Abstract
The purpose of this investigation is to quantify the influence of the peak wavelength shifts in commercially available LEDs on the characteristics of the mixed-LED white-light sources. For this purpose, a tetrachromatic spectrum was optimized and then subjected to deviations in the peak wavelengths. A total of 882 combinations of peak wavelength values were evaluated, and the results are reported in terms of correlated colour temperature, colour-rendering properties, and radiant luminous efficacy. The results show that there can be significant changes in the characteristics of the source under these conditions. Such changes are highly likely to present problems when dealing with applications where an effective and accurate white-light source is important.
1. Introduction
White light can be produced by additively combining the outputs of multiple monochromatic light-emitting diodes (LEDs) [1–6]. Thus, by fine-tuning the spectral intensity of individual LEDs, which emit different narrow bands of radiation, a white-light source characterized by a good colour-rendering index, , and high luminous efficacy of radiation, , can be designed.
Creating a stable white light using multiple LEDs is a complex task since both colour rendering and luminous efficacy of the mixture depend on the emitted spectrum of the individual LEDs. Therefore, any change in the LED parameters (peak wavelengths, spectral widths, lumen outputs, etc.), for example, due to variations in junction temperature of the LEDs, causes a change in the spectrum of the LED devices and consequently a change in the spectrum of the white-light source [7, 8]. The amount of change will depend on the magnitude of the deviations for each LED in the mixture. Keeping the mixture stable is further complicated by the fact that different types of LEDs are affected differently even when they are working under the same conditions [9]. Therefore, designing a simple yet accurate control system to maintain the white point within acceptable tolerances is one of the key challenges [7, 8, 10, 11].
We demonstrated that white-light sources based on LEDs have the potential of becoming the optimum choice for high-colour-rendering tasks [1], and in [2] we introduced our approach to intelligent spectral design. However, implementing a stable mixed-LED white-light source based on a theoretical (optimized) spectrum is an exacting task since there is no guarantee that a given set of real LEDs will exactly match the parameters used during the spectrum design. Hence, we have investigated the sensitivity of an optimized 4-band LED mixture to possible changes in the peak wavelengths of any one or more of the four LEDs. The aim was to quantify the influence of peak wavelength shifts in commercially available LEDs in terms of changes in correlated colour temperature, colour rendering, and luminous efficacy.
2. Background
2.1. Correlated Colour Temperature
Correlated colour temperature (CCT) of a light source is defined as the temperature of a Planckian (blackbody) radiator with chromaticity nearest to the chromaticity coordinates of the source on the CIE 1960 (u,v) diagram [12–14]. As the temperature of a blackbody radiator increases from 2000 K to 20000 K, the perceived colour of the white light changes from “warm” (very reddish) to “cool” (very bluish). For example, incandescent lamps (circa 3000 K) are characterized as being yellowish white, while fluorescent lights (4000 K–7000 K) are bluish white. In the text the correlated colour temperature is symbolized as . Since a given change in colour temperature expressed in kelvins (K) at different temperatures results in unequal changes in chromaticity [13], the colour temperature (or correlated colour temperature) is often expressed in reciprocal megakelvins, MK−1, and given the symbol , where , which provides more uniform chromaticity differences. Reciprocal megakelvins were formally known as “microreciprocal degrees”, abbreviated to “mireds.” In the text the correlated colour temperature when expressed in Kelvin degrees is symbolized as and as when is expressed in MK−1.
2.2. Colour-Rendering Indices (CRI)
Colour rendering is the characteristic of light sources that describes the visual effect of a light source on the colour of an object. Typically, at the present time, the colour-rendering properties of light sources are evaluated using the colour-rendering index [15]. In general, the higher the value of a light source, the more “natural” the colours of objects look under this source. Sunlight and incandescent lamps have , which is the maximum value a light source can have. The acceptable value of CRI depends on the application of the light source. Values of above 80 are considered sufficient for most social and commercial indoor lighting applications, while above 90 or 95 is desirable in colour-matching tasks.
