Author: Michael Richmond
Date: 970228
Revision: #2 970303: clarified local sky subtraction procedure,
added note on astrometric accuracy
Key Words: CCD, astrometry, observation, techniques
Tom Droege acquired a set of images with a triplet at his home near Chicago (longitude approx 88:20, latitude approx 41:50) during the month of February, 1997. He posted a message describing his dataset to the TASS mailing list, and urged members to try their hand at reducing the images. The images are largely I-band, with a few V-band; unfortunately, there are no fields covered in both passbands.
I spent about a week, on and off, trying to reduce the data. My goal was to produce lists of detected stars for each image, calibrated both astrometrically and photometrically. As I struggled to meet this goal, I found many bugs and inadequacies in the XVista software package. This project certainly has improved XVista, and I hope to release an improved version sometime soon.
This document describes my first attempt to reduce the data. I discovered that my choice of a five-sigma threshold for object detection was conservative: there are clearly many more stars visible in the images than are included in my analysis here. There are other improvements that could be made in the reduction process, too, but I have decided that it's more important to describe my work than to spend more time trying to make it marginally better.
Tom distributed a set of 20 images, consisting of
There are, therefore, a total of 15 images of the night sky, from two different nights. Note that the "dark" images were taken one week after any of the night-sky images.
Note also that there are no twilight-sky or "dome" flatfield images, which might yield better flatfield vectors than night-sky images. There was no choice but to use images of the night sky to try to flatten the target frames.
Below is a table showing the date, time, and central position
for each frame.
Table 1. Image names, positions, times
# H = high galactic latitude # L = low galactic latitude # # sky values for images g0493946,g0493955 re-calculated with bin=2, # to avoid even/odd errors in my reduction procedures # # the "RA" and "Dec" values are equinox 2000 coordinates # at the rough center of each image # pixel # name date time camera RA Dec sky skysig FWHM g0483967.fts 03-02-1997 11:13:48 0 I H 202.34 -1.90 -27918 55 3.4 g0483977.fts 03-02-1997 11:27:04 0 I H 205.67 -1.90 -28511 50 3.5 g0493669.fts 13-02-1997 04:03:37 0 I L 104.16 -1.88 -27710 104 3.6 g0493678.fts 13-02-1997 04:16:53 0 I L 107.49 -1.87 -27665 112 3.5 g0493946.fts 13-02-1997 10:42:37 0 I H 204.18 -1.89 -28030 48 3.3 g0493955.fts 13-02-1997 10:55:55 0 I H 207.52 -1.89 -27982 49 3.2 g1493669.fts 13-02-1997 04:03:37 1 V L 119.10 -1.04 -25080 185 2.3 g1493678.fts 13-02-1997 04:16:53 1 V L 122.42 -1.04 -25075 191 2.4 g1493946.fts 13-02-1997 10:42:37 1 V H 219.13 -1.04 -26547 46 2.6 g1493955.fts 13-02-1997 10:55:55 1 V H 222.46 -1.04 -26539 46 2.5 g2483921.fts 03-02-1997 10:07:23 2 I H 199.54 -0.79 -28884 49 3.5 g2483931.fts 03-02-1997 10:20:42 2 I H 202.90 -0.79 -28869 45 3.8 g2493623.fts 13-02-1997 02:57:18 2 I L 101.40 -0.76 -26748 82 4.4 g2493900.fts 13-02-1997 09:36:02 2 I H 201.36 -0.77 -28082 48 3.7 g2493909.fts 13-02-1997 09:49:22 2 I H 204.71 -0.77 -28010 56 3.8
Tom used Norman Molhant's data acquisition program TM3GET11 to read the data from his triplet. Norman's program quite properly converts the 16-bit unsigned camera output into 16-bit signed integers before storing them in FITS files; it therefore places a keyword BZERO = 32768 into the FITS header. My XVista software has inherited an unfortunate feature from the distant past (when computers didn't have enough memory to fit an entire image into RAM at once): it performs all calculations in 16-bit signed integers, and so will lost the top bit if it converts the FITS values back into their original range of 0 to 65535. I therefore modified the FITS header of each image file so that it contained BZERO = 0. Readers will notice that I quote many "dark" and "sky" values which are large, negative integers; you may find the value more familiar if you add 32768.
