Due to the random nature of seeing-induced error, the Strehl approximation for non-random aberrations, given by Eq. 56 becomes inaccurate for larger errors, considerably more than it is for conventional aberrations (FIG. 51). The effect is mainly due to the roughness error component, whose increase reduces the average relative size of wavefront irregularity, while at the same time increasing its average RMS error. Similarly to ordinary surface roughness, narrow zones and turned edge, the increase in the P-V (and thus RMS) error after a certain point begins to drain less energy out of the Airy disc, with the main effect gradually becoming merely spreading the energy out wider. As a result, the increase in the RMS (surface or wavefront) error is followed by relatively slower Strehl degradation, as given by the relation derived by Racine (The Telescopic Point-Spread Function, 1996) for long-exposure "seeing Strehl":

Size of r0 determines angular resolution of large telescopes as ~λ/r0 in radians (λ being the wavelength of light), as opposed to the "standardized" diffraction resolution given by ~λ/D. While the size of r0 results from a complex function, it can be expressed much more simply in terms of the resolution limit it imposes to large telescopes. For seeing imposed stellar resolution α in radians, and wavelength λc centered at 0.00055mm, it is given by:

r0= 1.27lc/α            (54)

Hence, an average ~2 arc second seeing at the zenith, for λ=0.00055mm, results from r0~72mm (2 arc seconds in radians is 2/206,265). Since r0 is changing in proportion to λ1.2 and (cosγ)0.6, γ being the zenith angle in degrees, a more complete expression for its size is given by:

Thus, the extracted limiting stellar resolution is:

where r0 is the atmospheric coherence length for λ=0.00055mm corresponding to the zenith angle γ. Since r0 for γ=0 is larger by a factor of 1/(cosγ)0.6, the corresponding limiting resolution (i.e. zenith "seeing") is αz=1.43λ1.2(cosγ)1.2/r0. Conversely, r0z=1.43λ1.2(cosγ)0.6/αz=r0/(cosγ)0.6.

So, for instance, at 30° from zenith (γ=30°) and the wavelength λ=0.0005mm, thus λ=0.909 in units of 550nm wavelength, atmospheric coherence length r0=100mm corresponds to the limiting stellar resolution ("seeing") α=1.43∙0.9091.2∙0.0005∙(cos30)0.6/100=0.00000585 radians, or 1.2 arc seconds (after multiplying by 206,265). Following table gives values of r0 and α in 2 arc seconds seeing for several values of zenith angle γ, for λ=0.00055mm.
 

For small amateur telescopes, limiting stellar resolution for these r0 values will be generally better, due to significantly smaller seeing-induced error level.

An interesting aspect of seeing-limited telescope resolution is that in imaging applications, either with photo-emulsion or CCD chip as a detector. The limit to resolution is determined by the diameter of first-order speckle structure. With the number of first-order speckles approximated by N~(D/2r0)2, and speckle angular center separation of ~2λ/D, in radians (thus with the speckle diameter ~2λF linearly, after multiplying the angular value with focal length), average linear radius of the stationary seeing FWHM for moderately bright stars, for (D/r0)≥3, can be roughly approximated as √NλF, or:

In the average 2 arc seconds seeing, with r0~72mm, a 200mm aperture with (D/r0) of ~2.8, average seeing FWHM radius is nearly 1.4λF linearly, still  not significantly larger than the Airy disc radius, but larger than system's FWHM (~1.03λF) by a D/r0 factor or, in this case, 2.8 times. This is approximation for the stationary speckle structure, i.e. for subsecond exposures.

For longer exposures (couple of seconds and up), the speckle movement caused by tilt wavefront error further enlarges the blur. If, for the purpose of obtaining a general idea of the magnitude of long-exposure enlargement, the tilt RMS wavefront error - from Eq. 52.1-2, rounded to 0.1(D/r0)5/6, in units of the wavelength - is assumed to be ~1/3 of the P-V tilt error W on the wavefront, angular displacement of the speckle structure around its center due to the tilt wavefront error is roughly αS~Wλ/D~0.3(D/r0)5/6λ/D. Corresponding average linear displacement from the center in the image plane is αSƒ, ƒ being the focal length, or 0.3(D/r0)5/6λF.

Since the linear radius of the stationary speckle structure for (D/r0)≥3 is, from Eq. 55, approximated by (D/2r0)λF, it indicates that the long-exposure radius is larger roughly by a factor 1+[0.6(D/r0)5/6/(D/r0)] than that of the stationary (short-exposure) image. For relatively good seeing conditions, with (D/r0)<3, the ratio of the seeing versus minimum (i.e. aberration-free) FWHM is roughly 1+0.6(D/r0)5/6. So, for instance, the long-exposure blur radius (i.e. seeing FWHM radius) for (D/r0)=1 would be ~1.6 times the system FWHM, while for (D/r0)=3 it would be 1.5 times its short-exposure blur radius of 1.5λF, or about 4.5 times the system FWHM of 1.03λF.

Table below summarizes approximate relation between optic's and seeing FWHM.
 

SEEING FWHM APPROXIMATIONS	(D/r0)<3	(D/r0)>3
SHORT EXPOSURE FWHM (λF=1)	~1 (somewhat larger)	D/r0
LONG EXPOSURE FWHM (λF=1)	1+0.6(D/r0)5/6	D/r0+0.6(D/r0)5/6

In terms of contrast transfer, the effect of atmospheric error is given by atmospheric OTF (Optical Transfer Function), which is for long-exposure given by:

and for short-exposure by

where exp(...) is ℯ(...), ℯ being the natural logarithm base, 2.718 rounded to three decimals.

In both relations ν is the normalized spatial frequency. Combined atmospheric and telescope contrast transfer is given by the product of their respective OTF's. It is the final OTF in the image plane of the objective. Obstructed apertures will have lower combined OTF due to the contrast-lowering effect of central obstruction, but not more. In fact, the larger obstruction, the larger relative size of r0 vs. annulus, resulting in the slower increase in phase variance over annulus area and, consequently, slower decrease in the average Strehl (as a measure of wavefront quality, independent of the effect of central obstruction). This beneficial effect partly offsets the negative diffraction effect of central obstruction.

Closer to the observer, it is terrain topography, immediate surroundings and the very parts of a telescope itself that can create layers of unsteady air resulting in wavefront deformations.