High-rate dead-time corrections in a general purpose digital pulse processing system

Abstract

Dead-time losses are well recognized and studied drawbacks in counting and spectroscopic systems. In this work the abilities on dead-time correction of a real-time digital pulse processing (DPP) system for high-rate high-resolution radiation measurements are presented. The DPP system, through a fast and slow analysis of the output waveform from radiation detectors, is able to perform multi-parameter analysis (arrival time, pulse width, pulse height, pulse shape, etc.) at high input counting rates (ICRs), allowing accurate counting loss corrections even for variable or transient radiations. The fast analysis is used to obtain both the ICR and energy spectra with high throughput, while the slow analysis is used to obtain high-resolution energy spectra. A complete characterization of the counting capabilities, through both theoretical and experimental approaches, was performed. The dead-time modeling, the throughput curves, the experimental time-interval distributions (TIDs) and the counting uncertainty of the recorded events of both the fast and the slow channels, measured with a planar CdTe (cadmium telluride) detector, will be presented. The throughput formula of a series of two types of dead-times is also derived. The results of dead-time corrections, performed through different methods, will be reported and discussed, pointing out the error on ICR estimation and the simplicity of the procedure. Accurate ICR estimations (nonlinearity < 0.5%) were performed by using the time widths and the TIDs (using 10 ns time bin width) of the detected pulses up to 2.2 Mcps. The digital system allows, after a simple parameter setting, different and sophisticated procedures for dead-time correction, traditionally implemented in complex/dedicated systems and time-consuming set-ups.

Keywords: cascade of dead-times; dead-time; digital pulse processing; time interval distribution.

Figure 1

The main operations and outputs of the digital pulse processing (DPP) firmware.

Figure 2

(a) The digitized waveform from the preamplifier (CSP output waveform) and the pulses from the fast SDL shaping. (b) A zoom of the signals clearly shows the fast detection of the pulses from the waveform; some piled-up pulses are also shown. The pulses represent X-rays from an Ag-target X-ray tube impinging on a semiconductor detector (CdTe detector) with an ICR of 2.2 Mcps.

Figure 3

Selection, through the PUR, of a time window of the CSP waveform for the slow shaping. Each selected time window is termed ‘Snapshot’, while the width of this window is termed ‘Snapshot Time’ (ST). The selection is related to the reference time of each fast SDL pulse: a pulse is accepted if it is not preceded and not followed by another pulse in the ST/2 time window periods; if two detected fast SDL pulses are within ST/2 of each other, then neither pulse will be selected. The PSHA is performed on the snapshot window with benefits at high ICRs (minimization of baseline shifts, etc.). The pulses represent X-rays from an Ag-target X-ray tube impinging on a semiconductor detector (CdTe detector) with an ICR of 2.2 Mcps. A ST of 2 µs was used.

Figure 4

Calculated time-interval distributions (TIDs) of the recorded counts of the fast channel (dead-time of type II) by using equation (2) at different ρτ_F values. (a) TID (thick gray line) at 220 kcps (ρτ_F = 0.03); there are no dead-time distortions at time intervals longer than 2τ_F and the exponential best fitting (thin red line), performed at times >2τ_F, gives an estimated ρ_FITTING equal to the true ρ. (b) TID (thick gray line) at 2.2 Mcps (ρτ_F = 0.3); here, there are dead-time distortions at time intervals smaller than 5τ_F; the exponential best fitting (thin red line), at time intervals >5τ_F, gives an estimated ρ_FITTING equal to the true ρ. (c) TIDs at ρ = 2.2 Mcps; the TID at ρτ_F = 0.3 (dashed gray line, τ_F = 138 ns) is compared with the TID at ρτ_F = 3 (solid gray line, τ_F = 1.38 us); the exponential fitting of the TID at ρτ_F = 3 gives an estimated ρ_FITTING = 1.3 Mcps (different from the true ρ = 2.2 Mcps), even at time intervals greater than 20τ_F.

Figure 5

Experimental throughput curve from the fast channel. The experimental points are in good agreement with the throughput function (red line) of a single paralyzable dead-time (the coefficient of determination is equal to 0.9999; this parameter indicates how well experimental data fit the model and a value close to 1 indicates that the model perfectly fits the data) (Draper & Smith, 1998 ▸). Errors of experimental points are too small to be visible in the figure.

Figure 6

Measured time-interval distribution (TID) of the events of the fast channel (thick gray line) at 2.2 Mcps (ρτ_F = 0.3) with a time bin width of 10 ns. The exponential best fitting (thin red line), performed at time intervals >5τ_F, is in good agreement with experimental data (the coefficient of determination is equal to 0.9997).

Figure 7

ρ_TID estimated from the measured time-interval distributions (TIDs) of the pulses of the fast channel versus the tube current (nonlinearity < 0.5%).

Figure 8

Measured time width distribution of the fast pulses at 752 kcps.

Figure 9

ρ values estimated through different dead-time correction methods. Each ρ value is related to the ρ_TID. The R _F values, related to ρ_TID, are also reported.

Figure 10

Ratio between the measured standard deviation of N _F and (N _F)^1/2 (i.e. the expected standard deviation in a Poisson process) versus the ρτ_F product values.

Figure 11

Measured throughput curve from the slow channel. The throughput function of the cascade of dead-time of type II and type III [equation (7)] is in good agreement with the experimental points (the coefficient of determination is equal to 0.9998). Errors of experimental points are too small to be visible in the figure.

Figure 12

Measured time-interval distributions (TIDs) of the events of the slow channel at (a) 201 kcps, (b) 752 kcps and (c) 2.2 Mcps, with a time bin width of 100 ns. The counts were normalized to the maximum number of detected events.

Figure 13

Ratio between the measured standard deviation of N _S and (N _S)^1/2 versus the ρ(ST − τ_F) product values.