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2008 IEEE Nuclear Science Symposium Conference Record M08-7 Pulse Width Modulation: a Novel Readout Scheme for High Energy Photon Detection Peter D. Olcott, Student Member, IEEE, and Craig S. Levin, Member, IEEE Abstract-In standard PET scintillation detection, the energy, timing, and location of the incoming photon are recovered using analog signal processing techniques. The energy and location information are processed using an analog-to-digital (ADC) converter that samples an analog value that is proportional to the integral of the charge created by the scintillation event. We propose to change the paradigm and modulate the width (rather than amplitude) of a digital pulse to be proportional to the integral of the charge created. The analog value of the outgoing digital pulses is recovered by using a time-to-digital converter (TDC) in the back-end electronics, without the need for an ADC. Note that in this new scenario the same TDC used to record the time of the event is used to recover the amplitude. The main performance parameter that must be optimized is the dynamic range versus the dead-time of the front-end detector. The goal is an 8-bit dynamic range for this pulse-width modulation (PWM) scheme, which is adequate for high resolution PET systems based on semiconductor detectors such as avalanche photodiodes (APD) or cadmium zinc telluride (CZT). A novel circuit has been designed, fabricated, and tested for the proposed PWM readout scheme. This circuit is different than previously developed time over threshold pulse width modulation circuits used in high energy physics. PWM techniques simplify the routing to the back end electronics without degrading the performance of the system. A readout architecture based on PWM processes digital rather than analog pulses, which can be easily multiplexed, enabling one to achieve very high channel density required for ultra-high resolution, 3-D positioning PET detector systems. • ANALOG BUS • FRONT-END ASIC • DIGITAL BUS • FPGA LOGIC (a) Light multiplexing is used to reduce the number of readout channels in a standard PET block detector readout. The most common architecture for the electronic readout is a low channel count (4-channel) ASIC, and four ADCs read each analog channel. • ANALOG BUS • FRONT-END ASIC • DIGITAL BUS • FPGA LOGIC (b) A multi-channel readout ASIC (32 or 64 channels) combined with triggering, an analog memory, and a single ADC reduce the number of channels to a reasonable level, but suffers from a high density analog bus. Index Terms-PET, Semiconductor detectors, PWM, Pulse width modulation, Time over threshold, Wilkinson ADC I. INTRODUCTION I N standard high energy photon (e.g. gamma ray or annihilation photon) detectors, information from individual interactions are recorded, such as the time of the event, the energy of the event, and the location of the event. These parameters are determined through certain processing algorithms applied to the analog signals that the detector generates. In evaluating the best architecture to implement very high channel count PET data acquisition systems, pulse width modulation (PWM) has significant advantages over previous generations of readout architectures (see Fig. 1). PWM architectures eliminate ADCs and dense analog buses. We are studying a PWM scheme • ANALOG BUS • FRONT-END ASIC • FPGA LOGIC ~ DIGITAL BUS (c) A high channel count digital architecture that consists of a low channel count front-end ASIC pulse width modulator and a high density digital bus. No ADCs are needed to digitize amplitude information. Fig. 1: Very high resolution PET systems [1], [2] require new data acquisition architectures to accommodate the large increase in the number of readout channels. The current acquisition systems (a) scale poorly in the number of ADCs required as the channel count increases. High analog channel count ASICs (b) have problems with dense analog busses. A new architecture (c) using pulse width modulation (PWM) eliminates the ADC and enables the move to purely digital high density back ends. Manuscript received November 14,2008. This work is supported in part by NIH research grants NIH ROI CA119056, NIH R33 EB003283, and NIH ROI CAI20474), and Society of Nuclear Medicine Molecular Imaging Predoctoral Fellowship. P. D. Olcott is a graduate student in the Bio-Engineering Department at Stanford University, 300 Pasteur Drive, Always Building Room Mool, Stanford, CA 94305, email: ([email protected]) Dr. Craig Levin is with the Department of Radiology and Molecular. . . Imaging Program, Stanford University, 300 Pasteur Drive, Always Building (see FIg. 2) that encodes the tIme, energy, and locatIon of R§~~~2U~mf~r087$'2~tio~~oi88~·edu). 