Patent Description:
Scintillator-based detectors are used in a variety of applications, including research in nuclear physics, oil exploration, field spectroscopy, container and baggage scanning, and medical diagnostics. When a scintillator material of the scintillator-based detector is exposed to ionizing radiation, the scintillator material captures energy of incoming radiation and scintillates, emitting the captured energy in the form of photons. A photosensor of the scintillator-based detector detects the emitted photons. Radiation detection apparatuses can analyze pulses for many different reasons. Continued improvements are desired. The patent publication <CIT> discloses a scintillator crystal coupled to a segmented photodiode.

Skilled artisans appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help to improve understanding of embodiments of the invention.

The following description in combination with the figures is provided to assist in understanding the teachings disclosed herein. The following discussion will focus on specific implementations and embodiments of the teachings. This focus is provided to assist in describing the teachings and should not be interpreted as a limitation on the scope or applicability of the teachings.

As used herein, unless otherwise stated, the term "energy resolution" (also referred to as PHR for pulse height resolution) refers to a parameter measured by recording a spectrum representing the activity of a source as a function of energy, this spectrum describing the full width at half maximum ("FWHM") of a peak which divided by the energy (abscissa of the peak maximum), multiplied by <NUM>%, gives the PHR as a percentage-the lower the PHR, the better the spectral resolution.

As used herein, the terms "comprises," "comprising," "includes," "including," "has," "having," or any other variation thereof, are intended to cover a non-exclusive inclusion. For example, a process, method, article, or apparatus that comprises a list of features is not necessarily limited only to those features but may include other features not expressly listed or inherent to such process, method, article, or apparatus.

The use of "a" or "an" is employed to describe elements and components described herein. This description should be read to include one or at least one and the singular also includes the plural, or vice versa, unless it is clear that it is meant otherwise.

The materials, methods, and examples are illustrative only and not intended to be limiting. To the extent not described herein, many details regarding specific materials and processing acts are conventional and may be found in textbooks and other sources within the scintillation and radiation detection arts.

The inventors have developed an arrangement of a photosensor applied to a scintillator to improve light collection efficiency and energy resolution. A photosensor, such as a semiconductor-based photosensor, can be very small and can be read out individually in an array. Thus, such a photosensor can be arranged in various patterns on a surface of a scintillator without covering the entire area of the surface. As will be discussed in more detail below, the arrangement of a photosensor on a scintillator surface can include placing a photosensor at each corner or along the peripheral edge of a scintillator surface, instead of at the center of the scintillator surface. Additionally, the aspect ratio of the scintillator can be selected to improve energy resolution.

Referring to <FIG>, a radiation detector <NUM> can include a scintillator <NUM> and a photosensor system <NUM> disposed on a scintillator surface <NUM>. In the embodiment illustrated in <FIG>, the photosensor system <NUM> is placed only on the scintillator surface <NUM>. In an embodiment, a photosensor can also be disposed on a side surface <NUM> of the scintillator <NUM>.

In the embodiment illustrated in <FIG>, the photosensor <NUM> does not cover the entire area of the scintillator surface <NUM>. In an embodiment, the photosensor system <NUM> can occupy a cumulative area of at most <NUM>%, or at most <NUM>%, or at most <NUM>%, or at most <NUM>%, or at most <NUM>% of the surface area of the scintillator surface <NUM>. Further, the photosensor system <NUM> can occupy a cumulative area of at least <NUM>%, or at least <NUM>%, or at least <NUM>%, or at least <NUM>%, or at least <NUM>% of a total area of scintillator surface <NUM>. Moreover, the photosensor system <NUM> can occupy a cumulative area within a range of any of the above minimum and maximum values, such as <NUM> to <NUM>%, or <NUM> to <NUM>% of the total area of the scintillator surface. For example, a total coverage of <NUM> to <NUM>%, or even <NUM> to <NUM>% can achieve approximately the same energy resolution as <NUM>% coverage for a NaI(Tl) scintillator. In the embodiment illustrated in <FIG>, the photosensor system <NUM> does not occupy any area within a distance of the center point of the scintillator surface <NUM> that is <NUM>% of the distance from the center point of the scintillator surface <NUM> to the nearest peripheral edge of the scintillator surface <NUM>. In an embodiment, the cumulative area can represent a total area occupied by the photosensor system or a total active area of the photosensor system.

