# Color Calibration of an Instrumental Photometric System

How to calibrate of an instrumental photometric system.

# Open cluster M 67

Open cluster M 67 is an old galactic cluster with a differently evolved stars which covers wide range of color indexes.

As the calibration stars, we are choose data which has been carefully measured by Arne Henden (M67 Standards Field).

## Sample Data

A sample data are available as munipack-data-m67.tar.gz. Use commands

    $ cd /tmp
    $ tar zxf munipack-data-m67.tar.gz

to unpack it to a desired directory. We will assume that the sample data are unpacked to `/tmp` directory as `/tmp/munipack-data-m67`.

## Photometry Calibration

The main goal of photometry calibration is to determine relations between instrumental fluxes (magnitudes) and fluxes (magnitudes) defined by a photometric system (with conventionally defined conditions, especially by transmission of filters).

General relations can by derived as an approximation of a set of functions (instrumental filters) by another set functions (standard filters) as a linear transformations. A simple example is the calibration of instrumental v-filter by a standard V-filter:

v - V = a + b*(V-R)

The goal is to determine coefficients a,b by a fit of a linear function. The precision depends on coverage of color index V-R and that is why we use the evolved cluster.

## Data Processing

There is an algorithm to get data for the calibration.

1. Prepare images for photometric corrections as describes Photometric Corrections Tutorial.
2. Stars detection and photometry

       $ munipack aphot M67_Green_*.fits
       $ munipack aphot M67_Blue_*.fits

3. Search an astrometric catalogue (required for astrometric calibration)

       $ munipack cone -o m67cat.fits -r 0.1 132.75 11.8

4. Astrometry calibration of all images

       $ munipack astrometry -c m67cat.fits M67_*.fits

5. Sum of all images

       $ munipack kombine -o M67_Blue.fits M67_Blue_*.fits
       $ munipack kombine -o M67_Green.fits M67_Green_*.fits

6. Aperture photometry of final frames

       $ munipack aphot -f 6 M67_Blue.fits M67_Green.fits

7. Preparation of results in tables

       $ munipack phframe --table -q IMAG --naperture 7 M67_Green.fits,M67_Green_res.fits
       $ munipack phframe --table -q IMAG --naperture 7 M67_Blue.fits,M67_Blue_res.fits

   The file M67_Green_res.fits contains the table:

   α [J2000] | δ [J2000] | instrumental magnitude | std. deviation
   --- | --- | --- | ---
   132.8228301 | 11.7562805 | 7.62841 | .00036
   … | … | … |

   The output table can be matched against to a standard field stars in equatorial coordinates. The calibration coefficients can be easy determined by the way.

   To match and visualize data, topcat (part of Virtual Observatory software) can be recommended.

M 67 calibration
M 67 calibration

## Notes

This example is illustrative only! The instrumental magnitudes are also affected by the atmospheric extinction and to get correct values, we need to determine extra-atmospheric magnitudes by observing of the field in different air masses and an extrapolation on null air mass.

Please also don't be confused from filters designation and graphs. The used filters are RGB photographic filters for a color imaging. That's why the linear dependence doesn't exactly fit the data.