Pixel Positions and Dimensions

If C$_{n}$ and W$_{n}$ represent the axis centre and width arrays for the n'th dimension of an NDF, then a pixel with index i in this dimension has its centre at coordinate C$_{n}$(i) and has a width of W$_{n}$(i) on the corresponding axis. It therefore extends along the axis from the point:

$C_{n}(i) - \frac{1}{2} W_{n}(i)$

to the point:

$C_{n}(i) + \frac{1}{2} W_{n}(i)$

In two dimensions the central ($x,y$) coordinate of a pixel with indices ($i,j$) would therefore be given by:

$(x,\: y) = (\: C_{1}(i),\: C_{2}(j) \: )$

and its size would be:

$\Delta x \: \times \: \Delta y = W_{1}(i) \: \times \: W_{2}(j)$

The axis variance array is used to represent any statistical uncertainty in a pixel's centre position and hence in the position of the pixel as a whole.¹⁶Like the NDF's main variance component (§), its values are estimates of the mean squared error in the pixel's position, so the value which would normally be quoted as the positional uncertainly (or used to plot error bars) is the square root of this value. Axis variance arrays may also be accessed directly as standard deviation values if required (see §).