Sky Simulation Tests
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[edit] Source Motion
The Sky Simulation Program was tested for motion of one source between frames. The position of the peak in different frames, shift from first frame, expected shift obtained from calculation and error in the observed peak compared to the expected are shown below. The IRAF 'imexamine' routine was used to get the position of peak of each source. The error is less than 1.2 % and hence the Sky Simulation Program is found giving very good result.
Pixel shift expected = 0.6007 (for DEC of 10 deg. calculated from expressions given below)
Observed Expected Error
frame# xcent ycent x_shift y_shift x_shift y_shift dx (in pixels)
------ ------ ------ ------ ------ ------ ------- -------------
0 623.40 741.74 - - - - -
4 621.02 741.73 2.38 0.01 2.4 0 0.02
9 618.13 741.64 5.27 0.10 5.4 0 0.13
14 615.13 741.65 8.27 0.09 8.4 0 0.13
19 612.10 741.77 11.30 -0.03 11.4 0 0.10
24 609.10 741.75 14.40 -0.01 14.4 0 0.0
29 606.19 741.83 17.21 -0.09 17.4 0 0.19
34 603.30 741.69 20.10 0.05 20.4 0 0.03
39 600.21 741.59 23.19 0.15 23.4 0 0.21
44 597.32 741.79 26.08 -0.05 26.4 0 0.32
49 594.27 741.70 29.13 0.04 29.4 0 0.27
The centroids of the same sources as detected by 'peak' of ECLIPSE package:
frame# xcent ycent
------ ----- -----
0 622.1 741.0
4 620.3 741.0
9 617.0 740.8
14 614.2 740.9
19 611.4 740.6
24 608.4 740.5
29 605.1 740.6
34 602.3 741.0
39 599.3 741.0
44 596.5 740.5
49 593.2 740.9
Parameters of the test file:
FWHM_PIX = 2 pixels
SCAN_RATE = 0.0041666 deg/sec
FRAMETIME = 0.128 sec
FIELD_VIEW = 0.9 deg
PROJECTION = TAN
PIXSIZE = 3.164 arcsec
RA_START = 5.0
DEC_START = 10.0
JITTER = 0
Pixel Movement was calculated using the steps:
pixelization = (0.9 x 3600)/1024 arc-sec/pixel
scanrate = (360deg x 3600)/(24h x 3600) arc-sec/s
pixshift_rate = scanrate/pixelization pixels/s
pixshift_frame = pixelshift_rate x 0.128 pixels/frame
= 0.61 pixels/frame
pixmov = pixshift_frame x cos(dec)
Another test result:
The x value shift by 1 pixel between certain frames and 0 between others. Ideally the shift should be 0.6064 pixel per frame in this data as calculated using the steps given below. Then the total shift should be 5.4 pixels for 9 frames against the 5 seen in the results. The error in shift for each frame is due to the round off in the simulation output data. The coordinates of peak are found by binning the x,y data in terms of frequency in software 'Origin'.
The values and parameters of test data are given below.
shift from first expected shift error
frame no x y dx dy dx (in pixels)
-------- -- --- --- --- ---- -----------
frame 1: 400 58 - - - -
frame 2: 399 58 1 0 0.606 0.4
frame 3: 399 58 1 0 1.212 -0.2
frame 4 : 398 58 2 0 1.818 0.2
frame 5: 397 58 3 0 2.424 0.6
frame 6: 397 58 3 0 3.030 0
frame 7: 396 58 4 0 3.636 0.4
frame 8: 396 58 4 0 4.242 -0.2
frame 9: 395 58 5 0 4.848 0.2
Parameters of test file:
FIELD_VIEW = 0.900000 (in degree)
PIXSIZE = 3.164000 (in arcsec/sec)
SCANRATE = 0.004167 (in deg/sec)
FRAMETIME = 0.128000 (in sec)
INTEGRATIONTIME = 0.012800 (in sec)
SCAN_REFVAL = 6.400000 degree Fixed DEC
RA = 10.200000
DEC = 6.400000 (in degrees).
The test files and image files can be dowloaded from the Uploads area [[1].
[edit] PSF Test:
Test file was created using UVS_simulate_sky program. Giving scan rate as zero, 100 frames were combined by taking frametime as 12.8 sec (0.128sec x 100) to get sufficient number of events. The IRAF imexamine routine was used to get the FWHM of each source. This was done by selecting each source manually. The possible error in doing it was determined by comparing with the source center values obtained by another method (',') of the same routine.
