Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry

For the study, the relative spectral power distributions of 1516 LED products of different types were measured; including AC- and DC-operated bulbs, spots, tubes, street lamps, LED strips, downlight luminaires, prints and textures by a large number of manufacturers. Measurements of the products were carried out in various laboratories, including manufacturers of LED products, test laboratories, and National Metrology Institutes (NMIs). The products included in the study were manufactured in the timespan of 2009–2016. Throughout the measurements, the products were operated in stable operating conditions using regulated voltage sources. The spectral data were measured using integrating spheres, goniometers, and optical rails, equipped with scanning or array spectroradiometers, in the wavelength range of at least 360–830 nm. The vast majority of the data were measured in $4\pi$ geometry. Table 1 lists the percentages of the spectra collected per type of the system used for the measurement.

Table 1. The systems used for acquisition of the spectral data.

Method	Spectroradiometer	Share ($\%$)
Sphere	Array	36.5
Sphere	Scanning	6.1
Goniometer	Scanning	30.2
Goniometer	Array	20.9
Bench	Array	6.3

The CCTs of the products were calculated using the minimum search method [18, 20], which determines the black body temperature that results in the smallest difference between the chromaticities of the light source and the point in the Planckian locus. Figure 1 shows the CCT distribution of the spectra collected for this study. Nine lamps with CCTs of over 20 000 K were marked off as outliers since they cannot be considered suitable for regular lighting purposes. The CCTs of the remaining lamps ranged from 1705 K to 17437 K with the median being 3149 K. The rightmost bin in figure 1 includes 22 spectra from 8100 K onwards and the leftmost bin contains three spectra below 1900 K. These spectra were retained because sources with such CCTs may turn up as LED products to be measured. However, removing these spectra from the analysis would still yield the same representative spectra.

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Due to the fact that the vast majority of the products were based on luminophore-converted blue LEDs, or blue-pumped white LEDs, this LED technology was chosen as the basis for the analysis of the RSPDs. Furthermore, luminophore-converted blue LEDs were considered most suitable for actual calibration sources due to the good availability, relatively simple design, and well behaving ageing characteristics compared with other white LED technologies.

Figure 2 shows the differences between the spectra of a luminophore-converted blue LED and Standard Illuminant A. Despite having similar CCTs, 2850 K and 2856 K respectively, the two spectral power distributions are disparate. The two local maxima in the LED spectrum are the peak caused by the blue LED element of the lamp, at 455 nm, and the broad luminophore peak, at 604 nm. Also plotted in the figure is the curve, CIE $V(\lambda)$, representing the spectral sensitivity of the human eye [21].

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In photometric measurements, the deviating spectral shapes of the lamp under test, or device under test (DUT), and the calibration source need to be taken into account using spectral mismatch correction factor F. This correction factor can be calculated using the equation [22]

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \label{eq:spectralMismatch} F = \frac{\int \it {\varPhi_{\rm DUT}}(\lambda) V(\lambda) \,\mathrm{d}\lambda} {\int \it{\varPhi_{\rm cal}}(\lambda) V(\lambda) \,\mathrm{d}\lambda} \cdot \frac{\int \it{\varPhi_{\rm cal}}(\lambda) s_{\rm rel}(\lambda) \,\mathrm{d}\lambda} {\int \it{\varPhi_{\rm DUT}}(\lambda) s_{\rm rel}(\lambda) \,\mathrm{d}\lambda}, \nonumber \end{align} \tag{ 1 }$$

where $\varPhi_{\rm DUT}(\lambda)$ and $\varPhi_{\rm cal}(\lambda)$ are the spectral power distributions of the DUT and the calibration source, respectively, and $s_{\rm rel}(\lambda)$ is the relative spectral responsivity of the photometer.

Equation (1) shows that if $\varPhi_{\rm cal}(\lambda) = \varPhi_{\rm DUT}(\lambda)$, then F  =  1, and thus the spectral mismatch correction is not required. Having an ideal photometer with $s_{\rm rel}(\lambda) = V(\lambda)$ would render the correction redundant as well. If no spectral data for the DUT are available, spectral mismatch errors must be included as a part of the measurement uncertainty budget.

