How to measure the color terms for your camera

Michael Richmond
Sep 7, 2011


How to compute color terms

Joe the Astronomer has a telescope, CCD camera, and two filters: B and V. The manufacturer stated that they were made to the standard Johnson-Cousins filter specifications, as described in

Joe decides to make a little test of this claim. He chooses a field in which there is solid photometry: PG1633+009, one of the equatorial calibration fields listed in the paper

The paper by Landolt provides this photometry (which you can also find in the Vizier system at http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=II%2F183A):

#Full  RAJ2000   DEJ2000   Star          RA2000     DE2000    Vmag     B-V     U-B     V-R     R-I 
#       "h:m:s"   "d:m:s"                "h:m:s"   "d:m:s"     mag     mag     mag     mag     mag 
#
    1  16 35 24  +09 47.8  PG1633+099   16 35 24  +09 47 50  14.397  -0.192  -0.974  -0.093  -0.116
    2  16 35 26  +09 47.9  PG1633+099A  16 35 26  +09 47 53  15.256   0.873   0.320   0.505   0.511
    3  16 35 34  +09 46.4  PG1633+099B  16 35 34  +09 46 22  12.969   1.081   1.007   0.590   0.502
    4  16 35 38  +09 46.3  PG1633+099C  16 35 38  +09 46 16  13.229   1.134   1.138   0.618   0.523
    5  16 35 40  +09 46.7  PG1633+099D  16 35 40  +09 46 43  13.691   0.535  -0.025   0.324   0.327

Notice that the stars cover a wide range of colors, with -0.192 < (B-V) < 1.134. The key to measuring color terms is to have simultaneous measurements of stars over as wide a range of colors as possible.

Joe takes a set of images of this field with his camera using both the B and V filters. He measures the brightness of the stars on each exposure and converts the raw counts to an instrumental magnitude. His data looks like this:


  #  star        b          v
    PG1633     16.759     15.749 
    PG1633A    18.812     16.602 
    PG1633B    16.878     14.348 
    PG1633C    17.242     14.582 
    PG1633D    16.905     15.050 

"In order to calibrate my photometry," thinks Joe, "all I have to do is to shift my measurements by a constant value, so that the instrumental magnitudes match up with the catalog magnitudes from Landolt's paper." However, because Joe fears his filters might have some problem, he decides to test this idea by plotting the results as a function of the instrumental colors of the stars. In other words, Joe

"Excellent!" exclaims Joe. "The difference between my measurements and the catalog values is the same for all the stars, both red ones and blue ones. I can simply average the differences to find the simple shift which will convert my instrumental "v" magnitudes into the standard Johnson "V" magnitudes."

Joe finds that the required shift is 1.36 magnitudes, so that


   Landolt V   =  instrumental v   -   1.36    (+/- 0.01)

On the other hand, when Joe compares the instrumental b-band magnitudes to the catalog magnitudes, he finds a different situation:

"Uh-oh!" says Joe. "The difference here depends on the color of the star: blue stars have smaller differences than red ones. If I try to use a constant shift to convert the instrumental magnitudes to catalog magnitudes, I'll end up with systematic errors ... and pretty big ones, too."

Joe decides that he can fit this data with a linear relationship, like this:


   Landolt V   =  instrumental v   +   z   +  k*(b - v)

where z is a zero-point shift, k is the first-order color term, and (b - v) is the instrumental color of the star. His calculator can do the arithmetic, finding the best-fit values of



    z   =   2.34   +/-  0.08
  
    k   =   0.19   +/-  0.04

"Well," says Joe, "I guess that my B filter isn't quite the same as the standard B filter. Still, as long as I include this extra term in my analysis, I can report my magnitudes on the standard Johnson magnitude scale."


