Chapter No. 18 Radiation Detection and Measurements , Glenn T. Knoll,

1. Multichannel Pulse Analysis Chapter No. 18 Radiation Detection and Measurements, Glenn T. Knoll, Third edition (2000), John Willey.

2. Ch 18 GK I SINGLE·CHANNEL METHODS IIGENERAL MULTICHANNEL CHARACTERISTICS • Number of Channels required • Calibration and linearity III THE MULTICHANNEL ANALYZER Basic components and functions • Analogue to digital converter • Linear Ramp Converter (Wilkinson type) • The Successive Approximation ADC • Sliding scale Principle • The Memory • Ancillory Functions • Multiscaling • Multiparameter Analysis • MCA dead time IV SPECTRUM STABILIZATION AND RELOCATION V SPECTRUM ANALYSIS

14. 18-11:The basic function of the MCA involves only the ADC and the memory. For purposes of illustration, we imagine the memory to be arranged as a vertical stack of able locations, ranging from the first address (or channel number 1) at the bottom the maximum location number (say, 1024) at the top. Once a pulse has been processed by the ADC, the analyzer control circuits seek out the memory location corresponding to digitized amplitude stored in the address register, and the content of that location is incremented by one count. The net effect of this operation can be thought of as one in which pulse to be analyzed passes through the ADC and is sorted into a memory location corresponds most closely to its amplitude. This function is identical to that described for the stacked single-channel analyzers illustrated in Fig. 18.1. Neglecting dead time, input pulse increments an appropriate memory location by one count, and therefore total accumulated number of counts over all memory is simply the total number of presented to the analyzer during the measurement period. A plot of the content of channel versus the channel number will be the same representation of the differential height distribution of the input pulses as discussed earlier for the stacked single-channel- analyzers. A number of other functions are normally found in an MCA.As illustrated in Fig.18.7, an input gate is usually provided to block pulses from reaching the ADC during the time it} is "busy" digitizing a previous pulse. The ADC provides a logic signal level that holds the input gate open during the time it is not occupied. Because the ADC can be relatively slow, high counting rates will result in situations in which the input gate is closed for much of the time. Therefore, some fraction of the input pulses will be lost during this dead time, and any attempt to measure quantitatively the number of pulses presented to the analyzer must take into account those lost during the dead time.

15. 18-12: To help remedy this problem, most MCAs provide an internal clock whose output pulses are routed through the same input gate and are stored in a special memory location. The clock output is a train of regular pulses synchronized with an internal crystal oscillator. If the fraction of time the analyzer is dead is not excessively high, then it can be argued that the fraction'of clock pulses that is lost by being blocked by the input gate is the same as the fraction of signal pulses blocked by the same input gate. Therefore, the number of clock pulses accumulated is a measure of the live time of the analyzer or the time over which the input gate was held open. Absolute measurements can therefore be based on a fixed value of live time, which eliminates the need for an explicit dead time correction to the data. Further discussion of the dead time correction problem for MCAs is given later in this chapter. Many MCAs are also provided with another linear gate that is controlled by a single channel analyzer. The input pulses are presented in parallel to the SCA and, after passing through a small fixed delay, to the linear pulse input of this gate. If the input pulse meets the amplitude criteria set by the SCA, the gate is opened and the pulse is passed on to the remainder of the MCA circuitry. The purpose of this step is to allow rejection of input pulses that are either smaller or larger than the region of interest set by the SCA limits. These limits, often referred to as the LLD (lower-level discriminator) and ULD (upper level discriminator), are chosen to exclude very small noise pulses at the lower end and very large pulses beyond the range of interest at the upper end. Thus, these uninteresting pulses never reach the ADC and consequently do not use valuable conversion time, which would otherwise increase the fractional dead time.

16. 18-13: If an MCA is operated at relatively high fractional dead time (say, greater than 30 or 40%), distortions in the spectrum can arise because of the greater probability of input pulses that arrive at the input gate just at the time it is either opening or closing. It is therefore often advisable to reduce the counting rate presented to the input gate as much as possible by excluding noise and insignificant small-amplitude events with the LLD, and if significant numbers of large-ampliude background events are present, excluding them with an appropriate ULD setting. The contents of the memory after a measurement can be displayed or recorded in a number of ways. Virtually all MCAs provide a CRT display of the content of each channel as the Y displacement versus the channel number as the X displacement. This display is therefore a graphical representation of the pulse height spectrum discussed earlier. The display can be either On a linear vertical scale or, more commonly, as a logarithmic scale to show detail over a wider range of channel content. Standard recording devices for digital data, including printers and storage media, are commonly available to store permanently the memory content and to provide hard copy output. Because of the similarity of many of the MCA components just described to those of the standard personal computer (PC), there is a widespread availability of plug-in cards that will convert a PC into an MCA. The card must provide the components that are unique to the MCA (such as the ADC), but the normal PC memory, display, and I/O hardware can be used directly. Control of the MCA functions is then provided in the form of software that is loaded into the PC memory.

