Wavefront error is one type of aberration, optical distortion that limits the observing ability telescopes. For the waves from distant objects, virtually plane waves, it is the degree to which the focal plane receives the wave before or after other parts. Rather than the crest of the wave reaching the focal plane simultaneously, parts may arrive early or late.
Such errors are inevitable both from the design of the telescope (which cannot be optically perfect, even by design), by flaws in the manufacture of its parts, and by changes in the telescope as it is used: from gravity due to movement, and from the temperature of different parts of the telescope. They are also be introduced by seeing conditions.
For a mirror, a contributor to wavefront error is its flatness, or rather the degree with which it adheres to its designed curvature. Direct measure of such flaws in the mirror are termed surface error.
A research telescope is designed to keep these within bounds, so design, construction and testing involves estimating and measuring the contributors. Adaptive optics 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.
Wavefront error is measured at a specific wavelength/frequency, essentially with some type of wavefront sensor. Measures are generally cited as a length, among them:
The Strehl ratio of a telescope includes the effects of this aberration, and others.