A method for positioning a muon and a method for imaging

Abstract

The application discloses a muon positioning method for a muon position sensitive detector, and the muon position sensitive detector comprises a plastic scintillator, three photomultiplier tubes arranged at the edge of the plastic scintillator, and a photomultiplier tube arranged on the upper surface of the plastic scintillator, wherein the photomultiplier tube arranged on the upper surface of the plastic scintillator is a silicon photomultiplier tube; the method comprises the following steps: S1, acquiring the distance difference r0 and r of the point, on which a muon hits the plastic scintillator, to each photomultiplier tube i ; S2, obtaining the coordinate value of the point, on which the muon hits the plastic scintillator. Compared with the prior art, the application can not only acquire the XY coordinate of the muon hitting the plastic scintillator, but also realize accurate positioning of the muon by acquiring the Z coordinate, thereby improving the imaging precision of the muon. On the other hand, the error caused by the random fluctuation of the signal in the scintillator due to the neglect of the volume of the photomultiplier tube and the scintillation photons generated by the muon can be eliminated.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of muon imaging, and particularly relates to a muon positioning method and an imaging method. BACKGROUND

[0002] Natural cosmic muons are secondary particles such as pions and kaons produced by the cascade shower effect of primary cosmic rays in the process of being shot at the earth's surface and the atoms in the earth's atmosphere. Since the charged pions and kaons have very short lifetimes, they will decay to produce muons.

[0003] The muon imaging technology has the characteristics of strong penetration, high detection accuracy, fast detection speed and no radiation hazard to the human body, so that the technology is widely used in various interdisciplinary researches. At present, the commonly used methods are the scattering and transmission imaging technology using the information of muons themselves and the imaging using the information of secondary particles generated by the interaction of muons and matter.

[0004] The accuracy of muon imaging depends on the accuracy of the position of the muon hitting the detector. Avery Cashion proposed a muon position sensitive detector formed by using an unsegmented large area plastic scintillator coupled with three PMTs (photomultiplier tubes) and a method for realizing muon imaging by using the muon position sensitive detector in the paper "Muon Tracker with Unsegmented Plastic Scintillator Panels". The disadvantage of the muon position sensitive detector imaging method is that only the XY coordinates of the muon hitting the plastic scintillator are solved, and the Z coordinate is regarded as a fixed value (i.e. the height of each plastic scintillator), ignoring the thickness of the plastic scintillator, which leads to inaccurate positioning of the muon and further leads to low imaging accuracy of the muon. SUMMARY

[0005] The present application provides a muon positioning method to solve the problem of inaccurate positioning of the muon and low imaging accuracy of the muon caused by the muon position sensitive detector ignoring the thickness of the plastic scintillator in the prior art.

[0006] To achieve the above object, the present application adopts the following technical solutions.

[0007] A muon positioning method for a muon position detector, the muon position sensitive detector comprising a plastic scintillator, three photomultiplier tubes arranged at the edges of the plastic scintillator, and a photomultiplier tube arranged on the upper surface of the plastic scintillator, wherein the photomultiplier tube arranged on the upper surface of the plastic scintillator is a silicon photomultiplier tube; the method comprising:

[0008] S1, obtaining the distance difference r0 and r of the point where the muon hits the plastic scintillator to each photomultiplier tubei ; wherein, r0 is the distance from the point where the muon hits the plastic scintillator to a certain selected reference photomultiplier tube, r i is the distance from the point where the muon hits the plastic scintillator to the ith photomultiplier tube; the ith photomultiplier tube is one of the other three photomultiplier tubes except the reference photomultiplier tube;

[0009] S2, coordinates (x, y, z) of the point where the muon hits the plastic scintillator are obtained according to the following formula:

[0010]

[0011] wherein, a i , i = 1, 2, 3 is the solution of AX = C, b i , i = 1, 2, 3 is the solution of AX = D;

[0012]

[0013] (x0, y0, z0) is the position coordinate of the reference photomultiplier tube, (x i , y i , z i ) is the position coordinate of the ith photomultiplier tube; Δr i is the distance difference between the ith photomultiplier tube and the reference photomultiplier tube, Δr i = r i -r0;

[0014] Since the plastic scintillator has a certain thickness (about 5 cm), when the muon hits the detector, the number of photons generated on the upper surface is small, while the energy deposition inside the detector is more, generating more photons, and the photon signal is stronger. Since the working principle of the PMT is to convert the light signal into an electrical signal by receiving the photon signal to obtain an output pulse signal, the response time of the PMT is actually the time for the photon to reach the photomultiplier tube from a certain height inside the plastic scintillator, rather than the time for the photon to reach the photomultiplier tube from the surface of the plastic scintillator, so the Z value of the hit coordinate needs to be obtained to realize accurate positioning of the muon. The above method not only obtains the XY coordinate of the muon hitting the plastic scintillator, but also realizes accurate positioning of the muon by obtaining the Z coordinate, thereby improving the imaging accuracy of the muon.

