  Quantitative and analytical analysis of modulation process of the collimator
is a great challenge, and is also of great value to the design and development
of Fourier transform imaging telescopes. The Hard X-ray Imager (HXI), as one of
the three payloads onboard the Advanced Space-based Solar Observatory(ASO-S)
mission, adopts modulating Fourier-Transformation imaging technique and will be
used to explore mechanism of energy release and transmission in solar flare
activities. As an important step to reconstruct the images of solar flares,
accurate modulation functions of HXI are needed. In this paper, a mathematical
model is developed to analyze the modulation function under a simplified
condition first. Then its behavior under six degrees of freedom is calculated
after adding the rotation matrix and translation change to the model. In
addition, unparalleled light and extended sources also are considered so that
our model can be used to analyze the X-ray beam experiment. Next, applied to
the practical HXI conditions, the model has been confirmed not only by Geant4
simulations but also by some verification experiments. Furthermore, how this
model helps to improve the image reconstruction process after the launch of
ASO-S is also presented.
