# Calculating Transformation Coefficients and the Use of Comp Stars

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WBY
Calculating Transformation Coefficients and the Use of Comp Stars

This is the continuation of a discussion that started in the thread "Which Software to use." Maxim DL is a common software used for photometry and the discussion digressed to systematic error that may be included in coefficients derived using Maxim since it doesn't provide "raw" magnitudes (defined as -2.5*LOG(netcounts*GAIN/EXPTIME) It requires a comp star.

When calculating a transformation you plot, for example V-vinst vs B-V for a whole bunch of different color stars. Maxim provides

vinst_target = vraw_target – vraw_comp + V_comp. (capital "V" denotes the standard magnitude)

Here is my concern using Maxim:
If the target and the comp are the same color then whatever color based systematic error exists (because my filter + camera pass band is not rectangular and extinction is frequency dependent) is the same for both stars. Therefore, the error cancels out. However, since you are plotting stars of a wide range of colors on the same graph to derive a slope, you end up with different systematic errors for different color stars being measured.

If I haven’t goofed up somehow, that will cause the V-vinst vs. B-V curve to tilt because the systematic error will vary with the color difference between target and comp. Further, the amount of systematic error for a given color difference will vary with extinction and instrumental frequency response.

We are trying to derive coefficients to apply consistently over a reasonably long period of time to correct our instrumental response to the standard system. The other two factors vary from night to night and field to field. Variation due to extinction is removed by adjusting the vinst values to extra-atmospheric values, vinst_o. Systematic error due to the difference in color between comp and the various measured stars wouldn't’t matter if I always used the same color comp in future photometry. I would always be adding the same offset for a given color target star and the extinction coefficient with that offset included would remove it. But that isn't’t going to happen. Comps will vary over a B-V range of 0.7 magnitudes, maybe more. However, If you just use the raw magnitudes of the individual stars, where mraw = -2.5*LOG(netcounts*gain/exptime), no systematic error is introduced by color difference between measured stars and the comp since there is no comp.

Ok. So much for theoretical musing. I am reasonably sure that using the vinst_o values is important due to fairly large variability in extinction from position and sky quality. Arne’s book seems to confirm that. It states in several places that you convert instrumental values to extra-atmospheric values before applying transformations.

I am not at all certain that any systematic error in transformation coefficients introduced by the color of the comp star is significant. Since it is a factor that can be eliminated, I just decided to use a procedure that eliminates it. The question remains whether it is worth it.

Maybe I am just all wet. Maybe I am concerned about the insignificant. This seems to be a topic that would benefit by comment from HQA.

HQA
transformation

Before I go into a detailed reply to Brad's comments, I'd like to hear from MaximDL users.  I seem to recall that there is a trick to defeat its zeropointing, namely to insert an artificial star into each image that has a constant magnitude (essentially a zeropoint), using it as the "comp", and then MaximDL gives you true differential photometry.  Let me know if I am wrong.

Arne

Richard Wagner
Maxim DL Photometry with Pseudo-comp Stars

Arne:

That's what I used to do: there is a plug-in for Maxim which inserts a 'perfect' Gaussian star of peak value 65536 in a 64x64 pixel box in the upper left corner of the frame.  I used it in Maxim's photometry tool as the comp star set to a magnitude of zero.  Then all target stars and real comp and check stars in the frame are selected as 'object' stars.  The photometry tool then gives magnitudes of all the real stars relative to the fake star.  It is then simple to convert this back to pseudo flux values which can be used for coefficient determinations or properly weighted averaging of ensembles.  By using the measured flux (in the Information Window) of the fake star to scale the fluxes I get back flux values for the stars which are very close to those measured in Maxim Information Window.

I have since switched to doing all my photometry with SExtractor as it gives fluxes (and flux errors) directly.

Richard Wagner

WCR

FJQ
Calculating Transformation Coefficients and the Use of Comp Star

[quote=Richard Wagner]

Arne:

That's what I used to do: there is a plug-in for Maxim which inserts a 'perfect' Gaussian star of peak value 65536 in a 64x64 pixel box in the upper left corner of the frame.  I used it in Maxim's photometry tool as the comp star set to a magnitude of zero.  Then all target stars and real comp and check stars in the frame are selected as 'object' stars.  The photometry tool then gives magnitudes of all the real stars relative to the fake star.  It is then simple to convert this back to pseudo flux values which can be used for coefficient determinations or properly weighted averaging of ensembles.  By using the measured flux (in the Information Window) of the fake star to scale the fluxes I get back flux values for the stars which are very close to those measured in Maxim Information Window.

