Detective efficiency of photon counting detectors with spectral degradation and crosstalk

Abstract

Purpose: Charge sharing and migration of scattered and fluorescence photons in an energy discriminating photon counting detector (PCD) degrade the detector's energy response and can cause a single incident photon to be registered as multiple events at different energies among neighboring pixels, leading to spatio-energetic correlation. Such a correlation in conventional linear, space-invariant imaging system can be usefully characterized by the frequency dependent detective quantum efficiency DQE(f). Defining and estimating DQE(f) for PCDs in a manner consistent with that of conventional detectors is complicated because the traditional definition of DQE(f) does not address spectral information. Methods: We introduce the concept of presampling spectroscopic detective quantum efficiency, DQE s (f), and present an analysis of it for CdTe PCDs using a spatial domain method that starts from a previously described analytic computation of spatio-energetic crosstalk. DQE s (f) is estimated as the squared signal-to-noise ratio of the amplitude of a small-signal sinusoidal modulation of the object (cortical bone) thickness at frequency f estimated using data from the detector under consideration compared that obtained from the photon distribution incident on the detector. DQE s for material decomposition (spectral) and effective monoenergetic imaging tasks for different pixel pitch is studied based on the multipixel Cram er-Rao lower bound (CRLB) that accounts for inter pixel basis material correlation. Effective monoenergetic DQE s is estimated from the CRLB of a linear weighted combination of basis materials, and its energy dependence is also studied. Results: Zero frequency DQE s for the spectral task was~18%, 25%, and 34% for 250 lm, 500 lm, and 1 mm detector pixels respectively. Inter pixel signal correlation results in positive noise correlation between same basis material estimates of neighboring pixels, resulting in least impact on DQE s at the detector's Nyquist frequency. Effective monoenergetic DQE s (0) at the optimal energy is relatively tolerant of spectral degradation (85-91% depending on pixel size), but is highly dependent on the selected effective energy, with maximum variation (in 250 lm pixels) of 17% to 85% for effective energy between 30 to 120 keV. Conclusions: Our results show that spatio-energetic correlations degrade DQE s (f) beyond what is lost by poor spectral response in a single detector element. The positive correlation between computed single basis material values in neighboring pixels results in the penalty to DQE s (f) to be the least at the Nyquist frequency of the detector. It is desirable to reduce spectral degradation and crosstalk to minimize the impact on system performance. Larger pixels sizes have better spatio-energetic response due to lower charge sharing and escape of scatter and K-fluorescence photons, and therefore higher DQE s (0). Effective monoenergetic DQE s (0) at the optimal energy is much less affected by spectral degradation and crosstalk compared to DQE s for spectra...

A detective quantum efficiency for spectroscopic X‐ray imaging detectors

“…There are two primary advantages of the DQE framework presented here relative to those presented by Persson et al 29 and Rajhanbandary et al 30,31 First, we have defined a DQE that is easily accessible experimentally. As described in the introduction, measurement of Persson et al's 29 task-independent DQE requires access to monoenergetic photon sources that finely sample the diagnostic energy range; Rajhanbandary et al's 30,31 approach requires imaging a series of pure sinusoid basis materials of varying amplitude and frequency. Both these approaches impose a high barrier to experimental DQE analysis.…”

“…Since the GLS estimator is the minimum-variance unbiased estimator, the DQE defined by Equation ( 12) is a measure of the quality of the data provided by an SXD independent of how the data are used to produce an image. There are two primary advantages of the DQE framework presented here relative to those presented by Persson et al 29 and Rajhanbandary et al 30,31 First, we have defined a DQE that is easily accessible experimentally. As described in the introduction, measurement of Persson et al's 29 task-independent DQE requires access to monoenergetic photon sources that finely sample the diagnostic energy range; Rajhanbandary et al's 30,31 approach requires imaging a series of pure sinusoid basis materials of varying amplitude and frequency.…”

“…Unlike traditional DQE analysis, this approach does not admit a task-independent DQE: the resulting DQE is a function of the signal-and-noise properties of the SXD and the imaging task. In addition, Rajbhandary et al's 30,31 approach requires computing the Cramer-Rao lower bound of estimates of the amplitudes of pure sinusoids for both ideal and real SXDs, which imposes a barrier to experimentation. Specifically, this approach requires many phantoms consisting of pure sinusoidal-varying basis materials with frequencies that span those relevant for a particular detector.…”

Photon-counting x-ray detectors for CT

“…A natural extension of the NEQ and DQE metrics to energy-resolving PCDs was proposed by Persson et al (2018b) and will be briefly outlined here. An equivalent spatial-domain description has been described by Rajbhandary et al (2019). Although it may be tempting to simply extend the NEQ to be dependent on incident photon energy in addition to spatial frequency, this definition does not work with broad-spectrum illumination since it fails to describe how different incident energies can be confounded during the detection process as described in section 4.4.…”

Assessment of Multienergy Interpixel Coincidence Counters (MEICC) for Charge Sharing Correction or Compensation for Photon Counting Detectors With Boxcar Signals

“…Zheng et al [42] also used the boxcar signals to assess the signal-difference-to-noise ratio with PCDs with CS. Rajbhandary et al [43] proposed a use of sinusoidal modulation of object thickness at frequency f to measure the spectroscopic DQE, DQEs(f ). We believe that it is very important to use spatially modulated signals, not flat-field signals, in the assessment of PCDs and PCD-CT for high spatial frequency tasks.…”