Some CCD chips contain "extra" columns at the edge which are shielded from photons. These can be very useful in removing bias/dark current from a raw image, because they provide an example of the value a pixel would have if no light touched it -- in other words, the zero point of the intensity scale. Based on Kodak's technical specs for the KAF-0400 chip, we believe that there are such columns in TASS images. Norman's program produces two sets of such pixels: if we start counting columns with zero (i.e. 0, 1, 2, ...), they are
For each of the dark images (one for each CCD), I created a "row vector" by finding the median value along every column. Thus, from an original image which was 895 rows by 896 columns, I created a "dark vector" which was 1 row by 896 columns.
Clearly, these dark images have a consistent pattern: the pixel values on the left-hand side (low columns) are higher than the rest, decaying quickly to the typical value. Therefore, I concentrated on the "dark columns" on the right-hand side of the chip (high columns), hoping to find values which would be representative of the columns covering the "data area". I discovered that pixels in columns 783-791 seem to satisfy my requirements:
Note that the Kodak spec sheet claims that columns 781 and 782 should also be "dark"; however, when I examined some of the target images, I noticed that these columns had slightly higher values than the others in a row which featured a bright star. Apparently, some of the charge "leaks" through to these columns.
Therefore, I decided to use columns 783-791 as the "bias/dark columns" in all the images.
Here's the idea behind their use: it's quite possible for the "bias level" of a CCD camera to vary slowly, over the course of several hours/days/weeks. One source of such change is very subtle variations in the input voltage, temperature of the electronics, etc. However, one can hope that the shape of the "dark vector" will remain the same, and that changes in the overall bias level merely shift the "dark vector" up or down by a constant amount. So, if one can measure the "dark vector" at any one time, one can apply it to an image taken at some other time merely by shifting it up or down so that the pixels in the "bias/dark columns" of the "dark vector" match the values in the image.
Therefore, I created "dark vectors" for each CCD chip, using the dark images Tom provided; the values of each dark vector are shown in the plot above. For each one, I calculated the mean level inside the "bias/dark area" in columns 784-791, and stuffed this into the FITS header of the "dark vector". Given some other image, I planned to subtract the dark current as follows:
In practice, I discovered that the values for Delta
ranged from -125 to +162 ADU.
Recall that the dark images were acquired at least one week
after the other images.
Unfortunately, after all data reduction and analysis, as I was writing this summary, I discovered that I had made a mistake the final step of this process during the preparation of flatfield vectors: instead of subtracting Delta, I added it instead. This means that my flatfield vectors must be in error (probably by a few percent), and consequently all my "final" images also must be in error. Rats. I can re-process all the data in the future, but I will continue writing this report; the reader should remember that there is an error derived from the bias/dark subtraction which affects all the results reported here.
We expect that the warmer a CCD chip is, the higher its dark current. Since Norman Molhant's data acquisition program TM3GET11 records the CCD temperature for each row of data, we can check to see if this relationship exists.
For each image, I measured the mean value inside the "bias/dark area", columns 784-791. I also measured the mean value in column 794, which is said to contain "CCD Temperature". Here's a graph of the "bias/dark" average versus the "CCD Temperture:"
There appears to be a correlation between the value of column 794 and the mean of the "bias/dark area." This would make sense if column 794 was proportional to the temperature. However, Norman's documentation states:
pixel 794: resi is the thermistor's resistance in kiloohms
pixel 795: resi is the thermistor's resistance in kiloohms
resi = (196592400 / (ADUs - 32768)) - 1000;
if (resi < 1300) resi = 1300;
temperature = 136.55 - 77.246 * sqrt (log (resi) - 7.1671);
which implies that the pixel values are inversely
proportional to temperture. So, if I'm interpreting all this
correctly, the figure implies that the "bias/dark area"
has larger pixel values when the CCD temperature decreases.
Does this make sense?
Remember that I made quite an error in generating these flats.
