Abstract:
A new adaptive filtering technique to reduce microphonic noise in radiation detectors is presented. The technique is based on system identification that actively cancels the microphonic noise. A sensor is used to measures mechanical disturbances that cause vibration on the detector assembly, and the digital adaptive filtering estimates the impact of these disturbances on the microphonic noise. The noise then can be subtracted from the actual detector measurement. In this paper the technique is presented and simulations are used to support this approach.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This U.S. application is a Continuation of PCT Application PCT/US2014/044537 filed Jun. 27, 2014, which claims priority to U.S. Provisional Application Ser. No. 61/840,062 filed Jun. 27, 2013, which application is incorporated herein by reference as if fully set forth in their entirety. 
     
    
     STATEMENT OF GOVERNMENTAL SUPPORT 
       [0002]    The invention described and claimed herein was made in part utilizing funds supplied by the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 between the U.S. Department of Energy and the Regents of the University of California for the management and operation of the Lawrence Berkeley National Laboratory. The government has certain rights in this invention. 
     
    
     BACKGROUND OF THE INVENTION 
       [0003]    1. Field of the Invention 
         [0004]    This invention relates generally to active microphonic noise cancellation. 
         [0005]    2. Brief Description of the Related Art 
         [0006]    Development of digital electronics, system identification and adaptive filtering techniques are allowing new approaches to improve the performance of radiation detectors. 
         [0007]    Powerful and affordable field programmable gate arrays (FPGAs), as well as high rate and resolution analog-to-digital converters are allowing cost effective digital processing algorithms specially designed for nuclear instrumentation. In this paper we are proposing an approach to reduce the microphonic noise and improve energy, timing, position and tracking resolution of radiation detectors. 
         [0008]    Microphonic noise in radiation detectors is associated with mechanical disturbances. These disturbances interact with the structure of the detector enclosure and its components, exciting mechanical vibrations. In one of the processes responsible for this noise, vibrations in the structure change capacitances inside the detector enclosure, injecting charge into the detector itself or its cables. This charge adds to the detector output and is measured as microphonic noise, degrading its performance. 
         [0009]    There are several sources for these mechanical disturbances. We will now describe a few examples. Vacuum pumps can be installed in the proximity of the detector, causing vibrations that are transmitted to the detector enclosure. In general, high resolution experiments require detectors operating at cryogenic temperatures to reduce leakage current. These temperatures can be achieved using piston driven cryocoolers mounted as part of the detector assembly (e.g., for portable radiation detector systems). The electrical motor and piston of the cryocooler generate vibrations that propagate to the detector enclosure. Other systems use cryostats with detectors cooled by Dewars mounted as part of the cryostat and with an external source of liquid nitrogen. The nitrogen “bubbling” inside the Dewar may cause vibrations. Even audible noise in the environment close to the detector may interfere with the detector enclosure. Therefore, microphonic noise is difficult to control and mitigate. 
         [0010]    Conventional filtering in nuclear spectroscopy is based on pulse shaping, substantially reducing the impact of microphonic noise (as well as other noise sources). However, if the mechanical resonant frequencies have components similar to the actual frequencies of the detector pulse, the shaper may allow the noise to propagate to the multichannel analyzer, degrading the energy resolution. 
         [0011]    The impact of microphonic noise can be more severe in multisegmented detectors, where the actual shape and amplitude of the detector pulse waveforms are used to estimate the interaction point and tracking of the gamma rays within the detector volume. Since information is contained on the shape and amplitude of the pulses themselves, there are fewer opportunities to filter the noise in these signals because traditional shaper filters cannot be used. 
         [0012]    The literature describes several approaches to reduce microphonic noise in high energy resolution radiation detectors. They are used mostly in nuclear spectroscopy. Various references propose an adaptive filter that uses a priori information about the exact form of the pulse signal after the charge sensitive amplifier, adapting a shaper to attenuate the microphonic noise deviating from this form. Other solutions deal with low-frequency periodic noise induced by mechanically cooling devices (e.g., cryocoolers). For example, variations on the shaper amplifier are used to minimize these contributions and another reference proposes a counterweight to mechanically minimize these system disturbances. However, observe that these approaches focus on improving the energy resolution by implementing enhanced shaper amplifiers, but they do not address microphonic noise in the detector output waveforms, which impact timing, position and tracking resolution. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]    The foregoing aspects and others will be readily appreciated by the skilled artisan from the following description of illustrative embodiments when read in conjunction with the accompanying drawings. 
           [0014]      FIG. 1  illustrates a block diagram of a scheme for active microphonic noise cancellation. 
           [0015]      FIG. 2  illustrates an example of the digitized output s(k) of the charge sensitive amplifier without microphonic noise. 
           [0016]      FIG. 3  illustrates an energy histogram for the 1.17 MeV line without microphonic noise: crosses are the energy histogram, line is the Gaussian fit. 
           [0017]      FIG. 4   a  illustrates simulated periodic mechanical disturbance v(k),  FIG. 4   b  its impact on the microphonic noise p(k) and  FIG. 4   c  the digitized output of the CSA s(k) with added microphonic noise for these conditions. 
           [0018]      FIG. 5   a  illustrates Microphonic noise cancellation y(k) as the LMS algorithm adapts,  FIG. 5   b  detail of the microphonic noise early in the adaption process, and  FIG. 5   c  after the parameters already adapted. 
           [0019]      FIG. 6  illustrates original microphonic noise p(k) (continue line) and estimated microphonic noise {circumflex over (p)}(k) (dashed line). 
           [0020]      FIG. 7  illustrates an improvement on energy resolution as the adaptive algorithms cancels the microphonics noise. 
       
