You cannot assume that a LED light source emits the "same color light" in all directions. Some do and some don't. And then what does "same color light" mean? Some answers are given in IESNA document LM-79-08, with the calculation of Delta u' v'.
Here are the results of measuring the spectrum of a LED light source at various angles from the horizontal:
If you compare the spectrum at 90° with that at 0° you can see they are quite different, as are the u'v' values. But the u'v' values are not wildly different, so can an average be taken and then used to assign a single u'v' value to the whole light source? According to
LM-79-08, within very specific limits, yes, but you must also give a number for the variation in color.
Imagine you have a whole set of measurements around the light source, in all directions. In many directions there'll be little or no light at all, so they should be ignored. The samples which should be ignored are those which have less than 10% of the peak intensity.
A weighted average of the remaining samples is made. The weighting is based on the intensity (candelas) and solid angle "occupied" by the sample. In the formula below you can see that the weighting depends on I (intensity at theta) and omega (solid angle at theta)...
In the above formula xa will be u' or v', the same formula is used for both coordinates of course.
So now you have a weighted average u'v' value. Delta u'v' (the spatial chromatic nonuniformity value) is the largest difference (in the 2d space of the u'v' diagram) in the samples from the average. Low delta u'v'means the color of the light does not change much with direction.
If we assume for the sake of argument and simplicty that the u'v' values in the image above have already been weighted, then the average u'v' is 0.222 and 0.495. That average point is shown in green in the image below. The five samples are shown in red. The distance to the most distant sample from the average is shown by the white line, and is 0.0227, which is the Delta u' v' value.
So Du'v' is a measure of non uniformity of color of a LED in different directions. (Du'v' is not to be confused with Duv, as explained here.)
The new edition of my book Candelas Lumens and Lux now has a chapter on the spectrums of light sources: