Calibration: Beginner

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Submitted by bkloppenborg on 20 February 2010

Below you will find instructions on how you can complete your analysis of photometric data. Below we will guide you through the process of converting your instrumental magnitudes into calibrated magnitudes that can be submitted to the AAVSO for long-term storage.  
What you will need:

  • A list of instrumental magnitudes for your variable star

  • A list of instrumental magnitudes for at least two comparison stars (six preferred)

  • An internet connection (to lookup catalogue values)

  • Excel or OpenOffice Calc

Computing Calibrated Magnitudes

We must first stress that this tutorial is suitable for calibrator-to-variable distances less than 3 degrees at zenith angles less than 34 degrees. Outside of this range, Air Mass must be taken into account to correctly calibrate your data. If your data does not meet these qualifications, please see the intermediate tutorial. The sample data provided by the DSLR Documentation and Reduction team is fine to use here.

Step 1:

  1. Download the Reduction for Beginners file that the DSLR Documentation and Reduction team has created for you.

  2. Fill in your name to the right of Observer, the Julian Date (a.k.a. JD) calculated using the USNO Julian Date Converter, and the time of your observation in UTC/GMT.

As you may have noticed, the spreadsheet contains cells filled in with yellow, green and orange. The green cells correspond to values looked-up in a catalogue, yellow cells are instrumental magnitudes that you provide, and orange cells are calibrated V magnitudes that *could* be reported to AAVSO.

Step 2:
As was mentioned in earlier portions of the tutorial, DSLR cameras record values in each of three colors: red, green, and blue. In the previous steps, you extracted the green portion of the Bayer array because it most closely corresponds to the photometric V-filter. The problem is that even though the filters are close, they are not exactly the same. Here we compute the necessary correction factors to convert your camera's Green filter into a V-filter.

Read More: Transformation Equations

Astronomers have already created a transformation equation that accounts for this change:
V = v - e * (B-V) - z
This equation describes how the catalog V-magnitude (capital V) changes in response to several parameters. From left to right, they are:

  • V = (upper-case V) the catalogue value for the V magnitude of the star

  • v = (lower-case v) the instrumental magnitude of the star

  • e = the color transformation coefficient (more on this later)

  • (B - V) = the mean catalogue "color" of the star

  • z = your camera's zero-point offset from the standard V filter.

For our calibration stars, the upper-case variables (V and B) are known and with a measurement the instrumental magnitude, v, is known too. This leaves only unknowns in the equation (e and z). With at least two calibrators and a little algebra we can determine both the transformation coefficient and zero-point offset.

Rearranging the above equation, we have:
V - v = -e * (B-V) - z
Which, with a few more parentheses:
(V - v) = (-e) * (B-V) + (-z)
Looks a lot like the equation of a line:
y = m * x + b
In our case, y = (V - v), m = (-e), and b = (-z). If we plot a series of calibrators in which the V, B, and v values are known and fit a line to them, we can pick off the slope and intercept and solve for 'e' and 'z'! There are, of course, other methods to solving this problem, but doing it this way allows you to solve for 'e' and 'z' simultaneously without doing any algebra! (It also allows you to solve for uncertainties in the slope and intercept which will be used in the advanced tutorial that includes a little error analysis).

Before we can solve this problem though, we must know V, B, and v for the calibration stars. As you recall, v is simply the instrumental magnitude for the comparison star your measured so we only need to find V and B. Therefore, we'll fill in these values in the spreadsheet using the calibration tables provided. If you always observe the same stars with your camera, you will only need to do this step once and re-use the data during later calibration sessions

As noted earlier, we have already chosen calibration stars for you. Look up the V Cat and (B-V) Cat values for the stars in the Target Star Table, Check Star Table, and Comparison Star Table and enter those values into the appropriate green cell. When you are done, your sheet should look something like what is shown below:

Step 3:
Now that you have filled in the V and B-V values, we simply need to insert the instrumental magnitudes for the comparison stars that you found earlier in the tutorials. Type in the values you found earlier in the yellow cells in the Comparison Star Table. As you fill in these values, you will notice the Transformation Coefficient graph to the right changing.

A “best fit” line will appear on the graph along with the data points. The slope of this line is the Transformation Coefficient (TC). The y-intercept is the Zero Point.


Read More: Slope and Intercept
After all of the values are inserted the graph will stop changing. We have used two functions (SLOPE and INTERCEPT) to extract the slope and intercept from the graph to make analysis a little easier. You should notice that the line displayed in the graph has the same slope value as the cell to the right of 'm' in the transformation coefficient (TC) table. Furthermore, the zero-point intercept in the graph is to the left of the 'b' cell in the TC table

Step 4:

Now we may insert check star and variable star insturmental magnitudes in order to compute a check star V-magnitude and variable star V-magnitude.

Type the instrument magnitudes for your check stars in the yellow cells of the “Check I Mag” column and for your variable star in the yellow “I Mag” column cells.

Read More: 

Here we apply the equation listed earlier:

V = v - e * (B-V) - z

With with (B-V) as defined earlier and 'e' and 'z' as determined from the graph / TC output table. To do so, we fill out the Target and Check Star Calibrated Magnitudes table. Fill in the image numbers used in the "IMAGES" column, and the instrumental magnitudes (I Mag) for the check and comparison stars in the yellow columns. You may need to drag down the formulas in the "Check V Mag" and "V Mag" columns if you have several images

Step 5:
Now we compute the average and standard deviation of the check star's "Check V Mag" column and "V Mag" column. We will first do this on the "Check V Mag" Column:

  1. In the cell immediately below the Target and check Star Calibrated Magnitudes table in column B type the word "Average". In the cell below that, type "StdDev" (for standard deviation). The table should now look like this:


  1. Now in the cell immediately below the check V-mag column, type "=Average(" (without the quotation marks) and then click and drag down through the orange cells in the Check V Mag column and then type the closing parenthesis ")". In my sheet the input looks what is picture below. (Notice that the cells C39 to C42 are the orange cells and you could have typed in C39:C42 inside the parenthesis.) If your input looks similar to mine, press return and the average should have been calculated for you.


  1. Now we are going to compute the standard deviation for the data. In the cell below the average we just computed, type "=Stdev(" then highlight the cells and close the parenthesis. Again your equation should look like what I have included below. If it is okay, press return. The standard deviation of your data (a measure of the spread around the average value) has now been calculated for you.

Repeat the last three points for the "V Mag" column (or, alternatively, copy cells from below the "Check V Mag" column and paste them below the "V Mag column".


Congratulations! You have now produced calibrated values for the variable star!

Step 6:
Now we check that our results make sense. Remember how we calculated the average and standard deviation for a check star? We can use this column to determine if our calculations were correct or in error. Compare the average V mag for the check star (which you just computed) to the catalog value for the check star (in cell B12). They should be in reasonable agreement, certainly within +/- 0.01 magnitude. If not please post in the Photometry section of the forum indicating that you had a problem with the tutorial and we'll try to help you.

Congratulations you are done with this part of the tutorial. Please proceed on to the Intermediate-Level reduction tutorial to learn how to do air mass corrections. If you wish to skip it, you can go directly to the Imaging and how to submit your data tutorials.



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