MPO Canopus – Photometry
The photometry side of Canopus is written primarily for lightcurve analysis and so many
of its features are designed towards that end. Some of the methods used are different for
asteroids than for variable star work but Canopus handles both. The concepts are a bit
involved but, with a little practice, should soon be familiar. The general method of
photometry is handled first, with occasional references to the more specialized work
required for lightcurve determinations. Afterwards, the specifics required for lightcurve
work will be covered.
A complete discussion of good photometric technique is beyond the scope of this
document. Arne Henden’s book, Astronomical Photometry: A Text and Handbook
for the Advanced Amateur and Professional Astronomer, co-authored with Ronald
Kaitchuck, is an invaluable resource and should be in the library of anyone doing
photometry.
Also recommended is A Practical Guide to Lightcurve Photometry and Analysis by
Brian D. Warner. This book is available from Springer and provides more in depth coverage
of the methods for obtaining and interpreting data to find lightcurve periods and
amplitudes for asteroids and variable stars.
The Measure of Magnitudes
Version 10 has adopted a "new-old" philosophy for photometry. It still
employs differential photometry but now you can store the magnitudes of the up to five
comparison stars and convert the target measurements to "true" magnitudes
instantly. If the catalog magnitudes for one or more of the comparisons should change, all
you do is update the value in the Sessions form of Canopus and click a single button to
calculate the updated values for the target. You don't have to remeasure your images.
For more on the new approach, see "What's
New in Version 10."
Setting the Measuring Apertures
The measuring apertures are seen whenever you click on an image. They can be three
squares or circles (or even rectangles/ellipses). The data completely within the inner
aperture is the "target data." The area completely within the "sky
annulus", i.e., the defined by the outermost and next inner circle in the image
above, is used to compute the background or "sky data." The middle region is the
"dead zone." This is used to keep pixels from being used for both the target and
sky data. It also helps avoid using pixels from stars adjacent to the target.
Using "k-clipping" and median values, the sky data pixel values are used to
compute a single sky background value, which is subtracted from the value for each pixel
in the target area. The resulting target values are then used to compute the centroid
position, signal-to-noise ratio (S/N), instrumental magnitude, and Full-Width Half-Maximum
(FWHM) value for the star.
Canopus has been well tested and its results compare well with well-known programs
using both rectangular and circular measuring areas. Tests on standard fields that
produced 0.01m and better photometry after finding the transforms and nightly zero points
and thousands of astrometric observations accepted by the Minor Planet Center fully
validate the methods and means of the Canopus system.
What Size Apertures?
There can and has been considerable debate concerning the proper sizing of the various
apertures, in particular, the inner most - which measures the sky and target, and the
outermost - which measures the sky background. Even among professionals, the computation
of the background value is one of uncertainty and numerous methods.
In general, a good rule for the innermost apertures is 3-5x the FWHM of the stars.
Remember that all stars are the same size on the image! Stars appear smaller because the
outer wings of the image profile fall near the level of the background and so are apparent
to the eye.
As for the background annulus size, many factors come into play, not the least of which
is if there are stars within the region. Without a good background algorithm, these can
artificially raise the background and so lower the apparent magnitude of the target. A
test of the background algorithm is to see how the instrumental magnitude of the target is
affected by including and excluding one or more stars from the background region. In tests
involving a nearby star of similar brightness to the target, the instrumental magnitude
changed by 0.003m. It took a star that was 1.2m brighter to affect the target by 0.01m.
Of course, you don't wan to use too large an annulus. After all, the point is to try to
determine the background under the target. However, assuming you have good flats, the
variations within 50 pixels of the target should not be so great as to cause an error of
more than a few millimags. The standard of 0.01m precision/accuracy is "good
enough" for the vast majority of situations. Millimag levels do require more work.
However, with care and judicious use, MPO Canopus and PhotoRed can achieve these levels.
Computing the Sky Background
One of the most important aspects of reliable and repeatable photometric results is the
accurate computation of the sky background. This is the area in the outermost annulus in
the set of measuring apertures discussed above. What follows presumes that you have good
darks and flats and that they have been applied to the primary image before measuring. If
not, then the subtraction routine and subsequent target measurements can and will be
affected to one degree or another.
