Thursday, March 27, 2014

Systematic Errors Yes and No

Does my data contain systematic errors?  You bet, it does.

Do those systematic errors make the data useless?  Not in the least.

The systematic errors are contributing to the overall error, but when the overall error is 2 - 4 percent, I'm not going to worry about them too much.

I spent all of yesterday looking at these errors and, while they're annoying, they appear to be in the raw data which means nothing I can do on the software end is going to change that.  I'm not going to try to explain to my readers what I'm seeing, because unless you've been looking at all of my data as much as I have, you probably won't see it.  However, this is the kind of plot I was looking at all day:

Figure 1: Photometry data from 23 Mar 2014 UTC

Now I guess that might look a bit scattered.  Staring at it a while will allow you to start seeing some patterns.  See them?  But consider the scale on the y-axis, plus the overall scale of the data (zero to 65535).  When I do this, I realize that the data in Figure 1 has an error of 2.18%.  This is well within my tolerances as far as having confidence that I'll be able to see variations in the lightcurves as these moons orbit Jupiter.

So now I can say, for the first time in this project, that I'm confident about the data that I have.  It seems consistent to a very reasonable tolerance.

I now, therefore, move on to more important matters.

Photometry versus Phase Angle

What I'm slowly moving towards is being able to plot phase angle versus photometric value.  When I do this, I should see variations similar to those shown in those USGS plots I did on a previous post.

To calculate the phase angle, I need to know three pieces of information:

  • The distance from the target to Jupiter
  • The direction of motion of the target (toward or away from Jupiter)
  • The side that the target is on (east or west of Jupiter)

I've created a little parameter file that will contain data used for this calculation (as well as the data needed to calculate the airmass of the observations -- needed to correct for atmospheric extinction).  In this case, the data is the distance (in AU) to Jupiter.  I need this in order to properly calculate the radius of the orbits for each moon in pixels.

The phase angle is then defined:

cos (phase angle) = measured distance / radius

I also need to know what "quadrant" the moon is in, and the direction of motion and the side tells me that:

Quad 1: east moving away
Quad 2: east moving toward
Quad 3: west moving away
Quad 4: west moving toward

So with all of this info, I can calculate the phase angle, which of course will go from zero to 360 degrees.  I've decided to define zero degrees as the point in the orbit when the moon is directly behind Jupiter and moving east.  This is an arbitrary definition and I'm not sure if it's the standard definition.  Once I find out what that is, it's likely I'll have to change mine to fit the accepted geometry.  No biggie.  The parameter file I mentioned above will also contain this information.

"Lost" Data

The other problem I'm trying to figure out is that a lot of data is "lost" because Jupiter is out of the field and therefore I can't compute a distance.  I've got an idea about how to deal with this and I'm hoping to try that out sometime very soon.  Callisto will especially suffer from this since it almost always is going to appear pretty far from Jupiter.  But as I said, I've got a possible solution and I'll see if that helps in any way to at least give me a way of looking at all of the data even though it may not be as exact as I would like it.

Data Reduction

I still have a backlog of new data to reduce.  I also need to go back and re-reduce all of my old data so I can start looking at this phase angle stuff.  Once I get the phase angle code running, I look forward to plotting all of this data to start looking for photometric variations.

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