Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R29/00—Arrangements for measuring or indicating electric quantities not covered by groups G01R19/00 - G01R27/00
  • G01R29/02—Measuring characteristics of individual pulses, e.g. deviation from pulse flatness, rise time or duration

Definitions

• a real IP device output signal viewed on a time scale comparable to ⁇ d, will then show a risetime region, whose shape may be difficult to describe mathematically, followed, after a period comparable to ⁇ r , by an exponential decay with time constant i -
• the output of a N- IP device will be similar, with additional distortions.
• steps-like we will refer to such signals, viewed on this time scale, as "step-like".
• Fig. IB shows a 5% residual T 2 component for ease of viewing: an exponential decay signal 25 with time constant T 2 , input to the P/Z network 20, produces either output signal 27 or 29, depending upon whether the residual T 2 term is positive or negative.
• RAUDORPH-1982 describes these issues. These risetime variations produce ballistic deficit by two paths, one direct, one indirect. The direct effect is well understood, per GOULDING-1988: the output filter's response varies with the time dependent shape of the charge arrival, being the convolution of the two. A trapezoidal filter greatly reduces this effect in the absence of exponential decay.
• HINSHAW-1991 and KUMAZAWA-1998 describe attempts to correct for ballistic deficit by capturing peak amplitudes from two filters which respond to the ballistic deficit differently, one an energy measuring filter and one a differentiating (or bipolar shaping) filter. Typically a significant fraction of their difference in peak heights is added to the energy filter's peak to correct it.
• cMOS correlated multiple output sample
• While embodiments of the invention use triangular and trapezoidal filters, the invention does not require specific filter shapes. Further, the invention does not require that the filter's capture times be precisely located relative to the step-like signal's leading edge. Rather, the method derives its accuracy from repeatably reproducing the set of prescribed time relationships between the sample values in the cMOS.
• the underlying capture method is therefore time-based rather than amplitude-based, which differentiates the invention from prior art methods which capture filter samples based on their maximum amplitudes.
• the measurement's noise is increased by the number N of additional filter samples required to compensate for the N-IP device's non-ideal terms.
• N may be reduced by creating a parameterized model of the non-ideal terms; making baseline measurements to determine the parameters; and then using them to correct area (e.g., charge) measurements made using simpler sets of filters which have less noise.
• these baseline measurements are cMOS values captured at times when the filters are not processing the step-like signals.
• the resultant implementation achieves the low electronic noise levels of conventional trapezoidal filters while also eliminating resolution loss due to both ballistic deficit and high count rates.
• Fig. 6A and 6B show a pair of purely digital circuits which implement the described method
• Fig. 7 shows a purely analog circuit which implements the described method
• Fig. 8 shows a hybrid analog/digital circuit which implements the described method.
• the invention has three basic steps: applying a set of filters to the preamplifier output; capturing a correlated multiple output sample (“cMOS") from the filter set in response to a detected event; and forming a weighted sum of these sample values to accurately recover the energy of the detected event.
• the cMOS is a set of samples bearing a prescribed set of time relationships between one another. The appropriate time relationships are achieved by setting the times of capture, inserting delays into the signal paths, or a combination thereof, and are independent of the specific risetime shape of any particular event.