The fundamental idea behind the calculation is a comparison of the colours of eight standard test colour samples, which have low to moderate chromatic saturation (Table 1, samples 1–8), illuminated, in turn, by the test and reference light sources. The reference source has to be a source with the same CCT as the test source, either a Planckian radiator for test sources having CCT below 5000 K or a phase of daylight for test sources having CCT at or above 5000 K. After accounting for chromatic adaptation with a Von Kries-type chromatic adaptation transform [13], the special colour-rendering index for each test colour sample is calculated as where is the colour difference for each sample between the two light sources, as computed in CIE 1964 W*U*V* uniform colour space [13].
Averaging the eight values results in the general rendering index :
The CRI metric was originally designed to assess the quality of traditional fluorescent lamps and is found deficient when applied to assessing the colour-rendering quality of narrow-band light sources, such as the LED-based white-light sources [16–20]. Hence, optimizing mixed-LED white-light spectra using only eight colour samples of low to medium saturation can result in spectra with good computed but actually providing poor rendering of saturated colours. Therefore, in an attempt to improve the descriptive power of colour-rendering index, the number of test samples was extended to 14 by the addition of six additional test samples (Table 1, samples 9–14) representing saturated red, yellow, green, and blue, plus light human complexion and leaf green. Averaging the additional six values gives what we term index , and averaging all 14 values results in an “overall” index .
In order to provide additional data on the colour-rendering properties of each source, we have chosen also to quote the lowest () and the corresponding sample number () for the colour yielding .
2.3. Radiant Luminous Efficacy
Radiant luminous efficacy, lm/W, compares the amounts of luminous flux and radiant flux emitted by the source: where is the spectral distribution of the light source, is the CIE spectral sensitivity function for photopic vision, and is the maximum luminous efficacy of radiation ( lm/W). The peak in the curve occurs for monochromatic radiation at 555 nm.
3. Method
Evaluation of the influence of peak wavelengths on the characteristics of LED-based light sources was performed on a tetrachromatic spectrum of commercially available LEDs, chosen from the Luxeon range, with a peak wavelength combination of 470, 530, 590, and 625 nm. The mixture was optimized using a differential evolution algorithm [2]. The peak wavelengths were taken from the Luxeon datasheet [21] and are shown in Table 2 as . The bracketed figures indicate the nearest available values in our data analysis which was based on a 5 nm wavelength interval. The optimized spectrum (Figure 1) has a correlated colour temperature of approximately 2919 K, good colour-rendering properties (), and high luminous efficacy ( lm/W). This spectrum is the reference against which all later comparisons are made.
The Luxeon data specifies wavelength ranges for the four LEDs in the mixture. The peak wavelength of the red LED can be anywhere between 620.5 and 645 nm, the amber LED between 584.5 and 597 nm, the green LED between 520 and 550 nm, and 460 to 490 nm for the blue LED (Table 2). For the purpose of quantifying the influences of values on the characteristics of the mixture, these ranges were divided into 5 nm bins (Table 3) and then the , the colour-rendering indices (, , , and ), and the values were calculated for all 882 possible combinations of . The first set of values was calculated at the values and the last at the values (i.e., , , , ).
4. Results
4.1. Summary of Results for
Table 4 summarizes the influences of each individual LED on the correlated colour temperature of the optimized tetrachromatic spectrum over the range of , showing values in kelvins calculated for all bin values of one LED at a time, while the of other three LEDs were kept at their typical values, , . For example, the values show the influence of changes in the red LED and were calculated with , , and and in the range from to . Note that the typical peak wavelength of the red LED is . Thus, shows the dependence of on , while other LEDs are at , shows the dependence of on , while other LEDs are at , and so on. In addition, Table 4 lists the average values for each dependency of , , and the difference between minimum and maximum values , the percentage change , and the differences in MK−1 defined as and rounded to nearest integer.
As seen in Table 4, the changes in and result in the biggest variations (i.e., MK−1 and MK−1, resp.), while the blue LED causes the smallest variations ( MK−1). The correlated colour temperature of the tetrachromatic spectrum increases with and and decreases with increasing and . It is evident that significant correlated colour temperature errors occur due to peak wavelength shifts in the red and green spectra and that the error caused by the shifts in the blue LED is one order of magnitude smaller.