In an embodiment, the photosensor system <NUM> can include a discrete photosensor <NUM> or a plurality of discrete photosensor <NUM> each arranged individually on the surface <NUM>. The discrete photosensor <NUM> can include a solid state photosensor, such as a semiconductor-based photosensor. The semiconductor-based photosensor can include, for example, at least one of Si, SiC, GaN, InP, CdTe, or any combination thereof. In a particular embodiment, the discrete photosensor <NUM> can include a silicon-based photosensor.

In an embodiment, as illustrated in <FIG>, an optical window <NUM> can be disposed between the scintillator <NUM> and the photosensor <NUM>. The optical window <NUM> can be transmissive to scintillation light given off by the scintillator <NUM>. In a particular embodiment, the optical window <NUM> can include a polymer film, a mineral glass, a sapphire, an aluminum oxynitride, a spinel, or any combination thereof. In a more particular embodiment, the optical window <NUM> can include an ultra thin mineral glass having a thickness of no greater than <NUM> microns.

Further, a layer of optical coupling material can be disposed on the photosensor <NUM>, the scintillator <NUM>, the optical window <NUM> if present, or any combination thereof. In an embodiment, the optical coupling material can include a grease, a resin, an adhesive, or any combination thereof, disposed between the scintillator <NUM> and the photosensor <NUM>. The optical coupling material can also be transmissive to scintillation light given off by the scintillator <NUM>.

In an embodiment, photosensor system <NUM> can include a discrete photosensor <NUM> disposed at a corner of scintillator surface <NUM>. In the embodiment illustrated in <FIG>, the photosensor system <NUM> includes a discrete photosensor disposed at each corner, in a corner configuration. In the embodiment illustrated in <FIG>, the photosensor system <NUM> includes a discrete photosensor <NUM> disposed at each corner and along each peripheral edge of the scintillator surface <NUM>, in an edge configuration. The edge configuration can include a single discrete photosensor <NUM> spanning each peripheral edge or a plurality of discrete photosensors arranged side-by-side to span each peripheral edge. Further, <FIG> illustrate the discrete photosensors <NUM> having a rectangular or square shape. In another embodiment (not illustrated), the discrete photosensors <NUM> can have alternative shapes that generally fit in the area near the corner or along the peripheral edges of scintillator surface <NUM>. For example, the discrete photosensors <NUM> can have a triangular shape such that a corner of the triangular shape is disposed on a corner of scintillator surface <NUM>.

In an embodiment, the photosensor system <NUM> can include a discrete photosensor <NUM> arranged such that a peripheral edge of the discrete photosensor <NUM> is flush with the nearest peripheral edge of the scintillator surface <NUM>. While it may be advantageous to have the peripheral edge of the discrete photosensor <NUM> as close to the nearest peripheral edge of the scintillator surface <NUM> as possible, achieving flush edges may not be possible in a particular application. In another embodiment, a discrete photosensor <NUM> can be arranged such that a peripheral edge of the discrete photosensor <NUM> is spaced apart from the nearest peripheral edge of the scintillator surface <NUM>. In an embodiment, the shortest distance from the peripheral edge of the discrete photosensor <NUM> to the nearest peripheral edge of the scintillator surface <NUM> is at most <NUM>, or at most <NUM>, or at most <NUM>. If not flush, the shortest distance from the peripheral edge of the discrete photosensor <NUM> to the nearest peripheral edge of the scintillator surface <NUM> may be at least <NUM> micron.

Further, the shortest distance from the peripheral edge of the discrete photosensor <NUM> to the nearest peripheral edge of the scintillator surface <NUM> can be at most <NUM>%, or at most <NUM>%, or at most <NUM>%, or at most <NUM>%, or at most <NUM>% of the shortest distance from the nearest peripheral edge of the scintillator surface <NUM> to the center point of the scintillator surface <NUM>. If not flush, the shortest distance from the peripheral edge of the discrete photosensor <NUM> to the nearest peripheral edge of the scintillator surface <NUM> may be at least <NUM>% of the shortest distance from the nearest peripheral edge of the scintillator surface <NUM> to the center point of the scintillator <NUM>.

