Diurnal And Seasonal Variations In The Atmospheric Structure Parameter (C n 2 ) That Affect The Atmospheric Modulation Transfer Function (MTF)

Abstract The atmospheric modulation transfer function (MTF) depends upon an integral of the index of refraction variations (Cn2) along the optical path. Cn2 undergoes large changes as a function of time and position within the l-3km thick planetary boundary layer. Diurnal and seasonal variations of Cn2 near the surface of south-central New Mexico are discussed.Introduct ionStochastic fluctuations in the atmospheric index of refraction degrade the propagation of electromagnetic energy by introducing beam spread, beam wander and scintillations of the intensity. Based upon work of Tatarski^, Hufnagel and Stanley2 , Fried3 , and Lutamirski and Yura4 , the atmospheric modulation transfer function (MTF) approach allows one to calculate the average degradation in image or beam propagation. Fried^ writes the long term atmos­ pheric MTF asMTF(f) = exp{-3.44(Af/ro) 5/3}, (1)where X is the wavelength of light, f is the angular frequency in cycles/radian, and ro is the transverse coherence length. For a plane wave, rQ depends on an integral of C 2 along an optical path of length L and may be expressed asro = 1.67{k2 J Cn2 (z)dz} 3/5, (2)where k is the wavenumber of the radiation (2-rr/X) .We have made an extensive set of rQ measurements for both desert and mountain locations^ / 6 ,7 . Most of the diurnal changes in r stem from C 2 variations within the planetary boundary layer'. C 2 is given byCn2 = /r12 , (3)which is a measurement of the random fluctuations in the atmospheric index of refraction, n. Cn2 is a mean square ensemble average of the difference in the index of refraction between two points n-]_ and n2 normalized by the distance between them, r12. Relations similar to Eq. (2) occur in most atmospheric propagation problems. Thus, measurements of C 2 are necessary to understand or predict the performance of optical systems. nExperimentally, the ensemble (spatial) average that occurs in Eq. (3) causes complexities. Convective plumes during the day and stratification at night produce abrupt inhomogeneities in Cn2. Scale sizes on the order of a few hundred meters to a few kilometers occur. Thus the choice of averaging scale size in Eq. (3) affects the mean and particularly the standard deviation of C 2. This ambiguity can be resolved by choosing an averaging scale that is consistent with the propagation path length L in Eq. (2) .Since it is difficult to make ensemble measurements using point probes, ergodicity allows us to make a time average as long as we are careful in choosing the time interval. For point probe measurements of Cn2 , we perform a fifteen minute linear time average of (n2 - n^)2. For a typical wind speed of say 3m/s this is equivalent to a ^3km optical path. Fifteen minutes is long enough to represent typical propagation path lengths without en­ countering significant diurnal trends. Since the probability distribution of the 15 minute samples is found to be approximately log-normal on a day to day basis, we compile a clima- tological mean and standard deviation by computing a log average of the 15 minute samples. The need for the mixed linear-log averaging is not obvious in the definition of Cn2 , Eq. (3).Point measurements of Cn2 are difficult to make directly; however, it is possible to measure the temperature structure parameter CT2 . CT2 is defined in a manner similar to Cn2