Fixed p attern noise comes about because of small centroiding errors resulting from the m ism atch between event profiles and the centroiding algorithm (C hapter 6). As a result, depending upon the severity of this m ism atch, a certain fraction of the events are cen troided in to the wrong subpixels in such a way th a t patterning w ith a period of 1 CCD pixel is superimposed onto the true image (F ig 3 .6 a).
Each event is centroided by firstly determining the event profile’s ’centre of gravity’ using th e 3-pixel centroiding algorithm
Centre Of Gravity = . ^ ^ ^ (3.1)
A + B - \- C ^ ^
where B is the peak d a ta value associated with th a t event. The algorithm outp uts answers in th e range of -0.5 to 0.5. In order to place the event into one of eight channels (sub pixels) this range of answers is initially subdivided into eight channels using boundary values which are separated by 0.125 CCD pixels. For example, an event would be placed
into Channel 1 if the result of the centroiding algorithm lay between -0.5 and -0.375 or would be placed in Channel 2 if the result of the centroiding algorithm lay between -0.375 and -0.25.
If the centroiding algorithm were to accurately centroid each event from a flat field, equal num bers of events would be centroided in to each subpixel and the o u tp u t image would appear ’flat’ (F ig S .6d ). However, fixed p a tte rn noise typically causes unequal numbers of events to be centroided into each subpixel if the subpixels have equally spaced boundary values.
The centroid position in x and y of each event is defined in w hat are called the cen troid lookup tables (C hapter 2). The position of a subpixel can be redefined in software by changing the d a ta stored in these centroid lookup tables. By changing th e subpixel boundary positions (i.e. by redefining the centroid positions of events), th e effect of fixed p attern noise can be minimized. A subpixel in which events are preferentially centroided can be made smaller by reducing the range of answers given by the centroiding algorithm , which apply to th a t subpixel. Similarly, a subpixel in which few events are centroided can be made larger by increasing the range of answers (from the centroiding algorithm ) which apply to it.
Finding by how much to change the position of each subpixel boundary is an iterative process and involves firstly sampling a fiat field image and analysing the count distribution in each subpixel. From a knowledge of this and the subpixel boundaries, the boundary positions can be changed in order th a t the next tim e a fiat field is sampled a more equal num ber of events are centroided into each subpixel (F ig 3 .6 b ). A new fiat field image is then resampled and the subpixel boundaries are changed until eventually (after several iterations) the ideal subpixel boundaries have been defined in the centroid lookup tables.
The fixed p attern noise can be corrected for by carrying out the following procedures; 1. Selecting a centroiding resolution of | of a CCD pixel so th a t d a ta in each of th e eight
subpixels is available. The centroiding resolution is set by executing F O R M A T and entering the num ber of subpixels/pixel required. This num ber is lim ited to 4 and 8 for XMM and so in this case the user should type F O R M A T 8.
2. Run the program L O O K U P which is used to analyse the count distribution in each subpixel and calculate the subpixel boundaries which are most likely to minimise the level of fixed p attern noise. A menu appears which asks the user w hether the
subpixel boundaries should be equally spaced (E ), reloaded from th e last tim e they were saved (R ), individually entered by the user (O ), or calculated from the subpixel count distribution of a flat fleld image (C ). The user has to firstly load th e centroid lookup tables w ith equally spaced subpixel boundaries in both x and y to provide the initial startin g boundary positions. The user types E a t the menu prom pt and then
X to specify in which direction the subpixel boundaries should be equally spaced.
L O O K U P is run again and at the menu prom pt the user retypes E and follows this by typing y to load the centroid lookup tables w ith equally spaced subpixel boundaries in y.
3. Carrying out an integration on a faint flat field image (to avoid a high proportion of coincident events), using a small section of the CCD. An integration is started , and continued until each subpixel has, on average, 10-20 counts in it. By co-adding rows or columns a cross section through this image will typically look like F ig 3 .6 a.
4. If, after im aging the flat fleld illumination, each subpixel does not contain an ap proxim ately equal num ber of events then the program L O O K U P is rerun in order to calculate a new set of subpixel boundary values. The user types C at the menu prom pt and then enters an area of the CCD over which the subpixel count distribu tion is to be calculated. This area should be free of the types of defect m entioned in Section 3.3.3 and have a size of typically 20x20 CCD pixels. The com puter proceeds to sum th e num ber of counts in each subpixel of a CCD pixel using Modulo 8 addi tion (e.g summing counts in the first subpixel (in x ) of every CCD pixel w ithin the specified area). By summing the counts in each subpixel over an area of the CCD, the subpixel count distribution has good count statistics w ith which to calculate new subpixel sizes. The program calculates the m ean num ber of summed counts/subpixel and then for each subpixel it estimates the change in boundary position required in order to minimize the degree of fixed pattern noise. For example, after analysing the count distribution in F ig 3 .6 a, the d ata shown in T a b le 3.3 m ight be presented.
C h an n el C o u n ta Old B o u n d ary V alues Suggested New B o u n d ary V alues 0 7600 0.6 0.5 1 7760 -0.376 -0.389 2 7786 -0.26 -0.282 7694 -0.126 -0.176 7360 0.00 -0.067 1064 0.126 0.047 7410 0.26 0.277 7640 0.376 0.386 0 .6 0 .6 M ean C o u n t/C h a n n e l» 6786