In an embodiment, the scintillator surface <NUM> can have a polygonal shape, an arcuate shape, an irregular shape, or the like. In an embodiment, the scintillator surface <NUM> has a polygonal shape having a plurality of corners, such as at least <NUM> corners, or at least <NUM> corners. In an embodiment, the polygonal shape has at most <NUM> corners, or at most <NUM> corners, or at most <NUM> corners. Further, in a particular embodiment, the polygonal shape includes a rectangular shape and, in the embodiment illustrated in <FIG>, the scintillator surface <NUM> has a square shape. In another embodiment, the scintillator surface <NUM> has an oval shape or a circle shape. After reading this specification, a person of ordinary skill in the art will conceive of a variety of different shapes for the scintillator surface <NUM>.

In an embodiment, the scintillator surface <NUM> can have an area of at least <NUM><NUM>, or at least <NUM><NUM>, or at least <NUM><NUM>. In an embodiment, surface <NUM> can have an area of at most <NUM><NUM>, or at most <NUM><NUM>, or at most <NUM><NUM>. For example, surface <NUM> can have an area in a range of any of the above minimum and maximum values, such as <NUM> to <NUM><NUM>, or <NUM> to <NUM><NUM>, or <NUM> to <NUM><NUM>.

In an embodiment, the scintillator surface <NUM> can have an average width WS calculated by taking an average of the shortest distance from the center point of the scintillator surface <NUM> to each peripheral edge of the scintillator surface <NUM>. For an arcuate shape, such as a circle or an oval, the average width WS is calculated by taking an average of the diameter along the major axis and the diameter along the minor axis. In an embodiment, the scintillator surface <NUM> has an average width WS of at least <NUM>, or at least <NUM>, or at least <NUM>. In another embodiment, surface <NUM> has an average width WS of at most <NUM>, or at most <NUM>, or at most <NUM>. Moreover, surface <NUM> can have an average width WS in a range of any of the above minimum or maximum values, such as <NUM> to <NUM>, or <NUM> to <NUM>, or <NUM> to <NUM>.

In an embodiment, the photosensor system <NUM> can be disposed on more than one surface of the scintillator <NUM>. In an embodiment the photosensor system <NUM> can be disposed on opposing scintillator surfaces, each having discrete photosensors <NUM> disposed thereon. In the embodiment illustrated in <FIG>, the discrete photosensors <NUM> are only disposed on opposing scintillator surfaces <NUM> and <NUM>. The scintillator surface <NUM>, and a discrete photosensor <NUM> disposed on the scintillator surface <NUM>, can have one or more of the features described above with respect to the scintillator surface <NUM>, and a discrete photosensor <NUM> disposed on the scintillator surface <NUM>. The size and shape of scintillator surfaces <NUM> and <NUM> can be the same or different. For example, the shape of the scintillator surfaces <NUM> and <NUM> can be the same while the sizes of surfaces <NUM> and <NUM> are different, such as a frustum of a cone or pyramid. Further, the arrangement of the discrete photosensors <NUM> on the scintillator surfaces <NUM> and <NUM> can be the same or different.

The scintillator <NUM> can have a length L measured from the scintillator surface <NUM> to the scintillator surface <NUM>. In an embodiment, the length L is greater than or equal to the average width WS of the scintillator surface <NUM>. In an embodiment, the length L can be at least <NUM>, or at least <NUM>, or at least <NUM>. In another embodiment, the length L can be at most <NUM>, or at most <NUM>, or at most <NUM>. Moreover, the length L can be in a range of any of the above minimum and maximum values, such as <NUM> to <NUM>, or <NUM> to <NUM>, or <NUM> to <NUM>. However, while the scintillator can have a length L within the values discussed above, after reading this specification, a person of ordinary skill in the art will understand how the photosensor system <NUM> discussed herein could be applied to the surface of a scintillator having a length L that is less than or greater than the values discussed above.

In an embodiment, the scintillator <NUM> can be a cube having the dimensions of at least <NUM> × <NUM> × <NUM> or at least <NUM> × <NUM> × <NUM>. In an embodiment, scintillator <NUM> can be a cuboid having the dimensions of at least <NUM> × <NUM> × <NUM>; or at least <NUM> × <NUM> × <NUM>; or at least <NUM> × <NUM> × <NUM>; or at least <NUM> × <NUM> × <NUM>. In an embodiment, the scintillator <NUM> can be a cylinder having a diameter of at least <NUM>, or at least <NUM>, or at least <NUM>, or at least <NUM>, or at least <NUM>, and a length of at least <NUM>, or at least <NUM>, or at least <NUM>, or at least <NUM>, or at least <NUM>. In a particular embodiment, the length L of the cylinder is the same as the average width WS of the scintillator surface <NUM> of the cylinder. In a further embodiment, the length L of the cylinder is greater than the diameter of the scintillator surface <NUM> of the cylinder, even at least twice the diameter of the cylinder.

