Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

Optical CCD image analysis, day 2 (with extra)

The goal today is to learn how to measure the brightness of stars in astronomical images. We'll use the clean images you created in the previous class, and focus on the process of measuring light. Our method is called aperture photometry, which is one of the simplest ways to determine the brightness of an object. Once again, we'll use AstroImageJ to do the work.

If you need to go back to the RAW images, you can find them at

What is aperture photometry?

An "aperture" usually means "a hole", or "an opening." Back in ye olde days, astronomers using single channel photometers would point their telescopes so that the light of just one star -- the target -- would fall into an honest-to-goodness hole in a piece of metal. Only that light would reach a detector and be recorded.

But in the world of CCDs, we create "synthetic apertures" on our images. To see what I mean, read this page:

Using AstroImageJ to perform aperture photometry

So, how do we do this in AstroImageJ? Let's use your cleaned image of the target, number 400, as our guinea pig.

Click on the "Aperture Photometry Tool" in the small AstroImageJ toolbar.

Then, move your cursor to one of the bright stars in the image, and left-click. A new text window should appear, with a set of measurements of the pixels near this star. Some of the data columns contain real measurements, but some contain bogus values, or no real data. Be careful!

The most important of these numbers is the "Source-Sky" value.

Part 1:

  1. What is the "Source-Sky" value for the star you chose?
  2. How large was the aperture for the Source?
  3. How large was the aperture for the Sky?

Now, before we try to use this value, we need to make sure that several of the parameters are set properly. You can open a big dialog window which controls these parameters by choosing in the image window's menu the Edit -> Aperture Settings option. The three most important settings are at the top:

In order to figure out the right values for these parameters, we need to look carefully and up-close at stars in our image(s). We want the object aperture to contain most of the object's light, but not too much background sky; and the background annulus should contain very little or no light from the star in question --- or from other stars, if possible.

As a very rough guideline, the object aperture might be 2 or 3 times the FWHM of the image, while the background annulus might run from, say, 5 to 7 or 10 times FWHM.

  1. What is the FWHM in your image?
  2. Set values for the object aperture and background annulus apertures
  3. Measure the star again with these parameters. What is the new "Source-Sky" value?
  4. What is the percentage change in brightness?

Faint stars and bright stars

When you measure bright stars, you will usually find that the choice of aperture parameters doesn't change very much. But when you examine faint stars, which rise only slightly above the background, even small changes in aperture can lead to significant changes in the measured brightness.

Let's investigate. In the same image, pick a much fainter star -- maybe the one near (224, 337). Use aperture photometry to measure its brightness:

Part 2:

  1. Using the default, "big" apertures: 25, 40, 60, what is the "Source-Sky" value?
  2. Using your smaller, customized apertures, what is the "Source-Sky" value?
  3. What is the percentage difference between these two values?

It turns out that using aperture photometry to measure both bright and very faint stars in the same image(s) can be a tricky business. As explained nicely in Howell, PASP 101, 616 (1989), one might want to use different apertures for different stars: big apertures for bright stars, and small apertures for faint ones. Doing so can provide slightly better signal-to-noise, but at the risk of systematic errors due to the different apertures. A technique called curve of growth analysis must be used to correct measurements through different apertures before the results can be used in further calculations. That is all outside the scope of this simple introduction.

Measuring a single star

You should have a set of 10 or 20 (or more) images of the V404 Cyg field. Here's a chart showing the region, with some stars labelled.

Choose the star labelled "D". Let's measure the brightness of this star in all the images in your set.

First, create an image stack with all your images.

Next, set the aperture parameters to reasonable values.

Now, the new part: use the menu above the image to choose Analyze -> Multi-Aperture . We are only going to use a single aperture, for a single star, this time ... but we'll use the full power of the tool later. Click on the Place Aperture button, and then left-click on star "D" in your image. Then press the Enter key to signal that you have finished marking stars to measure.

Lots of windows may pop up and appear. For now, pick the one which titled "Multi-plot Reference Star Settings". Choose Save Table, which will save the measurements of this star in ALL the images in a single, very wide, ASCII text file. Choose a name for the file, and save it.

What does this file contain? My version has 70 columns of data, separated by spaces. The first row of the table is shown below.

 	Label	slice	Saturated	J.D.-2400000	JD_UTC	JD_SOBS	HJD_UTC	BJD_TDB	AIRMASS	ALT_OBJ	CCD-TEMP	EXPTIME	RAOBJ2K	DECOBJ2K	Source_Radius	Sky_Rad(min)	Sky_Rad(max)	X(IJ)	Y(IJ)	X(FITS)	Y(FITS)	Source-Sky	Source_Error	Source_SNR	Peak	Mean	Sky/Pixel	Width	X-Width	Y-Width	Angle	Roundness	X(IJ)_T1	Y(IJ)_T1	X(FITS)_T1	Y(FITS)_T1	Source-Sky_T1	Peak_T1	Mean_T1	Source_Error_T1	Source_SNR_T1	Sky/Pixel_T1	X-Width_T1	Y-Width_T1	Width_T1	Angle_T1	Roundness_T1	X(IJ)_T2	Y(IJ)_T2	X(FITS)_T2	Y(FITS)_T2	Source-Sky_T2	Source_Error_T2	Source_SNR_T2	Sky/Pixel_T2	Peak_T2	Mean_T2	X-Width_T2	Y-Width_T2	Width_T2	Angle_T2	Roundness_T2	rel_flux_T1	rel_flux_err_T1	rel_flux_SNR_T1	rel_flux_T2	rel_flux_err_T2	rel_flux_SNR_T2	tot_C_cnts	tot_C_err

There are a LOT of numbers here, but the ones of interest right now are few. Which of these should we choose?

