# Patent

## Title
Method for detecting a moving radioactive source and associated device

## Abstract

A method for detecting a radioactive source moving on a linear path substantially parallel to an alignment of N detectors. The method includes: forming N×Nt pulse counting values Mi,t (i=1, 2, . . . , N and t=1, 2, . . . , Nt) from N×Nt detection signals delivered by the N detectors in the form of a succession over time of Nt sets of N signals simultaneously detected by the N detectors over a same duration Δt, a pulse counting value representing a number of pulses detected by a detector over a duration Δt; and computing, using a computer: a set of Nt correlation products Rt, a static mean R of the N×Nt counting values, a correlation condition for each correlation product Rt.

## Background
TECHNICAL FIELD AND PRIOR ART
The invention relates to a method for detecting a moving radioactive source and the associated device.
The invention has applications in many fields and, particularly advantageously, in the safety field.
For safety reasons, it is often necessary to detect the possible passage of a radioactive source in the vicinity of a place where an industrial process is taking place or during the supervision of an infrastructure.
The detection sensitivity of a radioactive source depends on the radioactive environment level (background noise), the source intensity, and the passage time of this source in front of the detection system. It is known to adjust an alarm threshold with respect to the level of statistical fluctuations in the radioactive environment in order to trigger a signal which proves the presence of a radioactive source.
Systems for detecting moving sources comprise a plurality of measuring channels. Some of these systems perform the detection of mobile sources by thresholding each measuring channel and measuring, by gross summation, signals delivered by the different measuring channels at the time of detection. In order to reduce the false alarm rates, systems which work based on an independent detection of each measuring channel and on an a posteriori detection correlation (cf. “Distributed detection of a nuclear radioactive source using fusion correlation decisions” A. Sundaresan, P. K. Varshney, N. S. V Rao in Proceeding of the International Conference on Information Fusion, 2007). If this approach indeed enables a reduction of false alarm rates, it does not suppress the conventional thresholding step which limits the intrinsic detection capacities of detectors.
The invention does not have this drawback.
DISCLOSURE OF THE INVENTION
Indeed, the invention relates to a method for detecting a radioactive source moving on a linear path substantially parallel to an alignment of N detectors, N being an integer equal to or greater than 2. The method comprises the following steps:

    
    
        forming N×Nt pulse counting values Mi,t (i=1, 2, . . . , N and t=1, 2, . . . , Nt) from N×Nt detection signals delivered by the N detectors in the form of a succession over time of Nt sets of N signals simultaneously detected by the N detectors over a same duration Δt, a pulse counting value representing a number of pulses detected by a detector over a duration Δt, and
        computing, using a computer:
        
            a set of NR correlation products RZ so that:

Rz=Πi=1NMi,[(N−i)z+1] (z=1,2, . . . ,NR)

            with
        
        
    
    






  
    
      N
      R
    
    =
    
      
        
          N
          t
        
        -
        1
      
      
        N
        -
        1
      
    
  
  ,




Nt being a very large integer ahead of N,

    
    
        
        
            a statistical mean R of the Nt products Πi=1NMi,t counting values such that:
        
        
    
    






  
    R
    _
  
  =
  
    
      1
      
        N
        t
      
    
    ⁢
    
      
        ∑
        
          t
          =
          1
        
        
          N
          t
        
      
      ⁢
      
        
      
      ⁢
      
        
          ∏
          
            i
            =
            1
          
          N
        
        ⁢
        
          
        
        ⁢
        
          M
          
            i
            ,
            t
          
        
      
    
  




    
    
        
        
            a standard deviation σ(R) of the Nt products Πi=1NMi,t such that:
        
        
    
    






  
    σ
    ⁡
    
      (
      
        R
        _
      
      )
    
  
  =
  
    
      
        1
        
          N
          t
        
      
      ⁢
      
        
          ∑
          
            t
            =
            1
          
          
            N
            t
          
        
        ⁢
        
          
        
        ⁢
        
          
            (
            
              
                R
                _
              
              -
              
                
                  ∏
                  
                    i
                    =
                    1
                  
                  N
                
                ⁢
                
                  M
                  
                    i
                    ,
                    t
                  
                
              
            
            )
          
          2
        
      
    
  




    
    
        
        
            a correlation condition for each correlation product Rt so that:
        
        
        if Rz≧R+K2σ(R), K2 being a scalar, a radioactive source is considered to have moved in front of the detectors, and
        if Rz<R+K2σ(R), no source is considered to have moved in front of the detectors.
    
