National Aeronautics and Space Administration

Background Calculation

Using the "optimized" background:

XIMAGE> BACK/OPT
 Calculating background: Poisson statistics assumed
          16  2.4067664E-03
          32  2.2978019E-03
          64  2.1534730E-03
         128  1.5703201E-03
 >>> Optimum box size = 128
 Background box size = 128
 Background =1.5703E-03 cts/original-pixel
            =1.0050E-01 cts/image-pixel
            =4.5730E-04 cts/sqarcmin/s
            =3.1757E-08 cts/original-pixel/s

The minimum background turns out to be the largest box considered (128), because the blank areas around the edge of the image bring down the average, skewing the background calculation.

XIMAGE> BACK/BOX=128/DRAW
 Calculating background: Poisson statistics assumed
 Background box size = 128
 Background =1.5703E-03 cts/original-pixel
            =1.0050E-01 cts/image-pixel
            =4.5730E-04 cts/sqarcmin/s
            =3.1757E-08 cts/original-pixel/s

Note that the areas with colored squares drawn around them have been rejected, while the remaining area in used to calculate the background.

Decreasing the box size to 64 improves the calculation, as less blank areas have been included. There are, however, still several boxes which are approximately half empty that are not rejected.

XIMAGE> BACK/BOX=64/DRAW
 Calculating background: Poisson statistics assumed
 Background box size =  64
 Background =2.1535E-03 cts/original-pixel
            =1.3782E-01 cts/image-pixel
            =6.2712E-04 cts/sqarcmin/s
            =4.3550E-08 cts/original-pixel/s

A box size of 32 appears to be a reasonable size, with sufficient resolution to reject nearly all of the blank areas.

XIMAGE> BACK/BOX=32/DRAW
 Calculating background: Poisson statistics assumed
 Background box size =  32
 Background =2.2978E-03 cts/original-pixel
            =1.4706E-01 cts/image-pixel
            =6.6915E-04 cts/sqarcmin/s
            =4.6469E-08 cts/original-pixel/s

Although the blank area is not a problem with a box size of 32, it's clear that there are sources being counted as background. There are three qualifiers in the background command which allow for further tweaking the background calculation.

The first adjustable criteria compares the distribution of counts in the top half of a background box with the bottom half and the left half with the right half. Using a chi-square test, the probability that the distribution of each half matches the other is calculated and compared with the BXHPROB value. Probabilities less than BXHPROB are rejected. By default BXHPROB is set to 0.0 and has no effect on the background calculation. Logically, BXHPROB can range in value from 0.0 to 1.0, however values in the 0.0 to 0.2 range are recommended, as higher values tend to be too restrictive. The red boxes have been rejected based on the BXHPROB setting.

XIMAGE> BACK/BOX=32/BXH=0.1/DRAW
 Calculating background: Poisson statistics assumed
 Background box size =  32
 Background =2.1473E-03 cts/original-pixel
            =1.3742E-01 cts/image-pixel
            =6.2531E-04 cts/sqarcmin/s
            =4.3424E-08 cts/original-pixel/s

The second criteria, BARYLIM, calculates a barycenter using the counts in each pixel as a weight. By default if the barycenter is greater than 0.35 of the box width away from the box center, the box is rejected. The light blue boxes have been rejected due to this criteria.

We can make this criteria more restrictive than the 0.35 default:

XIMAGE> BACK/BOX=32/BARY=0.1/DRAW
 Calculating background: Poisson statistics assumed
 Background box size =  32
 Background =2.2097E-03 cts/original-pixel
            =1.4142E-01 cts/image-pixel
            =6.4351E-04 cts/sqarcmin/s
            =4.4688E-08 cts/original-pixel/s

The next rejection criteria checks to see if the counts within the box conform to a Poissonian distribution. This test, which cannot be tweaked, primarily rejects blank boxes and strong sources. A yellow box is drawn for boxes which don't pass this criteria.

The final criteria depends on the boxes that have, thus far, not been rejected. The distribution of the average background in the remaining boxes is compared to a Gaussian distribution. Box values more that SIGMULT standard deviations away from the mean are rejected. The default value for SIGMULT is 3.0. The magenta boxes have been rejected due to this criteria.

XIMAGE> BACK/BOX=32/SIG=1.0/DRAW
 Calculating background: Poisson statistics assumed
 Background box size =  32
 Background =2.1436E-03 cts/original-pixel
            =1.3719E-01 cts/image-pixel
            =6.2426E-04 cts/sqarcmin/s
            =4.3351E-08 cts/original-pixel/s

A chat level of 20 (command: chatter 20 20) combined with the draw option of the background command will plot each box with a number, while Ximage prints the reason for each rejection. For more details about the background calculation, a chat level of 25 or more can be used.

XIMAGE> CHAT 20 20
XIMAGE> BACK/BOX=64/DRAW

           70 - Barycenter >   0.3500000     from center
           80 - Non-poissonian stats (Chi>9 or Back=0)
           50 - Background too far from avg  4.9560547E-02