Relationship of the temperature  SEEING  Temperature structure coefficient

Full Width Half Maximum

The Full Width Half Maximum (FWHM) of the seeing disk is the angular diameter at half height of the point spread function (PSF):

$$\theta = 2.591\cdot 10^{-5} \, \lambda^{-1/5}\left[ (\cos \gamma)^{-1}\int_{\rm H} C_{N}^{2}(z) dz \right]^{3/5}$$ (7)

  

For a vertical direction and $\lambda$ = 500 nm, the FWHM angle in typical conditions of astronomical mountain sites (pressure 770 mb, temperature 10$^\circ$C) is expressed as:

$$\theta = 0.94 \left[ \int_{\rm H}{C_{\scriptscriptstyle T}^2(z)}dz \right]^{3/5}$$ (8)

  

The diagram at fig. 2.2 illustrates the order of magnitude of the seeing effect with respect to a mean value of $\overline {C_T^2}$ and the integration distance. Depending on the geometric scale of the phenomenon causing seeing, the critical values of $\overline {C_T^2}$ will be very different: for instance, if we set at 0.1 arcsec an arbitrary threshold for "bad" seeing from a single cause, the corresponding critical (mean) value of C_T² will be

• for the dome interior (distance scale $\simeq$ 10 m): $\simeq 6\cdot$10^-3 K²m^-2/3;
• for the atmospheric surface layer (distance scale $\simeq$ 30 m): $\simeq 10^{-3}$ K²m^-2/3;
• for seeing caused by convection flow at the surface of the telescope mirrors (distance scale $\simeq$ 1-40 mm) the critical C_T² values are much higher, of the order of 10 K²m^-2/3.

Equations (7) and following show that the overall seeing effects may be considered a 5/3-exponent sum of different terms corresponding to the different atmospheric layers. Thus if $\theta_n$is natural seeing FWHM, caused by the boundary layer and upward, and $\theta_l$ is the local seeing, the overall seeing is:

$$\theta = \left( \theta_n^{5/3} + \theta_l^{5/3} \right)^{3/5}$$ (9)

   

 

 Figure 1: Parameterisation of seeing FWHM with respect to a mean value of $\overline {C_T^2}$ (K² m^-2/3) integrated over a distance z.

1998-07-05