As discussed previously in this disclosure, a significant improvement in energy resolution can be achieved by selecting a scintillator having the appropriate aspect ratio. As used herein, the aspect ratio of the scintillator <NUM> is equal to the length L of the scintillator <NUM> divided by the average width WS of the scintillator surface <NUM>. In an embodiment, the energy resolution decreases, which is desired, as the aspect ratio of the scintillator <NUM> increases from about <NUM>. The aspect ratio of the scintillator <NUM> is at least <NUM>, or at least <NUM>, or at least <NUM>, or at least <NUM>. If the aspect ratio is too high, the energy resolution can begin to increase, which is undesired. The aspect ratio of the scintillator <NUM> is at most <NUM>, or at most <NUM>, or at most <NUM>, or at most <NUM>. According to the claimed invention, the aspect ratio of the scintillator <NUM> is in a range of <NUM> to <NUM>.

Moreover, the aspect ratio of the scintillator <NUM> can be within a range of any of the above minimum and maximum values, such as <NUM> to <NUM>, or <NUM> to <NUM>, or <NUM> to <NUM>.

A radiation detector including a scintillator having an aspect ratio within the above ranges can show a decrease in energy resolution as compared to radiation detectors including scintillators having an aspect ratio outside of these ranges. For example, for an energy resolution of at most <NUM>%, scintillator <NUM> can have an aspect ratio of <NUM> to <NUM>; for an energy resolution of at most <NUM>%, scintillator <NUM> can have an aspect ratio of <NUM> to <NUM>; and for an energy resolution of at most <NUM>, scintillator <NUM> can have an aspect ratio of <NUM> to <NUM>. After reading the specification, a person of ordinary skill in the art will understand that the aspect ratios and relative improvement in energy resolution may depend on the particular composition of the scintillator and discrete photosensors <NUM> used.

Further, scintillator <NUM> can include a scintillator material that is particularly suited for a particular application, so long as a photosensor <NUM> can be disposed on scintillator <NUM>. In an embodiment, the scintillator material is an inorganic scintillator material. For example, the inorganic scintillator material can include a sodium iodide, a cesium iodide, a bismuth germinate, a lanthanum bromide, a cerium bromide, a lanthanum chloride, a lutetium oxyorthosilicate, a lutetium yttrium oxyorthosilicate, a cesium lithium lanthanum bromide, a cesium lithium lanthanum bromo-chloride, a cesium lithium yttrium chloride, or any combination thereof. In another embodiment, the scintillator is an organic scintillator material. For example, the organic scintillator material can include a plastic scintillator, an anthracene, a stilbene, or any combination thereof. In an embodiment, the scintillator <NUM> can be a monolithic scintillator.

An advantage of the radiation detector described herein includes achieving improved performance while the photosensor cumulatively occupies less than the full area of the surface of the scintillator. For example, the radiation detector <NUM> can have an improved single-end light collection efficiency and dual-end light collection efficiency. As used herein, the term "single-end," at least when used with respect to performance parameters of the radiation detector <NUM>, refers to a measurement taken from a single end surface of the scintillator, and the term "dual-end," at least when used with respect to performance parameters of the radiation detector, refers to a measurement taken from a two opposing end surfaces of the scintillator.

The radiation detector <NUM> can further include an analyzer device electrically coupled to the photosensors <NUM>, as illustrated in <FIG>. The analyzer device <NUM> can include hardware and can be at least partly implemented in software, firmware, or a combination thereof. In an embodiment, the hardware can include a plurality of circuits within an field-programmable gate array (FPGA), an application-specific integrated circuit (ASIC), another integrated circuit or on a printed circuit board, or another suitable device, or any combination thereof. The analyzer device <NUM> can also include a buffer to temporarily store data before the data are analyzed, written to storage, read, transmitted to another component or device, another suitable action is performed on the data, or any combination thereof.