Some good fields for measuring color terms

There are many fields throughout the sky with good photometry and stars covering a broad range of colors. The Landolt paper mentioned above is a good source of such fields; I'll pick out 4 of my favorites. I'll also include the cluster M67, which has been used by a number of authors for photometric calibration:



PG0231+051

Field center (J2000) 02:33:41 +05:18:40

#Full   RAJ2000   DEJ2000  Star          RA2000     DE2000    Vmag     B-V     U-B     V-R     R-I 
        "h:m:s"   "d:m:s"                "h:m:s"   "d:m:s"     mag     mag     mag     mag     mag 

    1  02 33 28  +05 19.7  PG0231+051E  02 33 28  +05 19 44  13.804   0.677   0.201   0.390   0.369
    2  02 33 33  +05 19.5  PG0231+051D  02 33 33  +05 19 28  14.027   1.088   1.046   0.675   0.586
    3  02 33 40  +05 17.6  PG0231+051A  02 33 40  +05 17 38  12.772   0.710   0.270   0.405   0.394
    4  02 33 41  +05 20.3  PG0231+051C  02 33 41  +05 20 19  13.702   0.671   0.114   0.399   0.385
    5  02 33 41  +05 18.7  PG0231+051   02 33 41  +05 18 40  16.105  -0.329  -1.192  -0.162  -0.371
    6  02 33 45  +05 17.5  PG0231+051B  02 33 45  +05 17 30  14.735   1.448   1.342   0.954   0.998



PG0918+029

Field center (J2000) 09:21:28 +02:46:03

#Full   RAJ2000   DEJ2000  Star          RA2000     DE2000    Vmag     B-V     U-B     V-R     R-I 
        "h:m:s"   "d:m:s"                "h:m:s"   "d:m:s"     mag     mag     mag     mag     mag 

    1  09 21 22  +02 47.5  PG0918+029D  09 21 22  +02 47 30  12.272   1.044   0.821   0.575   0.535
    2  09 21 28  +02 46.1  PG0918+029   09 21 28  +02 46 03  13.327  -0.271  -1.081  -0.129  -0.159
    3  09 21 34  +02 48.0  PG0918+029B  09 21 34  +02 48 01  13.963   0.765   0.366   0.417   0.370
    4  09 21 35  +02 46.3  PG0918+029A  09 21 35  +02 46 20  14.490   0.536  -0.032   0.325   0.336
    5  09 21 42  +02 46.6  PG0918+029C  09 21 42  +02 46 38  13.537   0.631   0.087   0.367   0.357



PG1633+099

Field center (J2000) 16:35:24 +09:47:50

#Full  RAJ2000   DEJ2000   Star          RA2000     DE2000    Vmag     B-V     U-B     V-R     R-I 
#       "h:m:s"   "d:m:s"                "h:m:s"   "d:m:s"     mag     mag     mag     mag     mag 
#
    1  16 35 24  +09 47.8  PG1633+099   16 35 24  +09 47 50  14.397  -0.192  -0.974  -0.093  -0.116
    2  16 35 26  +09 47.9  PG1633+099A  16 35 26  +09 47 53  15.256   0.873   0.320   0.505   0.511
    3  16 35 34  +09 46.4  PG1633+099B  16 35 34  +09 46 22  12.969   1.081   1.007   0.590   0.502
    4  16 35 38  +09 46.3  PG1633+099C  16 35 38  +09 46 16  13.229   1.134   1.138   0.618   0.523
    5  16 35 40  +09 46.7  PG1633+099D  16 35 40  +09 46 43  13.691   0.535  -0.025   0.324   0.327



PG2213-006

Field center (J2000) 22:16:28 -00:21:15

#Full   RAJ2000   DEJ2000  Star          RA2000     DE2000    Vmag     B-V     U-B     V-R     R-I 
        "h:m:s"   "d:m:s"                "h:m:s"   "d:m:s"     mag     mag     mag     mag     mag 

    1  22 16 18  -00 22.2  PG2213-006C  22 16 18  -00 22 15  15.109   0.721   0.177   0.426   0.404
    2  22 16 22  -00 21.8  PG2213-006B  22 16 22  -00 21 49  12.706   0.749   0.297   0.427   0.402
    3  22 16 24  -00 21.4  PG2213-006A  22 16 24  -00 21 27  14.178   0.673   0.100   0.406   0.403
    4  22 16 28  -00 21.2  PG2213-006   22 16 28  -00 21 15  14.124  -0.217  -1.125  -0.092  -0.110



M67 "dipper asterism"

Field center (J2000) 08:51:21 +11:46:16. The table below is from Chevalier and Ilovaisky, A&AS 90, 225 (1991)




For more information


Last modified 9/05/2011 by MWR.