# How to mix photometric data from different observers.

Dear all,

I am trying to mix light curve coming from different observers. I calculated differential magnitudes using the same C and K stars in the CCD fields. Then I converted all of the light curves to the standard system applying trasformation coefficents for each instrumental setup. Nonetheless the resulting curves are not precisely overlapped, showing some hundredths of a magnitude of difference. What could be wrong?

Thanks!

Massimiliano (MMN)

Photometry will never precisely overlay; there will usually be a small offset between observers even if things are properly transformed and the target star is free of unusual spectral features. How much of an offset depends on many factors, but for "clean" stars, it should be possible to get into the 0.01mag range.

A common misconception seems to be that CCD photometry is "perfect". But in reality ALL measurement systems have some degree of error or uncertainty. Even if one eliminates all known systematic errors and reduces random errors to absolute minimum, there will still be some remaining random error, due to a vast number of minor factors which are practically impossible to control and standardize between different observers using different telescopes, detectors, software, observing sites, techniques, etc.

But, just as in visual observing, combining measurements of a "random sample" of CCD observers yields an improvement in accuracy by the factor 1/SQRT(N), where N is the number of independent measurements so combined. This statistical approach using the combined measurements of a large number of visual observers, has resulted in very accurate light curves of the long term behavior of LPV's. So yes, mixing the data statistically improves the accuracy far better than any one observer can obtain.

Mike LMK

Dear Arne, dear Mike, thank you for your answers.

the color index of the comparison stars is obtained from the catalog APASS; calculation of the coefficients of extinction was performed according to the standard procedure also described several times on the AAVSO site and publications. The comparison stars have no other nearby stars that may contaminate the measurements.

In the awareness that differences of a few hundredths of a magnitude are of physiological from photometric measures coming from different instrumental setup, I'd like to know if, maybe, there are any mathematical procedures that can bring the measurements from different instruments to a kind of a common "zero point".

Thank you!

Massimiliano (MMN)

Hi Massimiliano,

How are you getting the color coefficient for the target star?

Ulisse Munari has had the most success at combining datasets from different observers, for pathological objects like novae and supernovae. You might look at:

http://arxiv.org/abs/1209.4692

http://arxiv.org/abs/1306.1501

which give the mathematical model he uses. Many CV researchers also combine light curves from different observers by using offsets, as long as the datasets overlap; look at papers from Joe Patterson and the CBA.

Arne

Are the offsets between different observers consistent, i.e. magnitude from A is consistently higher than B which is consistently higher than C etc, or do they seem to vary randomly from data set to data set? If the data sets overlap or you have commen check or standard star measurments for the sets you may be able to calculate offsets to bring them into closer agreement. If you have common transformed check star data from different observers, what happens if you offset the data so that the transformed check value matches the reference sequence value? that would be a simple first pass test to see the affect of applying offsets. I think Patterson uses more sophisticated methods.

How do the offsets among observers compare with the standard deviations for the transformed target star overlapping data or standard deviations of check star data for non overlapping data - 1 sigma or less, 2 sigmas or less, worse?

Where did the transformation coefficients come from? If they were supplied by the various observers do you have the data that was used to calculate the transformations so that you can determine if they were done on a consistent basis? For example, the transformations may have been done at different airmasses. If the transformations were done from a cluster like M67 or NGC 7790, the consistent airmass of all stars in the clustertakes care of first order extinction but if the transformation observations were at significantly different airmasses there may be second order extinction effects between observers. Also, observers often pick a particular star as the comp star for differential photometry of the others. If they have picked different stars, that can introduce a slight "color bias" between transformation coefficients. If you can get the images used to calculate transformation coefficients, you can calculate them on a consistent basis. I use an ensemble approach. I measure raw magnitudes (negative numbers) for all the standard stars in the cluster (at least all the ones I plan to use) and then calculate a zero point for each image by averaging all of the offsets from their standard magnitudes. Then I shift all the magnitudes in the image by that zero point and use those values as my instrumental magnitudes. That eliminates color bias based on any individual star, but of course you still have a color bias based on whatever the resultant "average" color is of all the standard stars but I can't think of a better way to do it. I also do each extinction regression twice. The first time uses all the standard stars I measured in the cluster. The second time I omit stars with residuals from the regression line with a t value that is outside the 98% confidence interval. For 30 stars that amounts to 2.5 standard deviations. I use the results of the second regression for my transformations.

