[Aavso-photometry] Determination and use of BVRI transformation coefficients with Maxim DL

Mon Jan 14 10:35:39 EST 2008

My goal is to improve the accuracy of my differential photometry results by
using transformation coefficients. This also converts magnitudes to the
standard system. To quantify the improvement in accuracy, I did the
following experiment. I took 12 exposures of the open cluster M67 in the
order BVRIBVRIBVRI using optec filters, a 10-inch Newtonian, and an SBIG
ST-2000XM camera. Each exposure was 60s long. I averaged the exposures for
each filter to increase the SNR without saturating the stars. Then I used
Maxim to calculate the (untransformed) magnitudes of 49 standard stars in
the field with Star 15 as my reference and differential photometry. I only
used stars that were not crowded by neighbours so as to have a clean
annulus. The lowest SNR was 255, so it is not a significant source of error.
I used standard magnitude data from the following source
http://binaries.boulder.swri.edu/binaries/fields/m67.html
I chose Star 15 as my reference because it has "average" colour indices
among all the other stars in the field, and its maximum ADU was about half
the range of my antiblooming CCD camera. Next, I calculated the average
absolute error of my untransformed differential magnitudes as follows:

Error (untransformed) = average {abs[mdiff(star) - mstd(ref)]}.

where N is the number of calculated stars (N=49), mdiff(star) is the
untransformed magnitude of a star obtained by differential photometry with
Maxim DL, mstd(ref) is the standard magnitude of the reference star taken
from Arne's data, and "abs" stands for absolute value. I obtained the
following results:
 Error V (untransformed) = 0.022
 Error B (untransformed) = 0.012
 Error R (untransformed) = 0.034
 Error I (untransformed) = 0.025

Next, I calculated the transformation coefficients and used the
transformation equations to calculate transformed magnitudes for all 49
stars. Finally, I calculated the average absolute error of my transformed
magnitudes as follows:

Error (transformed) = average {abs[mtrans(star) - mstd(ref)]}

where mtrans(star) is the transformed magnitude after applying the
transformation equations. I obtained the following results:

Error V (transformed) = 0.012
Error B (transformed) = 0.007
Error R (transformed) = 0.010
Error I (transformed) = 0.013

Therefore, applying the transformation equations reduced the error by a
factor of 2 to 3! I think that this is worthwhile if one is studying
variable stars whose range of variation is a few centimags. Interestingly,
the largest reduction in error was obtained for the R filter. 

Lionel 

-----Original Message-----
From: aavso-photometry-bounces at mira.aavso.org
[mailto:aavso-photometry-bounces at mira.aavso.org] On Behalf Of Jim Jones
Sent: Monday, January 14, 2008 2:06 AM
To: AAVSO Photometry
Subject: Re: [Aavso-photometry] Determination and use of BVRI transformation
coefficients with Maxim DL

Lionel

I have been following this thread and am having some problem 
understanding exactly what the problem is.  I am missing Gord Sarty's 
comments so suspect that they were not sent to the list.  Perhaps you 
could re-post them to the list.

When you select an object star (MaxIm's terminology)  and a reference 
star(s), MaxIm is obviously making a differential measurement.  However, 
MaxIm reports the instrumental magnitude of the object star if you have 
entered the magnitude of the reference star into the "Ref Mag" window.

Beyond that, I don't believe that the extinction and zero point ( Qv, 
Qvb,....) are normally needed when doing differential photometry so long 
as your FOV is not gigantic.  In Arne's book he mentions that "if the 
variable and comparison are separated by more than a degree it may be 
wise to apply an extinction correction".  I love quoting Arne ;>}  So I 
assume for reasonable CCD fields it can normally be ignored.

Maybe I'm missing something here.

BTW, I agree with Brad Walter's observations about the short comings of 
MaxIm.  I think that if we could ever produce a consolidated list of the 
data that we needed, Doug George would provide it.  I think if we 
approach him individually and present him with a moving target, he will 
pretty much ignore us.

Jim Jones

Lionel Catalan wrote:
> Based on comments from Arne and Gord Sarty, I thought that the most
> straightforward way of using Maxim photometry data to derive
> transformation coefficients would be to convert Maxim's differential
> magnitudes into instrumental magnitudes. This recognizes the fact that
> transformation equations are written in terms of instrumental
> magnitudes.
>
> Because the photometry analysis tool in Maxim DL only calculates
> differential magnitudes, a special procedure is required to derive
> instrumental magnitudes. Differential magnitudes in Maxim DL are
> calculated using a reference star with known standard magnitude as
> follows:
>
> mdiff (star) = minst (star) - minst (ref) + mstd (ref)
>
> where mdiff, minst and mstd refer to differential, instrumental and
> standard magnitudes, respectively. The instrumental magnitude of the
> reference star can be calculated as follows:
>
> minst (ref) = -2.5 log (Int(ref))
>
> where Int(ref) represents the intensity of the reference star
> calculated as the sum of all pixel counts within aperture less
> background. The value of Int(ref), which is simply called "Intensity"
> in Maxim DL, can be read from the information window in aperture mode
> by centering the aperture on the reference star while using the
> photometry analysis tool. One must be careful to ensure that the
> centroid of the reference star has the same coordinates when reading
> its intensity and when calculating the differential maginutes of the
> other stars.
>
> Combining the two previous equations gives:
>
> minst (star) = mdiff (star) -2.5 log (Int(ref)) - mstd (ref)
>
> This equation is applied to magnitudes obtained with the B, V, R, and
> I filters using Excel.
>
> Lionel
>
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