[0015] Since the photomultiplier tube itself has a volume, and the above positioning method regards the photomultiplier tube as a point, in order to eliminate this error, in some embodiments, S2 is followed by: S3, keeping the angle of the muon hitting the plastic scintillator unchanged, obtaining coordinate values of a plurality of points where the muon hits the plastic scintillator, and obtaining an estimated coordinate value (X, Y, Z) of the point where the muon hits the plastic scintillator by using the centroid method.

[0016] The random fluctuation of the pulse signal of the fluorescent photon generated by the interaction of the muon with the detector to the photoelectric conversion device will cause the error of the signal, and therefore, in order to eliminate the error, in some embodiments, S3 further comprises:

[0017] Constructing a pseudo-linear equation according to (X, Y);

[0018] Twice estimation calculation is performed on the pseudo-linear equation by using the weighted least square method, and the optimized horizontal and vertical coordinate values X' ', Y''of the point on the plastic scintillator hit by the muon are obtained;

[0019] X' ', Y''and Z are taken as the final coordinate values of the point on the plastic scintillator hit by the muon.

[0020] In another aspect, a muon imaging method is provided for a muon position detection device, the muon position detection device comprising a plurality of muon position sensitive detectors located above and below an object to be imaged, comprising the following steps:

[0021] According to the coordinate values of the points on the plastic scintillator hit by the muon, a muon track is obtained;

[0022] According to the muon track, an image of the object to be imaged is obtained;

[0023] The muon position sensitive detector is the muon position sensitive detector in the muon positioning method described above, and the coordinate values of the points on the plastic scintillator hit by the muon are obtained according to the muon positioning method described above.

[0024] The one or more technical solutions provided in the embodiments of the present application have at least the following technical effects or advantages:

[0025] 1. Not only the XY coordinates of the muon hitting the plastic scintillator can be obtained, but also the precise positioning of the muon can be realized by obtaining the Z coordinates, thereby improving the imaging accuracy of the muon.

[0026] 2. The error caused by neglecting the volume of the photomultiplier tube is eliminated.

[0027] 3. The error caused by the random fluctuation of the signal in the scintillator caused by the scintillation photon generated by the muon is eliminated. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 The flowchart of the muon positioning method of the present application;

[0029] Figure 2 The muon track obtained according to the muon positioning method of the present application is a schematic diagram (fixed position track);

[0030] Figure 3Fig. 1 is a schematic diagram of a muon track obtained according to the muon positioning method of the present application (fixed position track);

[0031] Figure 4 Fig. 2 is a schematic diagram of the structure of a muon position detection device according to the present application;

[0032] Figure 5 Fig. 3 is a single substance imaging diagram obtained according to the muon imaging method of the present application;

[0033] Figure 6 Fig. 4 is a multi-substance imaging diagram of different atomic numbers obtained according to the muon imaging method of the present application. DETAILED DESCRIPTION

[0034] In order to better understand the above technical solutions, the above technical solutions will be described in detail below in combination with the accompanying drawings and specific embodiments.

[0035] Embodiment One

[0036] Referring to Figure 1 A muon positioning method for a muon position sensitive detector, the muon position sensitive detector comprising a plastic scintillator, three photomultiplier tubes arranged at the edge of the plastic scintillator, and one photomultiplier tube arranged on the upper surface of the plastic scintillator, wherein the photomultiplier tube arranged on the upper surface of the plastic scintillator is a silicon photomultiplier tube; the method comprising:

[0037] S1, obtaining the distance difference r0 and r between the point on the plastic scintillator hit by the muon and each photomultiplier tube i ; wherein r0 is the distance between the point on the plastic scintillator hit by the muon and a selected reference photomultiplier tube, and r i is the distance between the point on the plastic scintillator hit by the muon and the i-th photomultiplier tube; the i-th photomultiplier tube is one of the other three photomultiplier tubes except the reference photomultiplier tube;

