Yes, that's a great idea. Send away! It'd be nice to get a solar measurement (solar + atmosphere, actually..) so I can play around a little. But the convolution is much simpler than it sounds, so you can experiment too.
so here's what
- some spectra measured with the line of sight from the sun to the sensor
as direct as possible using a white diffuser like a piece of paper (one photon bounce) or a pin-hole
(zero photon bounces), if you don't run into saturation.
- some spectra taken with lots of bounces. noon day pointed at the sky well off the sun (45 degrees, 60 degrees?).
My intuition is that a measurement of direct sunlight (perhaps with one "bounce" off a diffuser to lower the intensity) will be of more use for determining the bandpass than would be diffuse sunlight, since diffuse light that has been "through the atmospheric wringer" with multiple molecular scattering I think reduces the Fraunhoffer features in the solar spectrum which you'd use to estimate the bandpass. That said, it'd be cool to do both measurements, direct and diffuse, and compare. The ratio of the direct to diffuse might show something interesting since the properties of the RGB filter and other instrument peculiarities should cancel out in the ratio.
Yeah, these RGB color filters... I hear the next generation of CCD (and maybe CMOS) arrays will have one pixel in the mosaic that is left "white" so the signal would be RGBW. With enough light you might be able to just throw out the RGB channels and use the W. I also looked into the hobbyist astronomy sensors that don't have color filters so they can get better sensitivity, but they seemed a little pricey for the project. Unfortunately, my friend who knows a good bit about digital imaging told me that the RGB Bayer filters can be pretty variable in their transmission as a function of wavelength/color. That suggests to me that doing anything quantitative with intensity would best be done among a group if folks could standardize on a single make and model of web cam.
Incidentally, the convolution method is the same one as you might use to get a better sense of the RGB filter functions for the different pixels. And once you know those, you can reconstruct the total intensity of any experimental measurement from the separate RGB channels by de-convolving the measured spectrum -- essential applying an inverse of the convolution function.
The RGB transmission functions are complex, even after removing the IR filter, so you have to determine those empirically. I'm not sure how you could do that best, but there should be a simple approach. The slit-function is simpler. To the first order you can just assume it's a triangle function.
w = 1-abs(x-x0)/fwhw ; abs(x-x0) <= fwhm
w = 0 ; abs(x-x0) > fwhm
w: bandpass transmission
x : wavelength
x0 : center wavelength of your measurement
fwhm : width of the bandpass at 1/2 the peak height (aka full-width, half-maximum, or FWHM)
I've plotted this in the png attached. If this makes sense, the next step, the convolution, is simple. You just center the bandpass function at all of the solar reference spectrum wavelengths, the x0 in your spectrum, and use the bandpass function to compute weights at the neighboring wavelengths within x0 +/- FWHM. Then use these values as weights in a simple weighted average of the spectrum at each x0, which goes like this,
avg = sum(w*y)/sum(w)
where y is the intensity and w is as above.
If you do this all the way up and down the wavelength grid, you'll have converted (convolved) the high-resolution spectrum to what an instrument with an idealized triangular bandpass would "see".
It's simpler than it sounds. The fact that it's called "convolution" doesn't help, of course.
I'll find a reference solar spectrum and code an example in python that I'll send out this weekend.
If the solar spectrum idea doesn't work, maybe we could determine the bandpass by looking at how the spectrometer modulates ("sees") an easily available, sharp fluorescence feature. But the solar spectrum would provide better info if we can pull it.
Dave