Proportionality between Wiener spectra of quantum mottle and the squares of modulation transfer functions

Rossmann proposed that the Wiener spectra of the quantum mottle of radiographs made using screen-film systems were proportional to the squares of the modulation transfer functions (MTFs) of the screen-film systems. On the other hand, Lubberts theoretically pointed out that the shape of the Wiener spectrum of the quantum mottle depended on the sum of the squares of the MTFs for different depths in the screen phosphor layer, rather than the square of the sum of the MTFs for the different depths, i.e. the square of the MTF of the screen-film systems. The purpose of this study is to experimentally investigate the proportionality between the Wiener spectra of the quantum mottle and the squares of the MTFs of screen-film systems using two screen-film systems having different screen thicknesses. For this purpose, we determined correction factors for the square of the MTF of the screen-film system in the Wiener spectrum of the quantum mottle at each spatial frequency when the Wiener spectral values of the screen mottle were separated into those of the quantum mottle and structure mottle. The correction factor is the ratio of the normalized Wiener spectrum of the quantum mottle to the square of the MTF of the screen-film system. As a result, for a thin screen, the correction factors were unity for all spatial frequencies; on the contrary, for a thick screen, the factor increased with spatial frequency. By calculating the theoretical correction factors using the models for the MTF and Wiener spectrum of the quantum mottle of Nishikawa and Yaffe based on Lubberts' theory, we verified that our experimental results agreed with Lubberts' theory. Furthermore, by obtaining the screen thickness dependence of the theoretical correction factors for the two screens, we showed that, for screens thinner than 0.02 mm, Rossmann's theory can be applied to the relationship between the Wiener spectrum of the quantum mottle and the MTF of the screen-film system, whereas for screens thicker than 0.02 mm, Lubberts' theory should be applied.