Part 3:

  1. which column is a good measure of time?
  2. which column is a good measure of stellar brightness?

Okay, now that you know which ones to choose, can you figure out a way to make a plot showing the brightness as a function of time? You might choose to read the entire file into a spreadsheet program, and plot the contents of the proper columns inside the spreadsheet; or, you might figure out a way to plot them with some other program (like, say, gnuplot. Another option would be to pick out the columns of interest, write ONLY those values to a new data file, and then work on that smaller, more manageable data file. I found the following command useful.

   awk '{ print $5, $38 }' Measurements.xls > stard.dat 

  1. create a graph showing brightness as a function of time for star D

Measuring three stars

Let's do that again, but this time, we'll choose three stars to measure in all the images: the stars labelled "D", "F", and "V404".

Run the Analyze -> Multi-aperture command again, but this time, we'll mark one star as the TARGET and two stars as COMPARISONS.

The program should start measuring all three of these stars in all the images in the stack. When it finishes, use the Save Table button to save the results as a text file. My version of this text file has 88 columns!

Part 4:

  1. create a graph showing brightness as a function of time for stars D, F, and V404 Cyg
  2. comment on this graph

Very simple calibration

Suppose we want to convert our measurements from "counts" to something we can share with other astronomers. If we knew the magnitudes of the two comparison stars "D" and "F", we might be able to convert out measurements to magnitudes, at least to a rough degree.

Can you figure out the magnitudes of these two stars? I suggest using the Aladin tool to create a chart of the region around V404 Cyg. Then, inside Aladin's "Server Selector" window, use the "Surveys" option to select the "USNO B1.0" catalog. When you click "Submit", a set of overlaid dots should appear on top of some of the stars in the image.

Clicking on one of these dots will cause information to appear below the chart, showing properties of this star in the USNO B1.0 catalog. One of the pieces of information you can find is the I-band magnitude.

Part 5:

  1. What is the I-band magnitude of star "D"?
  2. What is the I-band magnitude of star "F"?
  3. Pick one image in your set; note the name and Julian Date
  4. What are the fluxes for stars "D", "F", and V404 Cyg in this image?
  5. Use the ratio of fluxes of stars "D" and "F" to compute the difference in their instrumental magnitude. Does this difference agree with the difference in their I-band magnitudes from the catalog?
  6. What is the (very rough) I-band magnitude of V404 Cyg in this image?

Homework: measure 5 stars in all images

Now that you have the basics down, it's time to apply your skills to a reasonably large dataset. For this assignment, you'll need to analyze all 70 of the V404 Cyg images in the given dataset (numbers 380 through 459), and measure a total of 5 stars in each image.

The stars of interest are shown in the chart below. They are

Part 6:

  1. Clean all 70 of the images
  2. Choose parameters for aperture photometry: write down the aperture radius, and radii of the sky annulus
  3. Perform aperture photometry on all 5 stars in all 70 images; save the results in a data file
  4. Make a light curve showing flux as a function of Julian Date for all 5 stars on a single graph. For the time axis, use (JD - 2,457,000), just to make the values easier to read
  5. Write down the mean counts for each stars, and the standard deviation from the mean. Aside from V404 Cyg, is there any relationship between the mean and stdev for the 4 stars? SHOULD there be a relationship?
  6. Convert each of the mean fluxes into an instrumental magnitude, using
                    instrumental mag  =  25 - 2.5*log10(flux)
  7. Look in the USNO B1.0 catalog to find the I-band magnitude for the 4 comparison stars (if it exists). Write down the values for each star, if you can find it.
  8. Compare the I-band magnitudes to the instrumental magnitudes. In a perfect world, there would be a single offset which you could apply to convert the instrumental mags to I-band mags, for all 4 stars. Do all 4 stars have the same offset? If not, propose reasons for the differences.
  9. Pick one of the stars as a "best" reference, and use it to convert all the instrumental magnitudes to I-band magnitudes. Explain your choice for "best" reference.

Bonus! Try out differential photometry

I am a big fan of "differential photometry", in which one uses the DIFFERENCES between measured magnitudes for stars in a single field as the basis for scientific analysis, rather than the measured magnitudes themselves. Why? Rather than explain, I'll let you try to figure it out for yourself.

Part 7:

  1. Plot a light curve for each of the 4 comparison stars individually, one star on each graph, so that you can see the fine details in each star's light curve. Plot instrumental magnitude on the y-axis, and (JD - 2,457,000) on the x-axis.
  2. Look at the four graphs. Do you see any gradual variation in each one? In other words, do the curves show any trends, instead of random noise around the mean value?
  3. Do you see any common features in these trends?
  4. Now, pick star "D" as a fiducial star; in other words, treat it as a special reference. For each star -- including "D" -- compute for all images
               diff mag of star X  =  (instr mag of X) - (instr mag of D)
    In other words, convert your table of instrumental magnitudes for each star into a table of (mag diff from star D).
  5. Make four graphs, one for each star, showing the differential magnitudes as a function of time.
  6. Do these graphs show gradual trends? If so, are those trends as big as the ones you measured earlier?

For more information

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.