2.1 Signal processing flow

A readout method is proposed to acquire energy and positioning information of incident γ photons. The concept of this method is shown in Fig.1. The incident γ photons deposit energy in the LYSO crystal to create fluoresce immediately, which is converted to photo-electrons on  photocathode of the H8500 PSPMT to, generate current signals.

Fig. 1Full-screen View

The concept of QTC-based readout for PSPMT.

The current signals from the PSPMT are processed by the charge division module (CDM) ^[22], which works to reduce the number of readout channels from sixty-four to I_A, I_B, I_C, and I_D, which are fed into the summing module (SM) (Fig.2a) designed to convert input current signals to voltage and reduce the number of output channels from four to V_X, V_Y and V_E. The V_X, V_Y and V_E are fed into the charge-to-time conversion module (QTCM) (Fig. 2b) composed of charge-to-time circuits and high speed comparators. The output digital pulses of T_X, T_Y and T_E (LVTTL levels) are finally generated with pulse width proportional to the integral of the input signal. The pulse width is measured using a TDC in the FPGA, and the data are transmitted to the computer via a gigabit network.

Fig. 2.Full-screen View

The circuits of SM(a) and QTCM (b).

2.2 Principle and circuit design

The SM circuit in Fig.2(a) is composed of current-sensitive preamplifiers, and inverting summing circuits with their gain being set to 1. So we can obtain Eqs.(1-3):

The QTCM circuit in Fig. 2(b) is composed of charge-to-time conversion circuits and high speed discriminators. The charge-to-time conversion circuit is designed according to the original QTC principle of the TOF detectors in BESIII. ^[19] Some appropriate improvement is made for the application in position sensitive detector. The comparator (ADCMP602) output digital pulse (LVTTL) can be directly fed into FPGA without any level translation.

For the signal flow of V_E ~ V_TE ~ T_E, the negative input signal (V_E) charges C_T via R_T and the constant source I_T also discharges C_T. The clamping diode (D) provides a DC route for charge-to-time conversion in order to clamp the output V_TE to the baseline (V_B) of about −300 mV at V_E =0. The charge Q_in fed into C_T is proportional to the integral of the input signal (V_E). So the discharge time interval T_E can be described as:

where a and b are coefficients associated with I_T, R_T, V_B and the threshold voltage of comparator V_REF. Note that the output V_TE will maintain V_B and T_E is zero, if charging current I_E is less than the discharge current I_T. So there is a tradeoff in pile-up at high event rates and the dynamic range. Specifically, the discharge current should be as small as possible for wide dynamic range which also lead to pile-up in high event rates.

Assuming that Q_A, Q_B, Q_C and Q_D are integrals of the current signals I_A, I_B, I_C and I_D, we have:

where Q_E is the total charge collected by PSPMT, which is proportional to energy of the incident γ photons (E_γ). Combining Eqs. (1), (4) and (5), we can obtain:

where A and B are coefficients associated with the SM and QTCM, and Q_E can represent the energy of incident γ photons. Similarly, we can obtain Eqs.(7) and (8):

So the γ photon position can be determined by Eqs.(9) and (10):

The outputs (TE, TX and TY) are received directly by the FPGA and measured by the TDC (64ps resolution) in the FPGA. The data TE, TX and TY are transmitted to the computer through the network and the energy and position information of the γ photons can be obtained using Eqs. (6), (9) and (10).

The experimental circuit was designed and tested with the H8500 PSPMT. Fig.3(a) is a photo of the circuit, with Parts 1, 2 and 3 being the CDM, SM and QTCM, respectively; while Fig.3(b) shows the VE, VTE and TE signals generated by the experiment circuit (captured by Tektronix DPO 3054 oscilloscope).

Fig.3.Full-screen View

The experimental circuit (a) and the signals of V_E, V_TE and T_E captured by oscilloscope (b). 1, CDM; 2, SM; 3, QTCM.

3.1 Linearity test of QTCM

In the linearity test of QTCM, pulses with adjustable amplitude (200 mV per step) from a function generator (AFG3252) were sent to the input stage of QTCM with the discharge current of 100 μA. A group of digital pulses was generated, and their time widths were obtained using TDC. As shown in Fig.5, the QTCM has a large dynamic range from 300 mV to 4 V, with the maximum time width of about 9 μs, the fitting coefficient of R² = 0.9997, and the integrated nonlinearity of 1.31%.

