Here is an idea how to do response curve calibration in a spectrometer.
An incandescent bulb produces light close to black body radiation. The problem is that its peak is way into far IR, so one cannot use it for calibration directly because the exact temperature cannot be measured.
My idea is to measure spectrum from the same bulb at two different voltages, resulting in somewhat different filament temperatures. Lets assume that both are simple black body radiations with two unknown temperatures, T1 and T2.
Each of the two measured spectra "I" is a dot product of the actual brightness curve "B" (black body radiation) and the spectroscope's response curve "R":
I1 = R*B1(T1)
I2 = R*B2(T2)
By dividing the two spectra (pixel by pixel), we get rid of the unknown response curve R, and get an analytic function of two unknowns - T1 and T2:
ratio = I2/I1 = B2(T2) / B1(T1)
Using the black body radiation equation, we get:
ratio(lambda) = (exp(A/(T1*lambda))-1) / (exp(A/(T2*lambda))-1)
(A is a constant: A=1.43877e7 when lambda is in nm.) This is a well defined, non-divergent function of T1 and T2. Using non-linear fitting (in Octave etc) one can derive both temperatures from the observed ratio(lambda)!
I did a test: generated two black body curves at T1=3000K and T2=2500K, computed their ratio, then provided initial guesses for both temperatures (2750K for both), and then recovered the original values for T1 and T2 (3000K, 2500K) by means of non-linear fitting of the ratio curve in Octave. Here is the plot for the log(ratio) I recovered:
Now that we know the two temperatures, to get the response curve R, we simply divide one of the measured spectra by the black body radiation for the recovered temperature value:
R = I1 / B1(T1)
In real world, the issues will be measurement noise, deviation of the incandescent light from black body radiation, and non-linearity of the measurements. But hopefully this will produce useful data.
One can use a 12V incandescent bulb (like they use in car turning signals etc) powered via power supply with voltage regulation.
I'll give it a try.
Edited by syam, 27 January 2021 - 09:51 AM.