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Transformation Coefficients & M67

CTX's picture
Joined: 2010-07-08

Transformation Coefficients and M67.

A transformation coefficient generally tells how your instrumental value differs from the true value as a function of star color.  This is usually a small correction; important if you need high accuracy but unimportant if your target and comparison stars are similar in color.  Hendon, Arne, 26 July 2007.

Frankly, I generally do not apply transformation coefficients to my observations unless there is a specific request for a specific target, self compelling or if I am running alternating filters (usually V & I) doing a time series. 

I am also not implying, herein, that M67 is the only or the best option for imaging as a Standards Field for your own computations.  There are other suitable FOV’s. 

I just finished up my annual computations from three nights of imaging M67 and thought I would share some information that might be of benefit for others.  When I say annual, it is true that I try to do this every year, but in this year’s case they are the first for my recent replacement scope.

In past years I have used the chart and data (Arne’s) located at:

Awhile back, Arne uploaded some revised and expanded M67 data to the VSD so that we can obtain a Standard Field Chart of that data from the VSP:

Enter the coordinates:  RA 08:51:24 + 11:45:00 and then select Yes, at the bottom of the VSP chart options, Would You Like A Standard Field Chart?

The field is quite crowded with photometry taking these standards as faint as ~ magnitude 16 and contains many duplicated values (which is OK for this purpose).

However, It can be a challenge, therefore, trying to use this Standard Field Chart, because of the crowding, and my first suggestion would be to reduce the number of standards by limiting the magnitude to say 13;  but that still leaves a number of duplicates which almost requires that you plate solve your own images or, as an alternative, use Aladin (down load to your desktop) to help you identify specific comps:

I choose to instead use the older chart for identifying the VSP’s standard stars as it is quite visible with its original number system and makes it easy to locate the comps when you are analyzing the data; I of course used the updated BVRI data from Standards Sequence. Once you examine the first links data you will catch on to what I am describing.

Choosing which standard stars to use and how many is, from my perspective, a bit of an art form as much as it is science.

I have made it a habit through the years to zero point on the number 1 star in the original published data and then to subtract all the following instrumental magnitudes from the standard values.  If I find differences greater than about .08 I simply do not use that standard star.  The twenty stars that I ended up selecting this year had standard deviations of the Standard value vs the zero pointed instrumental value of between .015 & .023, depending upon the selected filter.

The other issue is mixing of color choices (B-V) that go into your selections.  In my case the average B-V value was .634 with a median of .582.  This average seems to fit well with my typical targets. 

Here is the B-V data for each standard star that I choose.



So, as an FYI, I will share with you which specific 20 standard stars I used for my computations, with the first number being the matching star # from following link:

while the second data column is obviously the standard star AUID from the M67 Standards Field.

1          000-BLG-879 

2          000-BLG-886
3          000-BLG-887
4          000-BLG-888
5          000-BLG-889
7          000-BLG-891
10        000-BLG-892
11        000-BLG-893
13        000-BLG-895
14        000-BLG-896
15        000-BLG-897
16        000-BLG-898
17        000-BLG-899
20        000-BLG-901
23        000-BLG-903
24        000-BLG-904
25        000-BLG-905
31        000-BLG-910
33        000-BLG-911
37        000-BLG-914


I am not suggesting that you use these specific standards or this many or few; Just a starting point for your own research if you choose to image M67 for TC computations.

For those of you who are curious or would like to compare your own TC’s (and please keep in mind that they will vary a lot from system to system) here are my BVRI computed values:

Tbv = 1.008

Tvr =  1.091
Tri =   0.965
Tv =  -0.005
Tr =  -0.049

If you compute TC’s for two or more filters the formula’s can be found in the Sarty paper:

Here is my data for the two cases where I may just use two filters:

V & I filter: Tvi =  1.020

B & I filter: Tb =   0.003

Computing the Transformation Coefficients

I just read this morning in anther forum post, that Arne wrote they have a volunteer writing a program for computing your transformation coefficients as other progress towards making the process more user friendly.  That is great news for many observers:

In the meantime, however, I really like the Pricilla Benson paper as it lays out the whole process of how to generate your own transformation coefficients in a simple and straightforward manner and has enabled a lot of us to generate our own spread sheets for both the creation of the transformation coefficients as well as their application to observations.

There are other reference pdf’s that the AAVSO has available on this topic and here is another one:

Arne’s suggestions, to me, some years back, were, when following the Benson paper or any of the others, with similar suggestions, would be to:

1)      Instead of plotting (R-r) vs (R-I) for Tr to instead plot (R-r) Vs (V-I)

2)       Instead of plotting ((V-v) vs (V-R) for Tv to instead plot (V-v) vs (V-I)

V-cI has more change with star color and so results in a better transformation; V-Ic is also more sensitive to interstellar extinction; using Rc-Ic means you use Rc, a bandpass that has H alpha in it; which is a very prominent line that can be in emission or absorption causing an error in transformation, especially with novae, where H alpha emission can dominate the continuum in the Rc bandpass.  Arne

I have continued to follow this advice.

I hope some of this information may prove to be useful for your own efforts.