I have since switched to doing all my photometry with SExtractor as it gives fluxes (and flux errors) directly.

Richard Wagner

WCR

[/quote]

[quote=Richard Wagner]

Arne:

That's what I used to do: there is a plug-in for Maxim which inserts a 'perfect' Gaussian star of peak value 65536 in a 64x64 pixel box in the upper left corner of the frame.  I used it in Maxim's photometry tool as the comp star set to a magnitude of zero.  Then all target stars and real comp and check stars in the frame are selected as 'object' stars.  The photometry tool then gives magnitudes of all the real stars relative to the fake star.  It is then simple to convert this back to pseudo flux values which can be used for coefficient determinations or properly weighted averaging of ensembles.  By using the measured flux (in the Information Window) of the fake star to scale the fluxes I get back flux values for the stars which are very close to those measured in Maxim Information Window.

I have since switched to doing all my photometry with SExtractor as it gives fluxes (and flux errors) directly.

Richard Wagner

WCR

[/quote]

To Richard,

As I understand your proceedure above:

1.) Add artificial star plug-in, to the first set of images to photometrically reduce, Set this (as reference star) magnitude to 0.00.

2.)  Pick 3-5 stars with known (BV) magnitudes and variable star as 'object' stars in the set to reduce.

3.)  Export this data as a .cvs file for spreadsheet manipulation.

4.)  In the spreadsheet, convert these 'objects' offset magnitudes from the artificial reference star (previously assigned as 0.00 magnitude) to flux values.

5.)  Convert these flux values to 'true' instrumental magnitudes using  (-2.5*LOG(netcounts *GAIN/EXPTIME).  These will be the raw instrumental magnitudes that Maxim can't output directly.

At this point I can try to follow the proceedure Photometry Transformation Coefficients by Gordon Sarty (04Sep08) or the shorter, but more complicated (rigorous?) Standardization proceedures shown here: http://www.astro.caltech.edu/~aam/science/thesis/total/node15.html to get these magnitudes transformed.

I'm also looking at Bruce Gary's 'simplified' differential photometry page (http://brucegary.net/DP/) to get my transfomations done.  Too bad there is no step-by-step proceedure to derrive TCs without resorting to Linux/Unix hardcore software packages!

James

WBY
Artificial Reference Star

You can get the artificial reference star plug in from the maxim "Extras" page at

I have never used it and had forgotten about the artificial star Plug-in.  Bruce Gary mentioned it in his Exoplanet Observing Guide. By the time The EOG was published, however, I already had a photometry program that provides raw magnitudes (-2.5*LOG(netcounts *GAIN/EXPTIME) simply by not designating any star as a comp star.

jji
Transform Coefficients

An interesting discussion and I wish I could give it the attention it deserves.  But I incurred some damage in the observatory from passing electrical storms a week or so ago and my time seems to be spent shagging parts and generally trying to get stuff to work well enough to get me through the observing season.

But I don't think the effects you are describing tilt the curve so much as they bend the curve.  That is they make the relationship between vinst and  V-B nonlinear.  The curve v=mx+b will be "tilted" as a result but it should be tilted since that's what happens when we model a nolinear process with a linear curve.

I wish I had time to look it up, but my memory is that Arne talks about the secondary, nonlinear effects of transformation in his book and provides method methodology for handling it.

Like I said, an interesting discussion.

Jim Jones

WBY
Transformation Coefficients & Comp Stars

I am terribly sorry about the damage to your observatory. Aside from the lost observing time and all the work, aggavation and expense involved, it is like having a close friend who has been hospitalized suddenly with a serious illness.

It will be interesting to see Arne's comments. His question about the artificial star was illuminating. Using an artificial star is the same as using what I term raw magnitudes with a constant offset. It does the same job.

I'm glad this isn't a bore, though, many,  but many might have a different opinion. Like my wife, they would accue me of trying to tell them how a watch works whan all they want is the time.

jji
Observatory damage

Thank you Brad but it wasn't that bad.  Mostly a gigantic,  time consuming pain in the neck.

It got the focuser for sure which I think was just a blown RS232 driver.  "Seems" to be working now.  Probably some problems with the dome controller.  And some general flakiness.  But the major pieces, the camera and mount, seem fine.

