My interest is in high precision differential photometry
with the objective of being able to detect exoplanet transits. I
have set myself a target of being able to achieve 0.002 magnitude precision
for stars of magnitude 11 with an integration time of 2 minutes.
My technique is still developing, but the discussion
below will touch on several important elements. Bruce Gary has written
a great book that
describes how an amateur can observe exoplanet transits.
The Camera
- Linearity
The CCD camera used should have excellent linearity.
I currently use an SBIG ST-8XME without Anti-Blooming gates (NABG).
NABG gives the CCD higher sensitivity (QE), as well as greater well depth.
Both these factors help with collecting more photons and therefore reducing
photon shot noise.
I have also determined my CCD's limit of linearity.
Although the CCD will output > 60,000 ADU's (Analog Digital Units, or
counts) there is a point beyond which the CCD response ceases to be linear.
Photometry will not be precise if stars being measured produce pixel values
above this limit. Bruce Gary estimates that his ST-8 is linear up to
62,000 ADU but I have found that mine is linear only up to 40,000 ADU.
He uses a number of tests (described on his website) to arrive at his
conclusion, but I have found that for my CCD these tests were not
conclusive. Instead I noticed that when I plotted count Variance vs
ADU (the same process as for calculating CCD gain - see
http://www.mirametrics.com/tech_note_ccdgain.htm ) at 40,000 ADU the
Variance started to deviate significantly from a linear trend (chart
right). Beyond 40,000 ADU, variance is less than expected,
indicating onset of non-linearity. The full calibration sheet of my
CCD is here.
The Camera - Autoguiding
The ST-8XME has an additional chip built-in that enables
autoguiding with the one camera. I have found on the several occasions
that the guide star has been lost (e.g. cloud), photometric precision
suffers immensely.
Quantifying Errors
Given the importance of precision, it is very important
to be able to model the expected error from a measurement as well as
processing sequence. Being able to do this enables the selection of
acquisition parameters (exposure time, target star magnitude, filter),
calibration frames (no. of flat frames and ADU level, dark frames, bias).
My approach is based on the paper by Newberry (1991), "Signal-to
Noise Considerations for Sky-Subtracted CCD Data".
I have made a spreadsheet that calculates the expected
error given imaging and processing parameters. I offer it
here - but use with
caution - the output seems to match actual results, but there may still be
mistakes that have crept in.
Time series photometry software
Based on a
discussion in AAVSO, I have selected
Muniwin for this purpose.
Muniwin is excellent for time-series photometry. It is fast,
efficient, handles large datasets well, has automatic star detection as well
as full frame photometry (i.e. it measures all detected stars on the CCD
frames), permits use of multiple apertures - and runs on Windows XP.
The last point is important because all the important scientific photometry
packages seem to run mainly on Linux (e.g. IRAF).
Ensemble photometry
Ensemble photometry is the use of multiple comparison
stars rather than just one comp and one check star. It results in
improved precision is the comp stars are chosen such as to screen out those
that are variable on the timescale of the observation. The technique
is described in Everett and Howell's paper "A
Technique for Ultrahigh-Precision CCD Photometry", PASP 2001. My
implementation of this technique in a spreadsheet currently uses a maximum
of 20 stars.
U Sco campaign photometry
The U Sco campaign was a good
opportunity to test out these tools. Below is a light curve for 19th
Feb 2010, 23 days after eruption and when it had dimmed from 8th mag at peak
to mag 14.5. The light curve clearly show the eclipse of the dwarf
star by its companion. Note that the error bars are +- 0.02 mag,
far below the precision needed for exoplanet transits - but this is a mag 14
star, and I was using a V filter that significantly reduces the light.
