[Paper Review] True Gaussian shaping for high count rate measurements of pulse amplitudes

M. Yu. Kantor, A. V. Sidorov|arXiv (Cornell University)|Sep 6, 2018

Medical Imaging Techniques and Applications12 references4 citations

TL;DR

This paper proposes a digital true Gaussian shaper that converts short-rise-time, long-tail detector pulses into narrow, symmetric Gaussian pulses with full width at half maximum (FWHM) significantly shorter than the input pulse rise time. By achieving sub-rise-time pulse widths, the shaper enables higher output count rates—several times greater than standard trapezoidal shapers—while maintaining energy resolution and reducing amplitude variations due to charge collection time jitter.

ABSTRACT

A digital shaper for high-count-rate detection and amplitude measurement of pulses is proposed and analysed in this paper. The proposed shaper converts pulses with a short leading edge and a long exponential tail into a true Gaussian form. The width of Gaussian pulses can be several times smaller than the rise time of the input pulses, i.e. considerably shorter than the undistorted output pulses provided by standard shapers. Therefore, the proposed true Gaussian shaper resolves strongly overlapped pulses better and provides a higher output count rate. The capabilities of the proposed true Gaussian shaper are analysed with real and simulated output signals of a silicon drift detector of soft X-ray radiation, operating at a high count rate of the collected quanta. Our analysis shows that true Gaussian shapers can increase the count rate of spectrometer systems several times compared with the widely used trapezoidal shapers, while maintaining their amplitude resolution.

Motivation & Objective

• Address the limitation of standard shapers in high-count-rate pulse amplitude measurements due to minimum pulse width constraints.
• Overcome the trade-off between count rate and energy resolution in spectrometer systems using conventional pulse shaping techniques.
• Develop a digital shaper that produces true Gaussian-shaped output pulses with FWHM substantially below the input pulse rise time.
• Evaluate the performance of the true Gaussian shaper in terms of noise, dead time, resolving time, and energy resolution using real detector data.
• Demonstrate that true Gaussian shaping enables significantly higher output count rates than standard trapezoidal shaping while preserving energy resolution.

Proposed method

• Design a digital shaper using the transmission function derived as the ratio of the Fourier transform of the desired Gaussian output pulse to the measured impulse response of the detector system.
• Use measured impulse response data from an AXAS-D spectrometer with a KETEK H7 VITUS silicon drift detector (SDD) as the input for shaping.
• Apply numerical modeling based on calibrated system characteristics to simulate pulse shaping performance across varying Gaussian pulse widths.
• Compare the true Gaussian shaper with standard trapezoidal shapers by analyzing noise amplification, dead time, resolving time, and amplitude stability under varying charge collection times.
• Use the measured noise spectrum of the KETEK system to estimate signal-to-noise ratios and effective energy resolution for different shaper configurations.
• Analyze amplitude variations due to charge collection time jitter in SDDs by simulating pulse amplitudes across different integration times and pulse widths.

Experimental results

Research questions

• RQ1 Can a digital shaper produce true Gaussian output pulses with FWHM significantly shorter than the input pulse rise time?
• RQ2 How does the noise amplification in the true Gaussian shaper compare to that of standard trapezoidal shapers at high count rates?
• RQ3 What is the achievable output count rate of a spectrometer system using the true Gaussian shaper compared to standard trapezoidal shaping?
• RQ4 How do amplitude variations due to charge collection time jitter differ between true Gaussian and trapezoidal pulses at high count rates?
• RQ5 To what extent does the true Gaussian shaper maintain energy resolution while enabling higher count rates in SDD-based spectrometers?

Key findings

• The true Gaussian shaper achieves output pulse widths (FWHM) as low as 20% of the input pulse rise time, enabling significantly shorter inter-pulse intervals than standard shapers.
• The output count rate of the spectrometer system with the true Gaussian shaper is increased by a factor of 2–3 compared to standard trapezoidal shaping, while maintaining 139 eV FWHM energy resolution at 5.895 keV.
• Amplitude variations in true Gaussian pulses due to charge collection time jitter are less than 0.5% for the KETEK H7 VITUS SDD, remaining well below the system’s 139 eV energy resolution.
• For a fast SDD with larger area (AMPTEK XR100-SDD), amplitude variations reach ~20% at 100 ns integration time, but remain lower than those of short trapezoidal pulses.
• The resolving time of the true Gaussian shaper is shorter than that of trapezoidal shapers, enabling accurate amplitude measurement of strongly overlapped pulses.
• The shaper exhibits strong suppression of high-frequency components (≥1/Ts), which enables the generation of narrow pulses without excessive noise amplification, unlike standard shapers with similar pulse widths.