1. Introduction

We are pleased that our previous work has aroused interest as well as debate in the community [1, 2]. Here is a point-by-point rebuttal.

2. Rebuttal

2.1 Response to “Some CRI peak distortions are not present in the spectral loss simulation due to large wavelength step.”

By sentences in our article: “In order to gain more subtle plots for these sensitivities, we performed the same simulations as we did previously but limited the well-width to 1 nm, and process the results using the Eq. (1)”, we clearly stated that the CRI sensitivity to be employed in the guideline as a weighting function has the sole spectral resolution of 1 nm, and those with sample-rates other than 1 nm⁻¹ would be excluded.

Actually, the reason we introduced the spectral loss simulation was to facilitate the understanding of the concept of intrinsic spectrally resolved sensitivities (ISRS). It is well accepted that any loss in spectra would diminish the CRI to some degrees. Compared with this “CRI reduction”, the concept of ISRS is much more abstract. Hence, we started with presenting the well-accepted spectral loss simulation. By shrinking the well-width, we gradually transformed the “reduction” to “sensitivity” and finally came to the ISRS, which, in our opinion, would largely facilitate the understanding. The ISRS involved in the simulation in Eq.

By the way, we noticed that the sample rate of ISRS, s-SPD and r-SPD should be always identical to avoid any unnecessary oversampling or undersampling.

2.2 Response to “Poor correlations between MDs and CRIs at high CRI region”

We could not agree with his statement that we keep the CCT of r-SPD unchanged in the simulation. The fact is that, in our model, we do change the r-SPD, making its CCT same with that of s-SPD every time we change the intensity of the Gaussian peak, which has been clearly identified in the definition of r-SPD. By saying:”it is worth conducting comparisons between simulated SPDs (s-SPDs) and reference SPDs (r-SPDs) under the same CCT, in order to discover Ra and R9 sensitivity in different spectral regions.”, we meant to announce that the s-SPD and r-SPD should always have the same CCT, rather than “keeping the CCT of r-SPD unchanged”. Actually, in the standard algorithm of CRI, the s-SPD is supposed to be compared with the r-SPD with the same CCT of itself, to identify the color deviation between them. Hence we adjust the CCT of r-SPD according to the new s-SPD on each step before making the comparison, which means the shape of the r-SPD is changing with the s-SPD. As a theoretical model stemming from the standard algorithm of CRI, the spectra employed for comparison are all the same with its descent. If one changes the CCT of r-SPD according to the related s-SPD, it would not exhibit poor correlation between MD and CRI, as is shown in Fig. (3) [2].

Such confusion may result from the sentence “Since the ISRS shifts with the CCT, as discussed in previous sections, we only employed the moderate ones of Ra and R9 on 5455 K as the weighting function, for simplicity.” [1]. We were meant to indicate that only the ISRS of 5455 K, not the r-SPD, is employed in the following simulation. Because, if we also changed the CCT of ISRS, as we already did for r-SPD, the amount of calculation would be enhanced tremendously with only slightly increase in accuracy, which is clearly not worth considering.

2.3 Response to “No optimal peak wavelengths in the guideline for the CRI optimization”

The topic of this article is to investigate the correlation between SPD and CRI and, as a by-product, to present a guideline on how to approach the high CRI. In our two demos, we do give two SPDs with decent CRI, although not the highest. The achievement of our work is prominent, for the fact that it enables obtaining high-CRI multi-peak SPD by adjusting the intensity of each as-obtained spectral component. The question presented in [2], Guo et al… is obviously beyond the scope of this article. We have acknowledged that the model is a “basic one”, and “Therefore, in the future, more works are still needed to study the characteristic of the ISRS of each specific CRI in detail, and to uncover more information about the CRI.” We have been thinking about how to further refine the model, getting rid of defects, for example, as has pointed out in [2], Guo et al…, lack of accuracy among the high CRI region. We are pleased to find that the work presented in Table 4 and 5 [2], Guo et al… are such a refinement and optimization of our work, on which authors obtained a rough high-CRI SPD by using our model, and slightly changed the position or intensity of each peak to further improve the CRI. His work has just validated our theoretical model.

3. Conclusion

In summary, by the above explanations, we have demonstrated that our theory and model are solid and reliable. We established this model on our own, from the experiences accumulated from our daily works on spectra design. We agree with the viewpoint in [2], Guo et al… that, while CRI has been being used widely in lighting industry, it may be insufficient in identifying the color rendering ability of modern light sources, especially for those which comprise LEDs. Whereas the topic of [1], Lin et al… is “Study on the correlations between color rendering indices and the spectral power distributions”, therefore, any discussion on CRI’s validity is beyond its scope. Indeed we have been constructing a new standard that measures the illuminant’s color rendering ability in an advanced manner. At last, we apologized for the potential ambiguity in our language that may have led to some misunderstandings or confusions.