Coverage Simulations for WISE Detector Acceptance Testing

I. Overview

In support of WISE detector acceptance testing, simulated depth-of-coverage maps have been generated using bad pixel masks provided by the WISE project science office. The objective of these simulations is to help assess the impact of the bad pixel number and clustering on achieved WISE sky coverage.

Important Note - These simulations are not intended to represent what will be the net sky coverage from actual WISE observations. They make use of approximate mission design parameters and simple image coverage combination algorithms that may not be representative of the actual parameters.

II. Methodology

1. Inputs

1. Mask images provided by project office. 1024x1024 FITS format. Bad pixels denoted with a value "1", good pixels denoted with a value "0".

2. Procedure

1. Resample images to 512x512, preserving masked pixels, then upsample back to 1024x1024. Note: this simulates the 23μm band (W4)..
2. Optionally flip/rotate image. The projected orientation of the focal planes onto the sky is currently not specified. This step allows testing of various possibilities.
3. "Normalize" mask:
1. masked areas=0
2. unmasked areas= (Test A: 8 sec for exposure time) or (Test B and later: 1 for coverage)
4. Each frame is added into an 8000x4000 pixel field image.
5. Start in upper left of image and step down (-y) for orbits and across (+x) for new orbit.
6. Add in-scan step in y for each frame in an orbit (adjustable).
7. Add cross-scan step for new orbit (adjustable - can be positive or negative).
8. Add y phase change of (adjustable).
9. Repeat for new orbit.
10. Skip a specific number of orbits to simulate losses due to SAA avoidance maneuvers.
11. Crop out the central 2048x1024 of the field image and write out as FITS format coverage image.
12. Add header information.

3. Coverage Maps

The coverage maps generated by the procedure described above are 2048x1024 pixel FITS format images that represent the depth-of-coverage over two adjacent WISE fields-of-view. The pixel values in each maps are the accumulated number of coverages in that pixel (for Test A, the pixel is the accumulated exposure time). For Test B runs and later, the values will range from 0 to n, where n is the total number of coverages on the pixel. For the Test A run, pixel values are 0 to n*8. 8 seconds is used as the exposure time for simplicity. The actual net exposure time is 8.8 sec.

4. Caveats

The simulations do not take into account the following effects that can both increase and decrease achieved coverage.

1. Frame convergence off the ecliptic equator. The simulation approximates the coverage on the ecliptic. Coverage off the ecliptic will be better than shown in the simulation.
2. The effective "smearing" of bad pixels that will occur when the raw frame images are convolved with a smoothing kernel and resampled to a common pixel scale during the production of the WISE Atlas Images. This effect will increase the "sphere of influence" for each band pixel.
3. The true orbit-to-orbit scan path cross-stepping. In practice, the spatial offsets between adjacent orbits may not be evenly distributed because of the forward and backward "jumping" in the mission design.

III. Test Results

A brief summary of the results from each simulation are given below. Table 1 contains the basic parameters of each test, including the mask image used, array orientation (rotation), in-orbit and cross-orbit step sizes, orbit frame phase, and the number of orbits dropped to simulate SAA avoidance maneuvers. Click on the "X" in the "FITS map" column to download the gzip'd Coverage Map FITS image.

Following Table 1 are basic results from each test set. These include a simple histogram of the coverage statistics and JPEG views of the resulting coverage maps. The coverage histograms tables give the fraction of pixels having the specified depth-of-coverage (or for Test run A, exposure times in integer multiples of 8 sec). The JPEG representations of the coverage maps are shown in false color with black denoting smallest coverage and white denoting greatest coverages. For Test Run A, the color range corresponds to a minimum value of 55 sec (6.9 coverages) and a maximum of 112 (14 exposures). For Test Run B, the minimum display value is 6.9 and maximum is 14, and 8-deep coverage areas are indicated in dark blue. For Test Run C, the display range is 5.9 to 14, and 8-deep coverage areas are indicated in blue.

