Nonlinear Effect on Noise Power Spectrum for Quantum Mottle in Radiographs

Rossmann's formula on the power spectrum of quantum noise in a radiograph is based on an assumption that the relation between the spatial fluctuations of optical density and the relative spatial fluctuations of light energy irradiated from the intensifying screen due to absorbed x-ray quanta is linear. The reasonability of the assumption is not theoretically obvious because the relative spatial fluctuation of light energy increases as the number of absorbed x-ray quanta decreases. Based on the shot-noise theory, the power spectrum of quantum noise is calculated taking account of the second order of the spatial fluctuation of light energy and the spectrum is expressed as a function of the gradient, the modulation transfer function of the screen-film system, and the average number of absorbed x-ray quanta. The term caused by the nonlinearity between the spatial fluctuations of optical density and light energy per unit area for the noise power spectrum is also estimated using the m-hits model for the emulsion and it is found that the effect due to the nonlinearity is little in practice.