Ideally, one should create flatfield vectors from some source other than images of the night sky, for several reasons. First, there are many stars in the night sky, which tend to contaminate measurements of the background value. Second, the night sky is dark (surprise!), and so the signal-to-noise ratio is lower than it would be in images of a bright source. One might try using images of the twilight sky to create flatfield vectors (although there can be large gradients in the illumination of the night sky over the 3-degree TASS field of view); or one might try placing a diffuse screen over the camera during the day. However, since neither option was available to me for this dataset, I used the night-sky images themselves to create flatfield vectors.
The method was relatively simple:
Below are plots of the vectors derived in this way from each of Tom's raw images: for CCD 0, CCD 1, and CCD 2.
All the vectors have the same large-scale appearance: pixel values are small on the left, increase to the right, reach a peak near the middle of the chip, then decrease slightly to the right edge. However, there are small-scale differences between vectors from different cameras, and vectors taken at different times. Note that the vectors taken from images at low galactic latitude, where the stellar density is high, show many little bumps and wiggles; these are caused by contamination of the true background level by many stars.
I decided to make master flats for each camera, rather than use the median of each image to flatten itself (mostly because I wanted to avoid the little wiggles in the crowded fields). For each camera, I picked two consecutive images taken at high galactic latitude, and calculated the median vector, using all pixels in both images together.
I then used the master flat for each camera to reduce all the night-sky images taken with that camera.
When I finished with dark-subtraction and flatfielding, I discovered that there were still some large-scale features left in the images. Some of these are due to my error in creating the master flats (see above). Some of the variation, however, occurs in the other direction: variation from top-to-bottom within in image, which means variation with time. The images g0483967 and g0483977 clearly show large variations (around 400-500 ADU) over the course of the exposure, and there are smaller variations (around 50 ADU) in images g2493900 and g2493909.
In order to make a more uniform background for the next step in reduction (finding stars), I decided to try to remove the large-scale variations in those images which showed large effects. I created a box-shaped filter with diameter 57 pixels, and moved it over these images, replacing each pixel value with the median value of pixels near the filter's edge. The result was a very smooth version of the original image, from which stars and other small-scale features had been removed. I then subtracted this smooth version from the original, yielding an image with a relatively flat sky background and unmodified small-scale features.
These images were used only in the star-finding step, and not for photometry; I always used the "original" images to measure stellar magnitudes, even those with non-uniform backgrounds.
I made no such modification to the images which seemed to have a flat sky background.
For each frame, I determined an overall sky value by fitting a gaussian to the histogram of pixel values near its peak. In Table 1, you can see the values for the sky (the location of the peak of the gaussian) and the sky-sigma (the width of the gaussian).
For a couple of the images (g0493946, g0493955), I discovered that my reduction procedures had introduced a weird pattern in the final pixel values. The sky histogram appeared to be two interleaved distributions, one much higher than the other: somehow, the reduction preferentially yielded either even or odd integer values. In order to measure the sky value properly, I binned the pixel values into bins of width 2 ADU, so that the even/odd differences would disappear.
Once I had a clean, reduced frame for each field, I measured the FWHM of several bright, isolated stars interactively. My program calculated a local sky value in an annulus around the star I chose, subtracted the sky from all pixels within a small (5-pixel) radius around the cursor position, and calculated a central position by fitting a gaussian to the marginal sum in both directions. Using this center, the routine created a 1-D radial profile for each pixel within 5 pixels, and then fit a gaussian to that profile. I wrote down the FWHM values for several stars, typically finding a range of 0.4 pixel or so; I chose the center of the range as the characteristic FWHM for the image. You can find that value in Table 1.
I got the impression in several images that stars near the left-hand side of the frame (the Northern side) were a bit sharper than those in the middle, or near the right-hand (Southern) side. This may just be coincidence.
I ran a few preliminary tests to find stars. Examining the output, I found that my software measured values for FWHM which varied quite a bit within a single frame; faint stars usually had smaller widths than bright ones. I decided that my software might find widths that varied from the "typical" value by up to +/- 1 pixel.