17. 18-14: Some compromises in performance of the plug-in boards are often necessary because the noisy electronic environment inside the PC produced by the many digital switching operations is somewhat hostile to the sensitive analog operations required in ADCs. Thus there are also units in which the ADC operations are housed within an external NIM module that communicates with the PC through an interface cable. In some cases, the MCA is incorporated in a computer-based spectroscopy system that allows software control of the MCA functions as well as other settings such as detector voltage supply and parameters of the shaping amplifier such as gain, shaping time, pile-up rejection, and spectrum stabilizer operation (see later section in this chapter). B. The Analog-to-Digital Converter1. GENERAL SPECIFICATIONS The job to be performed by the ADC is to derive a digital number that is proportional to the amplitude of the pulse presented at its input. Its performance can be characterized by several parameters: 1. The speed with which the conversion is carried out. 2. The linearity of the conversion, or the faithfulness to which the digital output is proportional to the input amplitude. 3. The resolution of the conversion. or the "fineness" of the digital scale corresponding to the maximum range of amplitudes that can be converted. The nominal value of the resolution depends on the number of bits provided by the ADC, and is specified as the maximum number of addressable channels. Thus a 12-bit ADC will provide 212, or 4096 channels of resolution. From the previous discussion of ADC properties in Chapter 17, the effective resolution may be less than this value if electronic noise or instability result in typical channel profiles that are overly broad.

18. 18-15:For the types of ADCs generally chosen for use in MCAs, the effective resolution should not deviate greatly from the nominal value. The voltage that corresponds to full scale is arbitrary, but most ADCs nuclear pulse spectroscopy will be compatible with the output of typical linear Zero to 10 V is thus a common input span. Shaping requirements will also usually be specified for the input pulses, and most ADCs require a minimum pulse width of a of a microsecond to function properly. The conversion gain of an ADC specifies the number of channels over amplitude range will be spread. For example, at a conversion gain of 2048 channels, 0 to lO-V ADC will store a 10 V pulse in channel 2048, whereas at a conversion gain that same pulse would be stored in channel 512. At the lower conversion gain, a fraction of the MCA memory can be accessed at anyone time. On many ADCs, the conversion gain can be varied for the purposes of a specific application. The resolution of the ADC must be at least as good as the largest conversion gain at which it will be used. The conversion speed or dead time of the ADC is the critical factor in determining overall dead time of the MCA. Therefore, a premium is placed on fast conversion, but practical limitations restrict the designer in speeding up the conversion before linearity to suffer. The fastest ADCs, the flash or subranging type discussed in Chapter 17, are rarely used in MCAs because of their poor differential linearity. Two other types dominate in temporary MCAs: linear ramp converters and successive approximation ADCs. The first these, although the slowest, generally has the best linearity and channel profile specifications compared with the other types and has gained the most widespread application in MCAs. Successive approximation ADCs offer faster conversion times, but generally with poorer linearity and channel uniformity

19. 2. THE UNEAR RAMP CONVERTER (WILKINSON TYPE)-18-16 The linear ramp converter is based on an original design by Wilkinson and is illustrated in Fig. 18.8. The input pulse is supplied to a comparator circuit that continuously compares the amplitude with that of a linearly increasing ramp voltage. The ramp is conventionally generated by charging a capacitor with a constant-current source that is started at the time the input pulse is presented to the circuit. The comparator circuit provides as its output a gate pulse that begins at the same time the linear ramp is initiated. The gate pulse is maintained "on" until the comparator senses that the linear ramp has reached the amplitude of the input pulse. The gate pulse produced is therefore of variable length, which is directly proportional to the amplitude of the input pulse. This gate pulse is then used to operate a linear gate that receives periodic pulses from a constant-frequency clock as its input. A discrete number of these periodic pulses pass through the gate during the period it is open and are counted by the address register. Because the gate is opened for a period of time proportional to the input pulse amplitude, the number of pulses accumulated in the address register is also proportional to the input amplitude. The desired conversion between the analog amplitude and a digital equivalent has therefore been carried out. Because the clock operates at a constant frequency, the time required by a Wilkinson type ADC to perform the conversion is directly proportional to the number of pulses accumulated in the address register. Therefore, under equivalent conditions, the conversion time for large pulses is always greater than that for small pulses. Also, the time required for a typical conversion will vary inversely with the frequency of the clock. In order to minimize the conversion time, there is a premium on designing circuits that will reliably handle clock pulses of as high a frequency as possible. Clock frequencies of 100 MHz are representative of present-day commercial designs. The Wilkinson-type ADC leads to contiguous pulse height channels, all ideally of the same width. Because the linear ramp generation can be very precise, this design is characterized by good linearity specifications, accounting for its widespread popularity in MCAs. Variants of the Wilkinson design that lead to some improvement in speed are described by Nicholson and a clock frequency of up to 400 MHz can be achieved in advanced designs.

