Design and analysis of lens systems uses numerical calculations based upon geometrical optics. The calculation of the form of the image requires interpretation of these geometrical results by the use of physical optics. Closedform mathematical solutions are available only in a few relatively simple cases so that all realistic lens design is based upon manipulation of computed evaluations of the imagery produced by a lens.

The geometrical optical model is sufficient to define the properties of image formation by a lens and to relate them to the construction parameters of the lens. The geometrical ray-based model permits determination of image location and aberrations, and enables calculation of the pupil function describing the wavefront. Evaluation of the image quality requires the introduction of concepts of physical optics and wave propagation. The intensity distribution in the image is calculated by applying a diffraction integral to the pupil function.

The basic optics of image location and size is established by the application of paraxial or first-order optics. Ray tracing is the basic tool used in optical design. Aberrations are defined as the deviation of the ray path for real rays from the paraxial basis coordinates. Physical optics and beam propagation extend the geometrical model to include diffraction and interference. Investigation of these models permits determination of the limits on image formation.

Optical glasses are the most commonly used materials, although many other materials have become important in modern optical design.