There are many techniques for computing the sky background, which has been the subject
of technical papers and much discussion over the years. In MPO software (all use the same
algorithm), the process follows these steps:
The pixels within the outermost aperture are stored in a
list, sorted by increasing value.
When using circular apertures, a pixel may not be entirely within the measuring area. In
this case, its value is weighted according to the amount of the pixel area that is within
the measuring area. For example, if 0.347 of the pixel is within the area, the value of
the entire pixel is multiplied by 0.347 and it is that result that is used for the value.
After the initial list of pixel values have been placed
into the sorted list, the hottest and coldest pixel are removed.
- From here an iteration process begins.
The values in the list are averaged and the
standard deviation is found.
All pixels differing from the average by more than one standard deviation are removed
from the list.
The average and standard deviation of the remaining pixels are computed.
The two averages and standard deviations are compared.
The iteration process continues until the two averages and standard deviations each
agree to within 0.5% OR the number of pixels remaining in the list after the elimination
step drops below a fixed number of pixels (80).
- If the iteration succeeds before reaching the pixel count minimum, the program continues
to find the centroid, instrumental magnitude, SNR, and other values reported or used by
the programs. If the iteration cannot reach a stable solution (measured by the averages
and standard deviations agreeing to 0.5%), then the program reports that it cannot find
the centroiding information.
It is extremely rare that the iteration cannot succeed and is usually long
before reaching the minimum number of sky pixels. For example, if the inner aperture is 9
pixels, the dead zone is 2 pixels, and the sky annulus is 9 pixels, this results in
approximately 620 sq. pixels in the sky annulus alone [A = (15.52 - 6.52)
* p = 622.03]. How many are used in the final
result depends on the number and brightness of any stars in the annulus but in typical
situations, the number is usually > 300 sq. pixels.
Stars in the Sky Annulus
Stars in the sky annulus, unless handled properly, will raise the background level
higher than it is. This results in the measurement for the target to be fainter than it
really is. In tests in both crowded fields and where a single star could be included or
excluded from the sky annulus, the measured instrumental magnitude was stable to at least
±0.01 mag - usually ±0.005 mag, even when the interloping star was several magnitudes
brighter than the target. When the annulus had several stars fainter than the target,
i.e., only 1-2 magnitudes above background level, the change in instrumental target
magnitude when excluding one or two was typically ±0.003 mag or less.
Far more important to the stability of the measurement was to assure that the faint
wings of the intervening star, especially when it was very bright and close to the target,
did not encroach into the measuring area (innermost aperture).
Important Concepts
Lightcurve
A lightcurve is a plot of magnitude versus time. Lightcurve parameters define
the period of the lightcurve and the amplitude. For asteroids, the overall (maximum)
amplitude is sometimes variable, due to seeing the asteroid along the axis of rotation at
one opposition while broadside to the axis at another. Assuming a typical bimodal curve,
with two maximums and two minimums, the amplitude between adjacent extremes may not be the
same. Think of a rotation football with one broadside painted black and the other white.
For any of these reasons and more, you’ll sometimes see a range of values listed for
the amplitude of an asteroid’s lightcurve.
Of course, generating a lightcurve and finding its parameters requires measuring the
brightness of the asteroid or variable star, i.e., performing photometry. However, Canopus
goes a few steps further by allowing you to do what’s called "differential
photometry" with up to five comparison stars. Using what are called
"sessions", you save the values for the stars and target along with other
important information. You can separate the observations by session (one night’s run
to the next), plot the raw data, compute a possible period from the data, and plot the
so-called "phased data", i.e., the observations converted to a value of 0% to
100% of the period.
Session
In Canopus, a session is a group of observations that that have the following in
common:
Target
Comparisons star set
Telescope/Camera
Filter Night (Date)
To qualify a little more, the Date requirement does not allow for mixing observations
made in the morning of one date and the evening of that same date. The idea is a continuos
set of observations made without interruption (presuming clouds don't get in the way). For
a fast-moving asteroid, you might have several sessions during the course of the night
since you may be required to use a different set of comparison stars as you keep up with
the asteroid's motion. |