For the comparison of different calibration spectra in the spectral mismatch analysis, the relative spectral responsivity data for 107 photometers were used. These data represent real photometers that are used in photometric measurements at NMIs, industrial test laboratories, and in the field. The spectral responsivities of the photometers were measured during a time period of several years. The dataset includes commercial instruments from eight different manufacturers ranging from handheld illuminance meters to laboratory grade photometer heads. The filter technologies of the detectors included mosaic, stacked glass, and thin-film interference filters. The general $V(\lambda)$ mismatch indices $f_1^{\prime}$ [23] of these photometers ranged from 0.005 to 0.088, with the average being 0.032. Figure 3 shows the mean of spectral responsivities of the photometers along with the range of responsivity values measured at each wavelength. The responsivities have been normalized to unity at 555 nm. The figure also shows the deviation of the mean responsivity from the ideal $V(\lambda)$ curve.

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For the LED spectrum in figure 2 as $\varPhi_{\rm DUT}(\lambda)$ and the 107 photometers, the spectral mismatch errors (F  −  1) would range from $-1.05\%$ to 1.46$\%$ when using Standard Illuminant A as $\varPhi_{\rm cal}(\lambda)$. This indicates the magnitude of spectral mismatch errors that can arise despite the similar CCT values of the DUT and the calibration spectrum.

In order to determine the new candidate LED illuminants, the collected LED spectra were first used to calculate the representative spectral power distributions for different CCT categories. Out of the collected spectral data, 1119 blue-pumped white LED spectra were normalised and binned according to their CCTs into eight bins based on American National Standards Institute (ANSI) standard C78.377.2011 [24]. The bins corresponded to the CCT categories of 2700 K, 3000 K, 3500 K, 4000 K, 4500 K, 5000 K, 5700 K, and 6500 K.

First, for each CCT bin, the centroid spectral power distribution (CSPD) was determined by finding the closest spectrum to all the other spectra in the bin. The closeness score C, quantifying the cross-similarity between the spectra of a bin, was calculated using equation

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \label{eq:centroid} C^{(b)}_i = \sum_{j\in b} 10^{-{d}(\varPhi_i(\lambda), \varPhi_j(\lambda))}, \nonumber \end{align} \tag{ 2 }$$

where $b = 1\ldots8$ represents the bin, i and j are the indices of the spectra in the bin, and d is the distance function defined as

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \label{eq:distanceFuction} {d}(\varPhi_i(\lambda), \varPhi_j(\lambda)) = \sum_{\lambda = 380}^{780}\sqrt{\left[\varPhi_i(\lambda) - \varPhi_j(\lambda)\right]^2}. \nonumber \end{align} \tag{ 3 }$$

Distance function d gives the Euclidean distance between the two spectra. The eight CSPDs were the spectra with the highest closeness score C in their bin. The step of l in the summation is 1 nm.

For the purpose of not favouring any specific commercial LED product in selection of the representative spectra, several different methods of averaging multiple spectra were tested [25]. Averaging a CSPD with the nine spectra closest to it in the bin was found to be the most suitable for obtaining a spectrum with feasible spectral features. Before the averaging, the spectral data were corrected for the bandwidths of the spectroradiometers employed in the measurements by applying Wiener deconvolution.

Finally, the eight spectra obtained by averaging each CSPD with the nine closest spectra, were smoothed using Savitzky–Golay filter [26] to reduce any ripples due to measurement noise. To avoid distorting the spectra in the wavelength range of 430–470 nm, corresponding to the blue peaks of the spectral distributions, smoothing of the averaged spectra was reduced in this region. This was done by combining the filtered and unfiltered spectral data by using gradual transition between each two datasets in the vicinity of the blue peaks. To further reduce errors in the lower wavelength regions caused by noise, and stray light in single grating spectroradiometers, the spectra were linearly extrapolated below 410 nm based on the filtered, logarithmically scaled data of the wavelength region from 410 nm to 430 nm.