Unless you have transformation data images from the observers at significantly different airmasses on a particular night or the observers can give you their 2nd order extinction coefficients you are stuck with any transformation differences from 2nd order effects due to airmass differences. If all of the airmasses are near 1.0 this probably is insignificant even at the 0.01 magnitude level. If some are at essentiall 1.0 and others at, say, 1.4, it might have a small affect at this level.

These tranformation issues are all small but if you are trying to correct for a couple of hundredths of a magnitude they could make a difference. My instincts tell me you are probably better off applying offsets to data sets than examining differences in transformation techniques, although you may want to examine everything to see if you can determine the root cause of offsets you apply.

Brad Walter, WBY

I have a little advice about this being elbow deep in a project like this myself.

My experience with this has also taught me the importance of how the apertures and sky annuli are set for different systems. Every telescope/camera combination has its own unique PSF. We all know from experience that selecting different apertures and annuli on the same image can yield different results. This can be vexing enough with one system and one PSF. These issues increase expodentially when combining data from different systems with different PSFs.

In my own work, I've tried to find ways to consistently pick the "same" apperture for all systems using their own unique PSF as a guide. I've found through experience it works best to pick a point at the 90-95% full peak value in the PSF as my apperture size. This appears to handle many of the PSF and seeing related variables pretty well.

I always also try to get a sky annulus that is well removed from the PSF that is really sampling background/sky for all PSFs while still sampling the roughly the same portion of the background (same sky coordinates) in all the images irregarless of the system.

I also whole heartedly endorse the references Arne gave earlier as well. The nice thing about those recipes are that they are numerical methods that just acknowledge there is a point where you can't calibrate everything out You'll just drive yourself nuts trying to do it anyway. At that point you just accept there are offsets between systems you will never be able to characterize ab initio but that all of them sampled the same "true" light curve. From there statistics can help you with the relative scaling of each system.

Arne, Brad & John,

thank you all for your valuable suggestions. I will try to put them into practice starting right from the work of Dr. Munari.

Greetings!

Massimiliano (MMN)

Hello John

Just to make sure I am interpreting your suggestion, this gives a very small aperture, capturing only a very few pixels around the peak. Am I correct?

It does seem like this would give the very highest SNR for the signal, based on typically only a few pixels. One must make sure that the sky measurement is well away from the wings, as your suggest.

Gary

I'm glad you asked cause I said that in a confusing way. I mean that that you need to include more pixels that include most of the wings.

I'lll edit this in my original response but it would be less confusing to say that you should include as much of the flux as you can (i.e. out to a point where the flux falls to a value 1%-5% that of the peak value). I avoided specifying this in sigma or FWHM because I have encountered PSFs that look very non-gaussian in the wings and following the 2.5xFWHM rule doesn't get you enough of the PSF to yeild the best results.

Sorry for the confusion.

Thanks, I had the same question. I assumed that you meant an aperture corresponding to 90%-95% of the peak net flux capture (peak of the growth curve).

Brad Walter, WBY

Hi Massimiliano,

What target star, and how are you applying transformation coefficients (that is, how are you obtaining things like color index for the target star, extinction coefficients, etc.)? Have you looked at the field to see if there might be contaminating companion stars that are included in one observer's digital aperture and not in another's aperture, for the target and the comp?

Photometry will never precisely overlay; there will usually be a small offset between observers even if things are properly transformed and the target star is free of unusual spectral features. How much of an offset depends on many factors, but for "clean" stars, it should be possible to get into the 0.01mag range.

Arne