20. 3. THE SUCCESSIVE APPROXIMATION ADC-18-17 The second type of ADC in common use is based on the principle of successive approximation. Its function can be illustrated by the series of logic operations shown in Fig. 18.9. In the first stage, a comparator is used to determine whether the input pulse amplitude lies in the upper or lower half of the full ADC range. If it lies in the lower half, a zero is entered in the first (most significant) bit of the binary word that represents the output of the ADC. If the amplitude lies in the upper half of the range, the circuit effectively subtracts a value equal to one-half the ADC range from the pulse amplitude, passes the remainder on to the second stage, and enters a one in the most significant bit. The second stage then makes a similar comparison, but only over half the range of the ADC. Again, a zero entered in the next bit of the output word depending on the size of the remainder passed from the first stage. The remainder from the second stage is then passed to the and so on. If 10 such stages are provided, a 10-bit word will be produced that will cover a range of 210 or 1024 channels. In its most common circuit implementation, the successive approximation ADC multiple use of a single comparator that has two inputs: one is the sampled and held voltage and the other is produced by a digital-ta-analog converter (DAC). For the stage comparison, the input to the DAC is set to a digital value that is half the put range. Depending on the result of the initial comparison, the second-stage is then carried out with the digital input to the DAC set to either 25 or 75% of the and so on. In this way, analog subtractions are avoided but the functional operation equivalent to that described above. For a given successive approximation ADC, the conversion time is constant and independent of the size of the input pulse. For typical converters with a 10-bit output, the conversion time can be a few microseconds or less. Adding stages to increase the resolution only increases the conversion time in proportion to the number of total stages or in proportion to the logarithm of the maximum number of channels. Their speed advantage is therefore most pronounced when the number of addressed channels is large. The major disadvantage of typical successive approximation ADCs is a more pronounced differential nonlinearity compared with linear ramp ADCs. Some refinements to their design to help overcome this limitation are described in

21. 4. THE SLIDING SCALE PRINCIPLE-18-18 The linearity and channel width uniformity of any type of ADC can be improved by employing a technique generally called the sliding scale or randomizing method. Originally suggested in 1963 by Gatti and co-workers,8 the method has gained popularity (e.g., Refs. 9 and 10) through its implementation using modern IC technology. It has been particularly helpful in improving the performance of both successive approximation and flash ADCs. Without the technique, pulses of a given amplitude range are always converted to a fixed channel number. If that channel is unusually narrow or wide, then the differential linearity will suffer in proportion to the deviation from the average channel width. The sliding scale principle is illustrated in Fig. 18.10. It takes advantage of the averaging effect gained by spreading the same pulses over many channels. A randomly chosen analog voltage is added to the pulse amplitude before conversion and its digital equivalent subtracted after the conversion. The net digital output is therefore the same as if the voltage had not Digital output been added. However, the conversion has actually taken place at a random point along the conversion scale. If the added voltage covers a span of M channels, then the effective channel uniformity will improve as \1M if the channel width fluctuations are random. The implementation of Fig. 18.10 derives the added voltage by first generating a random digital number and converting this number to an analog voltage in a DAC. The same digital number is then subtracted after the conversion

