Legendre Fitting Method in Image Processing of X-ray Focal Spot

Legendre fitting method is important for analyzing the compressed core image of the ICF experiments. The method is used to analyze the X-ray focal spot of a planar anticathode accelerator in this paper. The system setup for X-ray focal spot imaging and the fundamental of the Legendre fitting method is detailed. The asymmetry features caused by Legendre polynomials of different modes are revealed. The fitting results for contours at 15%, 20%, 25%, 50% of the maximum intensities are proposed. The main factors which influence the fitting results are analyzed. In general, the shape of the focal spot is close to a normal circle. Most magnitude of p<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>~p<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</inf> is less than 2% of p<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf>. It is a precondition to find the center coordinate precisely for a high quality fitting. Fitting the contours of the four quadrants respectively can reduce the residual error significantly at the expense of using four sets of p<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> to express the fitting curve. The new method can reveal more details of the symmetry for the X-ray accelerator, which is meaningful for improving the accelerator performance.