4 Theory of seeing

The relationship between the full width at half maximum (FWHM) of a stellar image point spread function (PSF) formed at the focus of a large telescope and Fried parameter r₀, is given by Dierickx (1992) as

$$\epsilon_{FWHM} = \frac{0.98}{r_{{\rm o}}}\lambda ,$$ (1)

where $\lambda$ is the wavelength. The value of $r_{{\rm o}}$represents the diameter of the telescope for which diffraction limited image resolution is equal to the FWHM of the seeing limited image (cf. Fried 1966).

 

 

Table 2: Instruments used in the survey and their technical characteristics

Seeing
Data handling	Pentium PC's
Telescope (Site 1)	52 cm; f ratio = 13
	Fork mounting
Telescope (Site 2)	38 cm; f ratio = 15
	Single pier mounting
Camera at each site	CCD (ST4); size = 192 $\times$ 165 pixels2
	pixel size = 13.74 $\mu$ $\times$ 16.0 $\mu$
Power supply (DIMM)	Generators
Date acquisition rate	every 10 millisecond
Meteorology
Meteorological all	Wind speed ($\pm$0.1 m/s)
weather station	Wind direction ($\pm$1 degree)
Configuration	Relative humidity ($\pm$1%)
Availability	Air temperature ( $\pm 0.01^\circ$C)
	Solar radiation ($\pm 0.001$ w/m2)
	Soil temperature ( $\pm 0.1^\circ$C)
	Rainfall ($\pm$0.25 cm)
Data acquisition rate	1 hour
Power supply (AWS)	Batteries
Microthermal tower	20 m tower and three sensors
	placed at heights of 6, 12 and 18 m
Data acquisition rate	every 1 s

The variance ( $\sigma^{2}$) of the two dimensional image position is (cf. Vernin & Muñoz-Tuñón 1995) given as

$$\sigma^{2} = 0.373 \epsilon_{FWHM}^{2}\left( \frac{r_{0}}{D}\right)^{1/3}.$$ (2)

Thus measuring the image motion at the focus of a telescope of aperture Dand at wavelength $\lambda$, the Fried parameter r₀ and hence the seeing can be deduced from Eq. (1). This technique of measuring image motion suffers from the erratic motion of the telescope and it is difficult to separate the image motions due to turbulence and those due to telescope, which includes wind shaking, guiding and dome effect etc. The differential image motion monitor (DIMM) measurements eliminate the effects due to the motion of the telescope and hence enables one to measure the contributions of the atmosphere to the image degradation. The DIMM principle is to produce twin images of a star with the same telescope via two entrance pupils separated by a fixed distance. The assumption that Kolmogorov turbulence theory accurately describes the effects of atmosphere upon images, enables us to assess the longitudinal and transverse (parallel and perpendicular to the aperture alignment) variance of the differential image motion. The variance of the image motion in the direction parallel to the line joining the subapertures is given by (see Sarazin & Roddier 1990)

$$\sigma_{{\rm l}}^{2} = 2 \lambda^{2} r_{0}^{-5/3}\left( 0.179 S^{-1/3} - 0.0968 d^{-1/ 3}\right ) ,$$ (3)

where S is the diameter of the two entrance pupils and d is the separation between them. The corresponding expression for the differential image motion perpendicular to the line joining the two apertures is

$$\sigma_{{\rm t}}^{2} = 2 \lambda^{2} r_{0}^{-5/3}\left( 0.179 S^{-1/3} - 0.145 d^{-1/3 } \right ) .$$ (4)

It should be noted that these relations are valid if S/d $\leq$ 0.5 (Sarazin & Roddier 1990 and references therein). Measuring $\sigma_{{\rm t}}$and $\sigma_{{\rm l}}$ enables us to estimate the respective r₀, which when used in Eq. (1) gives the longitudinal and transverse seeing respectively. In the present case the value of S/d is 0.15 and 0.21 for 52 cm and 38 cm telescopes respectively.

Figure 2: A comparison of longitudinal and transverse seeing for the two sites in Devasthal. Straight line has unit slope and zero intercept

Figure 3: Seeing at Devasthal Site 1 plotted against UT. The date of observation along with the median seeing value (inside bracket) and the number of points are indicated sequentially on each panel