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10 Photometry
and dark currents. These sources are collectively known as the background. The
method by which we deal with the background is the difference between aperture
and PSF photometry.
In aperture photometry, we drop an aperture, which is normally a circle, but
not always, onto the image of the target star. We then integrate the count constrained
within that circle. The diameter of this circle is important. The circle should contain
only pixels associated with that star and be wide enough to capture the vast majority
of the signal from the target. The circle’s diameter typically has a radius three times
the FWHM PSF of the star.
Recalling that the PSF should be Gaussian, you should see that an aperture of
this size contains 99.7% of the light from the star. Because the PSF is principally
a function of seeing, the aperture size should be constant for the whole field. The
difference between a bright star and a dim one on the image is not the width of the
PDF but the height.
Clearly, the integrated count within the aperture also includes a contribution from
the background. It is impossible to determine directly which are from the source and
which are from the background, so we must assume that the background is constant
at local levels. By dropping an annulus onto the aperture, where the inner ring of the
annulus is beyond the aperture, we can address the problem of a noisy background.
Typically, the area contained within the annulus is the same as that enclosed by the
annulus, but if not, it should always be larger. We can take the background to be the
integrated count within the annulus normalised for the area of the aperture. Hence,
stars falling into the annulus must also be avoided, as they would artificially heighten
the background. We subtract this area’s normalised background from our integrated
aperture count in order to get an instrumental count. As the count will depend on the
exposure time, we need to divide the count by the exposure time to get counts per
second.
The key drawback of aperture photometry is that it requires that an aperture
and annulus, without contamination from other stars, be fitted to the target. In very
crowded fields, such as those found in globular and open clusters, this clearly is not
possible.
The solution to this problem is PSF fitting. Given that a star’s profile is Gaussian
and a Gaussian is determined by its width and height, it is possible to estimate the
count by fitting a Gaussian to the PSF, whence PSF photometry. In this way, even
if the PSFs of two stars overlap, we can achieve a reasonable estimate of the count.
In most cases of PSF photometry, the PSF is used to detect and remove the stellar
contribution to the entire image count, and the remainder is used to determine the
background.
In general, PSF photometry is not as accurate as aperture photometry in ideal
conditions, but it outperforms aperture photometry in crowded fields. Many applications used for photometry can do both PSF and aperture photometry, and you should
judge which one you should use based on the field and the FWHM of the stars in
the image. You may have thought about the implications of unresolved binaries on
photometry, two or more stars being so close that they appear as one. Fortunately, as
luminosity increases by approximately M
3.5 , low mass companions contribute little
10 Photometry
and dark currents. These sources are collectively known as the background. The
method by which we deal with the background is the difference between aperture
and PSF photometry.
In aperture photometry, we drop an aperture, which is normally a circle, but
not always, onto the image of the target star. We then integrate the count constrained
within that circle. The diameter of this circle is important. The circle should contain
only pixels associated with that star and be wide enough to capture the vast majority
of the signal from the target. The circle’s diameter typically has a radius three times
the FWHM PSF of the star.
Recalling that the PSF should be Gaussian, you should see that an aperture of
this size contains 99.7% of the light from the star. Because the PSF is principally
a function of seeing, the aperture size should be constant for the whole field. The
difference between a bright star and a dim one on the image is not the width of the
PDF but the height.
Clearly, the integrated count within the aperture also includes a contribution from
the background. It is impossible to determine directly which are from the source and
which are from the background, so we must assume that the background is constant
at local levels. By dropping an annulus onto the aperture, where the inner ring of the
annulus is beyond the aperture, we can address the problem of a noisy background.
Typically, the area contained within the annulus is the same as that enclosed by the
annulus, but if not, it should always be larger. We can take the background to be the
integrated count within the annulus normalised for the area of the aperture. Hence,
stars falling into the annulus must also be avoided, as they would artificially heighten
the background. We subtract this area’s normalised background from our integrated
aperture count in order to get an instrumental count. As the count will depend on the
exposure time, we need to divide the count by the exposure time to get counts per
second.
The key drawback of aperture photometry is that it requires that an aperture
and annulus, without contamination from other stars, be fitted to the target. In very
crowded fields, such as those found in globular and open clusters, this clearly is not
possible.
The solution to this problem is PSF fitting. Given that a star’s profile is Gaussian
and a Gaussian is determined by its width and height, it is possible to estimate the
count by fitting a Gaussian to the PSF, whence PSF photometry. In this way, even
if the PSFs of two stars overlap, we can achieve a reasonable estimate of the count.
In most cases of PSF photometry, the PSF is used to detect and remove the stellar
contribution to the entire image count, and the remainder is used to determine the
background.
In general, PSF photometry is not as accurate as aperture photometry in ideal
conditions, but it outperforms aperture photometry in crowded fields. Many applications used for photometry can do both PSF and aperture photometry, and you should
judge which one you should use based on the field and the FWHM of the stars in
the image. You may have thought about the implications of unresolved binaries on
photometry, two or more stars being so close that they appear as one. Fortunately, as
luminosity increases by approximately M
3.5 , low mass companions contribute little