The term wavefront error (WFE) refers to a type of anomaly gained by light (EMR) passing through an optical system, such that incoming plane parallel waves diverge from what they "should" be, e.g., instead of a wave crest forming a moving plane, some parts pass through earlier and others later. This type of error underlies a number of the common aberrations and the Strehl ratio of a telescope includes its effects. The phenomenon can be due to inherent characteristics of the optical instrument (e.g., the telescope type), can be due to manufacturing flaws in mirrors or lenses, and/or can be due to seeing issues. It also results from changes in the telescope during its use: from changes in the effects of gravity due to its position and support when pointed in a certain direction, and from the effects of temperature changes of different portions of the telescope.
The term is also used for quantities that characterize the degree of the problem, which are often used regarding the design and manufacture characteristics of an optical instrument (e.g., telescope), and is often a quantity that can be usefully summed and budgeted: i.e., it can be used to predict the quality of a system based upon its parts, and the aggregate error can be planned based upon a combination of design and the manufacturing specifications and execution. Quantifications deal with how far ahead one portion of the wave is from other portions, some measures being:
Regarding manufacturing errors, wavefront error is a means of quantifying a mirror's divergence from its intended mathematical curvature. A more direct quantification of the same thing is the mirror's surface error.
Wavefront error is measured at a specific wavelength/frequency, using a wavefront sensor, and the result is presumed to apply pretty well to a surrounding spectral band. Adaptive optics (AO) aiming to work around seeing conditions includes the ability to do this during observations, making "real time" adjustments. Pre-testing parts, and testing and adjusting the telescope may use analogous equipment.