Table 1 - Coverage Simulation Test Summaries

Test Run	Test No.	Device	Mask Name1	Rotation (deg)	In-scan step (arcmin)	Cross-scan step (arcmin)	Frame Phase2	Dropped Orbit3	FITS map4
A	1	Si:As FPA25	fpa25_more_bad_pix_tot.fits	0	42.3	4.7	17%	0	X
	2	Si:As FPA25	fpa25_more_bad_pix_tot.fits	90	42.3	4.7	17%	0	X
	3	Si:As FPA25	fpa25_more_bad_pix_tot.fits	0	42.3	4.7	17%	1/8	X
	4	Si:As FPA25	fpa25_more_bad_pix_tot.fits	90	42.3	4.7	17%	1/8	X
	5	Si:As FPA29	fpa29_more_bad_pix_tot.fits	0	42.3	4.7	17%	0	X
	6	Si:As FPA29	fpa29_more_bad_pix_tot.fits	90	42.3	4.7	17%	0	X
	7	Si:As FPA29	fpa29_more_bad_pix_tot.fits	0	42.3	4.7	17%	1/8	X
	8	Si:As FPA29	fpa29_more_bad_pix_tot.fits	90	42.3	4.7	17%	1/8	X
B	1	Si:As FPA31	bad_pix_tot31.fits	0	41.538	4.69	random	0	X
	2	Si:As FPA31	bad_pix_tot31.fits	90	41.538	4.69	random	0	X
	3	Si:As FPA31	bad_pix_tot31.fits	0	41.538	4.69	random	1/8	X
	4	Si:As FPA31	bad_pix_tot31.fits	90	41.538	4.69	random	1/8	X
	5	Si:As FPA31	bad_pix_tot31.fits	0	41.538	5.87	random	0	X
	6	Si:As FPA31	bad_pix_tot31.fits	90	41.538	5.87	random	0	X
C	1	Si:As FPA25	more_bad_pix_tot25.fits	0	41.538	+30.65, -22.15	random	4/15	X
	2	Si:As FPA25	more_bad_pix_tot25.fits	90	41.538	+30.65, -22.15	random	4/15	X
	3	Si:As FPA29	more_bad_pix_tot29.fits	0	41.538	+30.65, -22.15	random	4/15	X
	4	Si:As FPA29	more_bad_pix_tot29.fits	90	41.538	+30.65, -22.15	random	4/15	X
	5	Si:As FPA31	more_bad_pix_tot31.fits	0	41.538	+30.65, -22.15	random	4/15	X
	6	Si:As FPA31	more_bad_pix_tot31.fits	90	41.538	+30.65, -22.15	random	4/15	X
	7	Si:As -	no bad pixels	-	41.538	+30.65, -22.15	random	4/15	X

Notes to Table 1

1. Name of FITS format mask image provided by project office.
2. Staggering of frames on adjacent orbits. Values expressed as percentages denote a constant offsets on successive orbits, in percentage of FOV. "Random" denotes a random frame offset applied to each orbit.
3. Fraction of orbits omitted from coverage map to simulate SAA avoidance maneuvering. A value of "0" indicates that no orbits were dropped. For Runs A and B, 1/8 indicates one orbit out of eight was omitted. For Run C, four consecutive orbits out of each 15 were omitted.
4. Click on this column to download the simulated coverage map in gzip'd FITS format.

1. Test Run A

Summary Software proof-of-concept run. Comparison of FPA25 and FPA29 Si:As devices. Fixed orbit frame phasing (unrealistic). <1% of pixels have <8 coverages if no orbits lost. <1% (FPA25) and 3.2-3.3% (FPA29) have <8 coverages if 1/8 orbits dropped.