Fig.5.Full-screen View

Linear fitting of the test results.

3.2 Energy spectrum test

The H8500 PSPMT coupled with a single 3.5 mm ×3.5 mm ×20 mm LYSO crystal was used to obtain the energy spectrum with ¹³⁷Cs and ²²Na sources. The high voltage source was −750V and the discharge current was 100 μA. Under the same experimental conditions, we obtained the energy spectrum by using the commercial 12-bit 40-MHz ADC (ADS5282 from TI) with the signal V_E being fed into the input of the ADC. Fig.6 compares the spectra obtained with the ADC and the QTC circuit, after appropriate scaling.

Fig.6.Full-screen View

Gamma-ray spectra of ¹³⁷Cs (a) and ²²Na (b) obtained with an ADC system and the QTC-based circuit.

From Table 1, one sees that energy resolutions of the peaks at 511 keV, 662 keV and 1.27 MeV by the two methods are close to each other. Although some distortion appears in low energy regions of both spectra, it can be seen that input signals cannot be detected by the QTC circuit if the input charge current is less than the discharge current I_T, as explained in Section 2.2. So a tradeoff between dynamic range and dead time has to be found in practical spectrum measurements.

3.3 Positioning resolution test

The H8500 PSPMT coupled with an 11×11 array of 3.5 mm ×3.5 mm ×20 mm LYSO crystal, and a ¹³⁷Cs source, were used to test the position resolution. The high voltage was −750 V, and the discharge current was 100 μA. Fig.7(a) shows the flood histogram and profile histogram, with the peak-to-valley ratio of about 5:1. It can be seen that the 11×11 crystals in the array can all be identified clearly. In comparison, using the ADC method, with the ADS5282 and the same combination of the H8500 PSPMT and LYSO crystal array, the profile histogram (Fig.7b) has a peak-to-valley ratio of about 6:1.

Fig.7Full-screen View

The raw flood histogram (left) and the raw profile histogram (right) by the QTC (a) and ADC (b) methods.

3.4 Linearity test of system

Gamma-ray spectra of ¹³⁷Cs, ²²Na and ⁶⁰Co were measured with the system (Fig.8a), and linearity of the test pulses generated by the function generator (AFG3252) was checked (Fig.8b), with the fitting coefficient of R² =0.9989 and the integrated nonlinearity of 1.38%, while it is 0.95% in the energy range using the ADC-based system (ADS5282).

Fig.8Full-screen View

Gamma-ray spectra (a) of ¹³⁷Cs, ²²Na and ⁶⁰Co, and the peak linearity fit (b).

3.5 Stability test of system

To test stability and credibility, the system was measuring the ¹³⁷Cs source at room temperature for 48 hours, recording a γ-ray spectrum every three hours. From Fig.9, the maximum deviation of peak position in 50 hours is 0.32%.

Fig.9Full-screen View

Stability of 662 keV peak position in 48 hours. The error bars are FWHM of gamma-ray peak.

3.6 Discussion

The readout performance of the experimental circuit for position-sensitive detectors indicates that the QTC-based circuit has good linearity and energy resolution, which are close to the results of conventional ADC-based systems. We noticed some distortion in low energy region of the spectra using the QTC method, so the best tradeoff between dynamic range and dead time should be evaluated. In the position resolution test of QTC-based circuit, all the crystals can be identified with a peak-to-valley ratio of about 5:1 though the flood histogram distorted slightly compared to that of the ADC method.

However, the proposed method does not outperform ADC-based systems in linearity, with integrated nonlinearities of 1.38% and 0.95% for the QTC and ADC methods, respectively. In fact, the QTCM output width T is not simply proportional to the input charge Q, some complicated calibrations should be performed for better energy and position resolutions, which means a more complicated system. The original QTC calibration method has been described in detail for BESIII’s TOF detector in Ref.[19]. To simplify the whole system including hardware and software design for the application in position sensitive detector, the QTCM output width T is considered to be proportional to the input charge Q in this paper and the results are acceptable. An advantage of the proposed method is that large number of interface lines between ADCs and FPGA can be simplified. It contributes to great simplification of electronic system and low power consumption (~100 mW per channel for ADC and ~30 mW per channel for QTC).