• the theory underlying the invention method is based on modeling the preamplifier's (or N-IP device's) step-like output response (the "output") to the input charge (or impulse: the "input”) generated by the event as the sum of a small number of analytical functions which are represented by the same number of amplitudes.
• the preamplifier's or N-IP device's
• the input charge or impulse: the "input”
• five amplitudes are used to describe: the ⁇ ⁇ and T 2 exponential components prior to the step-like signal, the ideal amplitude of the step itself, an error term due to the ballistic deficit, and a DC level.
• Step amplitudes obtained using the four-filter measurement method have almost a factor of 3 higher electronic noise than simple trapezoidal filters.
• the parameters must be compensated for their evolution in time, creating a time- compensated model.
• the description below is organized as follows In ⁇ 2, using a static, captured step-like signal, we locate several filters in the vicinity of its leading edge and mathematically describe their outputs in terms of the base amplitudes. In ⁇ 3, we use these results to set up and solve the set of linear equations to obtain the input charge.
• Fig. 4 shows a typical preamplifier step-like output signal as it might look if it were digitized by an analog to digital converter (ADC) and saved in a computer memory.
• ADC analog to digital converter
• the shown time scale is arbitrary, with zero set a little before the onset of charge collection for convenience. To simplify the image, only a few members of the set of discrete values have been identified explicitly: subscripted capital Q's denote values at specific instants since the signal really represents the charge integrated on feedback capacitor 15 by amplifier 13.
• the ⁇ ⁇ component has three regions: an exponential decay region 50 prior to the step (i.e., times less than 0), a charge collection region 52, and an exponential decay region 53 following the step (i.e., times greater than 1).
• the curve 55 showing how curve 50 would have continued to decay had the step not arrived, represents the continued time decay of all previous steps, that is, the preamplifier's first pole residual response to those previous steps.
• the signal's T 2 component has the equivalent four regions 57, 58, 60, and 62.
• the ⁇ ⁇ and T2 charges injected by the ⁇ -ray pulse decay independently, since the preamplifier is a linear device.
• Eqn. 3 also defines the division factor r j5 which is equal to the sum to infinity.
• ⁇ g ( ⁇ g+ - ⁇ g- ) of risetime g, whose sub tractive leg ⁇ g- sits precisely within the gap of ⁇ ⁇ .
• ⁇ g ⁇ g+ - ⁇ g- g-i
• the correction charge Q c defined in Eqn. 10 is the difference between the total ⁇ ⁇ collected charge and the amount remaining at the end of gap g.
• Q c will typically be of order 2% of Q g ⁇ .
• Q c will be relatively uncorrelated to Q g i3, so the set of linear equations we solve for Q g i3 and Q c be well conditioned under inversion.
• Q C2 becomes proportional to Q c to a high degree of accuracy. This may be seen by defining Q gl as the total ⁇ -ray charge collected at time interval i in the collection region. Since each Q gl decays independently, we can write for the two components:
• Q C2 is therefore quite small, being about 0.1% of Q c or 0.002% of Q g ⁇ .
• Q g ⁇ , Q c , Q g ⁇ and Q g23 we can therefore express any of our filters in terms of the four quantities Q g ⁇ , Q c , Q g ⁇ and Q g23 using:
• ⁇ 2.5 shows how all difference filters in the vicinity of the step's leading edge can be expressed as linear equations in the four amplitudes Q g ⁇ , Q c , Q g l 3 an d Q g 23 (non-difference filters will also require Bo). Therefore we must make four (or five) independent filter measurements to solve for Q g ⁇ . While a wide variety of filters could be used, certain sets will be better conditioned than others and will also require less measurement precision to accommodate step risetime variations. Research and experimentation have shown the following set to function well: 1) the trapezoidal "energy” filter of risetime m from Eqn. 6; 2) the triangular "risetime probe” filter of Eqn.
