Whereas most amateurs use a differential photometry procedure to
measure an unknown star's brightness, and professionals use a
"pipeline" linkage of programs to perform PSF-fitting, etc to
accomplish the same task, I prefer to use an "artificial star"
photometry procedure. I don't know if anyone else does it this way, so
in this web page I'll describe it in perhaps too much detail.
My philosophy for data analysis is to "be as close to the data as
possible." By that I mean that I only resort to automated procedures
after I've had sufficient experience with viewing the data in
spreadsheets to know what kinds of problems can be present so that the
automated procedure can safequard against being misled by bad data. For
example, clouds not only make photometric results noisier but they may
also prodcuce biases. Neither effect is desireable, so any analysis
procedure must explicitly reject cloud-contaminated data before
creating a transit light curve.
Another of my data analysis philosophies is to "always be on the
lookout for trouble." If something doesn't seem right, or something is
noticed that can't be explained, STOP and figure it out before
proceeding! This practice has saved me many wasted hours when I worked
with data before retirement, and I believe it is a good philosophy with
all types of data.
I like spreadsheets for the "learning phase" of any data analysis
procedure. I consider myself to be still learning to do photometry, so
as I flounder I like to see graphs of things in order to at least
confirm what I expect if not to notice things I don't expect.
Therefore, in what follows you will notice that the bulk of work is
done with Excel spreadsheets.
The following analysis is designed to identify bad images so that
they're not used in producing a transit light curve. An image can be
"bad" because a cloud passed through the line of sight during the
exposure, or the wind caused bad tracking (with an oblong shape for all
star images), or a downslope wind caused star field movement that was
too fast for the tip/tilt image stabilizer (the SBIG AO-7) to follow.
This last problem is common at my site. The downslope winds also can
produce a 'ballooning" of seeing that can last a few seconds, which I
assume is caused by the breakdown of Kelvin-Helmholtz waves at the top
of the downslope wind plume (at the interface with ambient air).
Rejecting "bad" images can be important in rescuing what would
otherwise be a useless observing session.
Preparing CVS-Files for Importing to Excel
Identifying a "bad" image is accomplished by comparing the measured
flux of a bright, unsaturated star (the same one for all images for
that night) with the flux of an artifical star that is placed in the
upper-left corner of each image before photometry readings are made. I
refer to the bright star as my "extinction star" for the night, for
reasons that will be obvious shortly. The next few paragraphs are
detailed enough that anyone using MaxIm DL (MDL) will be able to
reproduce my procedure, and anyone using a different image analysis
program should be able to follow the concepts and translate them to the
other program's requirements.
A group of ~30 images are loaded into MDL. They are subjected to a
"Calibrate All" command which applies a dark frame subtraction and flat
frame division. Next I create an artificial star in the upper-left
corner of each image using Ajai Sehgal's plug-in (that replaces a 64x64
pixel region with a star having a Gaussian shape). This takes a few
seconds, and here's what an image with the artifical star looks like.
Figure 1. An artifical star has been placed in the upper-left corner of this calibrated image, making it ready for photometry.
Next I use the MDL Photometry Tool to batch
process the group of 30 images in a way that allows the flux for a
chosen bright star to be related to the flux of the artifical star
(always the same, 1,334,130 counts). The same bright star has to be
used for all images taken during an observing session. [The rest of
this paragraph and the next one are tedious, so feel free to skip them;
they're just a "how to" if you're using MDL.] The specific
procedure using MDL, once a group of 30 images have the artifical star,
is to click Analyze/Photometry, verify that the boxes for "Act on all
images", "Use star matching" and "Snap to centroid" are all checked,
"New Object" (from the Mouse click tags pull-down menu), click on
the bright (unsaturated) star to be used for monitoring extinction for
the observing session, select "New reference star" from the pull-down
menu, and click on the artificial star. Then click on "View Plot"
(which displays a plot of the magnitude of the extinction star relative
to the artifical star, taken to be zero). Save this photometry solution
to a CSV-file ("comma-separated-variable). The CSV-file is
automatically placed in the directory "My Data Sources." As soon as
this CSV-file exists, open Excel and import the CSV-file data to a
cell. (Of course I use a worksheet template with many other cells ready
for later analyses; this concept will be obvious to any spreadsheet
user). Excel's data importing defaults to the CSV-file just created, so
with that file highlighted simply depress the Enter key. Complete the
import using Alt-N, Alt-C, Alt-F, Enter. The spreadsheet now has 3
columns: JD, the objects magnitde relative to the artificccial star,
and zero (for the artificial star's magnitude relative to itself).
If the above paragraph's procedure were repeated for all remaining
groups of images, and if each CSV-file data import is placed below the
preceding one, an analysis could be performed for deriving extinction
for the observing session and identifying bad images. However, since
MDL has calibrated and artificial star modified images in the
Photometry Tool work area, it is better to click "Back" on the
photometry graphical display and untag the the "Obj1" and "Ref1"
selections and proceed to perform pohotometry on the exoplanet star and
nearby reference and check stars. Select "New Object" and click on the
exoplanet star. Select "New Check Star" and click in a set sequence of
stars to be used in the spreadsheet as reference stars and check stars.
