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I am trying to compare the relative brightness of $H \beta $ and $H\alpha$ lines using a CCD spectrometer. In order to correct for the different grating efficiency at the two different wavelengths. I took the spectrum of a 100W bulb to use as a blackbody source. I also know the pixel location that correlates to the $H\alpha$ and $H \beta $ line.

I am wondering how to translate the blackbody spectrum to a relative intensity calibration. I thought to try to approximate the peak and use Wien's law to get the temperate of the filament and use that temperature in the Planck's law equation. However, I was unsure if there was a standard method of obtaining a relative intensity calibration for a spectrometer.

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If no answers come to this question after a couple days, you may want to consider posting it on astronomy. – Kyle Kanos Jul 9 '14 at 1:39
I don't know, but I have some warnings. 1.) The spectrum of a 100 W bulb differs somewhat from a blackbody curve due to the effect of the envelope and the variation of emissivity of the filament. Tungsten-halogen are different still. 2.) The peak of the blackbody spectrum for a typical light bulb is in the IR, and likely outside the range of the CCD 3.) the peak you observe in the recorded spectrum will be due to a combination of the spectral curve of the source and that of the detector. That is, it will not be the peak given by Wien's Law. – garyp Jul 9 '14 at 1:50
... BTW, calibrated incandescent sources can be purchased. Watch out, they may have quartz envelopes and emit enough UV to require that you wear special clothing to avoid any skin exposure. – garyp Jul 9 '14 at 1:52
Sorry about the third comment. I don't know why I neglected this: if you can get your hands on an optical pyrometer you can get an idea of the filament temperature. Better to use a clear envelope. – garyp Jul 9 '14 at 1:58
up vote 3 down vote accepted

What you're trying to do is called radiometric calibration.

The problem with doing it with an ordinary incandescent light bulb is that the bulb itself would have to be radiometrically calibrated to get a precise spectral calibration of the detector. That's because the bulb's spectral emissivity deviates from an ideal blackbody source with an emissivity vs. temperature curve following the Planck law.

Typically either calibrated blackbody sources, or calibration lamps emitting at known wavelengths, are used for radiometric calibration. Since you are working in the visible, and interested in specific emission lines, the calibration lamp approach is more common - blackbody calibration is more typical in infrared applications with greater bandwidth.

This is a link to a paper from NIST that goes into more detail about the procedures for radiometric calibration using a krypton lamp as a reference wavelength source.

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