Exact calculation of the minimal exposure for the secure detection of a transmission contrast signal.

In contrary to conventional screen film radiography digital radiographic methods allow the flexible adaptation of the visualisation of an image to a clinical question even after its generation. Nevertheless, the information content of an image is in addition to covering effects like anatomical noise ultimately limited by the applied exposure, its energy distribution and the dose to the detector. This limitation needs to be analysed quantitatively and in connection with efficiency properties of the image generation process. The random variation of pixel values in plane digital radiography is in general attributed to the limited number of imaging quanta. This allows determining a minimal number of applied quanta from requirements to the image information. The number of applied quanta is closely related to the entrance dose. It can be calculated by understanding the imaging process as the sum of many binomial sampling processes. This approach is useful for the separation and examination of the influences of the transmission, absorption and scattering properties of an imaging setup, including the used radiation quality. The model imaging task examined here is the detection of a thin contrast layer of one material behind a homogeneous main absorber of a second material by projection radiography. As the physical properties of the setup are dependent on the energy of the applied radiation, the energy leading to a minimal number of applied photons to achieve the required information can be calculated. It turns out to depend on the materials of both but on the thickness of only the main absorber. The efficiency of the exposure by other energies can be determined as the ratio between the minimal number and the number of quanta needed to achieve the same information. For monoenergetic exposures it is shown that changing the optimal energy by a fixed factor leads to the same loss of efficiency independent of the thicknesses of contrast layer and main absorber. The efficiency of the detection process can shift the optimal position. It directly follows that the optimal range of photon energy becomes smaller for thinner specimens. This clearly stresses the need for an adaptation of the applied energies to the physical properties of the patient especially when thin objects are examined.