PSF test (FWHM =2):
Calculated by IRAF imexamine routine(j,k and ',')
# Centroid Gaussian fit Error in centroid FWHM
X Y X Y error yerror xfwhm yfwhm mean_fwhm
---- ---- --- ---- ----- ------ ----- ----- --------
1 288.32 854.85 258.352 854.851 0.03 0 2.119 2.049 2.084
2 177.68 514.77 177.646 514.749 0.03 0.02 2.118 2.08 2.063
3 623.42 741.73 623.443 741.698 0.02 0.03 2.131 2.112 2.121
4 569.74 287.19 569.714 287.211 0.03 0.21 2.088 2.12 2.050
5 402.22 173.31 402.24 173.33 0.02 0.02 2.103 2.063 2.083
Calculated by 'peak'(peak -sF <file>):
# X Y fwhmx fwhmy mean_fwhm
---- ---- ----- ----- --------
1 287.4 853.9 2.28 2.09 2.18
2 176.5 513.6 2.27 2.20 2.23
3 622.5 740.8 2.39 2.26 2.32
4 568.8 286.1 2.19 2.20 2.20
5 401.1 172.2 2.16 2.17 2.16
CATALOG:
# RA DEC Counts/sec
---- ----- ---------
5.1 10.2 10000
5.05 9.8 8000
4.9 9.7 3000
4.8 10.3 1000
4.7 10.0 500
Parameters of the test file:
SCAN_RATE = 0 deg/sec
FRAMETIME = 12.8 sec (to add 100 frames)
FIELD_VIEW = 0.9 deg
PROJECTION = TAN
PIXSIZE = 3.164 arcsec
RA_START = 5.0
DEC_START = 10.0
JITTER = 0
PSF test (FWHM =3):
Calculated by IRAF imexamine routine(j,k and ',')
# Centroid Gaussian fit Error in centroid FWHM
X Y X Y xerror yerror xfwhm yfwhm mean_fwhm
---- ---- --- ---- ----- ------ ----- ----- --------
1 288.42 854.80 288.4 854.87 0.02 0.07 3.106 3.139 3.122
2 177.69 514.71 177.677 514.714 0.02 0.0 3.024 3.002 3.013
3 623.46 741.70 623.447 741.708 0.02 0.01 3.117 3.061 3.089
4 569.69 287.22 569.704 287.209 0.01 0.01 3.154 3.027 3.090
5 402.28 173.34 402.271 173.356 0.01 0.01 3.176 3.071 3.123
Calculated by 'peak':
# X Y fwhmx fwhmy meanfwhm
---- ---- ----- ----- --------
1 287.4 853.9 3.03 3.12 3.08
2 176.5 513.8 3.20 2.66 2.92
3 622.3 740.5 3.39 3.18 3.28
4 568.5 286.3 3.17 2.98 3.08
5 401.1 172.2 3.08 2.94 3.01
PSF test (FWHM =4):
Calculated by IRAF imexamine routine(j,k and ',')
# Centroid Gaussian fit Error in centroid FWHM
X Y X Y xerror yerror xfwhm yfwhm mean_fwhm
---- ---- --- ---- ----- ------ ---- ----- --------
1 288.28 855.02 288.33 855.016 0.05 0.04 4.129 4.081 4.105
2 177.65 514.79 177.739 514.762 0.09 0.05 4.046 4.107 4.076
3 623.47 741.68 623.463 741.73 0.01 0.05 3.95 4.059 4.0045
4 569.66 287.26 569.7 287.23 0.04 0.03 4.081 4.038 4.059
5 402.19 173.39 402.161 173.339 0.03 0.05 4.026 3.977 4.0015
Calculated by 'peak' of eclipse:
# X Y fwhmx fwhmy meanfwhm
---- ---- ----- ----- --------
1 287.2 853.6 2.81 3.75 3.25
2 176.4 514.0 3.95 4.36 4.15
3 622.5 740.2 4.10 3.97 4.04
4 568.4 286.4 4.29 3.98 4.13
5 401.6 172.6 3.60 3.87 3.73
The results show that the FWHM matches well with the given values hence the Sky Simulation Program is creating gaussian shaped sources. With zero scanning the FWHM in X and Y directions are nearly equal. The test files and image files can be dowloaded from the Uploads area [[2].