• ⁇ ⁇ Q ⁇ (l- ⁇ )A, ,m + ⁇ A 2 Q, d ⁇ , m +FA 2 jn + Q 13 [ ⁇ (l,m,-m-g)]
• the unknown parameters are of three types: 1) (Pi) the unknown charge Q g ⁇ (the area of the input impulse in the general case); 2) (P 2 ) charges describing the step's finite arrival time (Q g ) and the residual charges in the X] and X 2 decay modes (Q 1 3 and Q23) from previous events; and 3) (P3) a set of fixed parameters ⁇ xi, X 2 , ⁇ , m and g ⁇ which describe the preamplifier's (or N-IP device's) transfer function and the applied filters.
• Eqn. 23c has the advertized form: a weighted sum of the four filter outputs.
• the weighting coefficients Jy - 1 are computed only once for a particular set of filters and P3 parameters ⁇ ⁇ , X 2 , ⁇ , m and g ⁇ and then multiplied by the four filter outputs ⁇ ⁇ , ⁇ g /r ⁇ , 0 43 and ⁇ 2 i to obtain the total pulse charge Q g ⁇ (and hence the energy of the absorbed ⁇ -ray) for each captured event.
• the matrix can be inverted using least squares methods to obtain Eqn. 23b.
• ⁇ g is typically of order 0.25 ⁇ ⁇ , so the ⁇ g term is typically less than 2% of Q g ⁇ . In spite of its small size, however, ⁇ g carries the burden of the ballistic deficit correction, since it is the only filter that probes the step's risetime directly.
• Table 1 Modeled charge Q g ⁇ for 5 filters in the presence of varying risetimes and X 2 amplitudes for the case of ⁇ equals 0.02.
• the outputs of single filters can be captured multiple times. Filter outputs can be captured as they appear from the gate array or can be delayed for convenience. We will show several examples in ⁇ 6. Which method is best will depend upon implementation details and will vary from case to case. We therefore intend the phrase "cMOS" (for "correlated multiple output sample”) to cover the multiplicity of possibilities for capturing, in a real-time implementation, filter values whose time relationships are correct for the set of J "1 weighting coefficients that will be applied to them to recover the input charge from the detected event.
• cMOS for "correlated multiple output sample
• the cMOS capture is made in response to the detection of a step in the preamplifier's output signal, with the intention of using it to determine the charge deposited in the detector (in the general case the impulse area) and hence the gamma- ray's energy, we will often refer to it as an "energy cMOS capture” (or “charge cMOS capture” or “area cMOS capture” as appropriate).
• Fig. 5A shows the filter regions relative to the preamplifier output step 72.
• ⁇ ⁇ 74, 0 43 76, ⁇ 2 i 77, and ⁇ g 79 were all described earlier.
• ⁇ t 81 is a fast channel timing filter, as described by WARBURTON-1997, which is used to detect step-like signals in the preamplifier's output.
• the timing filter's output triggers a digital discriminator when it is located approximately as shown with respect to the leading edge of the signal step 72.
• Fig. 5B shows the second step: correcting for propagation delays. We note that these delays may exceed a microsecond in long time constant filters and typically increase with filter length.
• Fig. 6A shows a preferred implementation of Eqn. 24c.
• the digital processor 90 comprises an ADC 92, a real-time digital processing unit (RT-DPU) 93, and a digital signal processor (DSP) 95.
• the RT-DPU processes data at the ADC output rate while the DSP processes data at the event rate (impulse signal rate).
• the RT-DPU produces values ⁇ ⁇ , 0 43 , ⁇ 2 i, and ⁇ g , while the DSP multiplies them by the coefficients J " 1 to obtain Q g ⁇ .
• the RT-DPU 93 also has two parts, a fast channel 97 and a number of slow channels 98.
• the fast channel contains the fast timing filter ⁇ t 100, a digital discriminator 102, some pileup test and timer logic 103, a clock 104, and an output register 105.
