Author: Arne Henden Date: 970307 Revision: #1 970307 Key Words: CCD, astrometry, observation, techniques
As opposed to stare-mode observations, drift scanning uses the rotation of the earth to scan strips in the sky. Since what the CCD sees is a projection of the curved sky into the flat plane of the CCD, a mapping takes place. Like a Mercator projection of the earth, there are distortions in this mapping that affect both the image shapes and the astrometric quality of drift scan images. This note will discuss some of these affects.
The scale of a CCD camera is given by
scale (arcsec/pixel) = [206.265*p]/f
where p = pixel size in microns, and f = focal length in mm. For the
TASS cameras, where p = 9 microns and f = 135mm, this gives a scale of 13.75
arcsec/mm.
Strictly speaking, drift scanning has no distortion if the scan follows a Great Circle (a line in the sky that forms a plane that passes through the center of the earth). There are two obvious great circles at any given location: the celestial equator and the meridian. If you used a one-dimensional CCD (that is, a 1xn format) and lined the long axis up so that it faced and was parallel to the celestial equator, it would image a 1-pixel high strip along the equator with no distortions and a scan rate time equal to
rate (sec/pix) = 86164.09 (sec/sideral day)
---------
[[360*3600 (arcsec)]/13.75(arcsec/pixel)]
or 0.9142 seconds/pixel at the equator. For 512 pixels as in a TASS
camera, the integration time would be 0.9142*512, or 468 seconds.
If you used a one-dimensional CCD and lined the long axis up so that it
faced and was parallel to the meridian, then it would image an n-pixel
high strip with no distortions but with only a one-pixel integration
time.
If you are scanning away from the equator, the star takes longer to move the same angular distance on the chip. At the North Celestial Pole (NCP), a star takes an infinite amount of time to transit. The basic relation is
rate{dec} (sec/pix) = rate{equator}
------------
cos[dec]
Obviously, we have two-dimensional CCDs, and therein lies the problem. If you project the sky onto a two-dimensional flat surface, then near the equator you get nearly a square grid, but that becomes more and more distorted as you approach the NCP, where the grid lines become complete circles. For an arbitrary location away from the equator but nowhere near the pole, stars follow curved tracks across the CCD. For example, a star entering the CCD field of view at the northeast corner will track south until it crosses the meridian, and then track back north until it exits the CCD field of view at the northwest corner (assuming the chip is properly aligned). What you see in the final output image, in the declination direction, is a star that is spread out in the declination direction, where the length of the spread is proportional to the declination.
Likewise, in Right Ascension, stars near the top of the chip are at higher declination and therefore move slower across the chip than stars near the bottom of the chip. The scan rate is only correct for one declination in the field of view; all others will be incorrect. This means that there will be a smearing of images in the RA direction, with the smearing proportional to the declination distance away from the correctly scanned declination, and this smearing is further proportional to the center declination of the chip.
These two affects have the result of an output image that is smeared out, with a larger fwhm in both RA and Dec from equivalent images taken with the same camera in stare mode.
However, that is not the full story. Note that the Dec smearing is always towards the NCP, and is worse the closer you get to the NCP. This means that stars are less smeared near the bottom of the chip than the top, and therefore there is a scale magnification in Declination that is dependent on the central declination of the chip. Likewise, stars near the top of the chip are transiting slower than stars at the center, but are being 'pulled' forward by the selected scan rate. This results in the RA smearing to be towards the east at the top of the chip, and towards the west at the bottom of the chip. In other words, the image looks like it has been sheared.
The equations for the magnitude of the RA and Dec smearing are given in Stone, et. al., 1996 AJ 111, 1721. I've run a typical TASS camera through the equations with the results given in Table 1. At Dec=0 (the equator), the RA distortion (drne,drse) is of the same sign since the north edge faces the NCP and the south edge faces the SCP. As soon as you get above 1.5 degrees Declination, then both edges are facing the NCP and the smear starts having different signs. A similar affect occurs for the Declination smear (ddne,ddse).
The smear becomes the same size as a pixel by the time the central declination reaches 4 degrees. This is one reason why scanning +-3 degrees from the equator is the preferred strip with these cameras. Note, however, that the astrometric performance is compromised right from the beginning. The FASTT system described by Stone limits astrometric observations to the region where smear <= 1.7FWHM.
There are several methods to circumvent this astrometric problem:
However, only options 1 and 2 are available to TASS cameras.
Tom's February data showed a fwhm of around 3 pixels. Since his scans were at -1 degree on average, the smear due to drift scanning would be around 6 arcsec max, which is less than one pixel and probably does not contribute to the large observed image size.
The astrometric accuracy measured on Tom's nights was around 3arcsec. Note that the RA shear is about +-3arcsec, and so may be a major contributor to the error budget. I noticed in my reduction that there was a correlation between Declination and RA error, which is probably related to this shear.
