  X-ray scatter remains a major physics challenge in volumetric computed
tomography (CT), whose physical and statistical behaviors have been commonly
leveraged in order to eliminate its impact on CT image quality. In this work,
we conduct an in-depth derivation of how the scatter distribution and scatter
to primary ratio (SPR) will change during the spectral correction, leading to
an interesting finding on the property of scatter: when applying the spectral
correction before scatter is removed, the impact of SPR on a CT projection will
be scaled by the first derivative of the mapping function; while the scatter
distribution in the transmission domain will be scaled by the product of the
first derivative of the mapping function and a natural exponential of the
projection difference before and after the mapping. Such a characterization of
scatter's behavior provides an analytic approach of compensating for the SPR as
well as approximating the change of scatter distribution after spectral
correction, even though both of them might be significantly distorted as the
linearization mapping function in spectral correction could vary a lot from one
detector pixel to another. We conduct an evaluation of SPR compensations on a
Catphan phantom and an anthropomorphic chest phantom to validate the
characteristics of scatter. In addition, this scatter property is also directly
adopted into CT imaging using a spectral modulator with flying focal spot
technology (SMFFS) as an example to demonstrate its potential in practical
applications.