[0038] S2, calculating the coordinates (x, y, z) of the point on the plastic scintillator hit by the muon according to the following formula:

[0039]

[0040] wherein a i , i = 1, 2, 3 is the solution of AX = C, b i , i = 1, 2, 3 is the solution of AX = D;

[0041]

[0042] (x0, y0, z0) is the position coordinates of the reference photomultiplier tube, (x i , y i , zi ) is the position coordinate of the ith photomultiplier tube; Δr i is the distance difference of the ith photoelectric conversion device to the reference photoelectric conversion device, Δr i = r i - r0;

[0043] Since the time of muon incident hitting the plastic scintillator detector is unknown, only the pulse signals of the four-corner photoelectric conversion devices of the detector can be obtained, and the rising edge of the pulse signal is taken as the initial response time of each photoelectric conversion device, which is t1, t2, t3, and t4, respectively. The difference between the four response times is recorded as the response time difference τ i . In the process of passing through the plastic scintillator, the muon will excite and de-excite the orbital electrons to produce scintillation photons, and the wavelength of the scintillation photons is 425 nm, and the diffusion speed v in the plastic scintillator is about 0.633 times the speed of light c. Therefore, the distance difference between the hitting point and the four-corner detector can be obtained by multiplying the obtained response time difference by the diffusion speed v of the scintillation photons, which is 0.633c (c is the speed of light).

[0044] Based on the Geant4 simulation software, the size of the plastic scintillator detector is set to 76cm×76cm×5cm, and when the incident position of the muon is set to (20cm, 20cm), the time information of the rising edge of the pulse signal of each photoelectric conversion device at the four corners of the detector is t i , wherein t1=1.681ns, t2=3.308ns, t3=3.297ns, and t4=4.181ns.

[0045] The calculation process is as follows:

[0046] Suppose the muon incident point position O is (x, y, z). And n photoelectric conversion devices are set on the four corners of the plastic scintillator detector, and their positions are known, which are (x i , y i , z i )i=1, 2,..., n, i is the position of the photoelectric conversion device at the corner. The distance difference between the hitting point and the four-corner detector can be obtained by multiplying the obtained response time difference τ i by 0.633c (c is the speed of light).

[0047] Δr i = 0·633·c·τ i

[0048] One of the four photoelectric conversion devices is taken as a reference point, and its coordinates are set to (x0, y0, z0), and the positions of the remaining three photoelectric conversion devices are (x i , y i , z ii = 1, 2, 3, the distance difference to the reference point can be directly obtained by equation (1). If the distance difference is obtained in step 1, and the four detector positions are determined, the positions (x, y, z) of the detectors in the muon cluster can be obtained by equation (1) inversely, i.e. the distance difference Δr i Solve (x, y, z):

[0049]

[0050] where (x0, y0, z0) is the position of a selected reference photoelectric conversion device, (x i , y i , z i ) represents the positions of the remaining photoelectric conversion devices, the muon incident point position is (x, y, z), r0 is the distance from the hit point to the selected reference photoelectric conversion device, r i is the distance from the hit point to the remaining photoelectric conversion devices, and r i -r0 is the distance difference between the photoelectric conversion devices and the reference photoelectric conversion device.

[0051] After simplifying equation (1), subtract r0 from both sides 2 to obtain equation (2):

[0052]

[0053] Let , we obtain:

[0054] Δr i 2 + 2Δr i r0 = 2x (x0-x i ) + 2y (y o -y i ) + 2z (z0-z i ) + d i 2 -d0 2 (3)

[0055] After rearrangement, we obtain:

[0056]

[0057] Since there are i unknowns in equation (4), equation (4) can be expressed in matrix form as:

[0058]

[0059] According to the properties of linear equations, equation (5) can be written in the form of AX = B, where:

[0060]

[0061] The solution of AX = B can be obtained as the sum of r0 times AX = C and AX = D, and the equation of formula (7) is solved to obtain the coordinate of the incident point position:

[0062]

[0063] where a i , i = 1, 2, 3 is the solution of AX = C, b i , i = 1, 2, 3 is the solution of AX = D, and the matrix A, C, D are known quantities, and a i , b i can be solved.