453Bach high energy photon interaction in a detector using the Authorized licensed use limited to: Stanford University. Downloaded on May 20,2010 at 21:54:43 UTC from IEEE Xplore. Restrictions apply. High Energy Photon Detector Charge Charge Sensitive Preamplifier Voltage Peak Detector Start Dela Voltage Pulse Width Latch Timing Discriminator SET Start Timing Input Signal Amplitude Delay Circuit Integrated Charge Signal Start Constant Delay Circuit Rising Edge Peak Amplitude Sense Dependent 1~1~1 I I I I I I I I I I I I I I I I I I I I I I II Fig. 2: Pulse width modulation circuit converts the amplified and filtered electronic charge signal from the detector into .a digital signal. The timing is encoded as the first rising edge, and each edge transition encodes a unique analog value. In thIS current implementation, one energy and one time value is encoded into a single digital signal. different arrival times of various edges of a digital signal, rather than in the amplitude of an analog signal. This PWM scheme marries the fast CFD timing needed for PET and the time counter principles behind the Wilkinson ADC conversion technique for encoding amplitude. Because it is relatively simple to implement a very high degree of multiplexing using digital pulses, the proposed PWM readout architecture can potentially readout more channels than a high density analog readout architecture without using ADCs. With the advent of very high channel count FPGAs synthesized into very high performance TDCs [3], [4], the diginal back-end readout of PWM architectures, even with thousands of readout channels, can be easily realized using off the shelf components and simple high density digital buses. A. Time over Threshold II. PULSE WIDTH MODULATION CIRCUIT In this work, we tried to improve two aspects of these previous implementations of TOT for PET (see Fig. 2). In the first modification, a CFD encodes the arrival time and reduces time walk. Secondly, a peak detector captures the maximum signal from a Gaussian shaped signal and generates a ramp function that linearly decays to zero. By splitting the signal into two paths, the SNR of coincidence timing can be optimized at the same time as the SNR of the energy signal. One of the TOT ASICs developed in the past [11] either uses little or no shaping to attain the best timing performance, but this severely degraded the SNR of the energy channel. The second TOT ASIC [12] uses Gaussian shaping with good SNR for energy performance, but this slow shaping significantly degraded timing performance. A. Pulse width modulation and CFD timing In standard PET data acquisition, timing is performed by a PWM circuits utilizing time-over-threshold (TOT) were constant fraction discriminator (CFD) to reduce the amplitude some of the first methods to digitize amplitude information dependent time walk. In the proposed PWM circuit design, of nuclear decay and drift chambers [5], [6]. By setting a the scintillation pulse is driven into a CFD that sets a latch threshold voltage above zero, an amplitude dependent pulse started at the rising edge. The scintillation signal may have width can be generated from a Gaussian, or other CR-RC type some small amount of fast shaping to optimize the timing shaped pulse. The noise of time-over-threshold depends on the resolution. In terms of time pickoff, the proposed design is shaping circuits used and strongly depends on the inherit non- identical to and will have the same performance as standard linearity of the width versus amplitude dependence. [7] Since PET electronics. Thus, this paper will only focus on studying the decay of a Gaussian-shaped pulse falls off exponentially the proposed PWM scheme energy resolution performance. with the time 2 , it does not provide the good delay linearity needed for a robust PWM scheme. The data acquisition architectures of TOT are used in very high channel count physics B. Peak detection and linear ramp experiments using silicon vertex trackers and calorimeters[8], The pulse width modulation circuit can be seen as an [9], [10]. New high resolution PET systems have similar high ADC operating on the energy portion of the scintillation channel count needs as these high energy physics experiments. pulse. The scintillation signal is first shaped by a Gaussian Recently, two groups have developed TOT ASICs for PET shaper set with a time constant to maximize SNR.. B.eca~se applications [11], [12], but their choice of pulse shaping leads the Gaussian shaper is a linear transform of the SCIntIllatIon to deficiencies, as explained in the next section. 453~ignal, the time between the start of the pulse and the peak Authorized licensed use limited to: Stanford University. Downloaded on May 20,2010 at 21:54:43 UTC from IEEE Xplore. Restrictions apply. ~-~-------------------------_. ~------2--------:.iI:lI--1 (j~;MP ---(JPWM . Fig. 4: An input scintillation signal (black) enters a peak-detector with a linear ramp discharge (green). The blue dotted line represents the maximum of the signal and is proportional to maximum value of a Gaussian shaped signal. The red dotted line represents the threshold for firing the trigger. R'3 ~----......