Find most suitable vectors

Dear all,

i have a problem and don't know how to solve it. But i am sure you clever people can help me. Here is my problem:

I have 21 LEDs which emit light at different wavelengths. For each LED i have emission spectra for various setpoints (input power) ranging from 10% to 100% in 10%-steps. Therefore, i have 21 matrices LED01 ...LED21 with 10 columns each which contain the spectrum for each setpoint (for example in LED05 column 2 we find the spectrum of LED 05 measured at a setpoint of 20%)

Now i have a spectrum which i would like to imitate using these 21 LEDs. Lets say this spectrum is stored in a vector called aimed_spec. Thus, i would like to find which setpoint (i.e. column) i need to choose for each LED in order to get the least square error between the simulated spectrum sim_spec (which is the sum of the LED spectra) and the aimed_spec.

Furthermore, i have two diodes to measure intensities and their spectral response is stored in SR column 1 and 2. The boundary condition is that the measured intensity is equal to a given value ref. Thus, . alternatively we could of course also write SR.' * sim_spec / step = ref. Note that SR will change regularily and therefore the optimization needs to be performed regularily.

One possibility is to calulate each combination but this is probably very expensive and gets even more expensive when i reduce the setpoint-step from 10% to 0.1%.

Here is a graph where you see 21 different LED spectra (colored from blue to red) at certain setpoints. Furthermore the sum of all LEDs is shown as "simulated spectrum" as thick red curve and the Aimed spectrum (black line with grey area underneath). Note that this is an example where no optimization was done.

i attached a .mat file where the above mentioned matrices and vectors are stored. for example aimed_spec are the y-values whereas aimed_spec_wav are the x-values.

Is there any optimization tool which can be used for this problem?

I hope this is enough information for you.

Looking forward to your solution!

[Image Analyst]

Attach your spectral component data, and your desired spectrum that is the weighted sum of the component spectra in a .mat file with the paperclip icon.

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[Eike Köhnen]

Dear Image Analyst,

i edited my question and added a .mat file as you recommended.

thank you for your suggestion!