Julius Muschaweck

# JMO_Spectrum: A Matlab spectrum library

Updated: Mar 29, 2021

We deal routinely with spectra in illumination optics. We need to analyze LED spectra, compute color coordinates and color rendering values from spectra, integrate them, add spectra, multiply spectra with scalar weights and with other spectra (like transmission spectra), interpolate a given measured spectrum with non-equidistant wavelength values to a regular 1 nm array, and so on.
In practice, this is tedious: spectra come in various formats, and the problem of dealing with two spectra als tabulated values which have two different sets of wavelengths is annoying. And while the various algorithms to compute things with spectra should not be rocket science, their implementation is sometimes tricky. Over the years, I settled on a bunch of Matlab routines I wrote to do all these chores for me, nice and easy. And now, I'm making the code freely available.
So, this open source Matlab library is designed to make dealing with spectra easy and transparent. It is compatible with GNU Octave, and with Matlab for Mac and Linux.
Available for free download on __https://github.com/JuliusMuschaweck/JMO_Spectrum__.

The full __documentation__ contains all the details, but here is the flavor:

In this library, a spectrum is a struct which

contains a field named lam, which is a 1D real array with length >= 2, and strictly ascending values,

contains a field named val, which is a 1D real array with same length as lam.

That's it. Simple to create, by one of the two following ways:

```
% // a flat spectrum, known as CIE standard illuminant E
clear s1;
s1.lam = [360 830];
s1.val = [1 1];
% // the same spectrum, created with a convenience helper function
s2 = MakeSpectrum( [360 830], [1 1]); % // the same spectrum
```

I decided against making my spectra a Matlab class, because I wanted to make it simple to add fields in a flexible and extensible way:

```
s.name = "CIE standard illuminant E";
s.hopp = "topp"; % // anything you want
s.CCT = CCT(s); % // a common idiom: compute something, add it as field
```

This requires a tiny bit of discipline on the user's side, but this is outweighed by the simplicity, I believe.

There are routines to **add and multiply **spectra, where the "interweaving" of non-equal wavelength arrays is taken care of by the library.

You can **create standard spectra** like Planck blackboy, various CIE standard illuminants, (bell shaped) Gauss spectra, a typical white LED spectrum. You can read and write LightTools® spectrum files, which are supplied by LED vendors.

And you can do a lot of **colorimetric calculations, **like CIE 1931 XYZ color coordinates, correlated color temperature (CCT), dominant wavelength, color rendering index, and more.

I did my very best to get some tricky implementation details right. The Planck locus, for example, is computed as tabular values using a fine grid of absolute temperatures and the original formula by Planck. Then, I provide a spline interpolation function for the color coordinates, which is then used to find the CCT of a spectrum with a root finding algorithm with high precision:

```
lam = 360:830;
T = 5761.68;
ps = PlanckSpectrum(lam, T);
CCT(ps)-T
```

returns 0.00017 K.

Or, take linear interpolation, which is at the core of the "interweaving": For Matlab on Windows, I created a C++ DLL which is much faster than Matlab's interp1 function, to which the code falls back on other platforms.

There is more coming: I'm planning to include TLCI calculations, CIEDE2000 color difference formula, other color spaces like CIELAB, and more.

Enjoy using the code, and please send me feedback when you do.