Fried parameter

The Fried parameter[1] or Fried's coherence length (commonly written as r_0) measures the optical quality of the atmosphere. This parameter is usually expressed in centimeters and corresponds to an area over which the rms wavefront aberration is less than 1 radian. As such, r_0 indicates the size of a telescope which can just operate at the diffraction limit. Any larger and resolution will be seeing-limited, any smaller and it will be limited by the telescope itself.

Although not explicitly written in his article, Fried's parameter is usually written as

r_0 = \left [ 0.423 \, k^2 \, \sec \zeta \int_{\mathrm{Path}} C_n^2(z) \, dz \right ]^{-3/5}. [2]

where C_N^2 is the strength of turbulence versus altitude, k= 2 \pi / \lambda is the angular Wavenumber, and \zeta is the angle of the telescope, measured from zenith.

Typical values for r_0 are 10 cm for average seeing and 20 cm for good to excellent seeing on the best sites. The seeing-limited angular resolution is \lambda / r_0. Since almost all professional telescopes have diameter D larger than r_0, they employ adaptive optics to correct the aberrations and get diffraction limited images, with resolution of \lambda / D. Because r_0 varies with wavelength as \lambda ^{6/5}, it is usually specified at \lambda = 0.5 \mu m

See also

References

  1. ^ Fried, D. L. (October 1966). "Optical Resolution Through a Randomly Inhomogeneous Medium for Very Long and Very Short Exposures". Journal of the Optical Society of America 56 (10): 1372–1379. Bibcode 1966JOSA...56.1372F. doi:10.1364/JOSA.56.001372. http://www.opticsinfobase.org/abstract.cfm?id=53167. 
  2. ^ Hardy, Johw W. (1998). Adaptive optics for astronomical telescopes. Oxford University Press. p. 92. ISBN 0195090195. http://openlibrary.org/works/OL2633873W/Adaptive_optics_for_astronomical_telescopes.