    
    
     DETAILED DESCRIPTION 
       [0021]    In the discussions that follow, various process steps may or may not be described using certain types of manufacturing equipment, along with certain process parameters. It is to be appreciated that other types of equipment can be used, with different process parameters employed, and that some of the steps may be performed in other manufacturing equipment without departing from the scope of this invention. Furthermore, different process parameters or manufacturing equipment could be substituted for those described herein without departing from the scope of the invention. 
         [0022]    These and other details and advantages of the present invention will become more fully apparent from the following description taken in conjunction with the accompanying drawings. 
         [0023]    Various embodiments of the invention describe a filtering technique based on system identification and adaptive signal processing. A sensor (e.g., accelerometer, voltage detector, motion detector) measures the mechanical disturbances on the detector structure. System identification techniques estimate a model of the electro/mechanical system injecting microphonic noise by monitoring the vibrations and the detector output. As the estimated model converges, the microphonic noise is more precisely attenuated and, thus, increasing the energy, timing, position and tracking resolution of the system. Furthermore, temporal variations on the coupling of the mechanical disturbances into microphonic noise can be tracked and minimized. 
       Active Microphonic Noise Cancellation 
       [0024]      FIG. 1  shows the block diagram of the proposed scheme. In this diagram, we highlight that the microphonic noise p(t) is added to the detector signal d(t) and then amplified by the charge sensitive amplifier (CSA). The variable t is used to highlight that this portion of the circuit is on the continuous time domain. The CSA output s(t) is converted to digital by a sample and hold and analog to digital converter (ADC) circuit, generating s(k): 
         [0000]        s ( k )= r ( k )+ n ( k )+ p ( k ),  (1)
 
         [0000]    where r(k) is the charge deposited by the radiation, n(k) is the noise associated with the detector, amplifier, ADC and other components and k is the sample number in the discrete time domain. Of course, in a real system, the signal from the detector already contains the microphonics noise. Here, we are explicitly separating it from the detector signal for explanation purpose. 
         [0025]    In the block diagram, we assume that some mechanical disturbance cause vibrations that convolves with an electro/mechanical system H(t) generating the microphonics noise p(t). In the introduction, we illustrated a few examples of how these mechanical disturbances could be generated. Consider the case of a vacuum pump operating close to the detector. The pump vibrations are transmitted to the detector structure, and the structure itself then oscillates with its own resonant frequencies and damp factors and injects charge noise into the detector signal d(t). The system H(t) captures the electro/mechanical process by which these disturbances are coupled to the detector signal. 
         [0026]    In one embodiment, we measure the mechanical disturbance using some sensor (e.g., accelerometer). We intend to investigate options associated with possible location of this sensor, its sensitivity and implications on performance of the proposed scheme. This sensor is instrumented by its own ADC generating v(k). 
         [0027]    The objective now is to estimate the system H(t) using an identification algorithm that monitors the mechanical disturbances and the microphonic noise contained in the detector signal s(k). The identification algorithm adjusts the parameters of the system H(k) by internally minimizing the error between the estimated microphonic noise (k) and the measured p(k). The output y(k) is given by 
         [0000]        y ( k )= s ( k )−{circumflex over ( p )}( k )= r ( k )+ n ( k )+ p ( k )−{circumflex over ( p )}( k ).  (2)
 
