1. A radiation imaging system comprising: a radiation imaging device which includes: at least one grating provided in an emission axis direction of radiation; and a mechanism that carries a subject in an orthogonal direction which is at right angles to the emission axis direction or a mechanism that moves the radiation imaging device in the orthogonal direction, and obtains a plurality of periodic pattern images while carrying the subject or moving the radiation imaging device; and an image processing device including: a reconstruction unit which generates at least two reconstructed images of a differential phase image, an absorption image and a small-angle scattering image based on the periodic pattern images; and a detection unit which (i) performs regression analysis on signal values of at least two images of (a) the differential phase image, a differential absorption image generated by differentiating the absorption image, and a differential small-angle scattering image generated by differentiating the small-angle scattering image, or (b) a phase image generated by integrating the differential phase image, the absorption image, and the small-angle scattering image, the at least two images being a target of the regression analysis, (ii) calculates an indicator value of an indicator indicating a relationship between the at least two images, and (iii) detects image quality deterioration due to change in relative position of the radiation imaging device and the subject based on the calculated indicator value.