility that has been created using photogrammetry. Photogrammetry can be used with photographs, LIDAR measurements, SONAR measurements or RADAR measurements. Neural rendering involves using machine learning techniques to map the photograph, or LIDAR measurement, or SONAR measurement, or RADAR measurement to a 3D model of the facility (using the same imaging technique) to discern the position and orientation of the radiation imaging apparatus 100 at the time that the measurement was taken. This technique may be preferable when the apparatus 100 is in a facility with objects far away from it, e.g. when the apparatus 100 is outside. Simultaneous localisation and mapping (SLAM) is a computational technique for keeping track of location of the apparatus 100 within a map/model of the facility, as well as updating the map with each new observation made. Furthermore, odometry (i.e. the use of motion sensors to determine the change of the apparatus’ 100 position relative to some known position) and other live streams from sensors that measure parameters such as distance of the apparatus 100 from a given point, may be used to monitor the positon and orientation of the apparatus 100 in real time. The type of technique and measurement used to determine the position and orientation may be determined based on a number of parameters, such as the type of facility being studied. For example, SLAM may be used if there is a need to improve the map/model of the facility. Photogrammetry techniques may be more efficient in a facility containing a plurality of distinct shapes and colours of features, whereas photogrammetry may be less effective in a facility with a plurality of features of similar shapes and colours (e.g. many corridors with no distinct features) because photographs from different locations may look very similar. I Preferably, a position and orientation detector which determines an instantaneous position and orientation of the apparatus based on LIDAR measurements is used. The position and orientation detector may be configured to determine its location via any suitable algorithm, such as Monte Carlo localisation. Monte Carlo localisation is an algorithm which estimates the position and orientation of the apparatus 100 as it moves and senses the environment. Another example of simultaneous localisation and mapping includes the use of odometry and/or any suitable position and orientation sensors which may also output velocity commands to the motorised controllable platform 102. In an embodiment of the radiation imaging device comprising two or more alpha-detectors, it is preferable that the location and movement of the apparatus 100 are monitored with greater accuracy. This is because alpha-particles have a short range in air, and an accurate map of the distribution of alpha-particle sources can be obtained when highly accurate measurements of location and movement are available. Therefore, in an embodiment of the invention comprising alpha-particle detectors, it is preferable to use a high resolution LIDAR sensor. Alternatively, a low resolution LIDAR sensor may be used with another sensor for tracking the movement of the apparatus 100 , such as an optical flow sensor. Other types of sensors may be used. The position and orientation detector of the radiation imaging apparatus 100 may further comprise an orientation detector. The orientation detector is configured to determine at least one of an instantaneous yaw, an instantaneous roll and an instantaneous pitch of the radiation imaging apparatus 100 relative to the real world structures. The orientation detector is configured to measure the tilt of the radiation imaging apparatus 100 such that a correction factor can be applied to the position data to ensure it represents a more accurately horizontal plane. The apparatus 100 may include a radiation determination section which determines a distribution of radiation sources based on data of the ionising radiation detected by the radiation detector and number of detectors, combined with data of the position, orientation of the radiation imaging apparatus 100 relative to the real world structures. The radiation determination section may also determine a spatial distribution of the minimum detectable activity of radiation based on data of the ionising radiation detected by the radiation detector and number of detectors, combined with data of the position, orientation of the radiation imaging apparatus 100 relative to the real world structures. The determinations of the radiation source distribution and/or the spatial distribution of the minimum detectable activity may also be based on the speed of the detector. According to the present invention there is provided a method for calculating a distribution of radiation sources within a facility. The method according to the present invention calculates a distribution of radiation sources within a 3D facility. The facility is modelled by a 3D model which may be generated using a variety of techniques. For example, it may be generated using photogrammetry techniques and other sources of information such as technical drawings or existing CAD models of the facility. The simplest choice is to assume that sources are distributed over external surfaces of the model as this minimises the effects of shielding and eliminates the vast majority of potential source locations, improving the output of the process. However, care must be taken to ensure that the assumption made at this point is suitable to the facility in question. The source distribution within the selected region of the model is then parameterised. The choice of parametrisation is arbitrary at this point, provided that it has the following properties. Firstly, the parameterisation should be capable of representing all plausible source distributions to a greater degree of precision than could be solved for given the set of measurements that have been taken. Secondly, the radiation field at all points in space must be a superposition of the radiation field caused by the radiation sources described by each parameter. Mathematically, this condition may be expressed as:

Where R is the intensity of the radiation field at point (x,y,z) and f_n is a function giving the contribution of radiation source parameter s_n at point (x,y,z). There are many choices of parameterisation which satisfy these properties. In the case of surface sources a good parameterisation is to divide the surface into many small triangles, with the amount of source material within each triangle described by a single parameter. The triangles should be small in comparison to the distance between the triangle and the nearest measurement, and preferably close to equilateral in proportion, and may be generated using standard meshing techniques from computer modelling and graphics applications. In some cases, the simple triangular patch technique will result in a very large number of parameters, resulting in a computationally inefficient model. In these cases, the dimension of the parameterisation can be reduced by linking the values of neighboring triangles. The simplest technique is to assign groups of neighbouring triangles a single radiation source density described by a single parameter. A preferable method, which allows a smoothly varying radiation source distribution is to define the N single triangle radiation source parameters s_n as a weighted sum of a smaller number, M, of multi-triangle parameters s’_m Selecting the weighting functions w(n,m) (known as a basis) is a design issue, and conventional techniques can be used to adapt the choice to a specific mesh. Once the model is parameterised, the parameter values which generate the observed radiation field with the minimum Root Mean-Square amount of radioactive material are calculated. This assumption tends to produce results which are conservative in terms of the total amount of radioactive material, but prefers distributed sources to point sources, which is suitable for many contaminated facilities. It is emphasised that this is only one of several possible methods of selecting the best set of parameter values, the choice of which will depend on prior knowledge of the facility. This set of parameter values may be found as follows. For each measurement of the radiation field, r_k, an equation may be derived from Eq. 1, of the form:

Where x_k,y_k, and z_k are the space coordinates of the measurement. The system of equations generated in this way can be written in matrix form as follows:

Where F is a matrix, defined as:

and S and R are vectors of which the ith elements are r_i and s_i respectively. Typically, the number of parameters, N, and the number of radiation field readings, K, are different. This implies that F is non-square, which in turn implies that it has no inverse and that the system of equations cannot be ‘solved’. However, it is nevertheless possible to find the shortest length parameter vector S which generates the observed radiation readings R by finding the pseudo-inverse of F. The pseudo inverse, F⁺, is a well known tool for solving under and over determined systems of equations, defined as: Eq. 5 The method described above provides a means to estimate the best set of parameters, in a particular sense, provided that the physical relationship between the each parameter and each reading can be modelled by a function f_n(x_k,y_k,z_k). The derivation of these functions depends upon the adopted parameterisation, the nature of the facility, and the types of measurement made. In the present embodiment of the invention, it is assumed that the facility is a convex volume, with negligible shielding effects, and that a radiation source with fixed isotopic composition with known emission spectrum g(λ) (total counts per second per gram at a given wavelength λ) can be attributed to all source material. The radiation source may be a source of, for example, X-ray or gamma radiation. The model can also be used if it is assumed that the facility is a convex volume, with negligible shielding effects, and that a particle radiation source with fixed isotopic composition can be attributed to all source material. In the case that the radiation source is a source of particle radiation (such as alpha particles or beta particles), the count rate of the particles detected is used in the method below. c? In the case of gamma radiation, the count rate measured at a distance d from a point source using a total counts radiation probe is approximated by:

30 Where Kd is a calibration constant that accounts for the geometry and efficiency of the detector and μ(λ) is the wavelength dependent attenuation coefficient of air. In practice, the emission spectrum will be zero outside of a range of interest, and the integral need only be evaluated over this range. Since the triangles of the parameterisation mesh are much smaller than the distance to the nearest source, each triangle is well modelled by a point source located at its centroid. The parameters then correspond to the total mass of this point source and the functions f_n(x_k,y_k,z_k) given by:

