An experimental method to directly measure DQE$(k)$ at k = 0 for 2D x-ray imaging systems

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(k). Under conditions specified by Shaw, DQE(k) is the same as DQE0 at k = 0. The experimental measurement of DQE(k) 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(k) 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.