1. Si:As FPA25, 0° rotation, 17% frame phase, 0 dropped orbits

Coverage histogram for fpa25_more_bad_pix_tot_cov.fits:
Depth (secs) =  56.00  64.00  72.00  80.00  88.00  96.00 104.00 112.00
Frac         = 0.0000 0.0005 0.0383 0.3366 0.3227 0.2720 0.0283 0.0016

2. Si:As FPA25, 90° rotation, 17% frame phase, 0 dropped orbits

Coverage histogram for fpa25_more_bad_pix_tot_cov_90.fits:
Depth (secs) =  56.00  64.00  72.00  80.00  88.00  96.00 104.00 112.00
Frac         = 0.0000 0.0004 0.0361 0.3406 0.3225 0.2717 0.0271 0.0015

3. Si:As FPA25, 0° rotation, 17% frame phase, 1/8 dropped orbits

Coverage histogram for fpa25_more_bad_pix_tot_cov_8.fits:
Depth (secs) =  48.00  56.00  64.00  72.00  80.00  88.00  96.00 104.00
Frac         = 0.0001 0.0076 0.1412 0.3775 0.2880 0.1716 0.0133 0.0008

4. Si:As FPA25, 90° rotation, 17% frame phase, 1/8 dropped orbits

Coverage histogram for fpa25_more_bad_pix_tot_cov_8_90.fits:
Depth (secs) =  40.00  48.00  56.00  64.00  72.00  80.00  88.00  96.00 104.00
Frac         = 0.0000 0.0001 0.0071 0.1409 0.3797 0.2883 0.1703  0.0128 0.0007

5. Si:As FPA29, 0° rotation, 17% frame phase, 0 dropped orbits

Coverage histogram for fpa29_more_bad_pix_tot_cov.fits:
Depth (secs) =  48.00  56.00  64.00  72.00  80.00  88.00  96.00 104.00 112.00
Frac         = 0.0000 0.0005 0.0108 0.1003 0.3456 0.3315 0.1915 0.0190 0.0008

6. Si:As FPA29, 90° rotation, 17% frame phase, 0 dropped orbits

Coverage histogram for fpa29_more_bad_pix_tot_cov_90.fits:
Depth (secs) =  40.00  48.00  56.00  64.00  72.00  80.00  88.00  96.00 104.00 112.00
Frac         = 0.0000 0.0000 0.0009 0.0126 0.1026 0.3454 0.3202 0.1978 0.0195 0.0009

7. Si:As FPA29, 0° rotation, 17% frame phase, 1/8 dropped orbits

Coverage histogram for fpa29_more_bad_pix_tot_cov_8.fits:
Depth (secs) =  32.00  40.00  48.00  56.00  64.00  72.00  80.00  88.00  96.00 104.00
Frac         = 0.0000 0.0000 0.0015 0.0298 0.1923 0.3735 0.2724 0.1208 0.0092 0.0004

8. Si:As FPA29, 90° rotation, 17% frame phase, 1/8 dropped orbits

Coverage histogram for fpa29_more_bad_pix_tot_cov_8_90.fits:
Depth (secs) =  32.00  40.00  48.00  56.00  64.00  72.00  80.00  88.00  96.00 104.00
Frac         = 0.0000 0.0001 0.0021 0.0311 0.1933 0.3716 0.2672 0.1251 0.0089 0.0005

Figure 1 - Test A.1 FPA25	Figure 2 - Test A.2 FPA25	Figure 3 - Test A.3 FPA25	Figure 4 - Test A.4 FPA25
Figure 5 - Test A.5 FPA29	Figure 6 - Test A.6 FPA29	Figure 7 - Test A.7 FPA29	Figure 8 - Test A.8 FPA29
False-color 2048x1024 JPEG images of coverage maps produced in Test Run A. Color indicates exposure time (number of coverages). Color range is 55 sec to 112 sec in all images. Black regions have 55 sec or less exposure and white regions have 112 sec or greater exposure. 64 sec exposure (8 coverages) is indicated in dark blue. Click on the thumbnails to see full-size JPEG maps.

2. Test Run B

Summary Si:As FPA31 device. Random orbit-orbit frame phasing which should be more realistic. More precise value used for in-scan stepping (41.538 arcmin) based on 5720 sec orbital period and 11 sec duty cycle. Cross-stepping for runs B.1-B.4 analogous to Test Run A: Constant cross-scan step of 10% of FOV (4.69 arcmin). Runs B.3 and B.4 drop one out of 8 orbits. Cross-stepping for runs B.5 and B.6 represent extreme case in which cross-stepping is large enough to give only an average of 8 deep coverages (5.87 arcmin).

