„Two specimens having identical tristimulus values (object colors X, Y, Z) for a given reference illuminant and reference observer are metameric if their spectral radiance (reflexion) distributions differ within the visible spectrum“ [1]. Based on this definition the metameric index was determined. It can be changed the illuminant spectrum or the observer. Therefore there exist two indeces. Mainly the changed spectrum is used in practice, because this index can be used to characterize light sources. The metamerism index is the color difference ΔE*_{ab}of the two specimen illuminated by the test spectrum.
Please be aware, that this index has nothing to do with the color shift of one reflecting surface illuminated by two different spectra!
The calculation is done in the following way:
 Calculation of tristimulus values X, Y and Z for both specimen illuminated by the reference illuminant according to CIE recommendations [1]
 The respective values X, Y and Z for both specimen are equal by definition.
 If there is a small differnece between the values an adjustment method has to be applied.
 Calculation of tristimulus values X, Y and Z for both specimen illuminated by the test illuminant
 Calculation of color difference ΔE*_{ab}
 This color difference is the metameric index M_{ilm}

Such Metameric calculations with changed illuminant are used to characterize the quality of daylight simulators for visual appraisal and measurement of color [2]. One spectrum is the target illuminant, e.g. D65, and the other is the real achieved and measured one. There are defined several virtual specimen to get not only one metameric index. They give more information about the agreement of two spectra than the pure calculation of the color difference between them.
There were defined 5 specimen pairs for characterization of the pure visible reflexion (calculation of M_{v}) and additionally 3 pairs with inclusion of fluoerscence properties (M_{u}). All comparison specimens were defined for 4 different reference spectra (D50, D55, D65, D75). The following diagram shows two pairs for the calculation of the visible metameric index.


Examples of two metameric specimen pairs

The software JETI LiVal allows to calculate both M_{v} and M_{u} as well. The following screen shot shows the Metamerism index window. 

Screen shot of the metameric calculation window in JETI LiVal

First it is necessary to select the reference illuminant between D50, D55, D65 and D75. The CIE 1976 u´_{10} v´_{10} chromaticity difference is shown, marked in red when the limit of 0.015 is exceeded.
This is a first criterion of the match between the standard illuminant and the real one.The color differences dE for all 8 pairs are given. The averages for both versions are the metameric indeces M_{v} and M_{u}.
Additionally the resulting quality grade of the illumination is shown. M_{u} can only be calculated if a specbos 1211UV is used.

[1] Colorimetry. CIE publication 15:2004 
[2] ISO 23603/ CIE S 012/E:2005 