Note: This Technote is superceded by information available at the CXCDS Caveats Web Page.
(2/29/00 - dd)
ACIS processing to go from pixel-quantized event coordinates measured by the ACIS system to real-valued sky coordinates can be summarized by the equation:
X,Y = DETfromCHIP( CHIPX,Y + 0.5*RANDOM_M1_P1() ) - Aspect_solution(t)In words the CHIPX,Y values are randomized by +/- 0.5 uniform distribution and then transformed to sky coordinates including the aspect correction.
The combination of aspect solution in the presence of large scale dither and the randomization results in an ACIS response to an incident spatial delta function that is described by a triangular response function in both X and Y with width at the base of 2 pixels, e.g.: "_/\_". Deconvolution with this function should recover the HRMA + aspect_error PSF alone.
Because the aspect solution alone produces a one pixel wide ACIS response function ("_-_") it is tempting to leave off the additional +/- 0.5 pixel randomization to improve the overall PSF. As will be shown below, depending on the specifics of the aspect solution and analyses to be performed this may not be desirable: for some aspect solutions and analysis objectives, the aspect correction alone can leave a pattern that has artificial structure at sub-multiples of the period of the pixel. The addition of +/- 0.5 uniform random blur exactly removes these artificial components.
---> Because the improvement in PSF is slight and the aspect specifics unknown a priory, it is prudent from a general use perspective to include the +/- 0.5 randomization; reprocessing with reduced or zero randomization can then be carried out when suggested in a specific analysis. The IDL procedure "sol_plot.pro", see "Need" section below, can be used to assess possible effects.
Discussion of removing randomization has its basis in the improvement in PSF that occurs. The EE curve looks better in the 0.5 to 2.0 arc second diameter region, with the 1 arc second diameter fraction increasing from ~60% to ~ 65%. The projected 1-D FWHM is reduced from ~40.5 um to ~37 um.
The need for randomization can be understood from the following plots:
Noticable substructure is visible. Randomization of +/- 0.2 is applied here, lower right panel and is not enough to fully remove the pattern.
As above but the full +/- 0.5 pixel randomization is applied.
The pattern is not quite so pronounced before the randomization.
With many more dither cycles the pre-randomized events seem more uniform... would need to quantify this however...
Basically each pixel sees the same aspect correction as its neighbors to high accuracy, and so the distribution of the aspect corrected events in each sky pixel follows the same pattern (of course there does not have to be an event at each frame readout for each pixel but the possible sky locations are correlated.) The result is that if the aspect correction creates some pixel substructure in one pixel it will be repeated in others and produce a noticable pattern. Randomizing by +/- 0.5 pixels removes these variations.
Please send any comments to
Dan Dewey at firstname.lastname@example.org.