I used the stars program within the XVista software package to detect sources in each image. I set it to find
As mentioned earlier, the threshold I selected, five times the standard deviation of the sky, is a conservative one. I noticed quickly that some faint stars, clearly visible to the eye, were not being detected. Nevertheless, I found enough stars to exercise my reduction and analysis procedures. Keep this in mind when you read about the limiting magnitude below.
The number of stars detected in each image varied
greatly with galactic latitude, but was about the
same in the V and I passbands:
Table 2: number of stars detected
image filter subtract smoothed? latitude number of stars -------------------------------------------------------------------------- g0483967 I yes high 476 g0483977 I yes high 467 g0493669 I no low 1401 g0493678 I no low 1333 g0493946 I no high 494 g0493955 I no high 543 g1493669 V yes low 1400 g1493678 V yes low 1272 g1493946 V no high 456 g1493955 V no high 547 g2483921 I no high 481 g2483931 I no high 545 g2493931 I yes low 1315 g2493900 I yes high 559 g2493909 I yes high 526
The stars program measures the position of each star as follows:
I used the phot program in the XVista software package to measure aperture magnitudes for each star detected in the previous step. There are a number of choices I made here:
Here are the aperture sizes I used for Tom's images:
Table 3. Aperture sizes
image image aperture radii (pixels)
-----------------------------------------------------------------
g0483967 g0483977 3.5, 3.0, 4.5
g0493669 g0493678 3.5, 3.0, 4.5
g0493946 g0493955 3.2, 2.7, 4.2
g1493669 g1493678 2.4, 1.9, 3.4
g1493946 g1493955 2.6, 2.1, 3.6
g2483921 g2483931 3.7, 3.2, 4.7
g2493623 4.5, 4.0, 5.5
g2493900 g2493909 3.8, 3.3, 4.8
After I had processed all the star lists to extract instrumental magnitudes, I realized that the estimated uncertainty in magnitude was always listed as "99.00", a special value which means that the uncertainty could not be calculated. I must have introduced an error somewhere in the process of estimating this uncertainty. Certainly, should I choose to re-reduce these images, I will fix the problem; but, as results below show, the extracted magnitudes themselves are properly calculated.
One quick test of the accuracy of the procedure
which extracts magnitudes
is to compare the instrumental magnitudes of stars
which appear in the "overlap area" of two consecutive
images. Since these are not only the same stars, but
the same raw pixel values, one expects them to yield
nearly identical magnitudes;
there may be small differences in the dark subtraction,
flatfielding and perhaps sky subtraction between the two.
It was possible to find large samples of stars in the overlap
area only for the images near the galactic plane.
Table 4. Check on instrumental magnitudes
all stars bright stars
image image filt N delta sig N delta sig
---------------------------------------------------------------
g0493669 g0493678 I 27 -0.05 0.15 14 -0.01 0.02
g1493669 g1493678 V 16 0.01 0.04 8 0.00 0.01
Here, delta is the average difference in instrumental
magnitudes for a set of N stars in the overlap area,
and sig is the standard deviation from the mean.
I report the differences for all stars in common,
and for the brighest half of all stars in common.
Not surprisingly, the bright stars yield much
smaller difference and scatter than bright+faint stars.
Once I had a list of stars, with measured (row, col) position and an instrumental magnitude, I could try to match the stars with those from some astrometric catalog. My approach is a very simple one: I assume that there is a transformation of the following sort:
x = A + B*row + C*col
y = D + E*row + F*col
where (x, y) are the spherical coordinates of a star
projected onto a plane tangent to the center of the field.
This approximation is commonly used, and is certainly
appropriate for the small fields of view (5-15 arcmin)
found in most CCD cameras.
Since the TASS images span more than 3 degrees,
however, it is likely that this transformation may
yield very high accuracy over the entire field.
I had in the past written a program that attempted to find the position on the celestial equator from which a star list was created; this was the automatic astrometric calibration by E-mail facility. Over the past few months, I've discovered that this works only about half the time; for some fields, there just isn't enough overlap between the brightest 50 or so stars detected in an image, and the small catalog of stars (a subset of the Guide Star Catalog) for which I have pre-calculated some matching information.
