In

geometrical optics, the deviation of the behavior of

optical systems from

first-order theory, or

paraxial theory, which occur even for light that is

quasimonochromatic.

Paraxial theory results from the approximation of sin(θ) by just θ for small θ. This corresponds to taking just the first term in the Taylor Series expansion of θ:

sin(θ) = θ - θ^{3}/3! + θ^{5}/5! - θ^{7}/7! + ...

If we take the first two terms, then we get a

third-order theory. Differences between the first and third order theories result in the

primary aberrations (also called

Seidel aberrations). They are:

In addition, deviations of first-order theory from higher-order approximations are called

higher-order aberrations.