    


As mentioned above, the number NR of correlation products is given by the equation:




  
    
      N
      R
    
    =
    
      
        
          N
          t
        
        -
        1
      
      
        N
        -
        1
      
    
  
  ,




where N is the number of detectors and Nt the number of sets of N signals simultaneously detected by the N detectors over a same duration Δt. The numbers NR, Nt, and N are all integers. It is consequently clear that, for a given number N of detectors, the number Nt is chosen so that NR is also an integer. By way of non-limiting example, for a number N of detectors equal to 10, the number Nt can be equal to 10000, which induces a number NR equal to 1111.
It also appears from the formula of the correlation product RZ that all the measurements performed over the duration Δt are not used to compute the product RZ. It is an advantage of the invention not to use all the performed measurements, but only the measurements useful for forming the desired result.
According to an additional feature of the invention, as soon as a radioactive source is considered to have moved in front of the detectors, the speed V of the source is computed such that:

V=d/(T×Δt),

where d is the distance separating two neighbouring detectors and T is the rank t of a set of N pulse counting values for which the correlation product Rt is maximum.
According to another additional feature of the invention, as soon as a radioactive source is considered to have moved in front of the detectors, the intensity I of the source is computed so that:




  I
  =
  
    
      
        1
        N
      
      ⁢
      
        
          ∑
          
            i
            =
            1
          
          N
        
        ⁢
        
          
        
        ⁢
        
          M
          
            i
            ,
            
              
                
                  (
                  
                    N
                    -
                    i
                  
                  )
                
                ⁢
                T
              
              +
              1
            
          
        
      
    
    -
    
      
        1
        
          N
          ×
          
            N
            t
          
        
      
      ⁢
      
        
          ∑
          
            t
            =
            1
          
          
            N
            t
          
        
        ⁢
        
          
        
        ⁢
        
          [
          
            
              ∑
              
                i
                =
                1
              
              N
            
            ⁢
            
              
            
            ⁢
            
              M
              
                i
                ,
                t
              
            
          
          ]
        
      
    
  




In a particular embodiment of the invention, the pulse counting values are smoothed before the computing step implemented by the computer.
The invention also relates to a device for detecting a radioactive source moving over a substantially linear path, characterised in that it comprises means for implementing the method of the invention.



BRIEF DESCRIPTION OF THE FIGURES
Other features and advantages of the invention will appear upon reading the following description, made in reference to the appended figures, among which:
FIG. 1 symbolically shows a radioactive source moving in front of a set of detectors of the device for detecting a moving radioactive source of the invention;
FIG. 2 shows the schematic diagram of an exemplary device for detecting a moving radioactive source of the invention;
FIG. 3 shows a processing method involved in the method for detecting a moving radioactive source of the invention;
FIGS. 4A and 4B illustrate the method for detecting a radioactive source of the invention in the case of a low intensity and low speed radioactive source;
FIGS. 5A and 5B illustrate the method for detecting a radioactive source of the invention in the case of a low intensity and high speed radioactive source;
FIG. 6 shows the false alarm rate as a function of the number of used detectors, for a device of the invention and for a prior art device;
FIG. 7 shows the non-detection rate of a radioactive source as a function of the number of used detectors, for a device of the invention and for a prior art device;
FIG. 8 shows the detection rate of a radioactive source as a function of the intensity of the signal emitted by the source, for a device of the invention and for a prior art device;
FIGS. 9A and 9B each show the measured intensity of two radioactive sources of different intensity, as a function of the number of detectors, for a device of the invention and for a prior art device.



DISCLOSURE OF PARTICULAR EMBODIMENTS OF THE INVENTION
FIG. 1 symbolically shows a radioactive source moving in front of a set of detectors.
The radioactive source S which is wanted to be detected moves in principle over a linear path TL (road/conveyor/etc.). The N detectors D1, D2, . . . , Di, . . . , DN of the detection device are aligned parallel to the path TL. A distance d separates two neighbouring detectors and a distance D separates each detector Di (i=1, 2, . . . N) from the path TL.
FIG. 2 shows the schematic diagram of an exemplary detection device implementing the method for detecting a moving radioactive source of the invention.
The device comprises N detectors Di (i=1, 2, . . . , N), N processing circuits Ti, N pulse counting circuits Ki, a memory block B made of N FIFO memories Mi (FIFO stands for “First In First Out”), and a computer C.
Each detector Di (i=1, 2, . . . , N) which detects an incident radiation delivers a pulse signal. The pulse signal delivered by the detector Di is then processed by a processing circuit Ti, the latter comprising, for example, an amplifier Ai and a filtering circuit Fi. Each processing circuit Ti delivers an electronic pulse. The electronic pulses delivered by a processing circuit Ti are counted by a counting circuit Ki. Counting the electronic pulses is made by successive time slots of a duration Δt. The counting values which are delivered by the counter Ki are transmitted to the FIFO memory Mi. A FIFO memory Mi consequently contains a succession of counting values Mi,1, Mi,2, . . . Mi,t, etc., where t is the time position index of the counting values in the history of the FIFO memories.
According to the known principle which governs the FIFO memories, as soon as a FIFO memory is full, the oldest counting value which is stored in the memory is extracted to enable a new counting value to be stored. The counting values which are simultaneously extracted from different memories Mi are then transmitted to the computer C. In a particular embodiment of the invention (not shown in the figure), the counting values are smoothed by a smoothing circuit before being transmitted to the FIFO memory.
The computer C implements a method for processing counting values Mi,t. FIG. 3 illustrates this processing method.
In a first step (step 1), the computer C computes NR correlation products RZ (z=1, 2, . . . , NR) such that:
RZΠi=1NM[i,(N−i)z+1]+, with