[edit] Dark Count Test:
Different average dark counts were generated for 5000 frames (640 sec of frame time without scanning). Mean and standard deviation were calculated using the expressions given below for theoretical model values. The measurement was done by IRAF routine imstat.
Total cts over frame = Dark_count x Integration_time x total_pixels
= Dark_cout x 0.128 x 1024 x1024 = Dark_cout x 134217.7
Total cts over 5000 frames = Dark_cout x 640 x 1024 x1024
= Dark_cout x 671,088,640
Mean per pixel = cts over 500 frames / 1024x1024
= Dark_cout x 640
CALCULATED(using above expressions) MEASURED USING IRAF (imstat)
Dark ----------------------------------- Measured ------------------------------
Count Counts Mean STDDEV counts MEAN(/pix) STDDEV MIN MAX
------- ---- ------ ------ --------- ------ --- ---
0.000001 671.1 6.4E-4 0.008 512 4.883E-4 0.02209 0. 1.
0.000005 3355.4 0.0032 0.0565 2063 0.002482 0.04984 0. 2
0.00001 6710.8 0.0064 0.08 5223 0.004981 0.07063 0. 2
0.00005 33554.4 0.032 0.178 26252 0.02503 0.1588 0. 3.
0.0001 67108.8 0.064 0.253 52557 0.05012 0.2255 0. 4
0.0005 335544.3 0.32 0.565 263203 0.251 0.5187 0. 5.
0.001 671088.6 0.64 0.8 526600 0.5022 0.7556 0. 7.
0.005 3355443.2 3.2 1.78 2634317 2.512 2.056 0. 15.
0.01 6710886.4 6.4 2.53 5269221 5.025 3.453 0. 24.
The values show that the dark count statistics is nearly Poissonian (STDDEV is square root of MEAN) if the dark count is less than of 0.005 counts/sec/pixel. The test files and image files can be dowloaded from the Uploads area [[3].
Parameters of test file:
Frames taken = 5000
DARKCOUNT = x c/p/s (given above)
DT = 1 (Exposure time as a fraction of Frametime)
JITTER = 0.0
PIXSIZE = 3.164
FIELD_VIEW = 0.9
FRAMETIME = 640
SCAN_RATE = 0
FWHM_PIX = 2
[edit] Jitter Distribution:
Created simulation data with jitter (0,1 and 2 pixels) for 500 frames for two stars. Examined the variation of jitter by detecting centroids of the stars and finding the their distribution. The IRAF imcntr routine is used for finding centroids after converting 500 frames to fits using ascii2fits program (available in downloads page). The IRAF routine can be run for several files at a time. (eg: imcntr 1.fits,2.fits,3.fits,.... > outfile). The centroids were picked by a simple c program and created suitable ascii file with parameters (same as simulation o/p file). The fits file was opened in ds9 and FWHM and standard deviation are obtained using imexamine routine.
jitter (pixel) peak_x peak_y stddev_x stddev_y fwhm_x fwhm_y fwhm_mean ------ ------ ------ ----- ----- ------- ------ ------- 2 742.66 624.39 0.6999 0.7118 1.648 1.67 1.659 2 178.61 515.69 0.7179 0.7277 1.691 1.714 1.702 1 624.468 742.65 0.352, 0.42 0.8292 0.9891 0.909 1 178.648 515.68 0.4375 0.447 1.03 1.053 1.042 0 624.1 743 0.2949 0.01976 0.6945 0.0465 0.371 0 178.92, 515.985 0.3441 0.1571 0.8103 0.37 0.590
The FWHM (fwhm_mean) is found to be roughly the jitter applied (in first column). The error may be caused by round off in converting ascii to fits using ascii2fits program. The histograms created by IRAF phistogram routine show the distribution in the centroid. This roughly obeys the gaussian distribution. The test files and image files can be dowloaded from the Uploads area [[4].
Count Rate:
Is the distribution in the count rate random with the right shape and right error.? yes it is gaussian with right fwhm and standard deviation. For small number of counts it obeys Poissonian distribution.
Noise:
Is the noise distributed properly? yes (dark count test)
Position:
Do the x and y positions match the star coordinates?
Is the distortion correct?