22. 18-19: One of the disadvantages of the technique is that the original ADC scale of-H"C1iannels is reduced to N - M. If a pulse occurs that would normally be stored in a channel number near the top of the range, the addition of the random voltage may send the sum off scale. Other design also provoid this limitation by using either upward averaging (as described above) or downward averaging (by subtracting the random voltage) depending on whether the original pulse lies in the lower or upper half of the range. The choice of M can then be as large as N /2 to maximize the averaging effect without reducing the effective ADCscale. Because the sliding scale method involves converting a fixed pulse amplitude through different channels whose width may vary, a potential disadvantage is a broadening of typical channel profiles. If this broadening is severe enough, it will compromise the resolution of the ADC. Another potential problem is that, if the addition and subtraction steps are not perfectly matched in scale factor, periodic structures can be generated in the differential nonlinearity that appear as artifacts in recorded spectra. C. The Memory The memory section of an MCA provides one addressable location for every channel. Any of the standard types of digital memory can be used, but there is sometimes a preference for "nonvolatile" memory, which does not require the continual application of electrical. power to maintain its content. Then, data acquired over long measurement periods will not be lost if the power to the MCA is accidentally interrupted. Most MCAs make provisions for subdividing the memory into smaller units for independent acquisition and storage of multiple spectra. In this way a 4096 channel analyzer can be configured as eight separate 512 channel memory areas for storing low-resolution spectra, or as a single 4096 channel memory for a high-resolution spectrum. In most analyzers, provision is made for the negative incrementing of memory content as well as additive incrementing. In this "subtract" mode, background can conveniently be taken away from a previously recorded spectrum by analyzing for an equal live time with the source removed.

23. I:Ancillary Functions 18-20. 1. MEASUREMENT PERIOD TIMING Virtually all MCAs are provided with logic circuitry to terminate the analysis period after a predetermined number of clock pulses have been accumulated. One often has the choice between preset live time or clock time, which are distinguished by whether the clock pulses are routed through the input gate (see Fig. 18.7). Normally, quantitative comparisons or subtraction of background are done for equal live time periods, and this is the usual way of terminating the analysis period. 2. MULTISCALING Multichannel analyzers can be operated in a mode quite different from pulse height analysis, in which each memory location is treated as an independent counter. In this multiscaling mode, all pulses that enter the analyzer are counted, regardless of amplitude. Those that arrive at the start of the analysis period are stored in the first channel. After a time known as the dwell time, the analyzer skips to the second channel and pulses of all amplitudes at that memory location. Each channel is sequentially. One such dwell time for accumulating counts, until the entire memory has The dwell time can be set by the user, often from a range as broad as from 1 f.lS to minutes. The net effect of this mode is to provide a number of independent to the number of channels in the analyzer, each of which records the total number of Over a sequential interval of time. This mode of operation can be very useful in the behavior of rapidly decaying radioactive sources or in recording other urrle-llec,eul11 phenomena.

24. 3. COMPUTER INTERFACING-18-21 Stand-alone MCAs share many features with general purpose computers. In its most I' form, the MCA can only increment and display the memory, but more elaborate operatic"~ can be carried out if it is provided with some of the features of a small computer. ", example, one of the most useful functions is to allow summation of selected portions of.:“ spectrum, generally called regions of interest (ROIs). Cursors are generated whose position ~."‘ the displayed spectrum can be used to define the upper and lower bounds of the channel n~;bers between which the summation is carried out. This operation has obvious practical use fof;; simple peak area determination in radiation spectroscopy. Other operations, such as additiori~ or subtraction of two spectra or other manipulations of the data can also be provided. .More complex computer-based systems are also widely available that are based on p~~ with an appropriate ADC under software control. In this approach, the functions mentioned above can be duplicated through software routines that may be modified or supplemented by the user. Useful operations of this type can range from simple smoothing of the spectra to damp out statistical fluctuations, to elaborate spectrum analysis programs in which the position and area of apparent peaks in the spectrum are identified and measured. Current manufacturer's specification sheets are often the best source of detailed information in this rapidly eVOlving area.

