The basic principle in fiber-to-fiber coupling is simply to reimage the fiber end surface from the emitting feeding fiber towards the receiving process fiber. Using an optimized system, losses will be kept low both regarding power and beam quality (BPP).
In the nominal situation with the beam collimated between the two optics, the image of the feeding fiber is magnified with a factor M onto the process fiber.
The magnification factor M, does not only magnify the image size onto the process fiber, but also demagnify the incoming angle with the same amount. Larger magnification leads to a smaller incoupling angle with a decrease of the BPP losses as a result. When the magnification becomes too large and the fiber core become overfilled, the power losses increase significantly.