This set of images was no exception: some of them were successfully identified by the automatic procedure, some weren't. Therefore, I created a somewhat simpler matching procedure that relies upon the user to supply a decent position for the frame. Since Norman Molhant's data acquisition program TM3GET11 places an approximate RA and Dec into the header of each FITS image, I think this should not be hard to extract in some automated way.
Using this simple procedure, I was able to match (row, col)
positions for stars in each image to (RA, Dec) values
for stars in the Hubble Guide Star Catalog.
A rough position for the center of each image, equinox 2000,
is listed above in
Table 1.
Below I list properties of the astrometric solution for each field.
Table 5. Astrometric calibration
image B C E F scale Nstar sigma ----------------------------------------------------------------------------- g0483967 13.6932 -0.0551 -0.0035 -13.7403 13.7167 426 4.7 g0483977 13.6849 -0.0458 0.0003 -13.7442 13.7145 404 4.1 g0493669 13.6847 -0.0588 -0.0098 -13.7454 13.7150 1154 5.8 g0493678 13.6904 -0.0478 -0.0055 -13.7430 13.7167 1141 5.6 g0493946 13.7205 -0.0509 0.0064 -13.7506 13.7355 455 4.5 g0493955 13.7257 -0.0417 0.0006 -13.7488 13.7372 475 4.6 g1493669 13.6927 0.0454 -0.0012 -13.6487 13.6707 1009 5.2 g1493678 13.7036 0.0434 -0.0018 -13.6496 13.6766 915 5.1 g1493946 13.7360 0.0514 0.0014 -13.6510 13.6934 336 4.4 g1493955 13.7249 0.0488 -0.0012 -13.6568 13.6908 405 4.9 g2483921 13.7549 -0.0446 0.0034 -13.8192 13.7870 424 4.5 g2483931 13.7424 -0.0370 -0.0010 -13.8182 13.7803 471 4.3 g2493623 13.7006 -0.0500 -0.0063 -13.8182 13.7593 1050 7.1 g2493900 13.7649 -0.0420 0.0012 -13.8234 13.7942 432 4.4 g2493909 13.7535 -0.0356 0.0025 -13.8189 13.7861 449 4.4Here, the coefficients BCEF of the TRANS are listed, as well as the overall plate scale derived via the formula
scale = sqrt { abs(B)*abs(F) + abs(C)*abs(E) }
One can derive the angle of rotation between the chip's (row, col)
coordinate system and the catalog's (RA, Dec) from these coefficients,
but I have not done so.
The scale is given in units of arcseconds per pixel.
The results for each camera are reasonably consistent, although
the slight jump in scale on CCD 0 between early and late times
on the same night of Feb 12, 1997, is puzzling.
I accepted any stars which fell within a distance D=15 arcsec of a corresponding star in the GSC as "true matches." The penultimate column lists the number of "true matches" found in common on the image and in the GSC, from which the solution was derived. The final column lists the standard deviation between the measured position and the catalog position, in arcseconds.
The values in the final column are disturbingly large. They correspond to a precision of about 0.3 pixels. Now, a general rule of thumb is that one can find the centroid of a well-sampled, symmetric PSF to at least 0.1 pixels, and sometimes much less. There are three reasons that I might have calculated such imprecise positions:
Let me test the first hypothesis. If the errors are caused by distortions from one edge to the other of the field of view, I would expect them to be small in a sub-section of the entire image. I choose image g0493669 for testing, and extracted all the stars which fell within a box of size 200 rows and 200 columns, near the center of the image. Matching these stars alone to the GSC, I found
Another way to check if the scatter is caused by distortion is to compare the raw (row, col) positions measured from two different images for stars in the same part of the sky. One would expect that the distortion should be similar in each image, and therefore the scatter should be smaller in this comparison. I used star lists from images g2483931 and g2493900, both taken with the same camera.
I conclude that the unexpectedly large scatter in measured position is not primarily due to distortion across the field of view, but perhaps caused by some (variable?) asymmetry in the PSF, or perhaps due to errors in my software.