• Each slow channel comprises a triangular or trapezoidal digital filter and an output register with either a digital delay line (if Eqn. 29 is negative) or a timer (if Eqn. 29 is positive). Notice that ⁇ 4 3 and ⁇ 2 i, both being of length m/2, are being implemented using a single triangular filter 0 4 3 21 107. In operation, ⁇ t 100 processes ADC 92 data until a step-like signal arrives.
• Discriminator 102 detects this step and signals the pileup inspector 103, which strobes a trigger line 106 and initiates pileup inspection. If the step's arrival time is important, the output of clock 104 can be captured to output register 105 by the same strobe signal 106. Filter 0 4 3 21 's 107 output, delayed by t 2 i using 21-delay 108 if required by Eqn. 29 causality, is captured immediately in the 21 -register 109 by this trigger strobe, which also starts the 43-timer 110, ⁇ -timer 111, and g-timer 112 to time t 43 , t ⁇ and t g .
• the g-timer 112 Since t g is shortest, the g-timer 112 times out first, capturing filter ⁇ g 's 115 output in the g-register 116. Similarly, the 43-timer 110 and ⁇ -timer 111 time out at . 4 3 and t ⁇ to capture filter 0 4 32 1 107 and ⁇ ⁇ 117 outputs in the 43-register 118 and ⁇ -register 119. If this step is not piled up, then all four filter values are ready to be read into the DSP 95 via data bus 121.
• the pileup inspector can be implemented as taught by WARBURTON-1999 relative to the length of the ⁇ ⁇ filter and will not be discussed further.
• the invention method does specifically require that the number of filters equal the number of filter values to be captured.
• the number of filters equal the number of filter values to be captured.
• Fig. 6B shows an implementation of Eqn. 27 wherein the three filter values are captured just as the value emerges from the slowest ( ⁇ ⁇ ) filter.
• the primary physical difference between this implementation and that of Fig. 6A is that the timers 108, 109, and 110 have been eliminated and a second delay (g-delay 125) has been added to compensate for the differences between t ⁇ and t habit and t ⁇ 2 from Eqn. 29. All the remaining parts are the same and carry the same reference numbers as is Fig. 6A. Notice that the trigger line 106 now connects directly to the output registers, rather than through timers as before. For this topology, the functional operation of the pileup test and timer #1 103 is essentially identical to that presented by WARBURTON-1999.
• Fig. 7 shows an analog version of Fig. 6A.
• the topologies are identical up to the point where sample and hold circuits replace digital registers to capture the filter values, so the operation of the circuit up to this point will be clear to one skilled in the art, given the teaching presented herein.
• the derivation of the J matrix will have to proceed using weighting functions appropriate for the analog filters used.
• analog multipliers 160, etc.
• an analog adder 185 are used to implement the J" 1 coefficients and addition of Eqn. 24C.
• the multiply-and-add function is just an op-amp circuit with appropriate resistor inputs to its summing node. If the pileup tester 143 deems the value good, the gate and shape circuit 145 passes out the adder 185 output in a form suitable for multichannel analysis.
• Fig. 8 shows one such implementation 190.
• the topology is nearly identical to that of Fig. 6A. The major differences are: 1) that the fast channel 191 is implemented in analog circuitry identical to that of Fig. 7 (although the digital circuit of Fig. 6A could as easily be used); and 2) that, in the slow channel section 192, the digital filters 0 4321 10 , ⁇ ⁇ 117, and ⁇ g 115 have been replaced by analog filters 0 4321 193, ⁇ ⁇ 194, and ⁇ g 195 followed by ADCs 196, 197, and 198.
• the time behavior of this circuit is the same as was described for the asynchronous digital circuit in Fig. 6A. 7.
• the Eqn. 27 filter will have approximately 2.7 times as much electronic noise as a simple trapezoidal filter.
• the result for the Eqn. 24c filter is similar.
• a 4 ⁇ s filter whose electronic noise can be as low as 150 eV, this effect is significant at energies like 100 keV (Fano noise 415 eV) but not at 1 MeV (Fano noise 1,300 eV).
