XMM-Newton Science Analysis System


ommosaic (ommosaic-2.7.1) [xmmsas_20141104_1833-14.0.0]

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Cross-correlation

The cross-correlation coefficient, R $(\Delta x,\Delta y)$ between 2 images, $image_1 \quad and \quad image_2$, with offsets $\Delta x \quad and \quad \Delta y$ between their x and y origins, respectively, is computed from

R $(\Delta x,\Delta y) = \frac{sum_1}{\sqrt{sum_2 \times sum_3}}$ ,

where $sum_1= \sum_{i=1}^{nx} \sum_{j=1}^{ny} image_1(x_i, y_j) \times image_2(x_i+\Delta x,y_j+\Delta y)$ ,

$sum_2=\sum_{i=1}^{nx}\sum_{j=1}^{ny} image_1(x_i, y_j) \times image_1(x_i, y_j )$ ,

$sum_3=\sum_{i=1}^{nx}\sum_{j=1}^{ny} image_1(x_i, y_j) \times image_2(x_i+\Delta x, y_j+\Delta y )$ ,

where nx and ny are the image dimensions in the x and y directions, respectively. In the above formulae it is assumed that the mean image values have been subtracted from the images. R can vary from -1 to +1.