The eight RSPDs obtained as the result are shown in figure 4. The RSPDs were submitted to CIE Division 1 technical committee TC 1-85, in charge of updating CIE Technical Report No. 15: colorimetry [19]. Five of these RSPDs are considered to be included in the upcoming CIE technical report. These RSPDs correspond to the CCT bins of 2700 K, 3000 K, 4000 K, 5000 K, and 6500 K. In figure 4, they are presented using solid lines. Because the CCTs of the obtained spectral power distributions naturally deviate from the nominal CCTs of the bins, for this article, the RSPDs are named using BL prefix, describing their type (blue-pumped LED), followed by the first two digits of the CCT bin, e.g. BL27 for 2700 K.

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Table 2 shows the colorimetric characteristics of the five RSPDs potentially to be used as LED illuminants in colorimetry. In the table, x and y are the chromaticity coordinates of CIE 1931 colour space [19], and R_a and R_f are the CIE defined colour rendering and colour fidelity indices [27, 28], respectively.

The five RSPDs considered for use in colorimetry were taken as the starting point for selecting a potential LED reference spectrum for calibration of photometers. To determine the RSPD which would on average produce the smallest spectral mismatch errors, the average spectral mismatch correction factors were calculated for the five RSPDs using equation (1), with each candidate RSPD in turn as $\varPhi_{\rm cal}(\lambda)$, the 1507 measured LED spectra as $\varPhi_{\rm DUT}(\lambda)$, and the 107 spectral photometer responsivities as $s_{\rm rel}(\lambda)$. In addition to calculating the spectral mismatch errors once for every DUT, RSPD, and photometer combination, the DUT spectra were grouped according to their CCTs, and the groups were weighted to see the impact of different CCT distributions of lighting products available on the market. Furthermore, the possibility of having two or three calibration spectra of different CCTs was studied, including the effects of operator mistakes when selecting the optimal calibration factor for the instrument based on an estimate of the CCT of light being measured. The suitability of each RSPD for calibrating photometers measuring non-LED light was also investigated.

In the case of a single calibration spectrum, the spectral mismatch correction factors were calculated for every $\varPhi_{\rm DUT}(\lambda)$ and $s_{\rm rel}(\lambda)$ combination, while each RSPD, in turn, was acting $\varPhi_{\rm cal}(\lambda)$. The mean absolute spectral mismatch errors (MAE) were obtained for each candidate RSPD using

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \mathrm{MAE}_i = \frac{\sum\nolimits_{j = 1}^N |F_j-1|}{N} \cdot 100\%, \nonumber \end{align} \tag{ 4 }$$

where i is the index of the RSPD, j is the index of $s_{\rm rel}(\lambda)$ and $\varPhi_{\rm DUT}(\lambda)$ combination, and N is the total number of these combinations ($107 \times 1507$). For comparison, the analysis was repeated using Standard Illuminant A as the calibration spectrum $\varPhi_{\rm cal}(\lambda)$.

Due to the fact that the CCT distribution of the spectral data collected for the study did not necessarily represent the average market share of LED products, the data in each CCT bin were weighted by the market share data [29] published by the US Department of Energy. Figure 5 shows the CCT occurrence frequency for all LED products in the United States (red bars) and for industrial lighting only (green bars). The figure also shows the original distribution of the collected spectral data grouped into the respective five bins (blue bars). The uniform distribution, shown using purple bars, was used in the study to give further indication of the sensitivity of the final results to the weighting. The weighted spectral mismatch errors were calculated by randomly picking DUT spectra from the five CCT bins, which were selected according to the proportions of the bins for 'All products', Industrial, and the uniform distributions. The mean absolute spectral mismatch errors were then calculated for these DUTs using the five candidate RSPDs and the spectral responsivity data of the 107 photometers.

