Greenwood Frequency

Greenwood frequency ^[1] - the frequency or range of frequencies needed for optimal correction by adaptive optics systems . Depends on crosswind speed and atmospheric turbulence . It is clear that the faster the turbulent air masses move over the telescope, the stronger it is necessary to correct the wave fronts arriving at the telescope - and vice versa. There are several methods for calculating the Greenwood frequency, but all of them determine the frequency at which the nature of the distortions due to atmospheric turbulence changes. The inverse of Greenwood frequency is the Greenwood time constant or the atmospheric time constant denoted by t ₀ . Since the distortions hardly change during a period shorter than the Greenwood time constant, the use of adaptive optics systems with higher speed practically does not give any advantages. And vice versa: the efficiency of adaptive optics systems is significantly reduced if the response time of the system becomes lower than this constant, since this means that distortions change faster than they are corrected by the system. The Greenwood frequency is usually calculated in the range from tens to hundreds or even thousands of hertz . Under unusual atmospheric conditions or equipment, this value can vary significantly.

One of the expressions for determining the Greenwood frequency is written ^[2] as

$f_{\mathrm {G} }=2.31\,\lambda ^{-6/5}\left[\sec \zeta \int _{\mathrm {Path} }C_{n}^{2}(z)\,v_{\mathrm {Wind} }(z)^{5/3}\,dz\right]^{3/5}$ ${\ displaystyle f _ {\ mathrm {G}} = 2.31 \, \ lambda ^ {- 6/5} \ left [\ sec \ zeta \ int _ {\ mathrm {Path}} C_ {n} ^ {2} ( z) \, v _ {\ mathrm {Wind}} (z) ^ {5/3} \, dz \ right] ^ {3/5}}$ ${\ displaystyle f _ {\ mathrm {G}} = 2.31 \, \ lambda ^ {- 6/5} \ left [\ sec \ zeta \ int _ {\ mathrm {Path}} C_ {n} ^ {2} ( z) \, v _ {\ mathrm {Wind}} (z) ^ {5/3} \, dz \ right] ^ {3/5}}$ where $\zeta$ ${\ displaystyle \ zeta}$ $\ zeta$ - zenith angle $v_{\mathrm {Wind} }(z)$ ${\ displaystyle v _ {\ mathrm {Wind}} (z)}$ ${\ displaystyle v _ {\ mathrm {Wind}} (z)}$ - wind speed as a function of altitude, $C_{n}^{2}(z)$ ${\ displaystyle C_ {n} ^ {2} (z)}$ ${\ displaystyle C_ {n} ^ {2} (z)}$ - the dependence of the distribution of turbulence on height.

Notes

↑ Greenwood, Darryl P. Bandwidth specification for adaptive optics systems (English) // Journal of the Optical Society of America : journal. - 1977 .-- March ( vol. 67 , no. 3 ). - P. 390-393 . - DOI : 10.1364 / JOSA.67.000390 . - .
↑ Tyson, Robert K. Field guide to adaptive optics . - SPIE Press, 2004. - P. 14. - ISBN 0-8194-5319-6 .

[1] Greenwood, Darryl P. Bandwidth specification for adaptive optics systems (English) // Journal of the Optical Society of America : journal. - 1977 .-- March ( vol. 67 , no. 3 ). - P. 390-393 . - DOI : 10.1364 / JOSA.67.000390 . - .

[2] Tyson, Robert K. Field guide to adaptive optics . - SPIE Press, 2004. - P. 14. - ISBN 0-8194-5319-6 .

Greenwood Frequency

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