Finally, Select "New Reference Star" and click the artificial star.
View the photometry plot and save the solution to a CSV-file. Switch to
the Excel spreadsheet an import this data to the same row but different
column as its corresponding extinction star data.
Spreadsheet Extinction Quality Checks
Repeat the operation described in the previous two paragraphs for all
groups of 30 or so images. All remaining analyses will be done with the
spreadsheet. An example of what's been described is shown in the next
Figure 2. Photometry relative to an artificial star is shown
after importing CSV files to an Excel spreadsheet. Each row is for an
image (images numbers 20 through 39 are shown). Column D is the "extinction
star" magnitude realtive to the artificial star, column G is the same
for the exoplanet candidate and columns H through L are for stars that
will be used in the spreadsheet as reference or check stars. Column N
is air mass (calculated from image number, using a LS solution). Column
O is a prediction for column D data based on an extinction model (where
the user adjusts a zenith extinction to achieve a good fit, see below).
Column P is a percent difference of column D with respect to column O
(i.e., this column is a percent discrepancy between measured extinction
star flux and extinction model flux). Column Q is a repeat of column G
when the absolute value of column P is less than the criterion in cell
Q41 (2.5%). The last column is the deduced additional extinction caused
by clouds (or flus loss due to bad tracking, bad seeing, etc).
Yes, this is a lot of work, and it's done in a spreadsheet. Normally,
differential photometry is done by specifying reference stars and their
magnitudes when the Photometry Tool is invoked. I prefer to do as much
analysis as possible in a spreadsheet, where bad data can be easily
identified rejected. This will become clearer in the next few
In the previous figure notice that we have image quality information
for each image. By adjusting the value for zenith extinction in a cell
we can determine whether clouds were present and how much additional
extinction they contributed, image by image. This is shown in the next
Figure 3. Plot of magnitude difference of the "extinction
star" relative to the artificial star versus air mass. The straight
line is for a zenith extinction determiend to be 0.27 magnitude per air
This figure is for an observing session that started out near the
meridian when it was clear and gradually clouds moved in producing at
their worst ~4 magnitudes of additional extinction. The next figure
shows the "transparency" of clouds versus time, which is derived from
the difference between total extinction and model extinction.
Figure 4. Transparency of clouds during a 4.5-hour observing
session, based on comparing a bright star's flux with the artifical
star's flux and removing the effect of a normal clear sky extinction.
In this figure all departures from 1.00 are due either to clouds, bad
tracking or exceedingly bad seeing. These departures will not affect
the artificial star but will reduce the flux from a chosen "extinction
star." Visual inspection of the images show that for this observing
session there were no tracking errors or no seeing degradations (FWHM =
2.6 to 3.5 "arc). Clear conditions were present from ~3.4 UT to 4.9 UT,
and my observing log did indeed show that clouds were present after 4.9
I have established that by setting an acceptance threshold of ~2.5% all
accepted data appear to be useable for establishing an exoplanet light
Using Reference Stars
So far we haven't made use of reference stars (also called "comp" or
"comparison" stars - a leftover term from "visual" brightness
estimating days). Other columns are used to calculate magnitude shifts
that should place all stars on the correct magnitude scale using whichever stars for reference the user wants to try. Consider
the next figure.
Figure 5. Portion of the same Excel spreadsheet as in Fig. 2,
showing where reference stars (columns AJ - AM) are used to calculate a
magnitude offset (column AO) that is applied to the exoplanet
"instrumental" magnitudes (not shown) to arrive at corrected exoplanet
magnitudes (column AP). The same offset magnitudes are applied to the
reference and check star "instrumental" magnitudes to arrive at
corrected reference star and check star magnitudes (columns AT - AX).
Column AR is a repeat of another column where discrepancies are
calculated for the "extinction star" and a model (predicted value) for
the extinction star (the discrepancy provides a way to identify
cloud-contaminated images). Column AQ is a difference of the
exoplanet's magnitude for the image associated with its row and the
average of its 4 nearest neighbors; this also helps identify
outlier images. Column AS is a 5-point average (non-overlapping).
Columns AQ and AR are used to identify outlier data. Whereas the column
for additional cloud extinction (AR) is fairly straight-forward, an
outlier in column AQ may call for further consideration. A bad tracking
image would show up in AQ as an outlier without necessarily showing
anomalous extinction. When a row is judged to be unuseable it is
"rejected" by deleting the contents of the exoplanet magnitude (column
Another quality check is afforded by plotting corrected reference star
and check star magnitudes (columns AT - AX). If any of these stars are
variable, or noisy, then additional consideration is called for. On
more than one occasion I've had to reject a reference star from use
because it didn't behave well in one of these plots. Rejecting a
reference star is done simply by chaning which columns are averaged (AJ
- AM) to produce column AO. This is very easy, which contrasts with the
standard Ensemble Differential Photometry procedure that would require
a remeasurment of all
images with a different reference star assignment.