For 10% FOV cross-stepping, <1% of pixels have fewer than 8 coverages if no orbits are dropped. Approximately 1.5% of pixels have fewer than 8 coverages with one orbit in 8 is missed. For 12.5% FOV cross-stepping, 5.7-6.5% of pixels will have fewer than 8 coverages depending on the array orientation.

1. Si:As FPA31, 0° rotation, random frame phase, 0 dropped orbits

Coverage histogram for fpa31_bad_pix_tot31_cov.fits:
Depth (num) =   6.00   7.00   8.00   9.00  10.00  11.00  12.00  13.00  14.00  15.00
Frac        = 0.0000 0.0001 0.0032 0.0571 0.3521 0.3179 0.1653 0.0824 0.0215 0.0006

2. Si:As FPA31, 90° rotation, random frame phase, 0 dropped orbits

Coverage histogram for fpa31_bad_pix_tot31_cov_90.fits:
Depth (num) =   7.00   8.00   9.00  10.00  11.00  12.00  13.00  14.00  15.00
Frac        = 0.0001 0.0034 0.0648 0.3531 0.3083 0.1632 0.0824 0.0241 0.0006

3. Si:As FPA31, 0° rotation, random frame phase, 1/8 dropped orbits

Coverage histogram for fpa31_bad_pix_tot31_cov.fits:
Depth (num) =   5.00   6.00   7.00   8.00   9.00  10.00  11.00  12.00  13.00
Frac        = 0.0000 0.0006 0.0146 0.1572 0.3668 0.2762 0.1375 0.0426 0.0046

4. Si:As FPA31, 90° rotation, random frame phase, 1/8 dropped orbits

Coverage histogram for fpa31_bad_pix_tot31_cov_90.fits:
Depth (num) =   5.00   6.00   7.00   8.00   9.00  10.00  11.00  12.00  13.00
Frac        = 0.0000 0.0005 0.0159 0.1595 0.3713 0.2654 0.1379 0.0446 0.0050

5. Si:As FPA31, 0° rotation, random frame phase, 5.87' cross-can step, 0 dropped orbits

Coverage histogram for fpa31_bad_pix_tot31_cov_5.87.fits:
Depth (num) =   5.00   6.00   7.00   8.00   9.00  10.00  11.00  12.00
Frac        = 0.0001 0.0023 0.0548 0.3925 0.3352 0.1593 0.0469 0.0089

6. Si:As FPA31, 90° rotation, random frame phase, 5.87' cross-can step, 0 dropped orbits

Coverage histogram for fpa31_bad_pix_tot31_cov_5.87_90.fits:
Depth (num) =   5.00   6.00   7.00   8.00   9.00  10.00  11.00  12.00
Frac        = 0.0001 0.0028 0.0618 0.3870 0.3310 0.1568 0.0501 0.0103

Figure 9 - Test B.1 FPA31	Figure 10 - Test B.2 FPA31
Figure 11 - Test B.3 FPA31	Figure 12 - Test B.4 FPA31
Figure 13 - Test B.5 FPA31	Figure 14 - Test B.6 FPA31
False-color 2048x1024 JPEG images of coverage maps produced in Test Run B. Color indicates depth-of-coverage. Color range is 6.9 to 14 in all images. Black regions have 7 or fewer coverages and white regions have 14 or more coverages. 8 coverages is indicated in dark blue. Click on the thumbnails to see full-size JPEG maps.

3. Test Run C

Summary Si:As FPA25, FPA29 and FPA31 devices. Random orbit-orbit frame phasing. In-scan step size 41.538 arcmin (based on 5720 sec orbital period and 11 sec duty cycle). Cross-stepping simulates actual mission design: +30.65 arcmin followed by -22.15 arcmin. Sawtooth longitude stepping. After 15 orbits, this gives an average cross-scan step of 4.25 arcmin, which is slightly faster than the precession rate. Data loss due to SAA avoidance is simulated by dropping four consecutive orbits out of each 15.

Approximately 10%-14% of pixels have fewer than 8 coverages with FPA 25. 18%-20% of the area has fewer than 8 coverages with FPA29. With FPA31, 19%-22% of the area has fewer than 8 coverages.

