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Appendix 1

Parametric search for Fried's parameter on globular cluster

We compare the results obtained using parameter search method with the Fried's parameter obtained using a conventional method and show that the results obtained using two different methods are in good agreement.

Parametric search on a globular cluster (NGC 1409)

We were looking for an image with many point sources in order to estimate the Fried's parameter using conventional methods like fitting a Gaussian and using its FWHM as a measure of the Fried's parameter tex2html_wrap_inline1639. We chose an image of the globular cluster NGC 1409 (observed by Prof. Ram Sagar and Mr. Alok Gupta at the Vainu Bappu Observatory using the 2.34 m Optical telescope) for this purpose.

Figure 1: A) Contour map of globular cluster NGC 1409 observed using the 2.34 m optical telescope at Vainu Bappu Observatory, Kavalur. The mean wavelength of observation is 5656 Å

Figure 2: A) Plot of seeing estimate obtained using parametric search and seeing estimated using average of FWHM tex2html_wrap_inline2153 (the factor of 1.12 is multiplied with the FWHM to take care of the non Gaussian nature of the Fried's coherence function)

The image is a 1024 tex2html_wrap_inline2155 1024 pixel CCD image with a plate scale of tex2html_wrap_inline2157. The mean wavelength of observation is 5656 Å. The contour of the globular cluster NGC 1409 is shown in Fig. 1 (click here)A. The field is approximately 10 arcmin tex2html_wrap_inline2155 10 arcmin. The isoplanaticity of the sky is not expected to be of that size. We divide the observed image into smaller sections, each of 50 arcsec tex2html_wrap_inline2155 50 arcsec. The parametric search algorithm is run on each such small sub images and the Fried's parameter is estimated. Since the plate scale and the mean wavelength of observation is known, the Fried's parameter can be now converted to "seeing" in arcseconds in the real domain.

On each subimage there are several point sources. A best fit Gaussian is made for each point source in the sub image and the average FWHM is estimated. This directly gives the seeing in pixel units. The plate scale is known and hence seeing is calculated in terms of arcseconds. A factor of 1.12 needs to be multiplied to these values to take care of the non-gaussian nature of the Fried's coherence function.

Figure 2 (click here)A gives the plot of the seeing estimated both using the parameter search method and also using the average FWHM of the Gaussians (corrected for the non-gaussian nature of the atmospheric psf) in each sub image. We see a similar trend in the seeing estimated using the two different methods. The values obtained using the two different methods agree within the error limits.

Seeing estimated using Seeing estimated using
Average FWHM Parametric Search
Frame of Gaussian fit
number tex2html_wrap_inline2155 1.12
(in arcsec) (in arcsec)
1 2.29 tex2html_wrap_inline2165 0.22 2.28
2 2.32 tex2html_wrap_inline2165 0.12 2.50
3 2.27 tex2html_wrap_inline2165 0.33 2.28
4 2.40 tex2html_wrap_inline2165 0.07 2.40
5 2.32 tex2html_wrap_inline2165 0.09 2.27
6 2.53 tex2html_wrap_inline2165 0.04 2.50
7 2.27 tex2html_wrap_inline2165 0.23 2.28
8 2.32 tex2html_wrap_inline2165 0.14 2.45
9 2.35 tex2html_wrap_inline2165 0.46 2.67
10 2.33 tex2html_wrap_inline2165 0.14 2.57
11 2.50 tex2html_wrap_inline2165 0.10 2.85
12 2.36 tex2html_wrap_inline2165 0.09 2.40
13 2.44 tex2html_wrap_inline2165 0.33 2.76
14 1.96 tex2html_wrap_inline2165 0.21 2.26
15 2.05 tex2html_wrap_inline2165 0.30 2.92
16 2.65 tex2html_wrap_inline2165 0.26 3.42
17 2.11 tex2html_wrap_inline2165 0.14 2.31
18 2.50 tex2html_wrap_inline2165 0.20 2.85

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