[0064]

[0065] where,

[0066] where, r0 can be obtained by the following formula:

[0067] r0 2 = (a1r0+b1-x0) 2 + (a2r0+b2-y0) 2 + (a3r0+b3-z0) 2 (8)

[0068]

[0069] The equation of formula (8) is solved to obtain r0, where:

[0070]

[0071] where, A, B, C in formula (10) are parameters in the root-finding formula, and A, B, C are substituted into formula (9) to solve r0.

[0072] Since the plastic scintillator has a certain thickness (about 5 cm), when a muon hits the detector, the number of photons generated on the upper surface is small, and the energy deposition in the interior of the detector is more, generating more photons, and the photon signal is stronger. Since the working principle of the PMT is to obtain a response by receiving a photon signal, the response time of the PMT is actually the time for a photon to reach a photoelectric conversion device from a certain height in the interior of the plastic scintillator, rather than the time for a photon to reach a photoelectric conversion device from the surface of the plastic scintillator, so the Z value of the hit coordinate needs to be obtained to realize accurate positioning of the muon. The above method not only obtains the XY coordinate of the muon hitting the plastic scintillator, but also realizes accurate positioning of the muon by obtaining the Z coordinate, thereby improving the imaging accuracy of the muon.

[0073] Further, since the photomultiplier tube itself has a volume, and the positioning method above considers the photomultiplier tube as a point, in order to eliminate this error, the centroid method can be used to estimate the coordinate values, that is:

[0074] S3, keeping the angle of the muon hitting the plastic scintillator unchanged, obtaining coordinate values of a plurality of points on the plastic scintillator hit by the muon, and using the centroid method to obtain estimated coordinate values (X, Y, Z) of the point on the plastic scintillator hit by the muon.

[0075] Further, since the random fluctuations of the pulse signal of the fluorescent photons generated by the interaction of the muon with the detector to the photoelectric conversion device will cause errors in the signal, in order to eliminate this error, the estimated coordinate values of the point on the plastic scintillator hit by the muon obtained by the centroid method can be further optimized as follows:

[0076] S4, constructing a pseudo-linear equation according to (X, Y);

[0077] When the number of photoelectric conversion devices is increased to n≥4, the number of unknowns is less than the number of equations, which is an overdetermined equation set, that is, pseudo-linearization processing can be used for solving. Assuming that X, Y, Δr i are linearly independent, from the positioning algorithm formula (2) above where (x0, y0) is the position of a selected reference photoelectric conversion device, and (x i , y i , z i ) represents the positions of the remaining photoelectric conversion devices. Therefore, the above formula is rewritten in the matrix form as shown below:

[0078]

[0079] Simplified as a pseudo-linear expression: where

[0080] S5, using the weighted least squares method to estimate and calculate the pseudo-linear equation twice to obtain the optimized coordinate values of the point on the plastic scintillator hit by the muon.

[0081] After the first processing of formula (12) using the weighted least squares method, we have:

[0082] Z a ≈(G a T ψ -1 G a ) -1 G a T ψ -1 h (13)

[0083] where ψ = v2BQB, B = diag(r1, r2,..., rN), Q is the covariance matrix of the positioning algorithm measurement error. i where ψ = v2BQB, B = diag(r1, r2,..., rN), Q is the covariance matrix of the positioning algorithm measurement error.

[0084] where v is the propagation speed of the scintillation photons in the plastic scintillator, Q = E{(Δr i - E{Δr i}(Δr i - E{Δr i}) T}, E{...} means taking the average

[0085] At this time, the value of Δr i is close to the distance defined by it, so that the approximate value of B can be obtained, which can replace ψ in the approximation of Q, then:

[0086] Z a ≈ (G a T Q -1 G a ) -1 G a T Q -1 h (14)

[0087] When the distance between the position of the photoelectric conversion device and the position of the incident point is close, the value of B obtained by long distance is used to obtain ψ and the final value of Z a .

