  In polychromatic x-ray imaging for nondestructive testing, material science
or medical applications, image quality is usually a problem of detecting sample
structure in noisy data. This problem is typically stated this way: As many
photons as possible need to be detected to get a good image quality.
  We instead propose to use the concept of signal detection, which is more
universal. In signal detection, it is the sample properties which are detected.
Photons play the role of information carriers for the signal. Signal detection
for example allows modeling the effects which polychromaticity has on image
quality.
  $\mathit{SNR}$ spectra (= spatial $\mathit{SNR}$) are used as a quantity to
describe if reliable signal detection is possible. They include modulation
transfer and phase contrast in addition to noisiness effects. $\mathit{SNR}$
spectra can also be directly measured, which means that theoretical predictions
can easily be tested.
  We investigate the effects of signal and noise superposition on the
$\mathit{SNR}$ spectrum and show how selectively not detecting photons can
increase the image quality.