Note added Mar 3, 1997: Arne Henden points out that some of the GSC stars I used were much fainter than any star visible in the images; hence, some of the matches were spurious. He suggested restricting the GSC sample to bright stars, mag < 13. When I tried this on one field, g2493900, I found I could decrease the scatter in position from 4.4 to 2.9 arcsec.
Once each star list has its positions calibrated into (RA, Dec), one can compare it to a catalog of standard stars to find any standards which appears in the list. I have created a list of 669 stars with UBVRI measurements from papers written by Arlo Landolt:
Fortunately for us, each consecutive pair of Tom's images falls in one of the Selected Areas containing a photometric sequence of Landolt stars. Since I used the same aperture to extract instrumental magnitudes from consecutive images, I can transfer the photometric zero-point from one image to its neighbor with some hope of avoiding large errors.
Recall that the night of February 2, 1997, had occasional clouds. The images g0483967, g0483977, g2483921 and g2483931 therefore may be expected to have relatively poor photometry.
Unfortunately, there is no field for which Tom provided both V and I images. Therefore, the best one can do to calibrate these data photometrically is to assume that there are no color effects (i.e., that the TASS V passband matches the Landolt V passband perfectly, and TASS I matches Landolt I); with this assumption, one calibrates by
Now, as mentioned above, the threshold I chose for finding stars in these images was pretty high. Therefore, although a typical Selected Area might have 10 Landolt standards, which would all fit entirely within a single TASS image, I found only a few Landolt standards per field. I suspect strongly that lowering the threshold would yield more standards.
For each pair of consecutive images, I tried to match the
star lists with the Landolt catalog.
For each aperture (recall that I used 3 different aperture sizes
to extract instrumental magnitudes from each image),
I calculated the mean difference Dmag between instrumental
and Landolt magnitudes, as well as the standard deviation sig of
the differences from the mean.
Table 6. Photometric calibration
aper R aper R-0.5 aper R+1.0
image filt field Nstar Dmag sig Dmag sig Dmag sig
------------------------------------------------------------------------------
g0483967 I 0
g0483977 I SA105 2 4.021 0.024 4.125 0.041 3.887 0.004
g0493669 I SA98 2 3.677 0.003 3.793 0.003 3.523 0.003
g0493678 I 0
g0493946 I SA105 3 4.038 0.024 4.175 0.024 3.845 0.027
g0493955 I 0
g1493669 V SA99 6 3.695 0.021 4.084 0.028 3.576 0.025
g1493678 V 0
g1493946 V SA106 3 3.728 0.057 3.875 0.072 3.594 0.037
g1493955 V 0
g2483921 I 0
g2483931 I SA105 3 3.914 0.011 4.030 0.010 3.762 0.012
g2493623 I SA98 1 3.569 3.695 3.369
g2493900 I 0
g2493909 I SA105 2 3.853 0.059 3.957 0.071 3.707 0.044
It would, of course, be nicer to have more than 2 or 3 (or 1!)
standard per field, but this suffices for the current needs.
Note that the typical agreement between measured and Landolt magnitudes,
after making a single offset, is typically 0.05 magnitudes,
or about 5 percent.
This is similar to accuracies I've derived for other sets
of TASS data (see
Technical Note 19,
for example), but is probably not the best one can do.
Note also that there is little difference between the accuracy provided by each of the three apertures. It's nice to have evidence that the exact size of the aperture isn't critical.
I then applied the zero-points listed above to the instrumental
magnitudes for all stars in all images.
