5. Aberrations in optical systems

The previous paragraph presented the performance of ideal optics, limited by diffraction, and in the Gaussian approximation that enables images and pupils to be positioned. In practice, however, it is not always necessary, nor is it always possible (at least at reasonable cost), to access the diffraction limit.

A perfect lens generates a spherical or plane wave in response to a point source. The aberrations of a system characterize the defects of the real output wave with respect to a perfect sphere or plane. This method of evaluation is very useful, as it takes into account the effects of diffraction, and enables us to calculate the exact distribution of illumination in a plane of focus, or elsewhere.

What's more, aberrations can be expressed as the displacement of real rays from their ideal positions or directions. This approach takes...