Andrew Bennett: andrew.bennett@ns.sympatico.ca
Minor revisions: 1999 Feb 7
Revision 3: 1999 Dec 30
Revision 2: 1999 Dec 24
Revision 1: 1999 Dec 13
Sources which suffer even from severe saturation effects can still be used to produce magnitudes and positions which are not much less accurate than those for non-saturated sources.
Replicate measurements using calibration against Tycho magnitudes and correction for trends have a standard deviation around 0.04 magnitudes near 9th magnitude. Positions show a scatter around 0.00025 degrees (1/8 pixel or 900 mas.)
All image show consistent trends. Sources appear fainter/have a larger magnitude as one moves away from the first pixel to be read out of the CCD. This effect is in the same direction as the observed fall-off in saturation value.
I now have working a new and improved program to purge "Bright" sources from CD5 data working. This one copes with the very largest sources, including airplane trails. It also copes to some extent with varying background levels across the image. On its way to rubbing out the "Bright" sources, it adds up all their pixels records the sum. This enables me to compute a magnitude for them. But first; a definition of "Bright". Earlier examination showed that the highest values in the images had a trend from full scale (65535) at low X1 and low X2 down to around 43000 at high X1 and high X2. Many, but not all, of the sources with these high values were obviously saturated, with "wings" of roughly constant high values instead of a well defined centre. Being too lazy to do a position dependent fit to the highest values, I instead used a very crude global definition:
A "Bright" source has at least one pixel value greater than 37768. 37768 = 32768 + 5000; an arbitrary number that catches all the truly saturated sources and a few more for good measure. I originally used 40768 as the critical value; further examination showed some remaining sources with the typical saturation wings. The adopted value obviously catches a number of sources at low X1, X2 which are nowhere near to being saturated.
Removing the "Bright" sources enables Star to do a much better job of matching to the Tycho catalog; I am analysing the images in 3 strips with a width matching the MKIII images using a version of the Tycho catalog shifted in declination so that the MKIII Star program can find it. With the "Bright" sources left in, quite a few strips failed to match. This is because of the large number of wrong positions found by Star for the "Bright" sources, many of which were seen as two or four bright sources, none of them in the right place. Not a "bug" - one is supposed to flag off-scale pixels before feeding them to Star.
I have analysed all the CD5 images for "Bright" sources but have not yet processed all the results of the Star analysis of weaker sources. I am posting the results for one of the 3 strips for all of the V-band images now because the analysis bears on Tom's question as to how well one can do a series of magnitude determinations.
Here is V-band data for all the "Bright" sources. The quantity plotted is 21.0 - 2.5Log(A) - adjusted Tycho catalog magnitude, where A is the total adu's. I have plotted it against "time" or rather sample number.
Four of the 35 images show much larger differences which are obviously the effect of cloud. These were H3R1442.863, 867, 885 and 889. Cloud can be seen on several other images so some of the remaining scatter is the result of cloud.
Here is V-band data for the "Bright" sources, leaving out the four cloudiest images, plus some Star analysis.
I have plotted two of the sets of magnitudes produced by Star. The magnitude using the 11x11 aperture agrees fairly well with the "Bright" source magnitudes. The magnitudes using the PSF aperture are considerably higher: the PSF method used by Star seriously underestimates the total adu's. This is to be expected because of the core/halo nature of the PSF. This doesn't matter if the PSF remains constant, as we hope it does for the MKIII, but in this case, I am inclined to call this a "bug" rather than a "feature"!
In order to get an estimate of how well we are doing in replicate magnitude measurements, subsequent analysis was restricted to sources seen at least 6 times. Three of the four cloudy images had sources meeting this requirement and were included. Processed consisted of subtracting the mean difference in magnitude for each image, which is more or less what "Star" does, and of subtracting trends. Taking out trends up to second order (i.e. x, y, x^2, y^2, xy) has a considerable effect. "Bright" and "Star" sources were analysed separately. The mean magnitude differences subtracted had a correlation of 0.97 between those for "Bright" and those for "Star", including cloudy images. I find this high correlation comforting. The mean magnitude differences range over 1.5 magnitudes with the three cloudy images; 0.4 magnitudes without.
BRIGHT SOURCES: V s.d. 3)
Raw 0.451 0.399
1) 0.139 0.093
2) 0.107 0.058
"STAR" SOURCES: V s.d. 3)
Raw PSF 0.406
Raw 11x11 0.377 0.350
1) 0.198 0.105
2) 0.162 0.049
1) Each image calibrated against Tycho
2) Trends with RA and DEC removed up to 2nd order
3) s.d. of individual sources
As will be seen in the plot below, there is still a considerable remaining trend with magnitude and a good deal of scatter. Taking out the 3 remaining cloudy images helps a bit (results not shown). The error for replicate magnitude determinations has a minimum value near Vmag = 9 of somewhere around 0.04 magnitudes rms. I think this is quite encouraging in view of the removal of 1.5 magnitudes of variation.
Here is V-band data for sources seen 6 or more times, with these corrections applied, plus the Star analysis so far. Note that this includes 3 of the 4 cloudy images.
BRIGHT: V X1 X1^2 X2 X2^2 X1*X2 Peak-to-peak 0.129 -0.073 0.218 -0.134 0.067 s.d. 0.017 0.018 0.017 0.016 0.030 "STAR": V (partial, preliminary) Peak-to-peak 0.124 0.375 s.d. 0.070 0.040
The linear trends removed are of positive sign. That is, sources appear fainter/have a larger magnitude when they are seen at a larger pixel number, row number, column number or whatever you choose to call it. This effect is in the same direction as the observed fall-off in saturation value as one moves away from the [0,0] (and/or [1,1] or [1.5,1.5]) corner of the CCD. This is a much larger effect than could be introduced by "Flat" processing (see Retraction below) and appears to be a real "feature" of the CCD and/or electronics.
