Color Quality Scale: The definition of CQS
Generally, in order to meet the new demand of solid-state lighting (SSL) market and communicate with consumers about the color quality of lighting products, NIST (National Institute of Standards and Technology) has developed the light color quality meter, which evaluates light sources with 15 new colors.
The calculation method of color quality scale (CQS) is derived from the calculating method of color rendering index (CRI). This method evaluates the color quality of light sources in the 15 colors in the following table (Pic 1.1) to analyze the color quality of current solid-state lighting sources more accurately.
Pic 1.1 CQS Q1-Q15
Problem with the CRI
CRI was firstly designed for evaluation of fluorescent lamps, and it has no substantive changes in recent 30 years. With the rapid development of solid-state lighting (SSL), color rendering index (CRI) is no longer enough to evaluate new artificial light such as LED. Here is an example (Pic 2.1) below that shows high CRI value cannot prove good saturation in colors.
Pic 2.1 Limitation of CRI 
From the picture above, it is obvious to see that the spectrum is simulated by three LED dies at peak 457nm, 540nm and 605nm. Comparing the colors of reference light and LED light, the value of Ra (R1-R8) is very closed, however from R9 to R12, the colors are much distinctive. Hence, high CRI value sometimes is not able to present the color quality of LED, especially in saturated colors.
Pic 2.2 Limitation of CRI 
The picture shows another example of problem with the CRI. In this picture, the neodymium incandescent lamp has only CRI 77, however the normal incandescent is CRI 100. The neodymium incandescent lamp presents as nearly same color as the incandescent lamp, but the CRI value is much lower.
To replace the CRI
In that case, NIST developed CQS (Color Quality Scale) to evaluate light sources with 15 new saturated colors in order to:
- Fix the problem of the CRI
- Replace outdated formulae in CRI
- Works for all light source
- Initially developed with colorimetric simulations
Pic 3.1 New set of 15 saturated color samples of CQS
Calculation formula of CQS
The CRI makes it possible for a lamp to score quite well, even when it renders one or two samples very poorly. This situation is more likely with SPDs having narrowband peaks, such as LEDs.
RMS (Root Mean Square)
Color difference of 15 samples:
Pic 4.1 Formula of Ra (RMS) 
Pic 4.2 Comparison of Ra (mean) and Ra (RMS)
Case A presents the case that color qualities are at the same level.
Case B presents the case that most of colors are consistent, but few colors are distinct.
The example above (Pic 4.2) shows algorithm of RMS precisely present color qualities than algorithm of mean under some extreme circumstances. It can be clear to see that if colors of sample are closed to each other, the mean and RMS would get the same result. However, if there are only few colors are extremely high than rest of them, the calculation by RMS can clearly present the color quality than calculation by mean.
From what have been shown above, it can be summarized as follows.
- 15 new saturated colors are chosen by CQS which are more suitable to evaluate the application of solid state lighting.
- CQS modified some special cases that come with high CRI but poor color quality.
- The calculation of Ra by RMS is more accurate to present the color quality than by mean.
 Color Quality Scale (CQS), Measuring the color quality of light sources, Wendy Davis