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Figure 3
Method to find the effective displacement [\xi_{0,180}] of two projections at 0° and 180°. (a) For each displacement [-X \,\lt\, \xi \,\lt\, X] the mean squared difference [\delta^2(\xi)] (black curve) and its gradient [\nabla\delta^2(\xi)] (gray curve) is computed. (b) Zoom in to the offset position [\xi_{0,180}] at which the function [\delta^2(\xi)] exposes a minimum which is characterized by a notch-like shape, indicated by the biggest jump in the gradient [\nabla\delta^2(\xi)] (dashed line). (c) Detector systems with increasing signal-to-noise ratios (6, 20, 44 dB) have been simulated by adding Gaussian noise. The stability of the algorithm is demonstrated by using only five rows (dash-dotted lines) of each image to compute [\delta^2(\xi)].

Journal logoJOURNAL OF
SYNCHROTRON
RADIATION
ISSN: 1600-5775
Volume 17| Part 4| May 2010| Pages 550-559
doi:10.1107/S0909049510011830
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