CHAPTER 6: DETECTOR FABRICATION AND CHARACTERIZATION
6.4 DIGITAL SIGNAL PROCESSING FOR RADIATION DETECTION
Historically, analog pulse-shaping has been the only option for processing signals produced by radiation detection systems due to the high speed and accuracy required. However, in the past two decades, high-speed analog-to-digital converters (ADC) with high resolution have been invented, which allow digital processing of signals produced by radiation detectors. This allows for a wide variety of new data processing techniques to be applied to the radiation detection signals. Additionally, there are a number of advantages
gained by processing detector signals digitally. Digital processing allows for unlimited flexibility in implementing and changing shaping parameters, such as the shaping time, which is limited for analog circuitry. Furthermore, digital processing in theory will be more stable, because the processing will not depend on cable or environmental noise which can affect an analog system. However, one potential disadvantage of digital systems is that they may not be as fast as their analog counterparts.
For the purposes of radiation detection, two parameters are very important when performing analog-to-digital conversion of the signal: the ADC resolution, and the sampling rate. The resolution governs how accurately the digitizer can convert the analog voltage amplitudes to a digital value. A digitizer appropriate for radiation detection must have good ADC resolution in bits, while being able to sample the signal at a high frequency.
Figure 6.19. An example of an ADC coding scheme for an 8-bit resolution ADC [83]. A digitizer will convert the analog signal based on the coding scheme used for the ADC, which depends on the resolution of the ADC. Figure 6.19 shows an example of a coding scheme for an 8-bit digitizer. Depending on the number of bits of resolution available, the ADC will more accurately be able to store the analog voltages. If the
resolution is too poor, information will be lost from the signal being digitized. The voltage resolution, Vres, of an ADC can be determined by the following equation:
2 1 6.18
where EFSR is the voltage range being measured, and M is the ADC resolution in bits. If a
signal ranging from 0 to 10V is divided into the code levels available for an 8-bit ADC, then:
10 0
2 1
10
255 39.2 6.19
This means that an 8-bit ADC will resolve voltage levels in steps no less than 39.2 mV. For the purposes of radiation detection, this means an 8-bit ADC is not suitable, because voltage signals produced by a charge sensitive preamplifier can be as low as 10 mV in peak-to-peak amplitude.
For our laboratory, we have chosen to use a National Instruments NI-5122 digitizer card to perform digitization of detection signals. The NI-5122 has 14 bits of ADC resolution, which gives a Vres value of 0.61mV over a 10V range. This resolution is
adequate enough to capture pulse information about small or large pulses generated by the radiation detectors. Furthermore, the NI-5122 can capture signals at a rate of 100 Megasamples per second in real-time at 14-bit resolution. This sampling rate is fast enough to capture detector signals and reconstruct them for future use.
Figure 6.20. Schematic diagram of a digital nuclear detection measurement system.
In order to capture radiation detection pulses from a detector, the radiation detection system was configured in the manner shown in Figure 6.20. A CZT detector biased under high voltage is connected to the preamplifier, which sends its signals to the NI-5122 digitizer card. The pulses are also sent to the shaping amplifier, whose output serves as a reliable external trigger for the NI-5122. The NI-5122 resides within the PC, where the Labview software coded in-house captures the detection signals received and stores it for later use.
6.4.2
Digital Pulse Shaping
Once the detection pulses are stored, they must be shaped using a filtering algorithm. Pulse shaping typically uses a linear time-invariant filter, which convolutes the input signal with a filter which does not change its properties based on time. The convolution process for a digital signal can be expressed by the following equation:
6.20 where i is the time period between signal sample values, L is the filter length, V is the original signal, H is the response of the filter, and S is the discrete output signal. As the filter H is convoluted through the original signal values V, a discrete shaped signal S will be generated.
For analog nuclear detection systems, the most common pulse shaping method employed is CR-(RC)n shaping. This method, as seen in Figure 6.11, uses one differentiator circuit followed by n integrator circuits wired in series [84]. This style of filter is known as a semi-Gaussian filter, because the resulting pulse shape approximates the Gaussian shape. More integrator circuits provide more noise filtering and further approximation to a Gaussian signal. However, this increases the delay present in processing the signals, and increases the complexity and the number of components present in the processing system. Furthermore, noise reduction suffers from diminishing returns when increasing the integrator circuits [84]. For this reason, in pulse height measurements the typical value of n used is 4.
In a digital system, in order to use a filter on a discrete signal, the transfer function of the filter, in the Z-transform domain, must be used. The Z-domain transfer function of a CR-(RC)4 filter can be expressed by the following equation [84]:
4 12 11 12 11 4
24 6.21
where a = 1/τ, α = exp(-T/τ), T is the sampling rate in seconds, and τ is the time constant. Using this filter, it is possible to perform the semi-Gaussian CR-(RC)4 shaping performed by a shaping amplifier circuit in a digital processing system.
In order to process digital signals produced by the radiation detection system in our laboratory, code was implemented in MATLAB which would perform the necessary steps. First, the CR-(RC)4 filter would be initialized by MATLAB, which would use a given time constant. Next, the detection input signal would be read in by the software, and its vertical scaling would be adjusted so that the signal would start at approximately 0 V, also known as baseline adjustment. Finally, the baseline adjusted signal would be convoluted with the digital filter, yielding an output signal. Appendix C shows the MATLAB code implemented to filter the detection signal. Figure 6.21 shows a signal generated by a test pulser being shaped by the MATLAB software. Figure 6.21a depicts the original signal, whose baseline has already been corrected, and Figure 6.21b shows the signal after being shaped by the CR-(RC)4 filter.
Once a collection of pulse heights have been determined from the stored digital signals, a pulse height histogram can be generated. The histogram will “bin” the pulse heights, and show the number of counts of radiation seen within a range of pulse heights. This process is equivalent to the process an MCA and Genie 2000 undergo when generating pulse height spectrum using an analog system. Figure 6.22 shows an example pulse height distribution generated from detector pulses stored from a CZT detector irradiated using a 137Cs source.
Figure 6.22. Pulse height distribution generated using pulse heights calculated based on digitally stored detector pulses from a CZT detector using a 137Cs source.
(a) (b)
Figure 6.21. (a) Digitized test pulse prior to digital shaping. (b) Test pulse shaped using a CR-(RC)4 digital filter algorithm using MATLAB.
6.4.3
Rise-Time Distribution
In addition to calculating the pulse height digitally, information about the rise-time of a detector pulse can be determined using a digital system. The rise-time of a signal is defined as the time required for a signal output to rise from 10% to 90% of its final value. In the case of radiation detection, it is approximately the time taken for a charge generated due to radiation interaction in the material to travel through the detector material and induce charge on the contact electrodes. Thus, the rise-time gives approximate information about the depth of interaction within a nuclear detector. For high-energy gamma-rays, the depth of interaction can be anywhere along the bulk of the detector material. The longer the charge takes to reach the read-out electrode (typically the anode), the higher its calculated rise-time will be.
Figure 6.23. Oscilloscope snapshot showing pre-amplifier output of an alpha particle signal detected using CZT.
An example of the rise-time of an alpha particle interaction pulse is shown in Figure 6.23. Once enough pulses have been recorded, a histogram of rise-times can be generated as seen in Figure 6.24. This rise-time distribution is necessary for charge transport measurements, specifically for measuring the mobility of a CZT detector crystal.
Figure 6.24. Rise-time distribution generated using rise-times calculated based on digitally stored detector pulses from a CZT detector using a 137Cs source.