An X-ray system with a large area detector has high scatter-to-primary ratios (SPRs), which result in severe artifacts in reconstructed computed tomography (CT) images. A scatter correction algorithm is introduced that provides effective scatter correction but does not require additional patient exposure. The key hypothesis of the algorithm is that the high-frequency components of the X-ray spatial distribution do not result in strong high-frequency signals in the scatter. A calibration sheet with a checkerboard pattern of semitransparent blockers (a "primary modulator") is inserted between the X-ray source and the object. The primary distribution is partially modulated by a high-frequency function, while the scatter distribution still has dominant low-frequency components, based on the hypothesis. Filtering and demodulation techniques suffice to extract the low-frequency components of the primary and hence obtain the scatter estimation. The hypothesis was validated using Monte Carlo (MC) simulation, and the algorithm was evaluated by both MC simulations and physical experiments. Reconstructions of a software humanoid phantom suggested system parameters in the physical implementation and showed that the proposed method reduced the relative mean square error of the reconstructed image in the central region of interest from 74.2% to below 1%. In preliminary physical experiments on the standard evaluation phantom, this error was reduced from 31.8% to 2.3%, and it was also demonstrated that the algorithm has no noticeable impact on the resolution of the reconstructed image in spite of the filter-based approach. Although the proposed scatter correction technique was implemented for X-ray CT, it can also be used in other X-ray imaging applications, as long as a primary modulator can be inserted between the X-ray source and the imaged object.