The fiber bundle (FB) optical system is widely used in many fields, such as medical imaging and military reconnaissance, owing to its advantages of high design freedom, small volume, and light weight. The traditional theory for the optical transfer function is not suitable for such a discrete sampling optical system. Researchers have developed numerical calculation methods to analyze the imaging quality of the discrete sampling optical system, in which the geometric model needs to be established and the coupling region needs to be determined. We have developed a simple and computationally efficient imaging theory that is suitable for various combinations of FB and CCD detectors. The coupling modulation transfer function (coupling-MTF) of discrete sampling optical systems of square-arrangement fiber bundles (SFBs) and hexagonal-arrangement fiber bundles (HFBs) are analyzed. Simulation results demonstrate that although SFB has a higher coupling-MTF than HFB, the latter is more convenient in coupling alignment operation. Our results have proven the effectiveness and universality of the proposed theory, and it can be used to guide the system design.