10.4 Differential Photometry
157
in the change in magnitude M in a single band. As both the colour transform and
the zero points are time independent, these can be ignored under these circumstances.
Hence, in this case, we are interested only in the difference between the instrumental
magnitude of the target and the reference, although in general, multiple reference
stars are used in order to reduce errors. Obtaining millimagnitude uncertainties using
differential photometry is possible using a small telescope. However, you should be
aware of the sources of errors so they can be minimised.
There are a number of sources that contribute to system noise with regard to
photometry. Read noise (σ read ) is simply the noise generated by the electronics
during the read process. It is effectively the noise within the bias frame (although
not the bias current, which is systemic). The bias will vary across the chip and to
some extent between bias frames. In general, the bias noise is small, with much of
the variation taken out using a master bias, i.e., the mean of a number of biases.
However, using a combination dark and bias frame (remember that a dark has a
bias frame inside unless it is removed) is generally acceptable for imaging, although
it does increase uncertainties in photometric measurements and should be avoided
when photometry is being undertaken.
As discussed in Sect. 7.1, the dark current is the build-up of thermal electrons
within the CCD. It is effectively, but incompletely, removed by the subtraction of
the dark frame. So it is another source of random uncertainty (σ dark ). Again master
dark frames are used to reduce dark current noise. Remember, however, that a dark
frame includes a bias. Although the dark current will not vary across the frame as
much as the read noise, it is, unlike the read noise, dependent on the exposure time
and operating temperature.
Flat fielding, as discussed previously, is a challenging issue. For bright objects,
the quality of a flat field and the noise of the flat field (flat field noise) normally are
not significant. However, for a faint source or when measuring sources in multiple
locations in the frame, it can become significant, because it causes variation across
the field due to the field not being entirely flat. Therefore, a variation in pixel location
can result in a differential pixel response.
In general, when performing single target photometry, the best practice is to
keep the target in the centre of the frame, as this is where the frame is flattest.
However, when undertaking differential photometry, this might not be possible for
both reference star and target. We might require moving between the source and the
reference, nodding, so that each appears on the same pixels, thereby reducing flat
field effects.
As stated previously, because of atmospheric effects the light from a star does not
appear as a point source occupying one pixel, but rather a circle (ideally) occupying
multiple pixels. However, pixels are square and are spaced with gaps between them,
and a small amount of light will fall between them, and the edges of the star will cut
through pixels rather than completely fill them. This leads to interpolation errors.
For the most part, the software will deal with this problem, but you should be aware
of the problem if, for example, you are using DS9.
Another photometric precision problem is scintillation noise. Small-scale turbulence in the atmosphere Effectively scatters the light, causing the random nondetec-
157
in the change in magnitude M in a single band. As both the colour transform and
the zero points are time independent, these can be ignored under these circumstances.
Hence, in this case, we are interested only in the difference between the instrumental
magnitude of the target and the reference, although in general, multiple reference
stars are used in order to reduce errors. Obtaining millimagnitude uncertainties using
differential photometry is possible using a small telescope. However, you should be
aware of the sources of errors so they can be minimised.
There are a number of sources that contribute to system noise with regard to
photometry. Read noise (σ read ) is simply the noise generated by the electronics
during the read process. It is effectively the noise within the bias frame (although
not the bias current, which is systemic). The bias will vary across the chip and to
some extent between bias frames. In general, the bias noise is small, with much of
the variation taken out using a master bias, i.e., the mean of a number of biases.
However, using a combination dark and bias frame (remember that a dark has a
bias frame inside unless it is removed) is generally acceptable for imaging, although
it does increase uncertainties in photometric measurements and should be avoided
when photometry is being undertaken.
As discussed in Sect. 7.1, the dark current is the build-up of thermal electrons
within the CCD. It is effectively, but incompletely, removed by the subtraction of
the dark frame. So it is another source of random uncertainty (σ dark ). Again master
dark frames are used to reduce dark current noise. Remember, however, that a dark
frame includes a bias. Although the dark current will not vary across the frame as
much as the read noise, it is, unlike the read noise, dependent on the exposure time
and operating temperature.
Flat fielding, as discussed previously, is a challenging issue. For bright objects,
the quality of a flat field and the noise of the flat field (flat field noise) normally are
not significant. However, for a faint source or when measuring sources in multiple
locations in the frame, it can become significant, because it causes variation across
the field due to the field not being entirely flat. Therefore, a variation in pixel location
can result in a differential pixel response.
In general, when performing single target photometry, the best practice is to
keep the target in the centre of the frame, as this is where the frame is flattest.
However, when undertaking differential photometry, this might not be possible for
both reference star and target. We might require moving between the source and the
reference, nodding, so that each appears on the same pixels, thereby reducing flat
field effects.
As stated previously, because of atmospheric effects the light from a star does not
appear as a point source occupying one pixel, but rather a circle (ideally) occupying
multiple pixels. However, pixels are square and are spaced with gaps between them,
and a small amount of light will fall between them, and the edges of the star will cut
through pixels rather than completely fill them. This leads to interpolation errors.
For the most part, the software will deal with this problem, but you should be aware
of the problem if, for example, you are using DS9.
Another photometric precision problem is scintillation noise. Small-scale turbulence in the atmosphere Effectively scatters the light, causing the random nondetec-