  
    
      N
      R
    
    =
    
      
        
          N
          t
        
        -
        1
      
      
        N
        -
        1
      
    
  
  ,




Nt being a very large integer ahead of N.

The statistical mean R of the Nt products Πi=1NMi,t is then computed (step 2):




  
    R
    _
  
  =
  
    
      1
      
        N
        t
      
    
    ⁢
    
      
        ∑
        
          t
          =
          1
        
        
          N
          t
        
      
      ⁢
      
        
      
      ⁢
      
        
          ∏
          
            i
            =
            1
          
          N
        
        ⁢
        
          
        
        ⁢
        
          M
          
            i
            ,
            t
          
        
      
    
  




Next, the standard deviation σ(R) of the Nt products Πi=1NMi,t is then computed (step 3):




  
    σ
    ⁡
    
      (
      
        R
        _
      
      )
    
  
  =
  
    
      
        1
        
          N
          t
        
      
      ⁢
      
        
          ∑
          
            t
            =
            1
          
          
            N
            t
          
        
        ⁢
        
          
        
        ⁢
        
          
            (
            
              
                R
                _
              
              -
              
                
                  ∏
                  
                    i
                    =
                    1
                  
                  N
                
                ⁢
                
                  M
                  
                    i
                    ,
                    t
                  
                
              
            
            )
          
          2
        
      
    
  




Once the standard deviation is computed, it is verified whether there is a significant correlation of the time series among the Rt values (step 4). It is thus verified whether the following inequation is performed or not:

Rz≧R+K2σ(R)

where the magnitude K2 is a scalar chosen with respect to the false alarm rate desired for detection. The order of magnitude of K2 is a few units.
If the above inequation is not performed, no source is considered to have moved in front of the detectors (step 5: no source).
If the above inequation is performed, a source is considered to have moved in front of the detectors and its speed V and/or its intensity I (number of hits per second) are computed (step 6).
Among the Rt values, there is an Rt value which is maximum. Letting T be the rank t for which the Rt value is maximum, we therefore have:

V=d/(T×Δt),

where d is the distance separating two neighbouring detectors, and




  I
  =
  
    
      
        1
        N
      
      ⁢
      
        
          ∑
          
            i
            =
            1
          
          N
        
        ⁢
        
          
        
        ⁢
        
          M
          
            i
            ,
            
              
                
                  (
                  
                    N
                    -
                    i
                  
                  )
                
                ⁢
                T
              
              +
              1
            
          
        
      
    
    -
    
      
        1
        
          N
          ×
          
            N
            t
          
        
      
      ⁢
      
        
          ∑
          
            t
            =
            1
          
          
            N
            t
          
        
        ⁢
        
          
        
        ⁢
        
          [
          
            
              ∑
              
                i
                =
                1
              
              N
            
            ⁢
            
              
            
            ⁢
            
              M
              
                i
                ,
                t
              
            
          
          ]
        
      
    
  




As soon as the steps 5 and 6 are carried out, a new computing cycle is started (back to step 1).
FIGS. 4A and 4B illustrate the method for detecting a radioactive source of the invention in the case of a low intensity and low speed radioactive source.
The results illustrated in FIGS. 4A and 4B are obtained for a detection device made of five detectors. A low intensity radioactive source moves at a speed of 5 m/s in front of the detectors.
FIG. 4A shows the counting values Mi,t (i=1, 2, . . . , 5) associated with each of the five detectors involved in the detection device of the invention, as a function of time τ. With reference to the previously defined magnitudes t, and Δt, we have:

τ=t×Δt 

FIG. 4B represents the correlation product R computed as a function of a speed v representing the speed of the source. With reference to the previously defined magnitudes d, t and Δt, we have:

v=d/t×Δt 

It can be noticed that the correlation product clearly shows a peak P at a speed substantially equal to 5 m/s.
FIGS. 5A and 5B illustrate the method for detecting a radioactive source of the invention in the case of a low intensity and high speed radioactive source.
FIGS. 5A and 5B respectively correspond to the preceding FIGS. 4A and 4B. The speed of the source moving in front of the detectors is here equal to 17 m/s. A correlation peak P at a speed substantially equal to 17 m/s can indeed be noticed.
FIG. 6 illustrates the false alarm rate TF as a function of the number of detectors N, for a thresholding detection device according to the prior art (curve T1) and for a correlation detection device according to the invention (curve T2), all other things being equal. Very advantageously, it can be noticed that, beyond three detectors, the false alarm rate is very substantially lower with the detection device of the invention.
FIG. 7 illustrates the non-detection rate TND as a function of the number of detectors N, for a thresholding detection device according to the prior art (curve ND1) and for a correlation detection device according to the invention (curve ND2), all other things being equal. Also very advantageously, it can be noticed that the non-detection rate is very substantially lower with the detection device of the invention.
FIG. 8 illustrates the detection rate TD as a function of the signal intensity I0 (expressed as a counting rate or as a number of hits per second (cps)) between a thresholding detection device according to the prior art and a correlation detection device according to the invention. In each case, the detection device comprises six detectors. Curve D1 represents the detection rate of the prior art device and curve D2 represents the detection rate of the invention device. Particularly advantageously, it appears that the detection rate of the device of the invention is always very substantially greater than the one of the prior art device for a counting rate between 2 and 13 cps, both detection rates being equal beyond the counting rate of 13 cps.
FIG. 9A shows the measured intensity of a strong intensity radioactive source as a function of the number N of detectors, for a thresholding detection device according to the prior art and for a correlation detection device according to the invention. The intensity I0 of the source is, for example, equal to 100 hits per second. It appears that the intensity IS measured by the prior art device and the intensity IC measured by the invention device are identical and equal to I0, whatever the number of detectors. The measurement inaccuracy which is represented by the intervals Δi (i=1, 2, . . . , 6) in FIG. 9A is also identical for both detection devices.
FIG. 9B shows the measured intensity of a low intensity radioactive source as a function of the number N of detectors, for a thresholding detection device according to the prior art and for a correlation detection device according to the invention. The source intensity I0 is for example equal to 12 hits per second. It appears that the intensity IC measured by the invention device is very substantially equal to the emitted intensity I0 whatever the number of detectors. On the contrary, the intensity IS measured by the prior art device is very different from the emitted intensity I0. Similarly, whereas the inaccuracy Δi of the measurements read by the invention device is relatively low, the inaccuracy δi of the measurements read by the prior art device is high. Furthermore, a bias b of the measurements read by the prior art device appears, which is not the case of the measurement read by the invention device.

## Claims

1. A method for detecting a radioactive source moving on a linear path substantially parallel to an alignment of N detectors, N being an integer equal to or greater than 2, the method comprising:
simultaneously detecting N signals by N detectors;
delivering N×Nt detection signals from the N detectors in the form of a succession over time of Nt sets of the N signals simultaneously detected by the detector over a duration Δt, Nt being significantly greater than N, a pulse counting value representing a number of pulses detected by a detector over a duration Δt;
forming N×Nt pulse counting values Mi,t (i=1, 2, . . . , N and t=1, 2, . . . , Nt) from the N×Nt detection signals;
computing, using a computer:
a set of NR correlation products Rz so that:


Rz=Πi=1NMi,[(N−i)z+1] (z=1,2, . . . , NR)


with NR being an integer equal to






  
    
      
        N
        t
      
      -
      1
    
    
      N
      -
      1
    
  
  ,




a statistical mean R of the Nt products Πi=1NMi,t such that:






  
    R
    _
  
  =
  
    
      1
      
        N
        t
      
    
    ⁢
    
      
        ∑
        
          t
          =
          1
        
        
          N
          t
        
      
      ⁢
      
        
      
      ⁢
      
        
          ∏
          
            i
            =
            1
          
          N
        
        ⁢
        
          
        
        ⁢
        
          M
          
            i
            ,
            t
          
        
      
    
  




a standard deviation σ(R) of the Nt products Πi=1NMi,t, and
a correlation condition for each correlation product Rz; and

determining that a radioactive source moved in front of the detectors if Rz≧R+K2σ(R), K2 being a scalar, or
determining that no radioactive source moved in front of the detectors if Rz<R+K2σ(R).

