Spatial Analysis

Hopefully final reworking of CREATE/EXPOSURE_MAP (DOE/MPE 950601)

Principle of CREATE/EXPOSURE

The exposure map is based on an overlay of instrument maps. Instrument maps are measured flatfields of the ROSAT PSPC. They are available for different energy bands and can be found in the EXSAS calibration area. Since ROSAT moves (wobbles) during the observation and may have different roll angles, for creating the exposure maps an instrument map has to be shifted and rotated according to the attitude (taken from attitude.tbl) and added to the final exposure map. Doing this for each entry in the attitude table would cause excessive computing times. Therefore the entries in the attitude table are binned into an attitude histogram, reducing the number of necessary computations by a factor of 100 or so. Even then, CREATE/EXPOSURE is slow. The selection of the attitude entries takes into account the accepted times (read from the descriptors of the reference image). The instrument maps have to be transformed in several steps:

centering

The instrument maps as stored in the EXSAS calibration area are offset to the image center. The PSPC detector center is defined as (4119, 3929) in detector coordinates (detector pixels). In the instrument map image this corresponds to (257.936, 246.066) in image coordinates (image pixels). This is a shift with respect to the true image center (256.5, 256.5) of (1.436, -10.434) image pixels.

flipping

The instrument maps as stored in the EXSAS calibration area are flipped in y-direction.

scaling

The stepsize of the instrument maps is 16 detector pixels. With a detector pixel size of 0.9342 arcsec this corresponds to a stepsize of about 29.9 sky pixels. Note that that is very close to the standard for EXSAS PSPC images of 30 sky pixels. Close, but not close enough. They have to be rescaled.

rotating

The instrument maps have to be rotated according to the roll angle. Since the roll angle stays fairly constant during an observation and within the accepted times, this usually hast to be done only once. However, the program checks for this and re-rotates the instrument map if necessary.

wobbling

According to the attitude histogram, the rotated instrument map is shifted, multiplied with the exposure time corresponding to the bin of the attitude histogram, and added to the final exposure map.

What has been changed now

1. The rotating algorithm had a bug. This bug filled some pixels of the rotated instrument map twice, and others not. This resulted in unwanted noise of the exposure maps in the form of high and low streaks along the wobble direction. This bug has been fixed by rewriting the algorithm for filling the pixels in the rotated instrument map.
2. Centering, flipping, scaling, and rotating of the instrument maps was done in separate steps. Furthermore, centering, scaling and rotating were transformations using integer pixel coordinates (Result pixel coordinates were truncated to the nextlowest integer), causing slight sub-pixel artificial shifts. Now centering, flipping, scaling, and rotating of the instrument maps is done in one step. This saves time, since the coefficients of the transformation equations are computed in advance. Furthermore, the algorithm now interpolates between pixels instead of using truncated pixel coordinates. Artificial shifts are therefore removed. This has also the additional benefit that the exposure map is now smoother.
3. The binsize of the attitude list has now been fixed to the size of the image pixels of the reference image. This was also the default in earlier versions, but the user could set this parameter in the parameter file. Changing this parameter now is not possible anymore. This has the advantage that the wobble shift can now be measured in whole pixels, speeding up the operation a bit.
4. The bins of the attitude histogram and the corresponding shifts of the rotated instrument map were offset by 0.5 image pixel in each direction. This has been fixed now.

Consequences for the user

• The instrument maps now look smoother and have less noise.
• The alignment is slightly better. In extreme (and rare) cases the difference can be up to 2 image pixels.
• It is not possible anymore to specify the size of the attitude histogram binsize in X and Y. This value is now hardcoded to be equal to the image pixel size of the reference image. Old parameter files containing this parameter still work, but the parameter value for ATTREB given in the parameter file is not used anymore.
• CREATE/EXPOSURE is not compatible with HRI observations anymore. However, this is not a great loss since there are no instrument maps available for the HRI.
• The image size of the reference image must be 512 x 512 pixels. For other image sizes CREATE/EXPOSURE will work, but the resulting exposure map will not be aligned. This was so before the changes, too, but it should be noted here again.

R. Egger, R. Supper, S. Döbereiner 6/95

© X-Ray Group at MPE (group)
last update:1998/12/07 12:40:30, editor of this page:Stefan Döbereiner