** Up:** Microthermal measurements of surface

The correlation between the astronomical seeing and the atmospheric
turbulence has been investigated by various authors
(Barletti et al. 1974,
1976;
Ken Knight et al. 1977;
Marks et al. 1996). They have measured the
small scale temperature structure functions in order to evaluate the
refractive index structure constants for atmospheric layers. These
refractive index structures have widely been used for calculating
the astronomical seeing quality. Their investigations reveal that the
parameter which gives a measure of the optical turbulence intensity related
to the refractive index inhomogeneities is the refractive index structure
coefficient (Coulman 1969;
Vernin & Muñoz-Tuñón 1994),
which is a measure of the average variability of the refractive index of light
in the atmosphere (Erasmus & Thompson 1986). The parameter is
connected with the temperature structure coefficient of the
microthermal field variations, which produce fluctuations in the refractive
index at optical wavelengths (Coulman 1969;
Barletti et al. 1974). The
relationship between refractive index fluctuations () and thermal
irregularities () at height *h* is given by

| |
(1) |

where *P*(*h*) and *T*(*h*) are the pressure in millibar (mb) and the
absolute temperature in Kelvin (K) respectively at height *h* in metre.
Hence the knowledge of as a function of altitude is prerequisite
for the estimation of the astronomical seeing quality of any place. Following
Barletti (1974)
and Marks et al. (1996), the process for evaluating
involves the measurement of the temperature function
at points *P*_{1} and *P*_{2} at same
level *h*, but horizontally separated by a distance *r* given by

| |
(2) |

where, *T*(*P*) is the temperature at point *P* and angle brackets denote the
ensemble average. As defined by
Obukhov (1949) this is related to
by

| |
(3) |

In our case, measuring the temperature differences at two points which are
horizontally separated by one metre apart, the value of is
numerically equal to the value in
units. The
relationship between *r*_{0}, the Fried's parameter and as a
function of height *h* through the
atmosphere has been given by Fried (1966) as

| |
(4) |

where is the wavelength and is the refractive index
structure constant, which gives a measure of the optical turbulence intensity
related to the refractive index inhomogeneities in the atmosphere at height
*h*. Vernin & Muñoz-Tuñón (1992) have mentioned that each
turbulent layer at its altitude contributes to the degradation of the image
according to the intensity of the turbulence. Thus represents the
sum of the contributions from all turbulent layers in the atmosphere. From the
theory of wave propagation in turbulent media given by
Tatarski (1961) and its
relevant application to the astronomical seeing quality
(Roddier 1981;
Coulman
1985) the relationship between seeing () and *r*_{0} is given
by Dierickx (1992) as

| |
(5) |

where *r*_{0} represents the diameter of the telescope aperture for which
diffraction limited image resolution is equal to the full width at half
maximum (fwhm) of the seeing limited image. Thus, *r*_{0} takes into account
all the different turbulent layers encountered by the light beam before reaching
the ground (Vernin & Muñoz-Tuñón 1992). Using expressions (4)
and (5), it is possible to write seeing as a function of as

| |
(6) |

The refractive index structure constant in this case represents the sum of
the contribution from all turbulent layers in the atmosphere
(Marks et al. 1996).
Vernin & Muñoz-Tuñón (1992) have mentioned that, in order
to assess the quality of an astronomical site, it is not sufficient to measure
only the optical turbulence integrated over the whole atmosphere but
also to evaluate the relative contribution to the smearing of the image from
each intervening slab. This information is valuable for deciding height of the
telescope location above the ground level in order to obtain better angular
resolution images. The turbulence contributions to seeing ()
originating from different layers is given by

| |
(7) |

where is the seeing contributed by turbulent layer.

** Up:** Microthermal measurements of surface

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