Table 7. Distribution of measured magnitudes
name filter lat 6 7 8 9 10 11 12 13 14 15 ---------------------------------------------------------------------------- g0483967 I H 4 7 18 26 71 131 199 20 0 0 g0483977 I H 2 6 12 38 65 132 183 28 1 0 g0493669 I L 2 16 48 154 401 512 239 23 4 1 g0493678 I L 0 20 63 158 358 469 239 21 3 2 g0493946 I H 5 9 16 30 71 134 175 53 1 0 g0493955 I H 0 4 15 44 79 140 211 50 0 0 g1493669 V L 0 0 23 38 118 278 522 386 35 0 g1493678 V L 0 1 18 42 117 263 402 396 33 0 g1493946 V H 0 0 7 17 39 78 144 162 9 0 g1493955 V H 0 3 5 23 45 96 159 194 22 0 g2483921 I H 2 5 9 24 65 139 212 24 1 0 g2483931 I H 3 10 15 38 68 165 210 36 0 0 g2493623 I L 5 24 55 169 407 461 186 6 0 2 g2493900 I H 0 9 12 36 70 140 232 60 0 0 g2493909 I H 2 5 13 30 66 158 207 45 0 0In rough terms, the number of stars detected rises to mag 11 or 12, then drops pretty sharply. Let me re-iterate that I used a relatively high threshold for detecting stars, so that the true limiting magnitude for these images is somewhat fainter than this table would suggest.
There are a number of the I-band images (but not the V-band images) which cover common areas of the sky. One way to assess the accuracy of photometry is to compare the magnitudes of the same star in two different images. I have done that for all pairs of images covering the same area, and list the results in the table below. I give the differences between all stars in common, and between "bright" (I < 11.0) and "faint" (I >= 11.0) subsamples. There are three tables, one for each choice of aperture size (but the results are very similar in each).
Table 8. Comparison of magnitudes of from different images,
aperture radius = FWHM pixels
# all stars (I < 11.0) (I >= 11.0)
# image1 image2 filt N mu sig N mu sig N mu sig
------------------------------------------------------------------------------
g0483967 g0493946 I 186 0.028 0.080 92 0.024 0.036 94 0.032 0.107
g0483967 g2483921 I 22 0.101 0.101 9 0.164 0.026 13 0.058 0.112
g0483967 g2483931 I 225 0.101 0.106 97 0.100 0.068 128 0.102 0.128
g0483967 g2493900 I 175 0.081 0.115 74 0.088 0.057 101 0.075 0.144
g0483967 g2493909 I 83 0.011 0.083 35 0.006 0.042 48 0.015 0.104
g0483977 g0493946 I 201 -0.005 0.082 89 0.004 0.026 112 -0.011 0.107
g0483977 g0493955 I 173 0.039 0.081 87 0.053 0.062 86 0.026 0.096
g0483977 g2483931 I 50 0.014 0.090 24 0.011 0.043 26 0.018 0.119
g0483977 g2493909 I 164 -0.025 0.094 82 -0.015 0.048 82 -0.036 0.123
g0493669 g2493623 I 63 0.080 0.072 48 0.085 0.047 15 0.064 0.124
g0493946 g2483931 I 162 0.036 0.082 77 0.029 0.038 85 0.043 0.107
g0493946 g2493900 I 38 0.014 0.079 22 -0.002 0.041 16 0.035 0.111
g0493946 g2493909 I 212 -0.020 0.080 99 -0.011 0.040 113 -0.028 0.103
g0493955 g2493909 I 43 -0.051 0.076 24 -0.027 0.053 19 -0.082 0.089
g2483921 g2493900 I 189 -0.059 0.078 78 -0.055 0.028 111 -0.062 0.100
g2483931 g2493900 I 270 -0.049 0.080 117 -0.043 0.029 153 -0.053 0.103
g2483931 g2493909 I 190 -0.039 0.075 91 -0.038 0.027 99 -0.040 0.100
------------------------------------------------------------------------------
Table 9. Comparison of magnitudes of from different images,
aperture radius = FWHM-0.5 pixels
# all stars (I < 11.0) (I >= 11.0)
# image1 image2 filt N mu sig N mu sig N mu sig
------------------------------------------------------------------------------
g0483967 g0493946 I 186 0.029 0.074 93 0.027 0.036 93 0.030 0.099