The values are plotted in Figure 2. The five step-changes in the plot are caused by a change of from bin to bin () together with “reset” of other LEDs’ peak wavelengths to their minimum values, that is, , . There are six distinctive patterns in the plot, one for each shift (bin). A pattern is influenced by seven green shifts (), and each green pattern is influenced by the seven blue peak wavelength shifts (). There are three shifts per a bin. As seen in Figure 2, the wavelength shifts of the red LED to a higher value increase the correlated colour temperature of the spectrum. Close inspection of the plot reveals that the increases in are larger at the higher values; the change from (A) to (B) resulted in K (104 MK−1), while the change from (C) to (D) resulted in K (116 MK−1). The influences of values on the of the mixture are further explored in Figures 3–5 and Table 5.
Keeping the red, green, and blue LED at their while changing from bin to bin () resulted in having a maximum value ( K) at which decreases to its minimum ( K) at (Table 4), a change of 235 K (27 MK−1). Figure 3 shows the dependency of the correlated colour temperature change caused by the shifts from to , , and Table 5 summarizes the influence of and on .
The values are calculated as the red peak wavelengths change from to with the peak wavelength of the green LED being at a value, . The process was repeated for all and shifts. In Figure 3 , , , and to are labelled for reference. It is observed that the magnitudes of the discontinuities at the to increase at higher values (e.g., compare A and B). Table 5 reveals that the values at are lower than at for .
The influence of and on is shown in Figures 4 and 5, respectively. The values shown in Figure 4 were calculated with peak wavelengths at , , , and , and those in Figure 5 with peak wavelengths at , , , and . The correlated colour temperature of the optimized tetrachromatic spectrum decreases as the value increases. This is most easily observed by inspecting the plot in Figure 4. Seven values are calculated () for each of the six red LED bins. For the sake of clarity, only one set of to are labeled on the plot (at ). It is observed that is highest at the wavelength () and lowest at wavelength ().
The influence of the on the correlated colour temperature is not so obvious. In Figure 5 the values are plotted for all possible combinations of . The general trend is that increases with . However, close inspection of the plot reveals that, for some combination of (at the higher values of (i.e., and ) and lower values of (i.e., and )), the values exhibit a small drop in values instead of the increase observed elsewhere. This can be seen inspecting the circled part in Figure 5.
The collated results show that a change in could cause the correlated colour temperature, , of the optimized mixture to be as high as 3976 K when , , , and and as low as 2311 K at minimum peak wavelengths for the red and blue LEDs and maximum peak wavelength values for the green and amber LEDs (, , , ) or a difference of 1665 K (181 MK−1). The average value of was 3039 K with a standard deviation of 359 K. Using the specified set of LEDs, changes −21% to +36% of its value in the optimized mixture.
4.2. Summary of Results for Colour-Rendering Indices
Table 6 provides a summary of the effects of peak wavelength shifts on the colour characteristics of the optimized tetrachromatic spectrum, expressed in terms of colour-rendering indices , , and . The errors for each colour-rendering index, shown in Table 6, are calculated as and . It is seen that variations in colour-rendering characteristics are significant. In particular, the index is the most affected with (, , , ) and (, , , ). These rather high variations () mean that the colour rendering of the saturated colour samples will be poor. The most affected samples were Samples 9 (strong red) and 12 (strong blue); had the lowest 397 times (in 45 % of combinations) and 301 times (in 34% of combinations). Four more samples had the lowest : sample 11 (strong green) 142 times (in 16% of combinations), sample 10 (strong yellow) 38 times (4%), sample 3 (strong yellow green) three times, and sample 4 (moderate yellowish green) once. Significant changes were observed in , with being always below its optimized value .
It is also interesting to note the effect of the peak wavelengths of four LEDs on the colour-rendering characteristics as shown in Figure 6. For the sake of clarity, the values ( are not plotted. As expected, there are five discontinuities in the plot, caused by a change of from bin to bin together with “reset” of other LEDs’ peak wavelengths to their minimum values (,). The largest change is when changes from () to , . The size of decreases to at the () to () change, before increasing to 35.6 at the () to () change.