Where (x_n,y_n,z_n) are the coordinates of the centroid of the nth triangle. Thus, the readings attributed to the measured location are the combined effect of all the sources of radiation. The functions affecting attenuation ^{^}

and distance (^ ) can be parameterised into a single matrix F ^^ = ^ Eq. 8 Where R represents the readings at various locations in space, S is the potential source list in the same spatial reference and F is the matrix specifying reduction in signal expected from each potential source to each reading. In order to calculate the source term g(λ), the solution has to be calculated such that it produces non-negative activities (as negative activities are non-physical for a scaler measurement). In some cases, the previously described methods will produce, due to the effects of noise, some negative source intensities. Because negative source intensity is not physically meaningful, eliminating these from the model adds an additional constraint which can be used to improve the robustness and accuracy of the model outputs. Several algorithms that achieve this purpose are known. Although they are typically much slower than the method described above, they have an additional advantage that less computer memory space is required, making them also suitable for application to very large models. An example of such a technique that is well suited to this application is the projected Landweber technique. This is an iterative technique, which begins with an arbitrary estimate of the source parameter vector s° and iteratively calculates an improved parameter vector s^k+1 based on the fit of the existing parameter vector sk to the model according to the following equation:

Eq. 9 Here κ is a step size parameter that determines the rate of convergence of the algorithm, and (a)₊ is the non-negative vector whose entries are those of a, where positive, and zero otherwise. This iteration loop is repeated until some stopping criterion (such as number of iterations, time, or stability of solution) is satisfied. A range of other algorithms with similar properties are also available. These include, but are not limited to: Non-negative Constrained Algebraic Reconstruction; Multiplicative Algebraic Reconstruction; Expectation Maximisation; and Ordered Subset Expectation Maximisation (OSEM). The source activity distribution is calculated from solving the inverse of the parameterised model. The readings are also dependant on Poisson statistics which can create noisy, highly variable measurements for each location (x,y,z). In order to solve the equation a novel version of the projected Landweber algorithm is used with an automated step size calculation. The standard Landweber algorithm aims to minimise the error between the parameterised model and real readings. min‖^^ − ^‖ Eq. 10 Using an iterative method where: ^_^^^ = ^_^ − ^^^∗(^^_^ − ^) Eq. 11 Where ^ is a relaxation parameter defined by the user. This parameter has to be estimated separately for each scenario. An automated relaxation parameter has been developed for this application. The updated projection is calculated as: ^ = ^^^∗(^^_^ − ^) Eq. 12 And the relaxation parameter ^ is calculated as _{^ = ^ ∗} ^(∑ _^ ⁽ _{^^^ − ^} ⁾ _/ ^‖ _^ ^‖) _/ ^‖ _^ ^‖ _{Eq. 13} Where ^ is a simple step parameter of value approximately 0-1, typically 0.2. This automation makes the solution more robust to noisy datasets while allowing it to run in real time with no user actions required. Typically, the standard Landweber algorithm would require ^ to be estimated by trial and error and a fixed value used for each of the thousands of iterations required. This allows ^ to be updated in each iteration. According to the present invention, there is also provided a method for calculating the spatial distribution of the minimum detectable activity of radiation by taking into account one or more parameters. The parameters may be any one or more of: the data collected by the two or more radiation detectors 101, the number of detectors, the data of the position, orientation of the radiation imaging apparatus 100 relative to the real world structures, the speed of the radiation imaging apparatus 100 . The parameters may be selected based on the set-up of the survey and the type of radiation being detected. The activity of the radiation sources (which produce ionising radiation) can be assumed to be confined to the surface, rather than spread out throughout the material. In that case, it is not necessary to account for density or depth of the activity. If such an assumption is made, the minimum detectable activity (MDA) can be assumed to be the minimum detectable concentration (MDC). The following description refers to MDC, however, the same analysis can be performed to calculate the MDA. Making an assumption that the radiation sources are confined to the surface simplifies the mathematical model because fewer steps are involved in the calculation. Therefore, if this method is to be performed on a computer, the computational power required for the calculation is reduced. This is based on the background measurements as per the industry standard Currie calculation.