In the embodiment illustrated in <FIG>, the analyzer device <NUM> can include an amplifier <NUM> coupled to the photosensor system <NUM>, such that an electronic pulse from the photosensor system <NUM> can be amplified before analysis. The amplifier <NUM> can be coupled to an analog-to-digital converter (ADC) <NUM> that can digitize the electronic pulse. The ADC <NUM> can be coupled to a pulse shape discrimination (PSD) module <NUM>. In a particular embodiment, the PSD module <NUM> can include a FPGA or an ASIC. In a particular embodiment, the PSD module <NUM> can include circuits to analyze the shape of the electronic pulse and determine whether the electronic pulse corresponds to a neutron or gamma radiation. In a more particular embodiment, the PSD module <NUM> can use the electronic pulse, information derived from the electronic pulse, and temperature from the temperature sensor with a look-up table to determine whether the electronic pulse corresponds to a neutron or gamma radiation. The look-up table can be part of the FPGA or ASIC or may be in another device, such as an integrated circuit, a disk drive, or a suitable persistent memory device.

The analyzer device <NUM> can further comprise a neutron counter <NUM> and a gamma radiation counter <NUM>. If the PSD module <NUM> determines that an electronic pulse corresponds to a neutron, the PSD module <NUM> increments the neutron counter <NUM>. If the PSD module <NUM> determines that an electronic pulse corresponds to gamma radiation, the PSD module <NUM> increments the gamma radiation counter <NUM>. While <FIG> illustrates a dual mode radiation detector, in other embodiments the radiation detector could be single mode radiation detector and the analyzer could include only one of the neutron counter <NUM> or the gamma radiation counter <NUM>, or may the radiation detector may be used to identify a particular material based on the pulse energy.

Any of the scintillators as previously described can be used in a variety of applications. Exemplary applications include radiation detectors for security applications, oil well-logging detectors, gamma ray spectroscopy, isotope identification, Single Positron Emission Computer Tomography (SPECT) or Positron Emission Tomography (PET) analysis, and x-ray imaging. The radiation detectors for security applications can include a portal monitor radiation detector, a handheld radiation detector, and a personal radiation detector.

Many different aspects and embodiments are possible. Some of those aspects and embodiments are described herein. After reading this specification, skilled artisans will appreciate that those aspects and embodiments are only illustrative and do not limit the scope of the present invention. Additionally, those skilled in the art will understand that some embodiments that include analog circuits can be similarly implement using digital circuits, and vice versa.

The Examples are given by way of illustration only and do not limit the scope of the present invention as defined in the appended claims.

A simulation was conducted to determine the change in detector performance based on the arrangement of discrete photosensors on a scintillator surface. The simulation was based on cuboidal NaI scintillators having the dimensions of <NUM> inches (about <NUM>) × <NUM> inches (about <NUM>) × <NUM> inches (about <NUM>) and plurality of discrete photosensors placed on one or opposing surfaces of the cuboidal NaI scintillators in a corner configuration (see <FIG>), an edge configuration (see <FIG>), and a center configuration (see <FIG>).

The detector performance improvement was quantified by the width of an Impulse Response Function (IRF). For purposes of illustration, the "impulse" is a collection of pulses in a simulation that generate the same number of photons within the scintillator. In other words, a group of light pulses is generated with an energy resolution of <NUM>%. As the scintillation light propagates around the interior of the detector, the amount of light collected by the photosensors from each pulse will vary due to variance in absorption and extinction that the geometry will impose on the random photon paths. Thus, even if the energy resolution starts out at <NUM>%, the variation in light collection from different parts of the scintillator will worsen the energy resolution. This worsening is captured in the IRF, which has a non-zero FWHM. Detector performance is improved when the IRF FWHM is narrow. An energy resolution based on the IRF FWHM, which is referred to herein as "RTransfer," is calculated using the following formula: <MAT>, where the Mode Average refers to a distribution in the number of collected photons. The detector performance is considered to improve as the RTransfer decreases.

The single-end configurations and RTransfer results are provided in Table <NUM> and the dual-end configurations and RTransfer results are listed in Table <NUM>. For Tables <NUM> and <NUM>, the term "SiPM" refers to a silicon photomultiplier having an active area of <NUM> × <NUM><NUM>, and the term "PMT" refers to a <NUM> inch photomultiplier tube.

