wavefront error

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 the very slight changes in the telescope during its use: from sagging due to varying effects of gravity as the telescope is pointed in various directions, and from the effects of temperature-changes on 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), often for a quantification that can be usefully summed and budgeted, allowing it to 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. Such quantifications assert how far ahead one portion of the wave is from other portions, some measures being:

• rms wavefront error - results of an RMS calculation of the divergence from an ideal wave front: summing/budgeting these can be useful if the sources of wavefront error are independent of each other, to find a most likely aggregate.
• peak-to-valley wavefront error (P-V) - just the difference between the extremes: summing/budgeting it gives you something of a worst-case scenario.
• half wavefront error (HWFE) - I've seen this but I have not found a source explaining whether "half P-V" versus "half RMS" is typically meant, but I did see one site explicitly refer to a telescope's "rms HWFE".

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, which corresponds to half its wavefront error (if the mirror is off by some length, then the light-travel distance is off by twice as much), thus the use of the HWFE for budgeting.

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.