Degradation of the detective quantum efficiency due to a non-unity detector fill factor

Digital x-ray imaging detectors generally consist of an array of discrete detector elements. These devices may have regions between the elements which are insensitive to the input signal, but are often necessary due to fabrication or operational requirements. These insensitive regions can be quantified in terms of the detector ''fill factor'', defined as the active area expressed as a fraction of the physical detector area. It is conventional wisdom that the fill factor be as close to unity as possible, but this can be difficult or expensive to implement. The actual loss of image quality due to a non-unity fill factor has never been quantified in detail. In this paper, the spatial-frequency dependent detective quantum efficiency (DQE) is determined for a digital detector with a non-unity fill factor. For clarity, it is assumed that each element is independent with unity quantum efficiency and no additive noise, but these assumptions can easily be removed. It is shown that a decreased fill factor increases the noise pass-band of the detector which increases noise aliasing causing a decrease of the DQE. If the interacting quanta are uncorrelatted, the DQE is always degraded. The degradation is generally greatest at frequencies approaching the sampling cut-off frequency. This result applies to digital devices which detect x rays directly, such as selenium-based active-matrix arrays. If the incident quanta are partially correlated, the DQE is degraded less. This can occur when x rays are detected indirectly, such as detectors which make use of conversion screens. An expression is developed which allows for a simple check that can be made to determine whether the fill factor degrades the DQE significantly for a specific design.