4.3. Summary of Results for Radiant Luminous Efficacy
The effect of changes on is evident in Figure 7. The radiant efficacy has a maximum lm/W (, , , ) at A and a minimum lm/W (, , , ) at (which is +12% and −21% from the value in the optimized mixture ). The in 292 combinations of (in 33% of combinations) and was below 590 times (in 67% of combinations). Figure 7 also shows the step changes in that result from changing from bin to bin (e.g., at in the graph).
The influences of the green, blue, and amber LEDs are further explored in Figure 8, where is plotted for and of the other three LEDs changing from bin to bin. There are seven plots, one per each of seven bins and 21 values (for different and combinations) per each bin. For the sake of clarity, the points were marked only on the plot. It is evident that the wavelength shifts of the green LED to a higher value result in a increase; however, the increases are smaller at the higher values of . It is also evident that, as changes from its lowest value (at ) to its highest value (at ), one observes reductions in . Again for the sake of clarity, only one set of to values are labeled on the plot. Increasing leads to improvements in . The values at wavelength are lower than the values at . It was interesting to observe that the difference between the (A) and (B) values was constant (67 lm/W) across all plots.
5. Conclusion
We have investigated the sensitivity of an optimized tetrachromatic LED spectrum to changes in the peak wavelengths, , of individual commercially available LEDs. The sensitivity was quantified in terms of changes in correlated colour temperature, colour-rendering indices, and luminous efficacy calculated for 882 combinations of . The results emphasize the fact that the influence of peak wavelength shifts in commercial LEDs on the characteristics of the LED-based light sources cannot be ignored.
The correlated colour temperature increases with increases in the wavelengths of the red and green components but decreases with increases in the wavelengths of green and amber components. The changes are significant. The correlated colour temperatures deviate −21% and +36% from the original value. The maximum of 3976 K was calculated when the red LEDs had the highest peak wavelength value and other LEDs were at their lowest values. The minimum was at minimum peak wavelengths for the red and blue LEDs and maximum peak wavelength values for the green and amber LEDs. Changes in correlated colour temperature caused by the deviation of the blue LED was one order of magnitude smaller than the changes caused by the other three LEDs. The largest deviations are caused by the red LED (26%), followed by the green LED (18%) for the wavelength ranges investigated.
Colour-rendering properties were also significantly affected by the variations in peak wavelengths, particularly the colour-rendering index which is determined by saturated test colour samples. The results for show a difference of 53 between its maximum and minimum values, . These results make it clear that the colour rendering of strong colours can become very poor. The saturated test colour samples (red, blue, green, and yellow) had the lowest rendering index in 99.5% of all combinations. The index was less sensitive to the peak wavelength shifts, decreasing from to (). These changes in colour rendering and correlated colour temperature are significant and can be problematic in numerous applications.
This study has also demonstrated that the radiant luminous efficacy, , of the optimized tetrachromatic LED spectrum changes significantly due to deviations in peak wavelength values. Its maximum value was 438 lm/W and minimum was 308 lm/W. For 67% of combinations was below its optimized value lm/W. The values decrease with the increase in red and amber peak wavelengths and increase with the blue and green wavelengths. This influence is opposite to the influence caused by the same set of LED variations on the correlated colour temperature.
A possible criticism of this study is that we have used the colour-rendering index, CRI, for the rendering of the white-light spectrum. While we are aware of the need for a new metric, CRI has been widely used for a number of years and is still the only officially recognized CIE method for assessing colour-rendering properties of light sources. We intend to adopt the new metric when formally adopted. In the meantime, we believe that it is appropriate to supplement with our additional ratings, , , and .
This study is only focused on the tetrachromatic spectrum of the LEDs chosen from the Luxeon range, and therefore these results cannot necessarily be extrapolated to other commercially available LEDs. Nevertheless, these results make it clear that the characteristics of mixed-LED white-light sources change significantly with changes in the peak wavelengths of individual LEDs.
Acknowledgment
The authors wish to acknowledge the support of this work by the RDTT Fund of the Manukau Institute of Technology and by the EET School of the Manukau Institute of Technology.