An experimental method to directly measure DQE[Formula: see text] at k = 0 for 2D x-ray imaging systems

Abstract

The zero-frequency detective quantum efficiency (DQE), viz., DQE₀, is defined as the ratio between output and input squared signal-to-noise ratio of an imaging system. In 1963, R. Shaw applied Fourier analysis to generalize DQE₀ to the frequency-dependent DQE, i.e. DQE[Formula: see text]. Under conditions specified by Shaw, DQE[Formula: see text] is the same as DQE₀ at k = 0. The experimental measurement of DQE[Formula: see text] involves the measurement of system modulation transfer function (MTF) and noise power spectrum (NPS). Although the measurement of MTF is straightforward, the experimental measurements of NPS[Formula: see text] encountered several challenges. As a result, some experimental methods may yield a nonphysical NPS value at k = 0, which makes the measured DQE(k)| _k=0 deviate from the true zero-frequency DQE. This work presents new results from three aspects: 1) system drift is a significant error source when a large number of independent image acquisitions are involved in measuring NPS and DQE; 2) a cascaded systems analysis shows that the drift induces a global positive offset to the measured autocovariance function, and the offset is quantitatively related to the NPS error at k = 0; 3) based on the measured autocovariance data, drift-induced offset can be estimated, so that errors in the measured NPS(k)| _k=0 and DQE(k)| _k=0 can be corrected. Both numerical simulations with known ground truth for DQE₀ and experimental studies were performed to validate the proposed measurement method. The results demonstrated that the method mitigates the undesirable influence of system drift in DQE(k)| _k=0 and DQE₀, allowing the measured values consistent with the classical definition of zero-frequency DQE.

Figure 1.

Plot of the drift function used in the numerical simulation study.

Figure 2.

Measured DQE(0) of the simulated x-ray systems by using different l for correction. (a) System with white noise. (b) System with apodization (width = 4 pixels). (c) System with apodization (width = 20 pixels).

Figure 3.

Experimental demonstration of system drift. (a) Comparison of drift function f_t) measured from four quadrants of a 100 × 1000 ROI in a detector panel. (b) Comparison of f_t measured in two ROIs from two different detector panels in the PCD system.

Figure 4.

Radial profiles of 2D autocovariance functions of the experimental system. The horizontal wavy lines indicate broken vertical axes. (a) ACS off; 20 keV. (b) ACS off; 35 keV. (c) ACS on; 20 keV. (d) ACS on; 35 keV.

Figure 5.

Radial profiles of the 2D NPS of the experimental system. NPS measured without drift correction demonstrated abrupt elevation at the zero frequency. The proposed drift correction generated smooth NPS within the entire bandwidth, including the point of k = 0. The horizontal wavy lines indicate broken vertical axes. (a) ACS off; 20 keV. (b) ACS off; 35 keV. (c) ACS on; 20 keV. (d) ACS on; 35 keV.