[0088] In the previous, it is considered that each element in Z a is independent of each other, while actually Δr i is related to (X, Y), and has the relationship: The coordinates (X', Y') obtained by the first weighted least squares method can be used to construct a new linear equation system according to Δr i , and then the second weighted least squares method is used to estimate, and finally the optimized coordinates are obtained. The new constructed linear equation is as follows:

[0089] G a ′Z a ′-h′=0 (15)

[0090] where

[0091] The relationship between the estimated value and the true value is:

[0092] Z a，1 = X + e1, Z a，2 = Y + e2, Z a，3= r1+ e3 (16)

[0093] In the above equation, e1, e2 represent the difference between the coordinates obtained by the first weighted least square method and the estimated coordinates of the muon hitting the detector by the center of mass method. e1 = X - X', e2 = Y - Y', e3 = r1 - r1'

[0094] For Z a , the weighted least square estimation is performed to obtain:

[0095] Z a ≈ (G a 'χ T G -1 ) a T Q -1 G a χ -1 G a ) -1 (17)

[0096] In equation (17),

[0097] χ = 4B' cov(Z a ) B', B' = diag(Z a，1 - x1, Z a，2 - y1, Z a，3 ), cov(Z a ) = (G a 'χ -1 G a ) -1

[0098] Q = E{(Δr i - E{Δr i})(Δr i - E{Δr i}) T}

[0099] Thus, the optimized coordinates (X", Y") of (X, Y) are obtained:

[0100]

[0101] X", Y" and Z are taken as the final coordinate values of the point of muon hitting the plastic scintillator.

[0102] Example Two

[0103] A muon imaging method for a muon position detection device, the muon position detection device comprising a plurality of muon position sensitive detectors located above and below an object to be imaged, comprising the steps of:

[0104] According to the coordinate values of the points hit by the muons on each plastic scintillator, a muon track is obtained;

[0105] According to the muon track, an image of the object to be imaged is obtained;

[0106] The muon position sensitive detector is the muon position sensitive detector in the muon positioning method of Embodiment One; the coordinate values of the points hit by the muons on each plastic scintillator are obtained according to the muon positioning method in Embodiment One.

[0107] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of each embodiment of the present application.

Claims

1. A muon positioning method for a muon position sensitive detector, the muon position sensitive detector comprising a plastic scintillator, three photomultiplier tubes arranged at the edge of the plastic scintillator, and one photomultiplier tube arranged on the upper surface of the plastic scintillator, wherein the photomultiplier tube arranged on the upper surface of the plastic scintillator is a silicon photomultiplier tube, the method comprising: S1, obtaining the coordinate values (x, y, z) of the point on the plastic scintillator hit by a muon according to the following formula: S2, after S1, further comprising: S3, keeping the angle of the muon hitting the plastic scintillator unchanged, obtaining the coordinate values of the points on the plastic scintillator hit by a plurality of muons, and obtaining the estimated coordinate values (X, Y, Z) of the point on the plastic scintillator hit by a muon by using the centroid method; S4, after S3, further comprising: constructing a pseudo-linear equation according to (X, Y); using the weighted least squares method to perform twice estimation calculation on the pseudo-linear equation to obtain the optimized horizontal and vertical coordinate values X''', Y''' of the point on the plastic scintillator hit by a muon; and taking X''', Y''' and Z as the final coordinate values of the point on the plastic scintillator hit by a muon. S1, the difference between the response time of the ith photomultiplier tube and the reference photomultiplier tube multiplied by the diffusion speed of the scintillation photons, gives the difference in distance, Δr, from the point where the muon hits the plastic scintillator to the ith photomultiplier tube and to the reference photomultiplier tube i , Δr i = r i - r0; where r0 is the distance from the point where the muon hits the plastic scintillator to a certain selected reference photomultiplier tube, and r i is the distance from the point where the muon hits the plastic scintillator to the ith photomultiplier tube; the ith photomultiplier tube is one of the other three photomultiplier tubes other than the reference photomultiplier tube.

4. A muon imaging method for a muon position detection device, the muon position detection device comprising a plurality of muon position sensitive detectors arranged above and below an object to be imaged, the method comprising the steps of: obtaining a muon track according to the coordinate values of the points on the plastic scintillators hit by a muon; and obtaining an image of the object to be imaged according to the muon track. where a i i = 1,2,3 are solutions of AX = C, b i i = 1,2,3 are solutions of AX = D. (x0, y0, z0) are the coordinate values ​​of the reference photomultiplier tube, (x i y i , z i () represents the coordinates of the i-th photomultiplier tube; 2. The muon positioning method of claim 1, wherein, The muon position sensitive detector is the muon position sensitive detector described in claim 1, and the coordinate values of the points on the plastic scintillators hit by a muon are obtained by the muon positioning method described in any one of claims 1-3. ​ 3. The muon positioning method of claim 2, wherein, ​ ​ ​ ​ ​ ​ ​ wherein, ​

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