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Registered Member #1906
Joined: Sat Jan 03 2009, 05:06PM
Location:
Posts: 39
In short, I'm writing an essay for school and I could use a little help. I have obtained a few (20 or so) radiation spectra in the form of csv files. They show the radiation from a light bulb at different voltages and what I'd like to do is to *identify what temperature the filament is *and compare my curves to that of an ideal black body radiator.
Any ideas?
I'm thinking it should be possible to fit a curve based on planck's law over the plotted data to compare but I'm not sure how. I've tried MS Excel but I can't manage to get it to plot a planck's law curve. I've also tried searching the web for an alternative software but there are lots and what I've tried so far hasn't ben helpful due to the (relative) complexity of planck's law.
Registered Member #1792
Joined: Fri Oct 31 2008, 08:12PM
Location: University of California
Posts: 527
If the peak of spectrum is contained in the included data then it is a simple closed form solution. Then from this temperature plot the spectrum and compare it to your spectrum data, if it looks close then call it a day.
But if the measurement band is too narrow to include the peak then you'll need to do a fitting routine, the Matlab optimization toolbox is great for this. But with any computation software (Python(x,y) is my preferred free tool) you could make your own fitting algorithm. The slowest but simplest way is a search algorithm: specify a temperature range, for each temperature compare the predicted spectrum to measured spectrum and determine a figure of merit such as average RMS error between the test spectrum and measured spectrum. Then from this array pick the temperature with the smallest error.
Registered Member #1526
Joined: Mon Jun 09 2008, 12:56AM
Location: UK
Posts: 216
Then I`d just do a fit in Matlab as you have access. You can have it fit the data to the blackbody equation, you`ll have to fiddle with starting values a bit. It`ll even give you the standard error.
Registered Member #1792
Joined: Fri Oct 31 2008, 08:12PM
Location: University of California
Posts: 527
When doing a fit you should throw out bad looking data points since they can only make convergence more difficult. There is a spike at around 600 which looks like it shows up on all of the traces which makes me think the measuring device had a problem there. I'd just delete that data point from all the traces.
Registered Member #1906
Joined: Sat Jan 03 2009, 05:06PM
Location:
Posts: 39
Turns out MatLab wasn't straight forward enough for me. Not today at least... I ended up estimating the wavelengths and skipping the comparison with an ideal black body.
Registered Member #1526
Joined: Mon Jun 09 2008, 12:56AM
Location: UK
Posts: 216
If it`s a matter of interest I`d be happy to use my copy of Matlab to fit a curve to your data and post the results, I enjoy this sort of thing anyway.
Registered Member #1906
Joined: Sat Jan 03 2009, 05:06PM
Location:
Posts: 39
That's very kind of you Fraggle and it might turn out to be helpful. Here is one spectrum. If it doesn't take you long to do this kind of fitting, could you fit a planck's law curve of the right temperature to that? Once again, I really appreciate your offer
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Radiation spectras