--vvv------1 50 UI PI • ) y ~ 50 C2 Cl D2 lOpF Rl loopF lOOk R4 lOOk associated electronics to fire a sample-and-hold precisely at the peak of the signal. The peak detector has a capacitor to store the value. With a simple resistor, an approximately linear discharge current can be generated that decays based on a RC product. The peak detector will begin to decay as soon as the output of the Gaussian shaper falls below the value of the storage capacitor. On the other hand, a sample-and-hold circuit would not have this limitation and could begin decaying immedately after sampling the value. Therefore, for an ASIC implementation, a sample-and-hold circuit would be preferred over a peak detector because the ramp could decay faster than the falling edge of the Gaussian shaper, which would improve count rate performance. c. Fig. 3: Key to the PWM circuitry is a high speed analog peak detector with RC delay circuit. The high speed Shockley diodes D1 and D2 are matched. An offset voltage of the Shockley diodes is required due to the forward drop in the feedback of the opamp. The capacitor C1 holds the peak voltage, and when the input drops below the peak, the capacitor discharges with a time constant of Rl *Cl. The terminal of Rl is tied to VEE to improve linearity. The resistors and capacitors can be changed to provide better dynamic range and less quantization noise with a corresponding tradeoff in pile-up at high event rates. High speed comparator The output of the PWM with a linear ramp discharge is fed into a high speed comparactor with an adjustable threshold. The output of the comparator fires the reset of the latch. The final digital signal has the rising edge encoding the arrival time of the scintillation pulse and the falling edge encoding the width of the pulse. Other information can be tacked onto the end of the pulse such as channel id [12], but these can come with a large penalty to the maximum count rate. III. NOISE ANALYSIS The PWM circuit can be analyzed to understand its impact on energy resolution for a scintillation detector. Other figures of merit, including spatial resolution, can be easily derived from this framework. First, the variance of the PWM in time must be derived: of the Gaussian shaper will be constant. This is exploited in current PET detector readout electronics designs by firing a sample and hold to sample at this peak. To capture the peak of the Gaussian shaper, we implemented a very fast peak detector with a linear ramp discharge (see Fig. 3). For discrete implementations, a peak detector is simpler than th~532 Authorized licensed use limited to: Stanford University. Downloaded on May 20,2010 at 21:54:43 UTC from IEEE Xplore. Restrictions apply. (1) TABLE I: Definitions av/at a~i a~t Slope of discharge Variance of peak input voltage signal Variance of comparator voltage threshold O"~CAP Variance of voltage on capacitor a&PD Variance of CFD start timing a'bOMP Variance of Comparator stop timing a~WM Variance of pulse width modulation timing a}DC Variance of quantization error of time to digital converter max(~) VEE RC Maximum voltage of input signal Negative Supply Resistor and capacitor used to select slope The slope of the discharge is related to the value of the resistor Rl and capacitor Cl (see Fig. 3), and the negative supply voltage. The discharge is made more linear by connecting the terminal of the resistor to VEE. The slope is: 8V/8t ~ ~ Vi - VEE RC VEE - - because Vi RC « VEE (2) The variance of the PWM can be converted into energy resolution by optimizing the voltage headroom of the circuits (max(Vi) ~ VEE/2, and max(Vi) ~ scaled so that it accommodates the 5llkeV photopeak pulse height). (J"PWM max(Vi)/8V/8t (3) 2 2 (J"CFD 2 + 2(J"TDC 2 + (J"COMP + RC (J"2 VCAP + (J"2 + (J"2 t Vi V max(Vi) There is a clear tradeoff in choosing the RC constant. The longer the RC constant, the better the energy resolution (ie better SNR), but this will come with a penalty in deadtime. The dead-time of this PWM is different from ADC based converters. The dead-time of this PWM circuit is the same as that for a Wilkinson ADC, because the time to convert the amplitude is linearly related to the amplitude. For Wilkinson ADC or PWM circuits [14], the non-Poisson nature of the dead-time has been derived. The voltage noise terms of equation (3) should be made small relative to the input amplitude Vi. The noise Vca ; is simply the k;{ noise of the storage capacitor. Usually, the noise of the front end detector is much larger than the noise of these simple elements. IV. MATERIALS AND METHODS A discrete PWM test board (Figure 5) was fabricated and evaluated