150
10 Photometry
observing. If not, you should have images of nearby stars with known magnitudes
and at the same air mass as the target. The reduction process outlined here and in
the following practical is discussed in considerably more detail in Brian D. Warner’s
excellent book A Practical Guide to Lightcurve Photometry and Analysis, also published by Springer. There are techniques that claim better accuracy, but the gains
are marginal given the complex nature of photometric reductions and the inherent
uncertainties in small telescope systems, which are often based at sites that are less
than ideal. When imaging for photometry purposes, it is best to take multiple images
very close together in time. The use of multiple images increases the number of
data points in your photometry, thereby reducing uncertainty and ensuring that all
the images are taken at the same air mass. These advantages apply to reference star
images as well.
Previously in this chapter, I discussed how to set an aperture size and measure the
integrated count within the aperture and how to account for the sky. Your software
should, unless it’s very simple, like DS9, be able to automatically time normalise
the data. If it doesn’t, do not forget to divide the background subtracted count by
the exposure time in seconds. You should determine the instrumental integrated
background subtracted count for all the reference stars you are using and for every
image. Take the mean count value for each star and use this as the instrumental count
(and also calculate uncertainty from this). The mean instrumental count needs to be
changed to an instrumental magnitude using a modified version of Pogson:
m = −2.5 log(count),
(10.1)
where m is the raw instrumental magnitude, and count is the count within the aperture
minus the background.
The count does not represent the number of photons received; rather, it is a ratio
between the electrons generated and the gain of the camera. You will find the camera
gain in the camera manual or written into the FITS header as EGAIN. Note that gain
might also be determined by the binning. The gain is applied to the count before it
is logged. Hence, (10.1) becomes
m = −2.5 log(count × gain),
(10.2)
and your errors become
δ(m) = −2.5 log 1 −
count × Gain
δcount × Gain
,
(10.3)
where δflux is your calculated count error.
If you now perform aperture photometry on a star in a science frame and apply
(10.2), you will find that you obtain an odd-looking result, most likely a magnitude
with a very negative value. The reason for this is that your photometry is not reduced.
The process of reduction takes your raw instrumental magnitude and converts it into
a standard magnitude, one set up for observing above the atmosphere.
10 Photometry
observing. If not, you should have images of nearby stars with known magnitudes
and at the same air mass as the target. The reduction process outlined here and in
the following practical is discussed in considerably more detail in Brian D. Warner’s
excellent book A Practical Guide to Lightcurve Photometry and Analysis, also published by Springer. There are techniques that claim better accuracy, but the gains
are marginal given the complex nature of photometric reductions and the inherent
uncertainties in small telescope systems, which are often based at sites that are less
than ideal. When imaging for photometry purposes, it is best to take multiple images
very close together in time. The use of multiple images increases the number of
data points in your photometry, thereby reducing uncertainty and ensuring that all
the images are taken at the same air mass. These advantages apply to reference star
images as well.
Previously in this chapter, I discussed how to set an aperture size and measure the
integrated count within the aperture and how to account for the sky. Your software
should, unless it’s very simple, like DS9, be able to automatically time normalise
the data. If it doesn’t, do not forget to divide the background subtracted count by
the exposure time in seconds. You should determine the instrumental integrated
background subtracted count for all the reference stars you are using and for every
image. Take the mean count value for each star and use this as the instrumental count
(and also calculate uncertainty from this). The mean instrumental count needs to be
changed to an instrumental magnitude using a modified version of Pogson:
m = −2.5 log(count),
(10.1)
where m is the raw instrumental magnitude, and count is the count within the aperture
minus the background.
The count does not represent the number of photons received; rather, it is a ratio
between the electrons generated and the gain of the camera. You will find the camera
gain in the camera manual or written into the FITS header as EGAIN. Note that gain
might also be determined by the binning. The gain is applied to the count before it
is logged. Hence, (10.1) becomes
m = −2.5 log(count × gain),
(10.2)
and your errors become
δ(m) = −2.5 log 1 −
count × Gain
δcount × Gain
,
(10.3)
where δflux is your calculated count error.
If you now perform aperture photometry on a star in a science frame and apply
(10.2), you will find that you obtain an odd-looking result, most likely a magnitude
with a very negative value. The reason for this is that your photometry is not reduced.
The process of reduction takes your raw instrumental magnitude and converts it into
a standard magnitude, one set up for observing above the atmosphere.