When a Gaussian is not a Gaussian

I’ve been sitting in an ETLC computer lab for quite a few hours here trying to write a computer simulation of the phys 397 lab that Rob Joseph and I have been working on for the last month. What should have ended up being a “straight line” passing through a nice series of 60 data points is actually a straight line passing through a jungle of randonimity. What I believe turned out to be our problem was that when we approximated our “filter function” (the transmission spectrum of the IR filters being used) we just used e as the base of the exponent. Assuming that a bell curve is accurately described by a gaussian distribution is something that loads of people probably do every day. I mean we did it every day for a month in Statistical Mechanics when we use the Stirlings approximation of large factorials. There are situations, and unfortunately our lab turns out to be one of them where a Gaussian just doesn’t describe a bell curve very well at all.

Indeed it’s the difference between something being gaussian and something being a bit wider up top or more triangular that throws our data for a loop. When performing the numerical integration right near the peak of the blackbody curve the filter is much narrower than the peak of the spectrum. This means that the variation from one filter to another across this regions is not
extremly pronounced. When the filter funtion is poorly approximated it makes a big difference!

What really needs to be done is to replicate the bell curve of the filter using a numerically exact model. Since I don’t have any means to do this I’m going to have to switch my beautiful 60 data point set into 10 data sets (ten filters) with only 6 data points each.

I was also going to pursue a reverse derivation of the plank curve using a 3D curve fit of my data array, that would have made my lab something close to a manifestation of sheer beauty on paper. But with these results I think it’s not going to be
worth the effort, I know that the answer will be poor.

I’m not all that worried about poor data, If I can write a blog at 12:50 am on a Friday night about the intricacies of a Gaussian Distribution, I’m not going to have any trouble filling 5 pages in Latex on the topic.

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