Where ^ is the background counts in the energy region of interest, ^_^ is the confidence factor of a false negative and ^_^ is the critical level below which is likely to be a false positive. ^_^ is the limit of detection whereby counts measured above this limit can be considered true counts. An example spectrum of background radiation is shown on Figure 5A. An example spectrum including a signal measurement is Figure 5B. As illustrated in Figure 5B, the activity of a radiation source may be proportional to net peak area. In order to determine L_c, the following calculation is performed. The critical level L_c depends only on the uncertainty of the zero-reading signal (^_^). The variance of the net signal (^_^) is:

where ^_^^^ is the variance of the total measured signal (i.e. the sum of the net signal and the background signal), ^_^ is the variance of the base signal, S is the true signal count and B is the background signal count. But for the zero-reading, S=0. Therefore:

So, L_c can be expressed as: Eq. 17

Thus, the background signal is a function of the size and uncertainty of the background signal. Therefore, the limit of detection increases with uncertainty on the measurement. The uncertainty of the measurement increases with the speed at which the radiation imaging apparatus is travelling while collecting the measurements. The MDC is then calculated as the calibrated activity from ^_^ (Equation 14). !"# = #^_^ Eq. 18 In a single possible source of activity, C can be a single scalar value however in the mobile platform, there are a number of possible sources. In order to calculate the MDC from the nearest surface area to the detectors at that measurement time the limit of detection is projected onto that area using the inverse square law. The minimum detectable activity for each reading can then be calculated as: ! = #/$ ∑ ^_^ ⊘ ^_&'* Eq. 19 Where ^_&'* is the subset of the system matrix for just the nearest area of interest (a). As a result, the MDC value is calculated. In an embodiment of the radiation imaging apparatus comprising a single alpha-radiation detector configured to be moved to two or more predetermined positions with respect to a body of the radiation imaging apparatus, wherein the radiation detector is configured to detect ionising radiation at the predetermined positions, the minimum activity calculation may be calculated as follows. The energy of detected alpha-particles emitted by an alpha-radiation source is likely to be significantly higher than the background radiation energy levels. The activity of a radiation, A, may be calculated as follows, wherein , is efficiency of the detector for alpha particles at that energy, f is the abundance of alpha particles per disintegration and S is the count rate measured (counts per second, cts). B is the background count rate. A typical value of B may be approximately 0.1cps. ^ = ,-^ − ^ Eq. 20 For example, if the critical limit L_c is set such that the same uncertainty on background and signal is used, then k (confidence factor of a false negative) is 1.645. Conversely the MDA can be simplified to the following (Eq. 21). In the example below, MDA is expressed in units of Bq/cm². ^_^ ^2.71 !"^ = = ,-0

^_^ is the limit of detection, , is efficiency of the detector for alpha particles at that energy, f is the abundance of alpha particles per disintegration and g is a measure of the speed and size of the detector. 0 = ^/3 Where A is the active detector area (cm²) and v is the speed (cm/s). The MDA is proportional to the square root of the background and inverse proportional to the time taken to measure it, T. For example, the radiation imaging apparatus may detect alpha particles emitted by Am- 241 (americium-241). In an example embodiment, the alpha-particle detector efficiency (,) of the emitted alpha particles may be approximately 30% , the abundance of alpha particles per Bq (f) may be 1, the area of the detector may be 100cm², and the speed may be 10cms^-1. According to the example, the minimum detectable activity becomes: 2.71 + 4.65√0.1 !"^ = = 1.39^;/<>^{^} 0.3 ∗ 1 ∗ 100/0.1 Any of the methods described above may be performed by a computer program.

Claims

CLAIMS 1. A radiation imaging apparatus comprising: (a) two or more radiation detectors configured to detect ionising radiation, or (b) a single radiation detector configured to be moved to two or more predetermined positions with respect to a body of the radiation imaging apparatus, wherein the radiation detector is configured to detect ionising radiation at the predetermined positions; and a position and orientation detector configured to determine an instantaneous position and orientation of the radiation imaging apparatus in six degrees of freedom relative to real world structures as a fixed frame of reference.

2. A radiation imaging apparatus according to claim 1 further comprising an imaging device configured to image real world structures by taking photographs, or LIDAR measurements, or SONAR measurements, or RADAR measurements.

3. The radiation imaging apparatus according to claims 1 or 2 further comprising: a speed detector configured to determine a speed of the radiation imaging apparatus.

