I have recently started experimenting with generating transform coefficients for my Seestar S50. My question is not about the process of generating them, which I think I understand and have managed to do more or less correctly, but about how to evaluate the results. For example, I have so far done five nights of observation of the standard field Melotte 111 and have ended up with the coefficients shown below for the five nights. There was an average of probably 15 stars or so that “made the cut” in each analysis.
But I’m not quite sure how to evaluate these. For instance, how much variation between observing sessions is expected and how much should be a concern? And though I’m no expert in statistics, the very low R-squared values for Tv - bv seem like a problem. As an initial test I threw out the results from 6/1 (since they seemed most divergent from the others, at least for Tbv and Tv - v) and averaged the rest. Applying these to a few observations made in TG and TB produced what seemed to be reasonable results. (“Reasonable” meaning they produced transformed V and B estimates that were quite close to other uploaded B and V observations of that star.)
My personal take on your question is that everything is fine, particularly if you average your coefficients.
Your Tv_bv coefficients approach zero, meaning that the B-V difference between variable and comp stars will have a very small contribution to error in V magnitude calculations, and the transformation process minimises this further.
It is instructive to know the formulae for transformed magnitude calculations. They illuminate the contribution of variance in TC values to the transformed V magnitude error.
In the following V and B-V are calculated or catalogue values, and v and b-v are measured (instrumental) values.
(B-V)var = (B-V)comp +Tbv[(b-v)var – (b-v)comp] Formula 1
Formula 1 is used first. It calculates the transformed B-V colour index of the variable. That value is then plugged into Formula 2 (it is the second last term) to calculate transformed V. Similar formulae apply to other filters.
Even though there is some scatter in your Tbv values, and thus some scatter in the Tbv[(b-v)var – (b-v)comp] term in Formula 1, the fact that (edit) Tv_bv in Formula 2 is near zero means that your final error in V mag will be fairly small even if you didn’t average your coefficients.
My final comment is that the small r value for the (edit) Tv_bv is of no consequence. The plot itself is nearly horizontal (which is why (edit) Tv_bv is nearly zero), and hence r will be nearly zero. An r value of 1 (perfect correlation between x and y values on a plot) occurs when the slope is ’45 degrees’ if I can describe it that way. AAVSO published TC listings include the r values, which are really just indications of the slopes of the plots and do not inform about errors.
Thanks for your detailed response, it has cleared up a lot of my questions. I need to sit down and go through the formulae in detail so I fully understand what is going on and your explanation is very helpful.
I’m struggling with a similar issue: trying to pin down repeatable transform coefficients for a new camera+filter+telescope setup, but after tracking several standard fields like GD391 for several nights, I don’t see very consistent values. It seems hard to separate true Zero point from variable extinction coefficients per night, and even with 15-20 stars, even 1 outlier breaks the consistency of obtained Tbv, … per night. Even with careful aperture photometry with AstroImageJ, I cannot say I’m obtaining stable transform coefficients. Did you use a standard package to do the regressions, which also reports outliers?
I used Tycho Tracker to do the generation of transformation coefficients, the same app I use to do regular photometry. It creates a graph very similar to the one that VPhot creates and lets you discard outliers. One difficulty I had is that I don’t think there’s any hard and fast rule about when to stop discarding outliers and decide that what you have left is good enough. Discarding too many of the marginal outliers can leave you with very few stars remaining, which obviously isn’t good.
GD391 has only 9 stars in the standard field. Impossible to be “hand” or statistically filtering with so few stars. I would say try other fields with more stars. M-11, M-67, NGC-7790 are fairly compact. Mel-111 is great for those using wide-field systems. Some of Landolt SA fields have a good number of stars available.
It should not be that hard to get decent, acceptable transformation coefficients. Observe standard fields only on the best nights. Here on the east coast, the last few years clear is a rare thing esp. in the summer with all the fire smoke over us. Try to use standard fields with a large numbers of stars. Observe your standard fields regularly doesn’t hurt at all.
If you are hand filtering a lot of stars as outliers the problem is in your observing and you need to address that. Bayer matrix sensors are bit harder but only because you need to do all the things observing to sample the Bayer matrix well enough in all three filter colors.
I have transformed DSLR sensor photometry fairly well over the years. I do “average” all the nightly transforms into one main transformation set. I have never observed any aging in the transformation coefficient values over years.
For CCD photometry I have Astrodon and Optolong filters. Those transforms are much more stable from night-to-night but I still average them. Again I’ve seen no evidence of aging in those filter, sensor systems.
Arne just had an observational best practices course and I’m sure they are well worth taking. There is nothing like asking questions live and in person!
Whenever you ask these types of questions it is always worth giving us a bit of info on your observing system, sensor (type), filters, etc.
Many of the things Jim has mentioned are valid. Besides various instrumental issues, inconsistent zero-points could come simply from it not actually being cloud-free! Also I note that the GD 391 Landolt stars don’t really have a good range in colors, and the sequence includes fairly faint stars (are the data simply noisy?). It could be that GD 391 itself (a hot DA white dwarf) is skewing results since it is basically an outlier in terms of color-index compared to the other ordinary stars. You’d probably need quadratic color terms to include it, but also just more stars filling in the color range. The other stars are OK for zero-point, but you’d want to look elsewhere to get proper color terms. There are many other options, including SA 110, Landolt SA 41 stars, NGC 6940 (Peter Stetson photometry), etc.
