2. Performance of diffraction-limited optical systems

2.1 Illuminance distribution in the image plane

In optical design, it is important to know whether or not the limit is imposed by diffraction, so as not to spend unnecessary effort on optimizing an already perfect system. At short wavelengths, the resolution of a system is not very often limited by diffraction, but rather by the size of the detector(s) or other considerations at the level of the overall system.

According to Huygens-Fresnel theory, every point inside a light beam behaves like a source of spherical waves in phase with the incident wave. If the beam is limited by a diaphragm of arbitrary shape, the illuminance at a point beyond the diaphragm is calculated by summing the complex amplitudes (i.e. containing the phases) from all points inside the...