4. The radiation imaging apparatus according to any one of claims 1 to 3 further comprising: a radiation source determination section configured to determine a distribution of radiation sources based on data of the ionising radiation detected by the radiation detector and number of detectors, combined with data of the position, orientation of the radiation imaging apparatus relative to the real world structures.

5. The radiation imaging apparatus according to claim 4 wherein the radiation source determination section is further configured to determine a distribution of radiation sources based on the speed of the radiation imaging apparatus.

6. The radiation imaging apparatus according to any one of claims 1 to 5 wherein the radiation source determination section is further configured to determine a spatial distribution of the minimum detectable activity of radiation based on data of the ionising radiation detected by the radiation detector and number of detectors, combined with data of the position, orientation of the radiation imaging apparatus relative to the real world structures.

7. The radiation imaging apparatus according to claim 6 wherein the radiation source determination section is further configured to determine a spatial distribution of the minimum detectable activity of radiation based on the speed of the radiation imaging apparatus.

8. The radiation imaging apparatus according to any one of claims 1 to 7 wherein the radiation imaging apparatus is disposed on a motorised controllable platform.

9. The radiation imaging apparatus according to claim 8 further comprising a includes a path planning and collision avoidance system which is configured to allow semi-autonomous navigation avoiding mobile and fixed obstacles.

10. The radiation imaging apparatus according to any one of claims 1 to 9 further comprising a communication unit configured to communicate with the radiation source determination section, wherein the radiation source determination section is disposed remotely from the radiation imaging apparatus.

11. The radiation imaging apparatus of any of any one of claims 1 to 10, wherein the wherein the one or more radiation detectors are alpha-particle detectors.

12. The radiation imaging apparatus of claim 11 wherein the two or more alpha-particle detectors are disposed on at least one arm, such that each arm has at least one detector disposed on it.

13. The radiation imaging apparatus according to any one of claims 1 to 10 wherein the wherein the radiation detectors are beta-particle detectors, or gamma radiation detectors, or X-ray radiation detectors.

14. The radiation imaging apparatus according to any one of claims 1 to 13, wherein the position and orientation detector is configured to determine the instantaneous position and orientation of the radiation imaging apparatus using photogrammetry, or neural rendering, or simultaneous localisation and mapping based on photographs, or LIDAR measurements, or SONAR measurements, or RADAR measurements.

15. A method of estimating radiation source distribution within a facility comprising: obtaining a position of each radiological measurement within a 3D model of the facility by using geometrical measurements; ascribing radiological measurements to a distribution of sources restricted to defined locations within a 3D model of a facility; parameterising the source distribution over the defined source locations, where the number of parameters exceeds the number of radiological measurements; relating each parameter (si, s2,...) to a calculated observable radiation field, calculated using a physical model, at each measurement position; adjusting the parameters (si, s2,...) to optimize the correspondence between said plurality of radiological measurements and the calculated observable radiation field, to yield the distribution of radioactive material as defined by the adjusted parameters by using an iterative method wherein the step size is recalculated during the iterative method based on the difference between prediction of given iteration and actual measurement; adjusting the parameters subject to the constraint that all sources have non- negative values.

16. The method according to claim 15, wherein the geometrical measurements comprise photographs, or LIDAR measurements, or SONAR measurements, or RADAR measurements.

17. The method of claims 15 or 16 wherein the 3D model is generated from the photographs, or the LIDAR measurements, or the SONAR measurements, or the RADAR measurements using photogrammetry, or neural rendering, or simultaneous localisation and mapping taken by an imaging device.

18. The method of any one of claims 15 to 17 wherein the radiological measurements are acquired from two or more radiation detectors.

19. A method for estimating the spatial distribution of the minimum detectable activity of radiation by taking into account one or more parameters, wherein the parameters may be any one or more of: the data collected by the two or more radiation detectors, the number of detectors, the data of the position, orientation of the radiation imaging apparatus relative to the real world structures, the speed of the radiation imaging apparatus.

20. A computer program for processing radiation data configured to estimate the radiation source distribution via the methods of any one of claims 15 to 18.

21. A computer program configured to estimate the spatial distribution of the minimum detectable activity of radiation via the method of claim 19.