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In addition to using just one available calibration spectrum at a time, the analysis was repeated by allowing the combinations of two and three calibration spectra to be used for calibration of each photometer. When calculating the spectral mismatch correction for a DUT, the calibration spectrum was chosen based on the closeness of its CCT to the one of the DUT. In practical measurements, the operator would need to estimate the CCT of light being measured in order to select the calibration factor for the instrument.

Besides using the spectral responsivity data of the 107 photometers and the spectral data of individual DUTs, an alternative approach was also employed. In this approach, spectral mismatch index M was calculated for every combination of the five candidate reference spectra and all the eight RSPDs shown in figure 4. The spectral mismatch index was calculated using the equation

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \label{eq:mismatchIndex} &M_{i,j} = \int \left| \frac{\varPhi_{\mathrm{cal}, i}(\lambda)V(\lambda)} {\int \varPhi_{\mathrm{cal}, i}(\lambda')V(\lambda')\,\mathrm{d}\lambda'}\right. \nonumber \\ &\qquad - \left.\frac{\varPhi_{\mathrm{RSPD}, j}(\lambda)V(\lambda)} {\int \varPhi_{\mathrm{RSPD}, j}(\lambda')V(\lambda')\,\mathrm{d}\lambda'} \right|\mathrm{d}\lambda , \nonumber \end{align} \tag{ 5 }$$

where $i = 1\ldots5$ and $j = 1\ldots8$ are the indices of the candidate spectra and all the RSPDs, respectively. Qualitatively, this resembles having one representative spectrum as the calibration source and another one as the DUT. For comparison, the spectral mismatch index was also calculated for Standard Illuminant A against the eight representative distributions. In this approach each CCT category was weighted equally.

To study the effect of using LED-calibrated photometers in measurements of light sources other than LEDs, the analysis of spectral mismatch errors was repeated using the CIE Technical Report No. 15: colorimetry [19] illuminants as DUTs. These illuminants include spectral data for daylight (Standard Illuminant D65 and illuminants C, D50, D55, D75), incandescent (Standard Illuminant A), fluorescent (illuminants FL1–12), and high-pressure discharge (illuminants HP1–5) sources.

Figure 6 shows the mean absolute spectral mismatch errors for the five candidate RSPDs. By weighting the CCT bins of the DUT data by the 'All products' distribution, shown in figure 5, the BL40 calibration spectrum resulted in the smallest mean absolute spectral mismatch error of 0.30$\%$ (red bars). This distribution of 'All products' should be considered the most significant one. Calibrating the photometers using the BL40 spectrum would also, on average, produce the smallest absolute spectral mismatch error (0.28$\%$) if the CCTs of the DUTs were uniformly distributed (purple bars).

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The BL30 RSPD produced the smallest mean absolute spectral mismatch error of 0.27$\%$ when no weighting was used (blue bars in figure 6). This is due to the dominance of low CCT spectra in the measured LED products as seen in figure 5. Out of the five candidate RSPDs, the BL40 spectrum also produced the smallest maximum absolute error of 6.33$\%$. The maximum absolute errors for the other candidate RSPDs ranged from 7.03$\%$ to 7.71$\%$.

Because high CCT values are preferred in industrial lighting, calibration spectra with higher CCTs yielded lower spectral mismatch errors in these applications. The BL50 calibration spectrum resulted in the smallest mean absolute spectral mismatch error of 0.25$\%$ when Industrial CCT distribution was used (green bars in figure 6).

Apart from one, all the candidate RSPDs and weighting distribution combinations produced smaller spectral mismatch than Standard Illuminant A. Depending on the utilised CCT weighting distribution, the most suitable LED-based calibration spectra reduced the mismatch error by approximately a factor of two or three when compared with Standard Illuminant A.

The impact of using a similar spectral shape for the calibration source as that of the DUT can be seen from the decrease in spectral mismatch errors when using the BL30 RSPD as the calibration spectrum while measuring the 2850 K LED of figure 2. For the 107 photometers, the range of the spectral mismatch errors decreased to $-0.18\%$ ... 0.35%, despite the increased difference in CCTs between the DUT and the calibration source, compared with the case of using Standard Illuminant A as the calibration source.

