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12 High-Precision Differential Photometry
12.4 Scintillation Noise
Scintillation is what a layperson would call twinkling, a change in brightness of an
astronomical object due to the change of pathway caused by atmospheric turbulence.
Planets, at least the bright naked-eye planets (not counting Uranus, which is technically a naked eye object), do not appear to twinkle, because unlike stars, they are
resolved objects, and any change in the pathway is limited to the disk of the planet.
This is not entirely true, but it is not within the ability of the human eye to detect
such changes.
For an observatory at altitude h operating at an air mass X , with an instrument of
diameter D operating with an exposure time of t exp , the scintillation noise is given
by
σ scint = 0.004D
−
2
3 X
7
4 e
−
h
H (2t exp )
−0.5
,
(12.3)
where H is the scale height of the turbulence, which can be taken as 8000 m.
Equation 12.3 is a simplified and generalised scintillation noise equation. It ignores
such effects as wind speed and turbulence cell size, as these are generally out of the
control of the observer.
As can be seen, the best practice to reduce scintillation noise is always to observe
the target as it crosses the meridian and has the lowest air mass. However, for observations such as exoplanet transits this is impossible, as we are constrained to the period
of the transit, and long-period observations are going to be over a range of air masses,
with the highest scintillation noise occurring at the highest air mass. Increasing the
diameter of the telescope would appear to be the solution to this problem. However,
increasing the diameter of the telescope reduces the exposure time by the square
of the diameter. As we can see, increasing the exposure time decreases scintillation
noise, but we can expose only up to the point of linearity of the instrument, t max .
The solution to this problem is to bin the data postcalibration, sacrificing cadence
for reduced scintillation noise.
Increasing the aperture size of the telescope has an additional effect. The turbulence cell size is typically of order 30–50 cm. Hence, telescopes significantly larger
than the cell size have less scintillation noise, as it is more likely that the entire range
of possible photon pathways will reach the camera.
Returning to (12.4), we can see by increasing the exposure time, we reduce scintillation noise (although by the square root of the exposure time), although of course,
we would not be able to exceed t max .
A possible solution to scintillation noise is to implement a method known as
defocused photometry. The telescope is deliberately defocused to allow an increased
exposure time. This method works because defocusing spreads the photons over a
larger area, and hence the light falls on more pixels. Therefore, a longer exposure can
be made while keeping the CCD in its region of linearity. Defocusing can reduce,
but not eliminate, scintillation and other atmospheric effects as well as flat-field
errors. You should be aware that defocusing can increase sky noise, so care must
be taken to keep the target’s PSF only as large as required. It is also impossible to
12 High-Precision Differential Photometry
12.4 Scintillation Noise
Scintillation is what a layperson would call twinkling, a change in brightness of an
astronomical object due to the change of pathway caused by atmospheric turbulence.
Planets, at least the bright naked-eye planets (not counting Uranus, which is technically a naked eye object), do not appear to twinkle, because unlike stars, they are
resolved objects, and any change in the pathway is limited to the disk of the planet.
This is not entirely true, but it is not within the ability of the human eye to detect
such changes.
For an observatory at altitude h operating at an air mass X , with an instrument of
diameter D operating with an exposure time of t exp , the scintillation noise is given
by
σ scint = 0.004D
−
2
3 X
7
4 e
−
h
H (2t exp )
−0.5
,
(12.3)
where H is the scale height of the turbulence, which can be taken as 8000 m.
Equation 12.3 is a simplified and generalised scintillation noise equation. It ignores
such effects as wind speed and turbulence cell size, as these are generally out of the
control of the observer.
As can be seen, the best practice to reduce scintillation noise is always to observe
the target as it crosses the meridian and has the lowest air mass. However, for observations such as exoplanet transits this is impossible, as we are constrained to the period
of the transit, and long-period observations are going to be over a range of air masses,
with the highest scintillation noise occurring at the highest air mass. Increasing the
diameter of the telescope would appear to be the solution to this problem. However,
increasing the diameter of the telescope reduces the exposure time by the square
of the diameter. As we can see, increasing the exposure time decreases scintillation
noise, but we can expose only up to the point of linearity of the instrument, t max .
The solution to this problem is to bin the data postcalibration, sacrificing cadence
for reduced scintillation noise.
Increasing the aperture size of the telescope has an additional effect. The turbulence cell size is typically of order 30–50 cm. Hence, telescopes significantly larger
than the cell size have less scintillation noise, as it is more likely that the entire range
of possible photon pathways will reach the camera.
Returning to (12.4), we can see by increasing the exposure time, we reduce scintillation noise (although by the square root of the exposure time), although of course,
we would not be able to exceed t max .
A possible solution to scintillation noise is to implement a method known as
defocused photometry. The telescope is deliberately defocused to allow an increased
exposure time. This method works because defocusing spreads the photons over a
larger area, and hence the light falls on more pixels. Therefore, a longer exposure can
be made while keeping the CCD in its region of linearity. Defocusing can reduce,
but not eliminate, scintillation and other atmospheric effects as well as flat-field
errors. You should be aware that defocusing can increase sky noise, so care must
be taken to keep the target’s PSF only as large as required. It is also impossible to