General relations for optical design parameters under diffraction limited paraxial imaging

We searched for fundamental relationships among general optical system parameters assuming diffraction limited imaging in paraxial space. We demonstrated that the total twelve optical system parameters describing the optical imaging problem are unambiguously determined with a set of four of them. This holds for a diffraction condition, where the image permitted blur is of the same size for both the spot due to defocus and the diffraction spot. Depending on the combinations of the four input parameters there can be found up to 314 different optical system design approaches to fully describe the diffraction limited imaging problem. We demonstrated eight examples of optical system design approaches using different combinations of input parameters. It can be helpful for optical designers to decide if diffraction limited imaging is feasible for the desired combination of optical imaging system parameters. With the reduction of the optical system to a thin lens approximation, the number of the optical system parameters describing the optical imaging problem decreases to eight and its unambiguous determination is possible with a set of only three of these parameters. It provides, up to 54 optical system design approaches based on different combinations of input parameters.