12.6 Lucky Imaging and Adaptive Optics Photometry
177
Adaptive optics (AO) is a process involving the variation of the optics of the
imaging device in response to changes in the focusing of the optical system caused
by, in astronomy, atmospheric turbulence. To do this, a source in the field of view
needs to be monitored, and an active feedback system makes corrections to the optical
system, either a flexible mirror or lens in the optical pathway, in order to make the
point spread function of the observed target as small as possible. In low-cost systems
that are now being made available to amateurs and small observatories, the source
will be a star. At large observatories such as the VLT in Chile, a laser tuned to make
a visible spot at a specific layer in the atmosphere is used.
As the point spread function is reduced, we obtain the effects of improved seeing
and finer resolution of the telescope. This results in the target being spread over fewer
pixels, resulting in a reduced exposure time before we enter the nonlinear zone of the
detector. As we have seen, increasing the exposure time will decrease the uncertainness. As a result, AO is not suitable for aperture photometry in uncrowded fields. In
crowded fields, where aperture photometry is challenging, AO may reduce the crowding to the point where aperture photometry is possible. However, in crowded fields,
PSF photometry is the preferred photometric technique, and AO should increase the
reliability of PSF photometry in these fields.
12.7 Target and Check Star Noise
As light comes in discrete packets, photons, in any given period there is a chance of
receiving more or fewer photons than the mean number from a source of constant
luminosity. This is known as shot noise, and it takes the form of a Poisson distribution,
whereby the noise increases with the square root of the signal. Hence, the signal-tonoise ratio for source and check stars scales by
SNR =
N
√
N
.
(12.4)
Hence the only way to reduce target noise is to increase the signal by increasing
exposure time.
Check star noise, however, can be addressed in an alternative manner. Adding
more check stars decreases the overall check star shot noise by
1
√
N
. But beware!
Apart from the fact that there are diminishing returns (a sample of four will have half
the error of a single sample, but a sample of nine, over twice the work, will reduce
the uncertainty only by a third), there is an increased risk of a bad pixel or, perhaps
worse, a variation in the brightness of a check star.
This last point, magnitude variation in the check stars, is resolvable by careful
selection. We can pick a section of stars in the field with magnitudes similar to the
target’s magnitude and perform photometry on them. For each image within your
time series, find the mean count of the check stars and plot them. The plots should be
smooth, with a slight gradient caused by changing air mass. If there are spikes within
177
Adaptive optics (AO) is a process involving the variation of the optics of the
imaging device in response to changes in the focusing of the optical system caused
by, in astronomy, atmospheric turbulence. To do this, a source in the field of view
needs to be monitored, and an active feedback system makes corrections to the optical
system, either a flexible mirror or lens in the optical pathway, in order to make the
point spread function of the observed target as small as possible. In low-cost systems
that are now being made available to amateurs and small observatories, the source
will be a star. At large observatories such as the VLT in Chile, a laser tuned to make
a visible spot at a specific layer in the atmosphere is used.
As the point spread function is reduced, we obtain the effects of improved seeing
and finer resolution of the telescope. This results in the target being spread over fewer
pixels, resulting in a reduced exposure time before we enter the nonlinear zone of the
detector. As we have seen, increasing the exposure time will decrease the uncertainness. As a result, AO is not suitable for aperture photometry in uncrowded fields. In
crowded fields, where aperture photometry is challenging, AO may reduce the crowding to the point where aperture photometry is possible. However, in crowded fields,
PSF photometry is the preferred photometric technique, and AO should increase the
reliability of PSF photometry in these fields.
12.7 Target and Check Star Noise
As light comes in discrete packets, photons, in any given period there is a chance of
receiving more or fewer photons than the mean number from a source of constant
luminosity. This is known as shot noise, and it takes the form of a Poisson distribution,
whereby the noise increases with the square root of the signal. Hence, the signal-tonoise ratio for source and check stars scales by
SNR =
N
√
N
.
(12.4)
Hence the only way to reduce target noise is to increase the signal by increasing
exposure time.
Check star noise, however, can be addressed in an alternative manner. Adding
more check stars decreases the overall check star shot noise by
1
√
N
. But beware!
Apart from the fact that there are diminishing returns (a sample of four will have half
the error of a single sample, but a sample of nine, over twice the work, will reduce
the uncertainty only by a third), there is an increased risk of a bad pixel or, perhaps
worse, a variation in the brightness of a check star.
This last point, magnitude variation in the check stars, is resolvable by careful
selection. We can pick a section of stars in the field with magnitudes similar to the
target’s magnitude and perform photometry on them. For each image within your
time series, find the mean count of the check stars and plot them. The plots should be
smooth, with a slight gradient caused by changing air mass. If there are spikes within