Figure 7 shows the results for the alternative approach of calculating the spectral mismatch indices M using equation (5). The figure shows the indices for the five candidate reference spectra and for Standard Illuminant A. This approach supports choosing the BL40 distribution as the reference spectrum, as it presented the lowest average and maximum spectral mismatch indices, 0.13 and 0.21 respectively. Standard Illuminant A, in turn, has the average and maximum index values 0.19 and 0.29, respectively. On average, all the five candidate RSPDs produced smaller spectral mismatch indices than Standard Illuminant A. The results of this approach are in line with those obtained by calculating spectral mismatch errors using equation (1) and uniform weighting distribution shown in figure 5.

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Figure 8 shows the mean absolute spectral mismatch errors when all the combinations of two RSPDs were used as the calibration sources. The combination BL30/BL40 produced the best result (0.19$\%$) when the DUT data was weighted by the 'All products' distribution, although three other combinations of calibration spectra performed almost similarly. For the unweighted data, the smallest spectral mismatch error of 0.18$\%$ was also given by the calibration spectra combination BL30/BL40. For the Industrial distribution, the smallest spectral mismatch error of 0.20$\%$ was achieved by using the combination of BL40/BL50 calibration spectra. The combination of BL30/BL50 calibration spectra produced the smallest error of 0.22$\%$ for the uniformly distributed data.

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In the case of two calibration spectra, employing Standard Illuminant A as the second source would not reduce spectral mismatch errors compared with the case of having just one LED-based calibration source. The smallest mean absolute spectral mismatch errors for Standard Illuminant A as the second calibration source were 0.31$\%$, 0.33$\%$, 0.26$\%$, and 0.28$\%$ for 'All products', Original, Industrial and the uniform distributions, respectively. Except for Industrial distribution, for which BL50/Standard Illuminant A produced the smallest spectral mismatch errors, BL40/Standard Illuminant A was the best combination of LED/incandescent calibration spectra.

When compared with the case of using just one calibration spectrum, the decrease in spectral mismatch error is on average 0.05–0.11 percentage points depending on the weighting distribution. The decrease in the error comes at the cost of more complex measurement procedure, where the operator has to choose the correct calibration factor for the instrument during measurements. For instance, for the DUT data weighted using 'All products' distribution, if the operator chooses the incorrect calibration spectrum in more than 48$\%$ of the cases, the benefits of using two spectrally different LED calibration sources are lost. Adding a third calibration spectrum would reduce the mean absolute spectral mismatch errors by additional 0.02–0.04 percentage points but would make estimating the CCT of light being measured even more complicated for the operator.

Figure 9 shows the comparison of the mean absolute spectral mismatch errors for the BL40 calibration spectrum and Standard Illuminant A when using the CIE colorimetric illuminants [19] as DUTs. The illuminants employed in the analysis and presented in the figure are: standard Illuminant A (Ill.A), daylight (D and C), fluorescent lamp spectra (FL), and high-pressure discharge lamp spectra (HP). Out of the five candidate LED spectra, the BL40 distribution yielded the smallest mean absolute spectral mismatch errors when measuring light represented by these illuminants.

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Except for HP1, HP2, and for Standard Illuminant A itself, the LED-based BL40 calibration spectrum resulted in considerably smaller spectral mismatch errors (average MAE  =  0.45$\%$) than Standard Illuminant A (average MAE  =  0.67$\%$). For HP1, the performance of the two calibration spectra is similar, making HP2 the only non-incandescent-based source for which Standard Illuminant A results in notably smaller spectral mismatch errors. The latter result can be explained by larger differences between the $V(\lambda)$ weighted spectra of HP2 and BL40 than between HP2 and Standard Illuminant A. On average, all candidate RSPDs produced smaller mean absolute spectral mismatch errors than Standard Illuminant A, average of mean absolute spectral mismatch errors ranging from 0.45$\%$ (BL40) to 0.60$\%$ (BL27).