for energy resolution performance versus a standard peak-sampled ADC (see Fig 5). The PWM circuit comprises a peak-detector with a linear ramp discharge (see Fig. 3) and a high speed LTl171 comparator. The R was set at 10k and the C at 100pF giving a slope of 50 ::s. Linearity of the test board was tested by driving a pulser signal into the input preamplifier and measuring the output voltage after Fig. 5: We have developed a discrete pulse width modulation test board that accepts signals from scintillation detectors. Front-end programmable trans-impedance amplifiers (inside light blue box) convert high speed signals for driving an external CFD. Peak detector circuits (magenta box) produce a linear ramp from a Gaussian shaped signal. A high speed low noise comparator (LTll7l) (yellow box) compares the peak-detector output to a programmable threshold. TAC. For our tests the TAC followed by an ADC will mimic the TDC that is intended to be used in this PWM scheme (see Figure 2). After pulser linearity tests, a 10 !-Lei 22 N a source irradiated a 3 mm x 3 mm x 20 mm LYSO crystal connected to a single 3 mm x 3 mm solid state photomultipler (SSPM) pixel of the SENSL 4x4 SPMArray 3035G16. The test board contained a fast trans-impedance amplifier (500 Ohms) to amplify and invert the input signal for the input to an Ortec CFD-935. A CFD is key to the fast timing for the proposed PWM scheme (see Fig. 2). The output of the CFD was the start for the Ortec 567 TAC/SAC. For the energy channel, the signal was shaped by a Cremat-200 lOOns Gaussian shaping amplifier. The shaped signal was input to both the discrete PWM circuit and to a Ortec 427A delay amplifier. The latter channel enables comparison to the standard analog modulated processing chain. After level shifting to negative NIM voltage standard, the PWM signal was sent to the stop of the Ortec 567 TAC/SCA. The output of the delay amplifier and the TAC went to a NI-lll0 peak-sampling ADC. The Ortec 567 TAC/SCA is being used to convert the pulse width back into an amplitude for digitization to mimic the function of the TDC and generate the PWM equivalent of a pulse height spectrum. The 22 N a energy spectrum was acquired for both the standard analog-modulation, peak-sensing ADC chain and the PWM processing chain. V. RESULTS The linearity of the PWM cir~uit (see Fig. 6) ~ts very closely to a seco.nd order polynomIal ?ve~ the dynamIC r~nge of the PWM. ThIS second orde: be~avlor IS solely determl~ed Y the discharge of the capacItor In the peak-detector uSIng ls3S Authorized licensed use limited to: Stanford University. Downloaded on May 20,2010 at 21:54:43 UTC from IEEE Xplore. Restrictions apply. Pulser Linearity of PWM circuit 50 100 Input Pulse Amplitude (mV) 150 200 Fig. 6: The PWM suffers from some non-linearity because the RC discharge circuit is not a pure current source. Howver, the linearity is significantly improved over the previous TOT designs [9,10] and is sufficient for almost all scintillation applications for PET. Te~, M Pos: 216.Ons DISPLAY • Persist • Format 11 " CH1 1.00V CH2 '1.00\1 M100M "" IJse rnultff)urpo$t, knob ro adjust (:ontrasf > a resistor with a large voltage offset (see Fig. 3). A scope capture of the PWM test board output pulses (see Fig. 7) shows the working operation of the circuits for SSPM-based scintillation detection using 22 N a source irradiation. The dead-time for this circuit is approximately 600 ns for a 1.27 MeV photon pulse. For a 511 keV photon pulse, the dead-time would approximately 400 ns. The dead-time for just the 100 ns Gaussian shaper is approximately 300 ns or three times the shaping constant. Therefore, this discrete PWM circuit implementation does not have a significant dead-time penalty. A wide dynamic range (for PET) scintillation signal (0-1.27 MeV) was digitized for the PWM circuit versus the standard analog-modulated digitization (see Fig. 8). The correlation between the ADC and PWM is 1.0 with a 1.2% standard deviation. This PWM circuit is not fully able to linearize the low amplitude pulses from the lOOns Gaussian shaper (see Fig. 7 and Fig. 8). An RC constant with a larger time constant relative to the shaper constant can be used to remove this small amplitude non-linearity, but this will increase deadtime. However, we do not expect this small low-amplitude non-linearity to be a significant detriment to the method. VI. DISCUSSION The circuit evaluated in this paper is a very simple discrete prototype that was used as a proof of concept. There are many better, but more complicated, linear ramp circuits that could easily be implemented in ASICs or more discrete components could have been used to achieve much better linearity. The peak-detector with resistive discharge could easily be replaced by a sample-and-hold with current source discharge architecture in an ASIC design. This would