Wavefront aberrations not resulting from the inherent properties of optical surfaces are more than common: to some degree, they are affecting imaging quality of telescopes at all times. According to their origin, they can be result of: (1) air non-homogeneity, (2) alignment errors, and (3) forced surface deformations. Some induced aberrations may be identical in form to those inherent to conical surfaces - for instance spherical aberration created by despace error in multi-element systems, or due to thermal expansion or contraction - but they remain dependant of factors other than inherent properties of optical surfaces in their proper use and near-optimum environment.

5.1. Air-medium errors

Wavefronts can preserve their form only if the media they move through are optically homogeneous. In other words, when every wavefront point propagates at identical speed. Thus, inhomogeneous media induce random wavefront deviations, resulting in optical aberrations. Air is by far the largest media through which light travels before forming the image in a telescope. What causes air to be inhomogeneous medium for the light are thermal effects, creating randomly changing structures consisting of streams and eddies of air of varying temperatures. Since air optical density, and so the speed at which light propagates through it, changes with the temperature, such random thermal structures cause it to become an inhomogeneous optical media. In various forms, it begins in the high layers of Earth's atmosphere and extends all the way down to both, outside and the inside of a telescope tube, including layers of turbulent air forming right next to the optical surfaces.
 

5.1.1. Atmospheric turbulence

The two main mechanisms inducing seeing error in telescopes are (1) vertical air movement caused by warmer air raising and mixing with cooler air above, and (2) upper level winds carrying this relatively slowly changing turbulent structure consisting of air pockets varying in size, temperature and refractive indici, across the window of the aperture. Smaller-scale variations in air optical properties -  roughly at the level of an average turbulent cell - are the primary source of wavefront roughness. Compounding of optical variations at larger scale creates wavefront tilt deformation.

Exaggerated illustration below shows the basic mechanism of wavefront distortion by turbulent air. For simplicity, it is reduced to a single layer, darker hue representing cooler, optically denser air. Small aperture suffers low-level roughness, and mainly inconsequential tilt error tending to move the image as a whole in time intervals sufficiently long for the eye to follow (depends mainly on the wind speed). Large aperture is affected more by roughness, breaking diffraction pattern into a speckle structure, with individual speckles popping up, moving around and disappearing mainly as a consequence of the sideways movement of turbulent air, producing quickly changing patterns of turbulent cells and inducing variations of the tilt component. So the structure and extent of speckle pattern changes simultaneously due to a constant change in the air-cell pattern and change in the tilt component, the later causing movement of larger portions of the image.

Note that the above depiction of atmospheric coherence length (explained in more details ahead) is a statistical fiction; actual size of orthogonally projected atmospheric segments over which the error generated by wavefront doesn't exceed any given value varies more or less significantly around the average value.

Wavefront deformations caused by atmospheric turbulence are ever-present, only vary in amplitude. The effect is popularly called the seeing error, and measured either through empirical scales of seeing quality - such as Pickering's 1-10 (FIG. 49) and Antoniadi 1-5 scale - or analytically, as given by the optical theory's take on random aberrations. For given level of seeing quality, an average wavefront error induced by atmospheric turbulence increases with the aperture size.

Being random aberration, seeing error comprises many different aberration forms constantly varying in magnitude. The dominant long-exposure form is wavefront tilt. Short-exposure error is corrected for tilt, and the remaining roughness component consists of a large number of aberration components.

Different components of long-exposure wavefront error caused by atmospheric turbulence can be quantified for its time-averaged form using wide range of Zernike terms of appropriate magnitudes. Table below lists first 12 components (20 counting sine and cosine terms separately, and without piston) of the Zernike-modeled time-averaged turbulence error (source: Optical Imaging and Aberrations 2, Mahajan). Piston, or uniform aberration, has zero variance over the pupil (it only becomes source of aberration in a system with multiple pupils of unequal phase); thus the first row gives values for the total aberration. Every next row gives values after the specified aberration component is corrected; for instance, after correcting for the tilt component in both cosine and sine term, the residual phase variance (φ2) is 0.134, and the corresponding RMS phase error (analog but not equivalent to the RMS wavefront error) is 0.0583(D/r0)5/6.; since the RMS error differential to the error level before correction for tilt is 0.1032, it equals term-specific RMS phase error.
 

Since the total aberration is proportional to to 1.0148, the relative error contribution of each separate error component is closely approximated by their φ differential; for defocus it is 0.033 (3.3%) of the total aberration, and after the first 20 components are corrected, remaining aberration is 14.2% of the total aberration.

While the degree of turbulence varies constantly, an average error to the wavefront passing through it can be expressed in terms of atmospheric coherence length or atmospheric coherence diameter. This parameter is defined as a turbulence diameter over which the time-averaged error induced to the wavefront doesn't exceed one phase radian (1/2π of the full wave phase of 2π radians). It is usually called Fried parameter, and denoted by r0. The parameter is set so that the telescope's resolving power is limited by its aperture for r>D, and by the atmosphere for r0<D (needless to say, this division line is only approximate; averaged long-exposure FWHM is nearly 1/3 wider than the aberration-free FWHM).

In terms of r0 and the aperture diameter D, the long-exposure atmospheric error as a variation of the standard (phase) deviation in radians, averaged over the pupil, is given by:

The speckles, being formed by the energy coming from the fragments of the broken wavefront over the pupil that meet in phase at the points randomly scattered around Gaussian image point, approximate in size diffraction disc (this apply to the brightest, so called first-order speckles; fainter speckles are smaller in size). The diameter of the 1st-order speckles envelope, the bright central core of the entire star image, roughly analogous to the FWHM (Full-Width-at-Half-Maximum) of the PSF of aberration-free diffraction image, is approximated by λ/r0 in radians. This means that it is r0, not the aperture, that sets the resolution limit. The speckle phenomenon is not only characteristic of large professional telescopes. Even medium-size amateur telescopes in bad seeing begin to develop speckle structure.

Probably the simplest model to use for explaining the mechanism of speckle formation is to assume that the aperture of a telescope is, as a result of atmospheric turbulence, effectively broken into sub-apertures, each approximately of the diameter equal to r0. Resulting diffraction pattern is a product of superimposed sub-aperture patterns. Similarly to a multi-aperture telescope, the combined pattern shows tendency to segmentation - mostly in the rings area - with the number of first-order radial segments (spikes, lobes, etc.) approximately equaling that of sub-apertures. Unlike multiple-aperture telescope, the seeing-formed sub-apertures are in an optical disarray, poorly defined and in a constant motion. Thus the increase in number of "sub-apertures" quickly causes disintegration of the bright central disc and formation of the random speckle structure which is stationary only within time intervals smaller than ~50 milliseconds.

Since speckles originate from wavefront roughness, which is proportional to (D/r0)5/6, their number will be larger for larger (D/r0) values. The number of 1st-order speckles N can be approximated as a ratio of the area of the speckle envelope FWHM vs. area of a single speckle, N~[(λ/r0)/(2λ/D)]2=(D/2r0)2; hence the spackle structure begins to form at (D/r0)~3.

Seeing error negatively affects image quality, reducing both, resolution and contrast transfer. These effects are more closely specified by the determinant of limiting stellar resolution, seeing-adapted Strehl, and seeing OTF, addressed on the following page.