TABLE 1. SCAN DISTORTIONS FOR A TASS CAMERA
TASS camera Dec=768 RA=512 Scale=13.75
Dec drne ddne drse ddse rate
0 -2.305 0.769 -2.305 -0.769 0.91416
1 -5.448 1.293 0.839 -0.244 0.91430
2 -8.593 1.819 3.986 0.280 0.91472
3 -11.741 2.346 7.137 0.804 0.91542
4 -14.894 2.874 10.294 1.329 0.91640
5 -18.054 3.403 13.460 1.854 0.91766
6 -21.223 3.935 16.636 2.381 0.91920
7 -24.403 4.470 19.824 2.909 0.92103
8 -27.596 5.007 23.027 3.439 0.92315
9 -30.804 5.547 26.246 3.971 0.92556
10 -34.029 6.091 29.483 4.506 0.92827
11 -37.274 6.639 32.742 5.043 0.93127
12 -40.540 7.191 36.023 5.584 0.93459
13 -43.829 7.747 39.329 6.128 0.93821
14 -47.144 8.309 42.662 6.676 0.94215
15 -50.488 8.876 46.026 7.228 0.94641
16 -53.863 9.449 49.422 7.785 0.95100
17 -57.270 10.028 52.852 8.347 0.95593
18 -60.714 10.614 56.321 8.914 0.96121
19 -64.195 11.207 59.829 9.487 0.96684
20 -67.719 11.808 63.381 10.067 0.97283
21 -71.286 12.417 66.979 10.653 0.97920
22 -74.901 13.036 70.626 11.247 0.98596
23 -78.566 13.663 74.326 11.849 0.99311
24 -82.285 14.301 78.082 12.459 1.00068
25 -86.061 14.949 81.897 13.078 1.00867
26 -89.898 15.609 85.777 13.706 1.01710
27 -93.800 16.281 89.723 14.344 1.02599
28 -97.772 16.966 93.742 14.994 1.03535
29 -101.816 17.664 97.837 15.654 1.04521
30 -105.938 18.377 102.013 16.327 1.05559
31 -110.144 19.105 106.275 17.012 1.06649
32 -114.437 19.849 110.628 17.712 1.07796
33 -118.823 20.611 115.079 18.425 1.09002
34 -123.309 21.392 119.632 19.155 1.10268
35 -127.900 22.192 124.296 19.900 1.11599
36 -132.603 23.013 129.077 20.663 1.12997
37 -137.426 23.856 133.981 21.445 1.14466
38 -142.375 24.723 139.018 22.246 1.16009
39 -147.460 25.615 144.196 23.069 1.17631
40 -152.689 26.534 149.523 23.914 1.19336
41 -158.071 27.482 155.011 24.782 1.21128
42 -163.616 28.461 160.670 25.676 1.23013
43 -169.337 29.472 166.512 26.597 1.24996
44 -175.245 30.519 172.548 27.547 1.27084
45 -181.352 31.604 178.794 28.528 1.29282
46 -187.674 32.729 185.265 29.542 1.31599
47 -194.226 33.898 191.976 30.591 1.34042
48 -201.024 35.114 198.946 31.678 1.36620
49 -208.088 36.380 206.194 32.806 1.39342
50 -215.437 37.701 213.742 33.978 1.42219
51 -223.095 39.082 221.615 35.197 1.45262
52 -231.086 40.526 229.838 36.468 1.48485
53 -239.436 42.040 238.441 37.793 1.51901
54 -248.178 43.630 247.457 39.177 1.55527
55 -257.344 45.303 256.921 40.626 1.59380
56 -266.972 47.066 266.875 42.145 1.63479
57 -277.104 48.928 277.363 43.740 1.67848
58 -287.787 50.899 288.437 45.419 1.72510
59 -299.076 52.990 300.154 47.188 1.77494
60 -311.029 55.215 312.581 49.058 1.82833
61 -323.716 57.586 325.792 51.037 1.88561
62 -337.214 60.122 339.872 53.136 1.94722
63 -351.614 62.841 354.920 55.370 2.01362
64 -367.017 65.766 371.048 57.752 2.08536
65 -383.543 68.923 388.388 60.300 2.16310
66 -401.330 72.344 407.095 63.032 2.24756
67 -420.541 76.065 427.348 65.972 2.33962
68 -441.365 80.129 449.361 69.146 2.44033
69 -464.030 84.590 473.390 72.586 2.55091
70 -488.806 89.512 499.742 76.328 2.67284
71 -516.018 94.974 528.787 80.418 2.80790
72 -546.062 101.072 560.981 84.908 2.95830
73 -579.426 107.930 596.888 89.864 3.12672
74 -616.711 115.705 637.215 95.365 3.31655
75 -658.679 124.597 682.859 101.511 3.53206
76 -706.294 134.874 734.977 108.426 3.77876
77 -760.808 146.894 795.088 116.269 4.06383
78 -823.864 161.149 865.224 125.246 4.39688
79 -897.670 178.336 948.167 135.629 4.79099
80 -985.253 199.475 1047.834 147.782 5.26446
81 -1090.867 226.117 1169.906 162.211 5.84375
82 -1220.669 260.742 1322.963 179.629 6.56854
83 -1383.847 307.574 1520.575 201.084 7.50118
84 -1594.551 374.406 1785.543 228.174 8.74560
85 -1875.014 477.311 2159.283 263.467 10.48885
86 -2258.602 655.075 2725.519 311.350 13.10507
87 -2771.249 1026.156 3682.059 379.978 17.46722
88 -3119.750 2088.530 5630.935 486.316 26.19418
89 583.626 5578.479 11630.207 671.843 52.38039
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