I view it as a good excuse to do some serious software and hardware upgrades that I have wanted to do for some time.  Starting with getting rid of all the USP to RS232 converters (done).

Jim Jones

WBY
Transformation Coefficients and the Use of Comp Stars

I am working on a long post - short treatise - to analyze my concerns about using comp stars in establishing transformation coefficients. I think, conceptually, you can summarize the situation as a signal feeding sequentially through two filters, one for atmospheric effects and the other the overall effect of instrumentation. Each can be approximated as a summation of convolution integrals of linear systems on contiguous segments of the frequency (wavelength) domain. However, the atmospheric filter cannot be considered invariant over time frames of interest, which is why you apply transformation coefficients to instrumental magnitudes that have been extinction corrected to extra-atmospheric instrumental magnitudes.

Arne, do you agree this is a valid conceptual approach?

FJQ
Calculating Transformation Coefficients and the Use of Comp Star

This is a very illuminating discussion about Calculating Transformation Coefficients Use of Comp Stars. One thing that is confusing when discussing MaximDL.  When you are going to assign a mag value to a star, this is called "reference star" in MaximDL.  If you designate a "comp" star in MaximDL, there is no option to assign it a magnitude.  I know this sounds weird in terms other programs that use comp/reference stars, but I feel that is important to make this discussion as clear as possible.

James

A Confusing Vocabulary:
The terms raw, instrumental standard, differential and absolute are not uniformly used and can have conflicting meanings in different contexts or different meanings in the same context when used by different people. It leads to confusion. The term standard as used in the MTYPE field of WebObs, for example is a bit of a misnomer although it is completely explained in the link in the notes, if you read that far. I would only use the term standard to apply to the magnitude of a recognized standard star. I wouldn't even use it to describe a magnitude that had been transformed to a standard magnitude scale. I would use "transformed" to describe that. I don't even use "standard" to describe the chart magnitude of a comparison star. I use "sequence" magnitude or "reference" magnitude to describe comp star magnitudes (unless they are recognized standard stars) because most sequence star magnitudes are only transformed to a standard magnitude scale. They are not sufficiently measured to qualify as a photometric standard stars.

Cound't agree more!

jji
Comp stars and Reference stars in MaxIm

You have object stars, reference stars and check stars in MaxIm.  No comp stars.  MaxIm's reference stars are the AAVSO's comp stars.  The check stars are the same.  And of course the object star is the target star.

Jim Jones

FJQ
Comp stars and Reference stars in MaxIm

[quote=jji]

You have object stars, reference stars and check stars in MaxIm.  No comp stars.  MaxIm's reference stars are the AAVSO's comp stars.  The check stars are the same.  And of course the object star is the target star.

[/quote]

To:  Jim,

Yea the Reference star in MaximDL is the "Comp" star used in the usual photometry venacular.  I enclose a screen print of the Maxim photometry designation choices in the .jpg attachment.

I maybe barking up the wrong tree.  I dont think I'll ever be able to transform my data using just MaximDL, since I never do day-by-day anaylsis.  I usually wait 3-5 months (my visibility window for most variables) and do 100-200 observation at a time per variable star.  Since this "looses" the night by night variation needed to reduce 2nd-order transformation corrections, I might need to look at another program that can derrive nightly transformation from my comp/reference stars.

James

HQA
DIF vs. STD vs. other name choices

[quote=FJQ]

A Confusing Vocabulary:
The terms raw, instrumental standard, differential and absolute are not uniformly used and can have conflicting meanings in different contexts or different meanings in the same context when used by different people. It leads to confusion. The term standard as used in the MTYPE field of WebObs, for example is a bit of a misnomer although it is completely explained in the link in the notes, if you read that far. I would only use the term standard to apply to the magnitude of a recognized standard star. I wouldn't even use it to describe a magnitude that had been transformed to a standard magnitude scale. I would use "transformed" to describe that. I don't even use "standard" to describe the chart magnitude of a comparison star. I use "sequence" magnitude or "reference" magnitude to describe comp star magnitudes (unless they are recognized standard stars) because most sequence star magnitudes are only transformed to a standard magnitude scale. They are not sufficiently measured to qualify as a photometric standard stars.

[/quote]

Actually, if you look at the Extended File Format definition, the magnitude type "STD" means "standardized", not "standard".  It is a type of observation, and I think the name is appropriate, and goes along with the other possible choice (DIF=differential).  Transformed is a subset of the observation type, and is also properly identified.  If you are talking about an individual star and its magnitude and colors, then standard, secondary standard, reference, etc. come into play.  There are many definitions in the photometry vocabulary, and you need to keep them straight.

