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DETERMINATION OF CENTROID OF CCD STAR IMAGES The to! 
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C. Fosu® *, G W. Hein °, B. Eissfeller® grey le 
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3 Dent of Geodetic Engineering, KNUST, Kumasi Ghana - fosucoll@hotmail.com regard] 
Institute of Geodesy and Navigation, University FAF Munich Germany — object. 
(guenter.hein, eissfeller) unibw-muenchen.de centre 
Commission II, WG 111/8 CENT 
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KEY WORDS: CCD star images, image co-ordinates, astro-geodetic co-ordinates, precise geoid, PSF fitting, image given 
moment analysis, centroid estimation, sub-pixel level define 
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ABSTRACT: mass € 
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The new microchip and sensor technology, charged couple device (CCD), has assumed a permanent position as the axis. T 
natural transducer for optical input to a computer. The CCD combined with the microcomputer have revolutionised the figure, 
whole discipline of observational astronomy at all stages from data gathering to data analysis, presentation and use. Not of the 
only has it brought the convenience of digital imaging to field astronomy but has also great potential in determining centre 
very accurate astronomic co-ordinates of a point at great speed and ease, compatible to GPS for the determination of 
deflection of the vertical and local or precise geoids. Despite the numerous advantages of the CCD in astronomical B.. - 
work most CCD users agree that individual devices have imperfections or various problems that have to be dealt with. i 
In using CCD in geodetic astronomy one major problem that has to be considered is whether the measuring accuracy of B = 
the image co-ordinates will be enough for the determination of astronomic latitude or. longitude. Just clicking on a star 
object in a digital image to determine its position in the image yields pixel accuracy. But to meet geodetic accuracies, VARL 
sub-pixel accuracies are required. In this work we employed least squares smoothing techniques on data obtained from 
astronomical observations using CCD zenith camera. The star image co-ordinates were estimated using the two main momet 
methods of centroid estimation, viz., moment analysis and PSF fitting. This paper compares these two methods of 
estimating image co-ordinates to sub-pixel level and their accuracies. Results so far indicate that star image o. z 
measurement accuracies better than 0.3 arcsecond can be obtained. They also show that PSF fitting method is more à 
adaptive to automation. = 
chosen as the representative position. The centre of mass 3 
1. Introduction or centroid of the object estimates the centre of area. g 
; Also determining the position of a star by just taking object 
Stars are point sources. However the image (clicking on) the position of its maximum intensity 
formed of stars by focussing through a lens is not would at best give the precision of measurement to one From 
a point but a blurred spot. Thus point sources pixel. It is therefore highly preferable to determine the variant 
emit light which is processed by the optical centre of mass or centroid (Eisfeller and Hein, 1994; and se 
system, because of diffraction (and the possible Buil, 1991). : invarie 
presence of aberration) (Kovalevsky, 1995), this (Jain | 
light is smeared out into some sort of blur spot 2. Principles of Centroiding origin: 
over a finite area on the image plane rather than There are two basic techniques used to estimate the momei 
focus to a point (Jain, 1989). When this patch is centroid of a star object. They are: This i: 
scanned the distribution of intensities can be 1 the image moment analysis more 
described by a mathematical function. This 2 profile fitting or point spread function (PSF) fitting. (Horn 
function is known as the point spread function accura 
(PSF) of the lens. It is the impulse response of the 2.1 IMAGE MOMENT ANALYSIS algorit 
system whether it is optically perfect or not. In a When a set of values has a tendency to cluster around (Schik 
well-corrected system, apart from a multiplicative some particular value, then it may be useful to 
constant the PSF is the Airy irradiance characterize the set by a few numbers that are related to 22 P 
distribution function (Longhurst, 1967) centred in its moments, the sums of integer powers of the values The b. 
the Gausian image point. The value of the spread (Horn 1986 pp.34, Press et al 1992 pp. 610-613). If an image: 
function depends only on the displacement of that object in an image is defined by the function B (x, y), distort 
location from the particular image point on which then the moments generated by this function give same 
the PSF is centred (Bove, 1993; Horn, 1986). interesting features of the object. For digital images the intensi 
(k+L)th order is defined by Papoulus theorem (Gonzalez 1993). 
For an object spread across an area Or several and Wintz 1987 pp. 421). series. 
ixels the object is no more just a point. We must a” X S. KI 
E give a precise meaning to the term 'co- Bi "e m y B(x.) () M 
ordinates’ or ‘position’. In order to determine the 
co-ordinate of the object, the centre of area is 
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