As shown by the results of the simulations, the center configuration appears to the least favorable of the three configurations. However, the RTransfer decreases when the photosensors are in a corner configuration and even more when the photosensors are in an edge configuration, indicating that the photons can be better detected at the corners and the edges of the surface of the scintillator, rather than at the center.

Data were taken on cube NaI(Tl) scintillators exposed to <NUM> keV gamma rays from a Cs-<NUM> gamma ray source. The cube NaI(Tl) scintillators each had the dimensions of <NUM> inches (about <NUM>) × <NUM> inches (about <NUM>) × <NUM> inches (about <NUM>). Photosensors (SiPM, model: SensL 60035c at <NUM> V bias) were placed on a surface of each of the cube NaI(Tl) scintillators either in a corner configuration (see <FIG>) or a center configuration (see <FIG>). For each configuration, a series of cube NaI(Tl) scintillators was tested with a gradually increasing cumulative coverage of the surface by the photosensors. The cumulative surface area covered in percent of total surface area and pulse height for each cube NaI(Tl) scintillator are provided in the graph of <FIG> and the cumulative surface area covered in percent of total surface area and energy resolution for each scintillator are illustrated in the graph of <FIG>. The graph of <FIG> indicates that, for a given amount of surface coverage, the amount of light collected (proportional to Pulse Height) was greater when the SiPMs were in a corner configuration vis-à-vis a center configuration. The graph of <FIG> indicates that the energy resolution is also better when the SiPMs were in a corner configuration vis-à-vis a center configuration.

A simulation was performed to determine detector performance improvement based on aspect ratio of the scintillator. The simulation was based on cuboidal NaI scintillators having different aspect ratios but each having a volume of about <NUM><NUM>. A plurality of silicon photomultipliers (SiPM) each having an active area of <NUM> × <NUM><NUM> were placed on one of the end surfaces of the cuboidal scintillator in a corner configuration (see <FIG>). The active area of each photosensor was <NUM> × <NUM><NUM>.

The detector performance was quantified using RTransfer as described in Example <NUM>.

The different aspect ratios and the RTransfer results are provided in Table <NUM> below.

As shown by the results of the simulation, the RTransfer generally decreases as the aspect ratio approaches <NUM>. Further, the RTransfer is less than <NUM>% when the aspect ratio is in a range of <NUM> to <NUM>, and is less than <NUM>% when the aspect ratio is in a range of <NUM> to <NUM>. In addition, <FIG> and <FIG> include plots of various performance parameters versus aspect ratio. In <FIG>, the light collection efficiency (%) is on the left axis and represented by the line including circles, and RTransfer (%) is on the right axis and represented by the line including squares, each measured as the aspect ratio on the horizontal axis increases from left to right. Light collection efficiency refers to the fraction of photons that reach a photosensor and is proportional to pulse height. In <FIG>, the PHR at <NUM> keV (%) is on the left axis and is measured as the aspect ratio on the horizontal axis increases from left to right. Light collection efficiency improves as the percentage increases, whereas geometrical nonuniformity and energy resolution improve as the percentage decreases. Thus, as illustrated in <FIG> and <FIG>, performance increases as the aspect ratio approaches <NUM>, such as in a range of from <NUM> to <NUM>, or even <NUM> to <NUM>.

Claim 1:
A radiation detector (<NUM>) comprising:
a scintillator (<NUM>) having a first surface (<NUM>); and
a photosensor system (<NUM>) comprising a discrete photosensor (<NUM>) disposed on the first surface (<NUM>) such that a shortest distance from a peripheral edge of the discrete photosensor (<NUM>) to a nearest peripheral edge of the first surface (<NUM>) is at most <NUM>% of a shortest distance from the nearest peripheral edge of the first surface (<NUM>) to a center point of the first surface (<NUM>), and at least one of the following:
the photosensor system (<NUM>) occupies a cumulative area of at most <NUM>% of a surface area of the first surface (<NUM>), and
the photosensor system (<NUM>) does not occupy any area within a distance of the center point of the first surface (<NUM>) that is <NUM>% of the distance from the center point of the first surface (<NUM>) to the nearest peripheral edge of the first surface (<NUM>), wherein the scintillator (<NUM>) has an aspect ratio in a range of <NUM> to <NUM>, the aspect ratio being equal to the length (L) of the scintillator (<NUM>) divided by the width (WS) of the first surface (<NUM>).