         [0000]    Therefore, as Ĥ→H, so does {circumflex over (p)}(k)→p(k), and the microphonic noise in the output y(k) decreases. Observe that the identification of system H(t) does not need to be perfect to obtain reasonable noise minimization. The uncancelled portion can be small when compared with the remaining noise n(k). The output y(k), instead of s(k), is now used by the rest of the system for further processing. 
         [0028]    The literature describes several approaches for system identification with different performance characteristics and number of parameters to estimate. Here is the example of a few. Some of these methods are recursive and guarantee convergence to a global optimum solution based on relatively easy to obtain conditions. 
         [0029]    Examples of such methods include linear-in-the-parameters strategies, like the least mean square (LMS) algorithm adjusting finite impulse response (FIR) filters. Fixing poles in specific positions allow the use of infinite impulse response filters, which are more compact while still keeping the linear-in-the-parameters characteristics. Other algorithms are based on data block processing: first acquire a block of data and use it to estimate the optimum parameters at some specific time. 
         [0030]    An embodiment models the coupling of these disturbances to the microphonic noise using the transfer function H(t). We are assuming we can model H(t) using linear systems. However, observe that the need for linearity is associated with the connection between the mechanical disturbance and the microphonic noise; it is not associated with the process that causes the disturbance themselves. For example, references describe the complex dissipative process in dilution cryostats that generates vibrations on the detector structure. Since we are measuring the vibration, the process that generates these disturbances does not need to be modeled. Another aspect is that this coupling can be time varying, i.e. H(t) may change as time progresses. This can be addressed by an identification algorithm that tracks the changes. 
       Simulations 
       [0031]    Various embodiments used simulations to demonstrate the feasibility of the proposed scheme. We will now describe how they were performed and their results. Our simulations were based on the information described in Table 1. Specifically for energy resolution with microphonic noise we assumed a substantial degradation to illustrate the performance of the proposed scheme. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
               
             
               
               
               
             
               
             
               
               
               
             
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Parameters used for simulations 
               
             
          
           
               
                 Parameter 
                 Setup 
                 Unit 
               
               
                   
               
             
          
           
               
                 Detector ADC sampling frequency 
                 10 
                 ns 
               
             
          
           
               
                 Trapezoidal filter configuration 
               
             
          
           
               
                 Collection time 
                 4 
                 μs 
               
               
                 Integration time 
                 320 
                 ns 
               
               
                 Time constant of the CSA with resistive feedback 
                 50 
                 μs 
               
               
                 and pole/zero compensation 
               
             
          
           
               
                 Segment resolution for  60 Co sources (FWHM) 
               
             
          
           
               
                 Without microphonic noise 
                 ~2.4 
                 KeV FWHM 
               
               
                 With microphonic noise 
                 ~3.3 
                 KeV FWHM 
               
             
          
           
               
                 ADC output for the  60 Co lines: 
               
             
          
           
               
                 1.17 MeV 
                 940 
                 Counts 
               
               
                 1.33 MeV 
                 1060 
                 Counts 
               
               
                   
               
             
          
         
       
     
         [0032]    The radiation detected r(t) was generated using a Poisson distribution in time with an average rate of 400 Hz. This decreases the possibility of pile-up and avoids simulation of an additional pole-zero correction. Just the two  60 Co lines were used. Initially, the microphonic noise p(t) is set to zero. The detector noise n(t) was simulated using white noise. The amplitude was set such that we obtain an energy resolution of approximately 2.4 KeV FWHM after a trapezoidal filter with collection and integration time described in Table 1.  FIG. 2  shows an example of the digitized output of the CSA s(k) for such scenario.  FIG. 3  shows the energy histogram for the 1.17 MeV line. The crosses are part of the energy histogram, and the line is the Gaussian fit. 
         [0033]    We now add microphonic noise p(t) to the detector. For our simulations we will use two types of mechanical disturbances. The first one is white noise band-limited by a 6-poles Butterworth low pass filter with a 3 dB 20 KHz cutoff frequency. The low pass filter represents a mechanical vibration with limited bandwidth. This disturbance, for example, could simulate the “bubbling” of the liquid nitrogen inside the Dewar. The second disturbance used in the simulations is periodic, with a fixed 1 KHz rate. This could represent, for example, the mechanical vibration of a cryocooler coupling to the detector enclosure. 
         [0034]    In our simulations, H(t) is a second order transfer function representing a spring-mass system with friction and 7 KHz natural oscillating frequency. The amplitude of the disturbances, both band-limited white noise and periodic, are adjusted to degrade the energy resolution to approximately 3.35 KeV FWHM. For illustration,  FIG. 4  ( a ) shows the simulated periodic disturbance v(k),  FIG. 4  ( b ) its impact on the microphonic noise p(k) and  FIG. 4  ( c ) the digitized output of the CSA s(k) with added microphonic noise for these conditions. The amplitude of both disturbances were set such that the estimated energy resolution degrades to approximately 3.35 KeV FWHM when using the same trapezoidal filter configuration as before. 
         [0035]    We will now describe the details of the simulations used to cancel the microphonic noise. We selected a sampling frequency of 5 μs for the ADC connected to the vibration sensor (refer to  FIG. 1 ), which is enough to capture all information contained in the sensor output. When we refer to the 5 μs sampling time we will use variable q. The signal s(k) is decimated by a factor of 500 to match the sampling frequency of the mechanical disturbance (i.e., from 10 ns to 5 μs) and we use an FIR filter 
         [0000]      {circumflex over ( H )}( z )= ĥ   0   +ĥ   −1   z   −1   + . . . +ĥ   −(j+1)   Z   −(j+1)   (3)
 