25. 4. MULT/PARAMETER ANALYSIS-18-22 The simplest application of multichannel analysis is to determine the pulse height spectrum of a given source. This process can be thought of as recording the distribution of events over a single dimension-pulse amplitude. In many types of radiation measurements, additional experimental parameters for each event are of interest, and it is sometimes desirable to record simultaneously the distribution over two or more dimensions. One example is in the case in which not only the amplitude of the pulse carries information, but also its rise time or shape. Categories of events can often be identified based on unique combinations of amplitUde and shape, while a clean separation might not be possible using either parameter alone. In the example shown in Fig. 18.11, both the amplitude and shape (measured from the rise time) of each pulse from a liquid scintillation counter are derived in separate parallel branches of the pulse processing system. The object will now be to store this event according to the measured values of both these parameters. In any unit designed for multiparameter analysis, at least two separate inputs with dedicated ADCs must be provided, together with an associated coincidence circuit. The memory now consists of a two-dimensional array in which one axis corresponds to pulse amplitude and the other to pulse shape. Because both parameters are derived from the same event, they appear at the two inputs in time coincidence. The multiparameter analyzer recognizes the coincidence between the inputs and increments the memory location corresponding to the intersection of the corresponding pair of digitized addresses. As data accumulate, the intensity distribution then takes the form of a two-dimensional surface with local peaks representing combinations of amplitude and shape that occur most frequently. The data are sometimes displayed as a surface contour plot, or as an isometric view of the surface from a perspective that can be changed using software routines for best viewing. Multiparameter analyzers generally require a much larger memory than single parameter analyzers because, for equal resolution, memory requirements for two parameters are the square of the number of channels required for only one parameter. Often, however, one of the two parameters need not be recorded with the same degree of resolution so that nonsquare (rectangular) memory configurations will suffice. Three or more parameters require multidimensional memory allocations that can be impractical in size. In experiments in which many parameters are of interest for each event (for example, from multiple detectors recording coincident events), it may no longer be possible to dedicate a large enough memory to sort all the information in real time. An alternative mode of data recording called list mode acquisition can then be employed. Each of the multiple parameters is digitized with a separate ADC in real time, and the results are then quickly written to memory. A clock may also be read to provide a "time stamp" to record the time of occurrence of the event. As the measurement proceeds, the collection of data grows with each observed event but requires a memory whose size is only the product of the total number of events mUltiplied by the number of recorded parameters. After the conclusion of the measurement, the data can then be sorten off-line based on arbitrary criteria involving any or all of the recorded parameters. I. MeA Dead Time The dead time of an MCA is usually comprised of two components: the processing time of the ADC and the memory storage time. The first of these was discussed earlier and, for a Wilkinson-type ADC, is a variable time that is proportional to the channel number in which the pulse is stored. The processing time per channel is simply the period of the clock oscillator. For a typical clock frequency of 100 MHz, this time is 10 ns per channel. Once the pulse has been digitized, an additional fixed time of a few microseconds is generally required to store the pulse in the proper location in the memory. Thus, the dead time of an MCA using an ADC of this type can then be written N 'T = - + B (18.3) v 700 Chapter 18 Multichannel Pulse Analysis where v is the frequency of the clock oscillator, N is the channel number in which is stored, and B is the pulse storage time. The analyzer control circuits will hold gate closed for a period of time that equals this dead time. A dead time meter driven by the input gate to indicate the fraction of time the gate is closed, as experimenter. One normally tries to arrange experimental conditions so that the dead time in any measurement does not exceed 30 or 40% to prevent possible distortions. The automatic live time operation of an MCA described earlier is usually quite s factory for making routine dead time corrections. Circumstances can arise, howeve which the built-in live time correction is not accurate. When the fractional dead tim high, errors can enter because the clock pulses are not generally of the same shape duration as signal pulses. One remedyI2,13 is to use the pulser technique described on p. to produce an artificial peak in the recorded spectrum. If introduced at the preamp' the artificial pulses undergo the same amplification and shaping stages as the signal pu The fraction that are recorded then can account for both the losses due to pileup and analyzer dead time. Several authors14,15 have reviewed the live time correction proble and suggested conditions under which the pulser method is not accurate. To avoid pote tial problems, the pulse repetition rate must not be too high, and the use of a random ratherl than periodic pulser is preferred. Under these conditions, the pulser method can success~ fully handle virtually any conceivable case in which the shape of the spectrum does notl change during the course of the measurement. Additional complications arise if spectrum shape changes occur during the measurement, which lead to distortions and improper dead time corrections with the pulser method. A better method first suggested by Harms16 can accommodate spectrum changes but requires a nonstandard mode of MCA operation. In this method, the analysis is run for a fixed clock time. If a pulse is lost because the analyzer is dead (this can be sensed externally), compensation is made immediately by assigning a double weight to the next pulse and incrementing the corresponding memory location by two. Spectra that change during the course of the measurement are properly accommodated because the correction automatically takes into account the amplitude distribution of signal pulses at the time of the loss. This correction scheme has been tested by Monte Carlo simulation for a wide variety of spectrum shapes and time variations and has proved to be quite accurate in all casesP At higher rates, however, the assumption breaks down that only one pulse was lost during the dead time, and the Harms method begins to undercorrect for losses. One remedy is to modify the correction process by first calculating the expected number of counts lost during a dead period from a running measurement of the input pulse rate. The memory location corresponding to the next converted pulse is then incremented, not by two counts as above, but by one plus the calculated number of lost pulses. These artificial counts do not have the same statistical significance as the same number recorded normally, but they do maintain the total spectrum content as if there had been no losses. Normally called loss free counting,IS this technique is applicable in situations in which the dead fraction of the MCA is as high as 80%.19 It is particularly helpful in measurements from short-lived radioisotopes from which the counting rate may change by many orders of magnitude over the measurement period. IV. SPECTRUM STABILIZATION AND RELOCATION A. Active