Mirror seeing in still air

Free convection at the surface of the primary mirror, the cause of so-called mirror seeing, is a main problem for telescope designers. In earlier telescopes, the evidence of mirror seeing was possibly hidden in the background of larger dome seeing effects.

Mirror seeing is caused by natural or weakly mixed convection over a mirror warmer than ambient air. The seeing effect is generated in a thin region just above the viscous-conductive layer where the temperature fluctuations are largest and most intermittent. If its cause could be visualized, seeing would appear to come from a thin but very turbulent layer "floating" a few millimeters above the surface.

The results of several experiments performed by various researchers[2] [3] [10] , have been processed to get a homogeneous database[10] . In still air, mirror seeing appears not to depend on the mirror size. For the purpose of engineering parametric studies the following relationship is proposed:

$$\theta_{m} = 0.38\ {\rm arcsec}\ \cdot \Delta T_m^{6/5}$$

with a possible spread of 25%. This relationship is validated in particular by the author's analysis of the log files of all observations performed during the years 1991, 1992 and 1993 at the CFHT, where it is shown that mirror seeing is indeed the only remaining cause of observatory-made seeing[10].

The effect of mirror inclination is more controversial: it is reported to be large for a small 25-cm mirror[3] but does not appear in our analysis of the 3.6-m CFHT observations data.

The author[10] formulates the hypothesis that the average amplitude of the seeing would be essentially a function of the surface heat flux. The profile of $C_{\scriptscriptstyle T}^2$ can then be described by a similarity equation (19), valid down to the interface with the tiny viscous-conductive layer.

The maximum value of $C_{\scriptscriptstyle T}^2$ will be found at the top of the viscous conductive layer, the thickness of which is computed by the expression from [5] as:

$$z_0 = \left(\frac{\kappa T}{g q_s}\right)^\frac{1}{4}$$

$C_{\scriptscriptstyle T}^2$ is zero at the surface and will be linearly interpolated in the viscous conductive layer. Thus the vertical profile of $C_{\scriptscriptstyle T}^2$ is described by

$$C_{\scriptscriptstyle T}^{2}(z,q_s) 2.68 \left( \frac{g}{T} \right)^{-\frac{2}{3}}\left( \frac{z}{q_s} \right)^{-\frac{4}{3}}\; \; \; \; {\rm for} \; \; z \geq z_0$$ = (19)

$$C_{\scriptscriptstyle T}^{2}(z,q_s) C_{\scriptscriptstyle T}^{2}(z_0,q_s) \cdot \frac{z}{z_0}\; \; \; \; \; \; \; \; \; \; \; \; \; \; \;{\rm for} \; \; z < z_0$$ = (20)

 The seeing FWHM angle is then obtained by integrating equation (7) twice over the height significant for seeing effects:

$$\theta = 5.182\cdot 10^{-5} \, \lambda^{-1/5}\left( 80 \cdo......ght)^{3/5}\left[ \int_{\rm H}{C_T^{2}(z)} dz\right]^{3/5}$$ (21)

 Integral seeing values computed by means of this model are plotted in fig. 6 below over various experimental data. The good agreement indicates that a similarity model as described above does account well for the observed seeing effects.

 

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Figure 6: Mirror seeing for an horizontal mirror in free convection for T_m > T_a. Laboratory data experiments ^{2, 3, 10} performed in various ranges of temperatures are compared with expression (18) and with the similarity model (19).

1998-07-05