Fried parameter
The Fried parameter or Fried's coherence length (commonly designated as formula_1) is a measure of the quality of optical transmission through the atmosphere due to random inhomogeneities in the atmosphere's refractive index. In practice, such inhomogeneities are primarily due to tiny variations in temperature (and thus density) on smaller spatial scales resulting from random turbulent mixing of larger temperature variations on larger spatial scales as first described by Kolmogorov. The Fried parameter has units of length and is typically expressed in centimeters. It is defined as the diameter of a circular area over which the rms  wavefront aberration due to passage through the atmosphere is equal to 1 radian, and typical values relevant to astronomy are in the tens of centimeters depending on atmospheric conditions. For a telescope with an aperture, formula_2, the smallest spot that can be observed is given by the telescopes Point spread function (PSF). Atmospheric turbulence increases the diameter of the smallest spot by a factor approximately formula_3 (for long exposures). As such, imaging from telescopes with apertures much smaller than formula_1 is less affected by atmospheric seeing than diffraction due to the telescope's small aperture. However, the imaging resolution of  telescopes with apertures much larger than formula_1 (thus including all professional telescopes) will be limited by the turbulent atmosphere, preventing the instruments from approaching the diffraction limit. Although not explicitly written in his article, the Fried parameter at wavelength formula_6 can be expressed in terms of the so-called atmospheric turbulence strength formula_7 (which is actually a function of temperature fluctuations as well as turbulence) along formula_8 the path of the starlight : formula_9 where formula_10 is the wavenumber. If not specified, a reference to the Fried parameter in astronomy is understood to refer to a path in the vertical direction . When observing at a zenith angle formula_11, the line of sight passes through an air column which is formula_12 times longer, producing a greater disturbance in the wavefront quality. This results in a smaller formula_1, so that in terms of the "vertical" path "z", the operative Fried parameter formula_1 is reduced according to: formula_15 At locations selected for observatories, typical values for formula_1 range from 5 cm for average seeing to 20 cm under excellent seeing conditions. The angular resolution is then limited to about formula_17 due to the effect of the atmosphere, whereas the resolution due to diffraction by  a circular aperture of diameter formula_2 is generally given as formula_19. Since professional telescopes have diameters formula_20, they can only obtain an image resolution approaching their diffraction limits by employing adaptive optics. Because formula_1 is a function of wavelength, varying as formula_22, its value is only meaningful in relation to a specified wavelength. When not stated explicitly, the wavelength is typically understood to be formula_23.