Arne

Richard Wagner
James: That's the process.

James:
That's the process.  And if the images are of a target variable star then I include it as well in the group of object stars.  And the object stars become the comp (ensemble) and check stars in the final analysis.

It's actually a lot quicker than it sounds.

Richard

WBY
Calculating Transformation Coefficients and the Use of Comp Star

Well, take a look at the attached spreadsheet and see it that is any help.

I don't guarantee that I have made no errors is the formulas. I put this together several years ago and updated as I found errors. I did it to keep straight how extinction and transformation interact and to have a crib sheet to look at when doing. the idea for this came from Bruce Gary's method and then I sat down with Arne's book to figure out what he was doing. This was the result. I didn't use an artificial star because I could get raw magnitudes from the program I use. using an artificial star accomplishes the same thing.

FJQ
To:  Richard, Thanks for

To:  Richard,

Thanks for the verification on how to get v (instrumental magnitudes) from MaximDL.  Also thanks Brad for the spreadsheet notes!

One other question,  before applying the TC to the v, do we first need to change it to an "extra-atmospheric" magnitude? I see a typical formula (for b-mag) shown as this: bo=b-kb*X, where bo is the extra-atmospheric b-magnitude, b is the instrumental magnitude, kb is the excitation coeffieceint for the b-filter observation, and X is the air mass [Sec(z), where z is the altitude].  The kb or more gerally k-lambda or Kl is usually derrived from the Zero-point(k') and color coefficient(k") such as kl=k'+k"(B-R); for transformations with B & R terms.

Sorry for the long post, but are these (1)Zero-point and (2)Color coefficient the same terms B. Gary uses as (1)Zero-shift value and (2)Star Color Sesitivity in his DP photometry pages?  Thanks for all the help!

James

HQA
extra-atmospheric magnitudes

[quote=FJQ]

One other question,  before applying the TC to the v, do we first need to change it to an "extra-atmospheric" magnitude? I see a typical formula (for b-mag) shown as this: bo=b-kb*X, where bo is the extra-atmospheric b-magnitude, b is the instrumental magnitude, kb is the excitation coeffieceint for the b-filter observation, and X is the air mass [Sec(z), where z is the altitude].  The kb or more gerally k-lambda or Kl is usually derrived from the Zero-point(k') and color coefficient(k") such as kl=k'+k"(B-R); for transformations with B & R terms.

Sorry for the long post, but are these (1)Zero-point and (2)Color coefficient the same terms B. Gary uses as (1)Zero-shift value and (2)Star Color Sesitivity in his DP photometry pages?  Thanks for all the help!

[/quote]

The transformation coefficient is applied to the extra-atmospheric color index.  For differential work (a target and a comparison star in the same field), many of the complications drop out, especially if the target and the comp are roughly the same color.  The nightly zeropoint goes away, and first order atmospheric extinction can be ignored if your field of view is small and you are observing at low airmass. That is why we generally try to choose comp stars that are either similar to the target, or at least similar to other comp stars that you might use in an ensemble or later in the star's light curve.

Don't make things too difficult.  Brad's conceptual description of transformation being composed of a time-varient aspect (the atmosphere) and a nearly-stable aspect (the instrumentation) is correct, and is why you can calculate transformation coefficients (which only directly apply to the instrumentation part) once, and use them for many months.  I recommend that you calculate your coefficients using standard clusters, like M67, rather than trying to do it the more rigorous way of using Landolt standards spaced across the sky, as you eliminate most of the atmospheric problems.  I also recommend that, once you determine your coefficients, you use them with comparison stars of known magnitude/color, and at reasonable airmasses, so that you can ignore the atmosphere as much as possible.

Arne

FJQ
extra-atmospheric magnitudes & Vtrue or Vcorr magnitude

" I recommend that you calculate your coefficients using standard clusters, like M67, rather than trying to do it the more rigorous way of using Landolt standards spaced across the sky, as you eliminate most of the atmospheric problems. I also recommend that, once you determine your coefficients, you use them with comparison stars of known magnitude/color, and at reasonable airmasses, so that you can ignore the atmosphere as much as possible.

Arne"

Thanks Dr. Arne!  I actually got the Zero-shift value and Star Color Sesitivity for my system on M67; abiet with Maxim's non-instrumental magnitudes.

James