• the problem will worsen at higher energies. We therefore consider how to obtain the benefits of correcting for both ballistic deficit and pole-zero errors without paying the additional filter noise price.
• Classes 1 and 2 (Pi, P 2 ), as before, which include Q g ⁇ , Q c , and Q13; Class 3 (P3), Q 2 3 and Bo, which describe the preamplifier's "non-ideal" behavior, Q23 being the amplitude of its second pole's response to any previous steps and Bo being the DC offset; and Class 4 (P4): all the remaining fixed parameters (e.g., ⁇ ⁇ , ⁇ , ⁇ , m, g) which describe both the filters' and the preamplifier's transfer functions.
• Eqn. 35A is therefore a transform function (the first bracketed term) between the Eqn. 34 cMOS filter values ⁇ ⁇ + , ⁇ ⁇ ., and ⁇ g- and the desired detector charge Q g ⁇ , minus an error term L L s T + B QJ A m ⁇ ⁇ - s tne transform's response to the non-ideal (NI) preamplifier terms Q 2 3 and Bo- Using Eqn.
• NI non-ideal
• Eqn. 38 has two significant problems: 1) increased noise, due to the noise in the single baseline measurement, which is the same size as in the measurement itself and degrades resolution by sqrt(2); and 2) it increases deadtime by at least a factor of two if the two measurements are independent and so separated by at least 2m+g in time. It is therefore useful to be able to make multiple, independent measurements of Bo and Q 23 and average them in order to reduce their variance. We present a method for doing so below.
• the noise contribution of the correction term in Eqn. 42 can be made much smaller than in the single baseline correction procedure of ⁇ 8.2. Since the weighting function of ⁇ g- is small compared to unity, the measurement noise in Eqn. 42 will then be determined primarily by ⁇ ⁇ + and ⁇ ⁇ _, and will be approximately the same as for a trapezoidal filter of the same peaking time and about a factor of sqrt(2) better than by using Eqn. 38.
• Bo (1 measurements can be averaged, as noted above, to obtain ⁇ Bo>, a low variance estimation of Bo, for use in Eqn. 35a. From Eqn. 45, it is clear that the longer the time interval ⁇ t, the more accurate the measurement of Bo will be, since both the numerator and denominator are small differences of large numbers. In any case, enough values Bo, ⁇ can be averaged so that errors in ⁇ Bo> do not contribute substantially to the error in Q g ⁇ .
• the P 4 parameter ⁇ needs to be precisely known and stable over time. Else both the extrapolations of Q 13 and increments in Q 2 3 will incorporate systematic errors which will propagate into the Q g ⁇ calculations.
• the proposed Q 23 baseline measurements offer a method to monitor ⁇ and either refine its value or track it in time.
• AALSETH-1998 "Using pulse shape discrimination to sort individual energy deposition events in a germanium crystal", C.E. Aalseth, F.T. Avignone III, R.L. Brodzinski, H.S.
• KUMAZAWA-1988 U.S. Patent No. 4,727,256, issued Feb. 23, 1988 to Y. Kumazawa for "Semiconductor radiation detector”.
• MILLER-1994 U.S. Patent No. 5,347,129, issued Sept. 13, 1994 to W.H. Miller and R.R.
• TAKAHASHI-1994 "A Multiparametric Waveform Analysis of Ge Detector Signal Based on Fast ADC Digitizing Technique", by H. Takahashi, S. Kinjoh, J.

Landscapes

• Physics & Mathematics (AREA)
• General Physics & Mathematics (AREA)
• Measurement Of Current Or Voltage (AREA)
• Measurement Of Radiation (AREA)

Priority Applications (3)

Applications Claiming Priority (2)

Publications (1)

Family

ID=22537001

Family Applications (1)

Country Status (5)

Cited By (2)

Families Citing this family (9)

Citations (10)

Family Cites Families (13)

• 2000
  • 2000-08-21 US US09/643,705 patent/US6587814B1/en not_active Expired - Lifetime
  • 2000-08-24 WO PCT/US2000/023333 patent/WO2001017103A1/en not_active Ceased
  • 2000-08-24 EP EP00959390A patent/EP1206832A4/en not_active Withdrawn
  • 2000-08-24 JP JP2001520938A patent/JP2003508764A/ja active Pending
  • 2000-09-24 AU AU70724/00A patent/AU7072400A/en not_active Abandoned

Patent Citations (10)

Non-Patent Citations (1)

Also Published As

Similar Documents

Legal Events