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# diy spectroscopy w/o diffraction

diy spectroscopy w/o diffraction using rgb leds and ccd
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Exploring a cheapo diy spectrometry possibility.

The standard spectro meter uses eg. reflected light bounced off a diff. grating. One modern twist is to put this light onto a ccd, then diferent parts of ccd get different colors, and the resultant intensity vs. color is the spectrum.  No moving parts.

However another poss. I am trying to grok is doing this without a grating,  instead using eg rgb leds. It would require de convoluting a signal that is due to known combo of led spectra * unknown reflection spectrum. I cant figure if the information is 'inthere' or hopelessly smeared out.  Take for example 2 leds and vary their percent contribution to illumination,  call this percent p,  freq. is w, and the individual led spectra are led1(w) and led2(w) . The combined illumination is then

L(w,p)= p led1(w) + (1-p) led2(w)

Assuming the sample is 'nice' and doesnt play any frequency shifting tricks (i believe this is quite rare and limited eg to some crystals that can do frequency doubling, anyway it seems this must be an assumption of optical spectroscopy ) then it has an unknown  reflection spectrum R(w) to be found.

Finally assume that the detector has flat spectrum - this can be done by normalizing the actual response, i dont think it helps anything to include the detector sensitivity curve in this analysis. Use two or more detectors e.g. Rgb values from a ccd if that helps matters, I dont think it does. So the problem is to use the detected signal D(p) from the light detector/ccd, which is a weighted average of the intensities at each freq., to find R.

======== ============= ========== ==============

D(p)= integ over w of  (L(w,p)*R(w))

= integ over w of ( p led1(w) R(w) + (1-p) led2(w) R(w))

Knowing D(p) (and led1, led2) can R be found?

======== ============= =========== =============

Alternatively / maybe equivalently, is there only one solution for R ( in which case numeric solution is possible if nothing else). Use 3 leds if necessary, etc. Differentiating wrt p does not seem to help matters. Any maths whizzes able to shed some spectrum on this?

Take a gander at [see link] which does something close, I am not convinced he extracts a spectrum however.

 — spalpeen, Dec 23 2011

led 'spectrometer' http://www.creative...ology.net/MAKE.html
led 'spectrometer' [spalpeen, Dec 23 2011]

Full spectrum tunable LED http://cerncourier..../article/cern/46530
Build it with one of these. [Wrongfellow, Sep 19 2012]

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Annotation:

 The linked article seems to use 5 different LED wavelengths to get a _very_ crude spectrograph - one with 5 frequency values.

If you're suggesting that by illuminating a sample with mixtures of light from different LEDs you can get more information than by illuminating it with each LED in turn, then I fear you are mistaken.
 — spidermother, Dec 23 2011

 >>If you're suggesting that by illuminating a sample with mixtures of light from different LEDs you can get more information than by illuminating it with each LED in turn, then I fear you are mistaken.

Thats my suspicion as well - that the varying linear comb. of two spectra is not 'variable enough'. But I do not directly see it from the math. If a single led with variable center frequency were available then it almost surely could be use for this purpose. If the center freq. can be varied slightly with power/temp, then a spanning set of LEDs would do.
 — spalpeen, Dec 23 2011

 AFAIK spectral transmittance is strictly linear, except in extreme cases such as heating of the sample by the light such that its optical properties change. If so, your idea is mathematically useless.

 Your best bet might be to get a large number of LEDs of different frequencies. Even LEDs of a single type from a single manufacture have slightly varying frequencies, and are sometimes divided into different frequency bins for sale. You then have to calibrate for each LED, but that might end up being an almost trivial software problem.

Altering the LED's frequency function using temperature or power can certainly be done, but it might not be very repeatable (read - reliable) if it tends to damage the LED, which I suspect it might.
 — spidermother, Dec 23 2011

I was thinking about a prism. But you wouldn't need to spread the frequencies across the CCD, just physically move the CCD through the nicely expanded spectrum in a sweep. Then you can simply integrate the signal from the entire CCD to gain sensitivity. However if you're cooling the CCD with single or series Peltier units, it will be bulky. It might be easier to sweep the light path across the CCD by pivoting the prism. Still trivial though.
 — bs0u0155, Dec 23 2011

I assumed sensitivity and noise were always problems....
 — bs0u0155, Dec 23 2011

[+] for a prism. KISS (keep It Simple S*****)
 — csea, Dec 24 2011

//Keep It Simple Sirrah// Yebbut, then it becomes a Perfectly Ordinary Spectrophotometer. And you're just replacing one kind of complexity with another - you'll need a stable smooth- and wide-spectrum light source, a slit, a prism or grating, and a CCD array or physical scanning mechanism, all precisely aligned.
 — spidermother, Dec 24 2011

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