Ad Astra,

Tim Crawford, CTX

Thanks Tim
BPO's picture
Joined: 2010-07-28

Thanks Tim,

Lot's of great information there, the Benson paper especially, as you say lays out the whole process in a straight forward manner, I already feel I have a grasp on the subject.

Many thanks again,


Transformation Coefficients and M67
CNY's picture
Joined: 2010-07-23


Thank you for that great post! I will take you up on that offer t go over my M67 data in more detail. The next month or so is very busy , but you will hear from me soon after that....

Tim, Thanks for
nmi's picture
Joined: 2010-08-01


Thanks for sharing


Ooops; Actually it looks like
CNY's picture
Joined: 2010-07-23

Ooops; Actually it looks like you didn't really offer that. You just provided some of your data for comparison. I didn't remember it correctly when I read it quickly yesterday.

Thank you for the great post and information. This will help me a great deal!

Picking M67 Stars
WBY's picture
Joined: 2010-07-24

So now that I have added a corrector to my Dahl Kirkham telescope I am recalculating transformations. This time using M67. Is there any particular reason that I shouldn't simply pick the first 30 stars in Arne's original sequence, excluding variables and suspected variables? These appear to be the 30 brightest ones. I use a smaller than normal aperture size when measuring cluster stars per Arne's recommendation in another string on transformations. Therefore, crowding doesn't seem to be an issue for more than a couple of these stars (like #22 and #12.  #11, #18 and #30 seem to have sufficient separation). For M67 an aperture radius of about 5.25 arcsec (10.5 arsec diameter) seems to work well. In my images this amounts to radius of about 1.7 FWHM (diameter 3.4 x FWHM)  I also do a two-pass regression. I calculate a regression for all the measured stars. Then I eliminate stars with residuals from the regression line outside the 98% confidence interval and run the regression a second time. From past experience on NGC7790 most frequently no measurements are rejected and even for relatively noisy data rejection of more than 1 measurement out of 30 is rare. 

So, Anyone know why I shouldn't just pick the non varying stars in the first 30?


I don't know what aperture size Arne used to calibrate the cluster in his original PDF sequence and its relationship to the image FWHM.  Can anyone supply that information? 

I don't pick a single star as a comp for the others. My software allows me to use an ensemble approach. I measure the raw magnitudes of all the selected stars calculate a zero point for the image based on the average of all of the offsets and then add the zero point to the individual raw magnitudes to get instrumental magnitudes. So the "effective color" of my comparison is the average color of all the stars I measure.  This probably doesn't do significantly better than just picking one of the standards with B-V in the range of 0.5 to 0.7.

IGNORE THE FOLLOWING PARAGRAPH: As Arne points out below, the "color bias" from choosing a specific star affects the Y intercept of the regression lines. It doesn't affect the slope and the coefficients are the slope or are calculated from the slope. The Y intercept doesn't matter for this purpose. Star #1 is bright and uncrowded and would be a good choice if positioned correctly for the part of the field you image; so my appologies to Tim. WBY

If I were using a single comp to measure the others, I would not choose #1 because it is quite blue compared to most of the standards in the cluster. I think #4 (B-V = 0.576) would be better choices. The numbering is from Arne's old PDF M67 finder chart. 

Brad Walter, WBY

m67 choices
HQA's picture
Joined: 2010-05-10

Hi Brad,

Picking the first 30 is fine.  What I tend to do is make sure that a couple of very red stars and very blue stars are included.  The majority of stars in any field will have "average" color, so you have to work a little harder to get the extreme ranges.

Remember that the zeropoint is just some arbitrary constant - it doesn't matter whether it is a number you created out of thin air, or the value of a single star, or of an ensemble, as you are not using that zeropoint to calibrate any other field.  It just creates an offset for the least squares line, and you are only interested in the slope of that line.  So don't go overboard worrying about that aspect.


Zero Point
WBY's picture
Joined: 2010-07-24

Arne, your absolutely right about the zero point. I use the residuals between the instrumental mag and the standard mag as a quick check to see if I have made a mistake in my photometry take-offs (as in selecting the wrong star or the aperture being out of position) or have a problem in a particular image (an unfortunately positioned cosmic ray hit, for example). Also, I rarely have just one image. I essentially always have at least two in each filter because I take images ithrough multiple filters in pairs, IRVBBVRI for example, so that the average airmass of all colors is essentially the same. If the offsets from standard magnitude for a star are very different in the two images, that also gives indication that I have a problem with that star in at least one of the images. If I have the time I try to do this initial check while the synthetic apertures are still in place on the images. If I have made an error,I can correct it easily and get the revised data quickly.  If you only have a couple of stars on a couple of images it doesn't save much time, but if you have to reset 30 apertures on several images that are shifted, it saves quite a bit of time and eliminates a lot of swearing. I don't align the images because the software I use for photometry does very precise centroid alignment - even if just shifting images without ratation or scaling. That means the alignment is sub pixel and flux gets shifted between adjacent pixels. I could do a single star alignment in Maxim first without using centroids. That simply shifts images by full pixel values without any reallocation of flux among pixels. I'll have to do that next time I have a bunch of shifted images. Now let's see; which bit of string around which finger is supposed to remind me to do that?

Brad Walter, WBY

AAVSO 49 Bay State Rd. Cambridge, MA 02138 617-354-0484