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\label{chap:abtheta}
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\label{chap:abtheta}
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These parameters are intended to describe the detected object as an elliptical
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These parameters are intended to describe the detected object as an elliptical
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shape. {\tt A} and {\tt B} are its \index{semi-major} semi-major and \index{semi-minor axis} semi-minor axis lengths,
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shape. {\tt A} and {\tt B} are its \index{semi-major} semi-major and \index{semi-minor axis} semi-minor axis lengths,
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respectively. More precisely, they represent the maximum and minimum spatial
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respectively. More precisely, they represent the maximum and minimum spatial
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\rms dispersion of the object profile along any direction. {\tt THETA} is the
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\rms dispersion of the object profile along any direction. {\tt THETA} is the
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position-angle between of the {\tt A} axis relative to the {\tt NAXIS1} \index{image} image axis. It is
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position-angle of the {\tt A} axis relative to the first image axis. It is counted positive in the direction of the second axis. Here is how they are computed:
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counted counter-clockwise. Here is how they are computed:
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2nd-order \index{moments} moments can easily be expressed in a referential rotated from the
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2nd-order \index{moments} moments can easily be expressed in a referential rotated from the
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$x,y$ \index{image} image coordinate system
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$x,y$ \index{image} image coordinate system
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by an angle +$\theta$:
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by an angle +$\theta$:
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\begin{equation}
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\begin{equation}
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