I asked the moderator to move this thread to ATM Optics and DIY.
I finally got back to my original idea - using the ratio of the incandescent bulb spectra measured at two different temperatures - to recover both temperatures, and then use them to compute the response curve for the spectroscope. This relies strongly on the assumption that the incandescent bulb spectra are very close to blackbody radiation, which as I posted here earlier is not quite the case.
Anyway, before trying something more fancy (like using published incandescent bulb spectra, in place of blackbody approximation), here is what I got with the simplifying blackbody assumption.
I used a 12V/20W automobile incandescent bulb at 5 different voltages (from 12V*1.60A=19.2W down to 7.4V*1.25A=9.25W). I used the same diffuser as with LEDs (thick white paper), the bulb was ~5cm away from the slit. With ToupTek B&W astrocamera, I used 150ms exposures at the maximum (1000) gain. I averaged 500 frames per spectrum, and then also computed the dark frame from 1000 frames. I used the same spectral calibration as with LEDs.
First - the five raw spectra (for the five filament temperatures), the bluer the hotter:
Interestingly, I see the same zigzaggy effect on the red side of the spectrum as I saw before with my CFL bulb spectra - so these are obviously artifacts from my spectroscope, not real features.
Next - the same spectra, only normalized to the same brightness. Effects of the changing temperature on the shapes of the spectra are more obvious now (the hotter the filament is, the more to the blue the spectrum is shifted):
Now to the interesting part. Assuming all these spectra are blackbody radiation with unknown temperatures, I used my method of dividing one spectra by another, and then fitting an analytical division of blackbody radiations at two temperatures to the former, to derive both temperatures by means of non-linear fitting (using Octave). I instantly discovered that the results strongly depend on which two of the five temperatures I used in my analysis - not a good sign! I suspect this is primarily because the actual spectra are rather different from blackbody radiation.
Interestingly, using different pairs (out of 5) of spectra, many produced very poor fit in my analysis. For example, using temps #1 and #4 (#1 being the hottest, #5 being the coldest), I get this rather poor fit:
The recovered temps are also not good - 2001, 1816K (where I expected them to be around 2500-3000K). Worse still, once I expand the range of temps used in non-linear fitting, the recovered temps tend to approach zero (and still being not a good fit to the data).
Then I tried all possible combinations of the spectra, and got a much better fit when using temps #3 and #4 - the std went from 0.0095 dex in the above plot, down to 0.0006 dex. This fit looks quite believable:
The temperatures recovered are still not realistic - 4521K, 4138K (they are like factor of 2 larger than expected). But the point is the temperatures do not have to be exactly realistic - I am just trying to find two values of "blackbody temperatures" which produce blackbody spectra similar to the observed ones, in the given spectral window.
Finally, I used the above recovered "temperatures" to compute my spectroscope's response curves from both spectra - #3 (red line) and #4 (blue line):
Again, this is all based on the assumption that blackbody radiation is a very good fit to incandescent bulb spectra, which is not the case. Still, the above response curve looks quite interesting, and almost believable. It is quite symmetric. It has a bump around 640nm which I'm sure is an actual feature of my response curve, as I saw this feature on other pairs of spectra. The two response curves (red and blue) are very close to each other, which is a promising sign. Even the fine-scale structure (zigzag between 600 and 700nm) are practically identical for both red and blue lines - so I can actually get rid of this artifact in all my spectra by using this response curves! Meaning that I shouldn't try to fit a polynome to these curves, but rather use them as is, with all these fine features.
This response curve is very different from the one I derived previously, based on LED spectra. Probably meaning they are both rather wrong.
Nevertheless, I think I am moving in the right direction, so I will try to do a better job with the same data - instead of blackbody radiation assumption, I'll try to use published incandescent spectra for this analysis. (Of course once you start getting into such details, different bulbs have different spectra, at the same temperature, which makes the analysis more difficult.)
Edited by syam, 07 February 2021 - 04:42 PM.