2. The method according to claim 1, the method further comprising computing, by the computer, a speed V of the radioactive source as soon as a radioactive source is determined to have moved in front of the detectors, such that:


V=d/(T×Δt),

where d is a distance separating two neighbouring detectors and T is a rank t of a set of N pulse counting values for which the correlation product RZ is maximum.

3. The method according to claim 1, the method further comprising computing, by the computer, an intensity I of the radioactive source as soon as a radioactive source is determined to have moved in front of the detectors, such that:




  I
  =
  
    
      
        1
        N
      
      ⁢
      
        
          ∑
          
            i
            =
            1
          
          N
        
        ⁢
        
          
        
        ⁢
        
          M
          
            i
            ,
            
              
                
                  (
                  
                    N
                    -
                    i
                  
                  )
                
                ⁢
                T
              
              +
              1
            
          
        
      
    
    -
    
      
        1
        
          N
          ×
          
            N
            t
          
        
      
      ⁢
      
        
          ∑
          
            t
            =
            1
          
          
            N
            t
          
        
        ⁢
        
          
        
        ⁢
        
          
            [
            
              
                ∑
                
                  i
                  =
                  1
                
                N
              
              ⁢
              
                
              
              ⁢
              
                M
                
                  i
                  ,
                  t
                
              
            
            ]
          
          .

4. The method according to claim 1, further comprising smoothing the pulse counting values before computing.

5. A device for detecting a radioactive source moving over a substantially linear path, the device comprising:
N detectors (Di, i=1, 2, . . . , N) substantially aligned parallel to the linear path of the radioactive source, N being an integer equal to or greater than 2, the N detectors simultaneously delivering N detection signals over duration Δt,
N processing circuits (Ti, i=1, 2, . . . , N) connected to the N detectors, each processing circuit being configured to deliver an electronic signal corresponding to a detection signal delivered by a different detector,
N counting circuits (Ki, i=1, 2, . . . , N) connected to the N processing circuits, each counting circuit being configured to count, during Nt successive counting durations Δt, a number of electronic pulses delivered by a different processing circuit and to deliver, for each counting duration Δt, a pulse counting value (Mi,t) (t=1, 2, . . . , Nt), Nt being significantly greater than N,
a memory block (B) that stores the N×Nt pulse counting values delivered by the N counting circuits during the Nt successive counting durations,
a computer configured to compute:
a set of NR correlation products Rz so that:


Rz=Πi=1NMi,([N−i)z+1] (z=1,2, . . . , NR)


with NR being an integer equal to






  
    
      
        N
        t
      
      -
      1
    
    
      N
      -
      1
    
  
  ,




a statistical mean R of the Nt products Πi=1NMi,t such that:






  
    R
    _
  
  =
  
    
      1
      
        N
        t
      
    
    ⁢
    
      
        ∑
        
          t
          =
          1
        
        
          N
          t
        
      
      ⁢
      
        
      
      ⁢
      
        
          ∏
          
            i
            =
            1
          
          N
        
        ⁢
        
          
        
        ⁢
        
          M
          
            i
            ,
            t
          
        
      
    
  




a standard deviation σ(R) of the Nt products Πi=1NMi,t, and
a correlation condition for each correlation product Rz, the computer being further configured to determine that:
a radioactive source moved in front of the detectors if Rz≧R+K2σ(R), K2 being a scalar, or
no source moved in front of the detectors if Rz<R+K2σ(R).

6. The device according to claim 5, the computer being further configured to compute a source speed V if Rz≧R+K2σ(R), such that:


V=d/(T×Δt),

where d is a distance separating two neighbouring detectors and T is a rank t of a set of N pulse counting values for which the correlation product RZ is maximum.

7. The device according to claim 5, the computer being further configured to compute a source intensity I if Rz≧R+K2σ(R), such that:




  I
  =
  
    
      
        1
        N
      
      ⁢
      
        
          ∑
          
            i
            =
            1
          
          N
        
        ⁢
        
          
        
        ⁢
        
          M
          
            i
            ,
            
              
                
                  (
                  
                    N
                    -
                    i
                  
                  )
                
                ⁢
                T
              
              +
              1
            
          
        
      
    
    -
    
      
        1
        
          N
          ×
          
            N
            t
          
        
      
      ⁢
      
        
          ∑
          
            t
            =
            1
          
          
            N
            t
          
        
        ⁢
        
          
        
        ⁢
        
          
            [
            
              
                ∑
                
                  i
                  =
                  1
                
                N
              
              ⁢
              
                
              
              ⁢
              
                M
                
                  i
                  ,
                  t
                
              
            
            ]
          
          .