g0483967 g2483921 I 22 0.123 0.096 9 0.178 0.030 13 0.084 0.107
g0483967 g2483931 I 225 0.113 0.104 97 0.109 0.071 128 0.116 0.123
g0483967 g2493900 I 175 0.083 0.108 74 0.087 0.059 101 0.081 0.133
g0483967 g2493909 I 83 0.008 0.085 36 -0.001 0.044 47 0.014 0.106
g0483977 g0493946 I 201 0.002 0.075 90 0.009 0.027 111 -0.004 0.098
g0483977 g0493955 I 173 0.048 0.075 87 0.060 0.062 86 0.035 0.085
g0483977 g2483931 I 50 0.021 0.086 25 0.016 0.045 25 0.025 0.115
g0483977 g2493909 I 164 -0.026 0.091 83 -0.016 0.049 81 -0.037 0.119
g0493669 g2493623 I 63 0.124 0.064 48 0.129 0.045 15 0.109 0.103
g0493946 g2483931 I 162 0.041 0.079 77 0.035 0.040 85 0.047 0.103
g0493946 g2493900 I 38 0.013 0.076 22 -0.007 0.037 16 0.039 0.105
g0493946 g2493909 I 212 -0.026 0.080 99 -0.018 0.041 113 -0.033 0.102
g0493955 g2493909 I 43 -0.052 0.071 24 -0.038 0.052 19 -0.070 0.087
g2483921 g2493900 I 189 -0.075 0.073 78 -0.074 0.027 111 -0.075 0.092
g2483931 g2493900 I 270 -0.060 0.076 119 -0.056 0.027 151 -0.064 0.098
g2483931 g2493909 I 190 -0.050 0.067 92 -0.050 0.026 98 -0.050 0.090
------------------------------------------------------------------------------
Table 10. Comparison of magnitudes of from different images,
aperture radius = FWHM+1.0 pixels
# all stars (I < 11.0) (I >= 11.0)
# image1 image2 filt N mu sig N mu sig N mu sig
------------------------------------------------------------------------------
g0483967 g0493946 I 186 0.018 0.092 93 0.007 0.038 93 0.029 0.124
g0483967 g2483921 I 22 0.058 0.112 9 0.141 0.028 13 0.001 0.113
g0483967 g2483931 I 225 0.079 0.114 97 0.078 0.067 128 0.080 0.140
g0483967 g2493900 I 175 0.066 0.133 73 0.082 0.055 102 0.055 0.167
g0483967 g2493909 I 83 0.003 0.093 36 -0.003 0.045 47 0.008 0.118
g0483977 g0493946 I 201 -0.021 0.097 90 -0.014 0.030 111 -0.027 0.128
g0483977 g0493955 I 173 0.018 0.094 88 0.031 0.062 85 0.005 0.117
g0483977 g2483931 I 50 -0.011 0.096 24 -0.004 0.046 26 -0.018 0.127
g0483977 g2493909 I 164 -0.030 0.104 83 -0.021 0.047 81 -0.039 0.141
g0493669 g2493623 I 63 -0.005 0.088 48 -0.004 0.060 15 -0.006 0.149
g0493946 g2483931 I 162 0.030 0.089 76 0.026 0.035 86 0.033 0.118
g0493946 g2493900 I 38 0.030 0.089 22 0.001 0.045 16 0.069 0.117
g0493946 g2493909 I 212 -0.014 0.087 97 0.000 0.043 115 -0.026 0.110
g0493955 g2493909 I 43 -0.044 0.090 24 -0.009 0.069 19 -0.088 0.097
g2483921 g2493900 I 189 -0.040 0.093 78 -0.037 0.027 111 -0.042 0.119
g2483931 g2493900 I 270 -0.036 0.095 116 -0.029 0.038 154 -0.042 0.122
g2483931 g2493909 I 190 -0.030 0.086 92 -0.029 0.031 98 -0.032 0.116
------------------------------------------------------------------------------
To summarize the information in the above tables very briefly, the scatter between independent measurements of the same stars in different images is about 0.05 magnitudes for "bright" stars (with I < 11.0), and about 0.10 magnitudes for "faint" stars (with I > 11.0).
Looking just a little bit deeper, one can see that, for the "faint" star subsample, large apertures give slightly smaller offsets and larger scatter than small apertures, which is just what one would expect from normal sources of error.
Here I list the major points of my analysis for quick review.
You can find pointers to the raw images upon which this work was based, and the calibrated star lists I created, on Data Archive for Tom Droege's February 1997 images.
Back to Index of Technical Notes
Back to TASS home page