remove the non-linearity for small signals that the peak-detection method may suffer from with small RC constants used to improve dead-time performance. Even in its current form, our results (Figs. 6 and 8) suggest this discrete circuit would perform in well in PET scintillation applications. This circuit can be used to capture the signals from a light sharing block detector[reference] or 3D positioning sensitive detectors [references to our workLevin 2008 and Pratx 2008] because of the improved linearity and optimal SNR as compared to previous TOT designs for PET [9,10]. The timing CFD of the front end may also be replaced with a fast leading edge discriminator. The amplitude information may be used to remove the time walk. However, the same comparator that is used for timing should not also be used for the energy signal, otherwise a poor tradeoff between timing and energy SNR will result. VII. CONCLUSION A proof of concept, discrete pulse width modulation circuit for PET has been analyzed and built. This PWM circuit provided a simple method to study the trade off of dynamic range and linearity versus dead-time by adjusting the slope of a ramp reset circuit. We achieved a dynamic range, linearity and SNR with a very simple circuit that can meet performance parameters needed in PET data acquisition designs. The proposed scheme preserves the low jitter of CFD based triggering while deriving a pulse width from an optimally shaped signal 453lchieving a high SNR energy signal. Fig. 7: Scope capture of PWM evaluation circuit with the input to the CFD (blue), output of the PWM (magenta) and the logic output of the PWM that represents the integrated charge for each analog pulse (yellow). It takes approximately 600 ns to digitize the max signal amplitude for the 1.27 MeV line of the 22 N a source using a resistor of 10k and a capacitor of 100pF. Authorized licensed use limited to: Stanford University. Downloaded on May 20,2010 at 21:54:43 UTC from IEEE Xplore. Restrictions apply. REFERENCES Correlation between PWM and ADC .. 't' • ~1' •• i"" • 2.5 .... ~:~ . ~. 2 0.5 0.5 1.5 ADC 2.5 2 (a) Histogram of the ADC sampled pulse height of the standard analogmodulated processing chain (x-axis) versus the PWM processing chain y-axis for 22 N a irradiation of a LYSO-SSPM scintillation detector Na-22 Energy Spectrum 3000 -ADC -PWM 2500 2000 II) E ::J 0 U 1500 1000 500 0 a 0.5 1 1.5 Pulse height (V) 2.5 (b) Energy spectra of the ADC sampled pulse height of the standard analogmodulated processing chain versus the PWM processing chain for 22 N a irradiation of a LYSO-SSPM scintillation detector [1] Levin, C.S.; Foudray, A.M.K.; Olcott, P.O.; Habte, E, "Investigation of position sensitive avalanche photodiodes for a new high-resolution PET detector design," Nuclear Science, IEEE Transactions on , vol.5!, no.3, pp. 805-810, June 2004 [2] Albuquerque, E.; Bento, P.; Leong, C.; Goncalves, E; Nobre, J.; Rego, J.; Relvas, P.; Lousa, P.; Rodrigues, P.; Teixeira, I.C.; Teixeira, J.P.; Silva, L.; Silva, M.M.; Trindade, A.; Varela, J., "The Clear-PEM Electronics System," Nuclear Science, IEEE Transactions on , vol.53, no.5, pp.27042711, Oct. 2006 [3] Fries, M.D.; Williams, J.1., "High-precision TDC in an FPGA using a 192 MHz quadrature clock," Nuclear Science Symposium Conference Record, 2002 IEEE, vol.l, no., pp. 580-584 vol.l, 10-16 Nov. 2002 [4] Jinyuan Wu; Zonghan Shi; Wang, I.Y., "Firmware-only implementation of time-to-digital converter (TDC) in field-programmable gate array (FPGA)," Nuclear Science Symposium Conference Record, 2003 IEEE, vol.l, no., [5] Verweij, H., "Electronics for Drift Chambers," Nuclear Science, IEEE Transactions on , vol.22, no.!, pp.437-440, Feb. 1975 [6] Kephart, R., Kerns, C., "'E-537 MWPC amplifier". 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IEEE , vol.6, no., pp.4612-4614, Oct. 26 2007-Nov. 3 2007 [13] Pratte, J.-E; Junnarkar, S.; Deptuch, G.; Fried, J.; O'Connor, P.; Radeka, V.; Vaska, P.; Woody, C.; Schlyer, D.; Stoll, S.; Maramraju, S.H.; Krishnamoorthy, S.; Lecomte, R.; Fontaine, R., ''The RatCAP front-end ASIC," Nuclear Science Symposium Conference Record, 2007. NSS '07. IEEE, vol.l, no., pp.l9-25, Oct. 26 2007-Nov. 3 2007 [14] Pomme. S., and Uyttenhove J., "Statistical precision of high-rate spectrometry with a Wilkinson ADC", Journal of Radioanalytical and Nuclear Chemistry, Vol. 248, No.2 (2001) 263-266 Fig. 8: (a) The PWM energy 22 N a energy spectra results correlated very well with the analog-modulated scheme (b). The energy resolution of the two conversions schemes is identical at 19.3 + / - 0.4% FWHM at 511 keY. There is some non-linearity for small amplitude signals from the PWM circuit that can be seen in (a) and (b). 4535 Authorized licensed use limited to: Stanford University. Downloaded on May 20,2010 at 21:54:43 UTC from IEEE Xplore. Restrictions apply.