         [0000]    to represent Ĥ(k), where j=200 adjustable parameters and z refers to the z-transform. 
         [0036]    For simplicity,  FIG. 1  does not show the decimation on s(k) and we assume it is part of the identification algorithm block. The identification algorithm we used to test is the recursive LMS, due to its simplicity, easy implementation and linear-in-the-parameter characteristic (i.e., adapts to a global minimum given the persistent excitation condition). Of course, as pointed before, the literature describes several identification algorithms with different performances. In this invention we are not looking for the most suitable algorithm for such application, but rather on demonstrating the usefulness of the proposed microphonic noise cancellation scheme. We will now describe the LMS algorithm used for both disturbances. Define the vector 
         [0000]      {circumflex over ( H )}( q )=[ ĥ   0 ( q ) ĥ   −1 ( q ) . . .  ĥ   −(j+1) ( q )] T   (4)
 
         [0000]    formed by the adjustable parameter of the finite impulse response (FIR) filter (capital letters in the equations are used to identify vectors). Also, construct the vector 
         [0000]        V ( q )=[ v ( q ) v ( q− 1) . . .  v ( q−j+ 1)] T   (5)
 
         [0000]    where v(i) is time delayed samples of the vibration sensor and initialize Ĥ(q)=0. The recursive algorithm starts here. First find the estimated output 
         [0000]      {circumflex over ( p )}( q )= Ĥ   T ( q )· V ( q ).  (6)
 
         [0000]    Then the error e(q) between the measured signal and the estimated output of the adaptive filter 
         [0000]        e ( q )= s ( q )−{circumflex over ( p )}( q ).  (7)
 
         [0000]    Finally, update the parameters of the FIR filter 
         [0000]      {circumflex over ( H )}( q+ 1)={circumflex over ( H )}( q )+μ V ( q ) e ( q ),  (8)
 
         [0000]    where μ is small and positive number. Repeat the algorithm. The parameter μ has to be adjusted to avoid divergence of Ĥ(q). A variation of the LMS algorithm is the normalized LMS, which uses the input V(q) to weight on μ, making it a more robust algorithm. 
         [0037]    During the simulations, we observed that when radiation is detected, the signal r(k) was capable of disrupting the adaptive algorithm quite substantially. This can be understood observing the LMS algorithm. In our simulations, when radiation is detected, s(k) is substantially larger then p(k), and the error e(k) is large. Then, the recursive process (Eq. 2) significantly upgrades the parameters of Ĥ(q), but in the wrong direction. To handle this effect, we changed the algorithm to turn off the adaptation while s(k) is above the threshold of 150 ADC counts. 
         [0038]    To generate now {circumflex over (p)}(k) (i.e., in the 10 ns sampling time), we up-sampled the output {circumflex over (p)}(q) (the opposite operation of decimation) to 10 ns and interpolate the signal using a low pass filter. Again, for simplicity this process is not shown in  FIG. 1  and is considered as part of the block Ĥ(k). We can now subtract {circumflex over (p)}(k) from s(k) to cancel the microphonic noise (Eq. 2).  FIG. 5(   a ) shows the LMS algorithm adapting Ĥ(k). Observe that at the beginning, the parameters of the FIR filter are mostly very close to zero due to the initialization Ĥ(q)=0, and there is almost no cancellation of the microphonic noise ( FIG. 5(   b )). As time progresses, the algorithm more precisely models H(t) and the noise decreases ( FIG. 5(   c )). 
         [0039]    With the adaptive cancellation running, we now estimate the energy resolution of y(k) using the same trapezoidal filter as before and for both disturbances. For the 1.17 KeV line, the energy resolution is now 2.42 KeV for the band-limited white noise disturbance and 2.46 KeV for the periodic disturbance. The proposed scheme mostly recovers the original energy resolution before microphonic noise was added. Also, observe that the waveforms in y(k) ( FIG. 5(   c )), which depicts the cancelled microphonic noise for the periodic disturbance, are mostly similar to the waveforms without microphonic noise ( FIG. 2) . 
         [0040]    Table 2 summaries the results of these simulations, both for the  60 Co 1.17 MeV and 1.33 MeV energies and for the two disturbances (band-limited white noise and periodic). Note we have set the amplitude of the disturbance such that, for these two energies, the resolution with microphonic noise degrades by the same amount. Then, when we turn on the identification algorithm, the performance for both  60 Co lines improves by the same amount, almost recovering the original energy resolution. Now we estimate the actual energy (i.e., the mean) in the output of the trapezoidal filter to detect if the proposed scheme introduces some bias on the energy itself. We used the two lines for the case without microphonic noise as the “calibration” to estimate the other energies. The results are also summarized in Table 2. Observe that for the 1.17 MeV line the energy did not change with microphonic noise or when it was cancelled. However, we measured a small fluctuation of 1 KeV for the 1.33 MeV line before microphonic noise cancellation (i.e., 1.329 MeV). 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Results of the simulations of the microphonic noise cancellation 
               