For reference, a test of a hypothetical "perfect" Si:As detector with no bad pixels was run with the same scanning pattern. The test includes the 4 pixel wide "reference pixel" border as the other arrays, but no masked pixels. The results are shown in the entries for Test Run C.7 in the table below and in Figure 21. Even with no bad pixels, approximately 9.5% of the area receives fewer than 8 samples.

1. Si:As FPA25, 0° rotation, random frame phase, 4/15 dropped orbits

Coverage histogram for fpa25_more_bad_pix_tot_cov.fits:
Depth (num) =   4.00   5.00   6.00   7.00   8.00   9.00  10.00  11.00  12.00  13.00  14.00 
Frac        = 0.0000 0.0001 0.0086 0.1289 0.2844 0.2908 0.1679 0.0882 0.0260 0.0048 0.0003

2. Si:As FPA25, 90° rotation, random frame phase, 4/15 dropped orbits

Coverage histogram for fpa25_more_bad_pix_tot_cov_90.fits:
Depth (num) =   5.00   6.00   7.00   8.00   9.00  10.00  11.00  12.00 
Frac        = 0.0001 0.0063 0.0972 0.2579 0.3522 0.2083 0.0653 0.0128 

3. Si:As FPA29, 0° rotation, random frame phase, 4/15 dropped orbits

Coverage histogram for fpa29_more_bad_pix_tot_cov.fits:
Depth (num) =   4.00   5.00   6.00   7.00   8.00   9.00  10.00  11.00  12.00  13.00  14.00  15.00 
Frac        = 0.0000 0.0015 0.0243 0.1736 0.3024 0.2703 0.1505 0.0513 0.0171 0.0059 0.0028 0.0001

4. Si:As FPA29, 90° rotation, random frame phase, 4/15 dropped orbits

Coverage histogram for fpa29_more_bad_pix_tot_cov_90.fits:
Depth (num) =   3.00   4.00   5.00   6.00   7.00   8.00   9.00  10.00  11.00  12.00  13.00  14.00  15.00 
Frac        = 0.0000 0.0000 0.0013 0.0210 0.1580 0.2916 0.2637 0.1539 0.0745 0.0287 0.0067 0.0005 0.0000 

5. Si:As FPA31, 0° rotation, random frame phase, 4/15 dropped orbits

Coverage histogram for more_bad_pix_tot31_cov.fits:
Depth (num) =   3.00   4.00   5.00   6.00   7.00   8.00   9.00  10.00  11.00  12.00  13.00 
Frac        = 0.0000 0.0001 0.0025 0.0305 0.1596 0.3376 0.2704 0.1391 0.0507 0.0092 0.0003

6. Si:As FPA31, 90° rotation, random frame phase, 4/15 dropped orbits

Coverage histogram for more_bad_pix_tot31_cov_90.fits:
Depth (num) =   3.00   4.00   5.00   6.00   7.00   8.00   9.00  10.00  11.00  12.00  13.00 
Frac        = 0.0000 0.0001 0.0029 0.0345 0.1839 0.3139 0.2860 0.1353 0.0376 0.0057 0.0001

7. Hypothetical "perfect" array - No bad pixels, random frame phase, 4/15 dropped orbits

Coverage histogram for perfect-cov.fits:
Depth (num) =   6.00   7.00   8.00   9.00  10.00  11.00  12.00  13.00 
Frac        = 0.0043 0.0922 0.3081 0.3129 0.1750 0.0845 0.0217 0.0013 

Figure 15 - Test C.1 FPA25	Figure 16 - Test C.2 FPA25
Figure 17 - Test C.3 FPA29	Figure 18 - Test C.4 FPA29
Figure 19 - Test C.5 FPA31	Figure 20 - Test C.6 FPA31
Figure 21 - Test C.7 "Perfect" Array
False-color 2048x1024 JPEG images of coverage maps produced in Test Run C. Color indicates depth-of-coverage. Color range is 5.9 to 14 in all images. Black regions have 6 or fewer coverages and white regions have 14 or more coverages. 8 coverage areas are indicated in blue. Click on the thumbnails to see full-size JPEG maps.