The quadratic trend is fairly small and negative for both X1 and X2 for the bright sources. This suggests that I have managed to overcorrect a little with my crude Flat process for any lens fall-off. On the other hand, the quadratic trend is large and positive for the "Star" results: sources appear dimmer in the corners. This is obviously a result of the coma; even the 11x11 aperture sees less and less of the true amplitude as one approaches the corners of the image.
I retract my previous accusation that the linear gradients result from my "Flat" processing. The observed effect is much too large. I still don't think the median flat is good enough but it is not introducing effects that great. So: there is a significant effect for Tom to worry about.
I-band data: "Bright" sources plus H4R1438.878. Cloudy images omitted from this plot but not from the subsequent analysis.
BRIGHT SOURCES: I s.d. 3)
Raw 0.429 0.382
1) 0.268 0.154
2) 0.226 0.089
1) Each image calibrated against Tycho
2) Trends with RA and DEC removed up to 2nd order
3) s.d. of individual sources
X1 X1^2 X2 X2^2 X1*X2
Peak-to-peak 0.027 -0.133 0.438 -0.184 -0.051
s.d. 0.021 0.020 0.021 0.020 0.037
This shows much the same thing but with larger scatter. The rms error after processing is over twice that for V-band. A good deal of this scatter is, I think, in the Tycho magnitudes. The scatter for individual sources is much smaller, including a number of mostly very red stars which are up to a magnitude brighter than the extrapolated Tycho magnitude. My comparison is with all the Tycho sources, not just the "Good" ones. Obviously, I am including the "Bad" and the "Indifferent" too.
The pixel sum for the "Bright" sources allows one to make a useful estimate of their magnitudes. It does not appear that charge is lost when the CCD wells overflow.
The rms replication error of 0.058 magnitudes for the V images is not much worse than the 0.049 magnitudes for the corresponding "Star" analysis. This includes some contribution from cloud. The measured rms scatter is worse for the I images but a major part of this scatter arises from extrapolating the Tycho magnitudes.
A while ago I posted preliminary astrometry for a raw CD5 image. I have now repeated this with my crude Dark/Flat processing, both for the "Bright" sources and for the weaker sources processed by "Star". Using a quadratic fit, the rms residuals for the "Star" processing (from Tycho) are
RA Dec
raw 0.00056 0.00038 degrees
processed 0.00032 0.00025
RA Dec
raw 2.0 1.4 arc seconds
processed 1.2 0.9
The pixel size is about 7.5 arc seconds.
Just think how much better things will get when we get proper Dark/Flat processing!
I have looked at the proper way of doing the astrometry that somebody posted recently. Expanding the formulae in powers of pixel position confirms the empirical result that the second order approximation is adequate for our needs unless we can get the scatter down a lot or unless we choose to observe near the pole. Any distortion in the lens is also adequately dealt with by the second order approximation.
Surprisingly, results are quite good for the "Bright" sources ...
RA Dec
"Star" fit 0.00351 0.00367 degrees rms
New fit 0.00064 0.00040
RA Dec
"Star" fit 12.7 13.2 arc seconds rms
New fit 2.3 1.4
... provided one uses an appropriate fit. This is a measure of the extent to which the coma is affecting the very different methods of extracting position. I used the centre of gravity of the comatic image down to a level 200 ADU above background for my "Bright" sources. The difference from the "Star" fit is around 3 pixels in the corners of the image. Ouch!
I think this scatter (from the new fit) is remarkably small. Being able to do things with the brighter sources greatly expands the usable magnitude range for the MK IV. (Just think what happens when the MK IV gets somewhere really dark and somebody cranks up the exposure. Mag 10 stars will be saturating and there won't be any non- saturating Tycho stars on an image, let alone Good Tycho stars.)
Dark frame median of the three dark images
in each case. [a bug was later discovered in this code so all
results are not as good as they might have been]
Flat using median of 35 images
each dark corrected and scaled using median.
In view of the severity of the cloud problem on four of the images,
this obviously needs to be done again, if only to show that dropping
the four images does not make a substantial difference ... I hope!
Processing applied by program ProcCD5.
"Bright" sources removed for separate analysis and image split
into 3 overlapping strips in MKIII format by new and improved
(I've taken out some of the bugs) program
Splt_CD5.
Analysis by MKIII "Star".
Positions and magnitudes from Tycho: in order to get the MKIII version
of Star to work, I have subtracted an offset from both RA and DEC
and have scaled the remainder by the ratio of pixel sizes. The
current version inadvertently includes some of the "zero-magnitude"
Tycho sources. I thought I had got rid of them, as I did with the
earlier attempts.
Catalog matching manual for "Bright" sources, fully automatic for
remainder. Manual matching was done by first processing the remaining
sources with Star for one image. The catalog match then gave a fit
for (modified) RA & DEC as a function of X1, X2 for that image and
also the range of declination. I then prepared a selected catalog
covering that range of declination and sources brighter than a
carefully selected magnitude. Laying this alongside the list of
"Bright" sources in the spreadsheet, with a computed approximate
declination, it was usually fairly simple to pick out the match
from declination alone. Often, as many as three or four successive
catalog sources matched before one came to one too faint or just
outside the range of declination. In more complicated cases, one had
to hunt around and cross check with RA vs X2. Tedious and time
consuming!