             
          
           
               
                   
                 Resolution 
                   
               
               
                   
                 (FWHM) 
                 Energy (MeV) 
               
             
          
           
               
                   60 Co line 
                 1.17 MeV 
                 1.33 MeV 
                 1.17 MeV 
                 1.33 MeV 
               
               
                   
               
               
                 Without microphonic 
                 2.37 
                 2.37 
                 1.170 
                 1.330 
               
               
                 noise d(t) 
               
               
                 With microphonic noise 
                 3.35 
                 3.35 
                 1.170 
                 1.329 
               
               
                 s(k) 
               
             
          
           
               
                 Cancelled 
                 White noise 
                 2.42 
                 2.42 
                 1.170 
                 1.330 
               
               
                 micro- 
                 disturbance 
               
               
                 phonic 
                 Periodic 
                 2.46 
                 2.46 
                 1.170 
                 1.330 
               
               
                 noise y(k) 
                 disturbance 
               
               
                   
               
             
          
         
       
     
         [0041]      FIG. 6  shows the original microphonic noise p(k) (continue line) and its estimation {circumflex over (p)}(k) (dashed line) for the case of periodic disturbance. Observe that p(k) and {circumflex over (p)}(k) did not have to precisely match to obtain the results described in Table 2. Actually, perfect identification is not possible in this case, since the detector noise n(k) will always generate an error e(q) (Eq. 7), which will then keep the parameters of the adaptive filter Ĥ(q) (Eq. 4) fluctuating around the optimum solution. As we pointed out before, a precise match is not needed, since the remaining microphonic noise (the subtraction of the continue and dashed lines in  FIG. 6 ) is small when compared with the detector noise n(k). 
         [0042]    We have also measured the energy resolution when the adaptive algorithm is still adapting to the disturbance. For this specific simulation we used the periodic disturbance and we measured the resolution at different times during the adaptation process.  FIG. 7  shows the results and it should be compared with  FIG. 5(   a ). Observe that, as the contribution of the microphonics noise is being cancelled, we already observe an improvement on the performance of the energy resolution. 
         [0043]    Observe that there is no requirement that the mechanical disturbances be periodic or with good period stability (as we have exemplified by the band-limited white noise versus periodic disturbance). However, good harmonic content of the disturbance is associated with the persistent excitation condition necessary for good modeling when algorithms like LMS are used. The good harmonic content exercise all poles and zeros of the transfer function H(t), allowing good modeling. In these simulations, both disturbances have good harmonic content for the transfer function H(t) and they are always present. Therefore, they meet the persistent excitation condition. However, the impact of imprecise modeling in this microphonic noise cancellation scheme can be small. For example, consider that the mechanical system modeled here had another resonant frequency above certain frequency, and that our disturbance was band limited to less than this frequency. The disturbance will not exercise these higher resonance frequencies and, therefore, the adaptive filter algorithm will not model these higher frequency poles and zeros. However, if one vibration mode of the detector structure is not excited because the disturbance is band limited, this one mode will not contribute to the microphonic noise, and therefore, there is no need to cancel it. Therefore, though the model identification is imprecise, the microphonic cancelation scheme proposed here can still yield good results. Also, the LMS algorithm may have to be turned off when there is no mechanical disturbance (i.e., the persistent excitation condition does not hold) to avoid the parameters of the filter drifting away from the optimum solution due to noise in the radiation detector and vibration sensor. Various embodiments describe a scheme that may become a very powerful tool to reduce microphonic noise in future systems.