Daylight Spectrum Index: A New Metric to Assess the Affinity of Light Sources with Daylighting

energies Article Daylight Spectrum Index: A New Metric to Assess the Affinity of Light Sources with Daylighting Ignacio Acosta * , Jesús León and Pedro Bustamante Instituto Universitario de Arquitectura y Ciencias de la Construcción, Universidad de Sevilla, 41001 Sevilla, Spain; [email protected] (J.L.); [email protected] (P.B.) *Correspondence: [email protected]; Tel.: +34-954-556-595 Received: 3 September 2018; Accepted: 20 September 2018; Published: 24 September 2018   Abstract: The current scenario of colorimetry shows a wide variety of different metrics which do not converge in the assessment of the color rendering of light sources. The limitations of the Color Rendering Index have promoted the emergence of new metrics, such as the Color Quality Scale. As in the case of the previous metric, these new concepts are based on the analysis of the deviation of different color samples in a color space, contrasting the results with those obtained with a light source reference, which can vary depending on the color temperature. Within this context, the Daylight Spectrum Index is proposed. This new concept aims to determine the affinity with daylighting of electric light sources, comparing the resulting spectral power distributions of the lamps studied and that observed under natural light. The affinity of an electric light source with daylighting allows for lower energy consumption due to the better performance of human vision. The new metric proposed is evaluated following the results obtained from 80 surveys, demonstrating the usefulness of this new concept in the quantification of color rendering of LED lamps and the affinity of electric light sources with daylighting. Keywords: colorimetry; color rendition; daylighting; light spectra; light sources; energy savings 1. Introduction and Objectives 1.1. State of the Art Nowadays, cutting-edge technology in electric lighting is promoting new metrics for the assessment of the color rendering of light sources currently used. LED lamps, with a wide presence in the market today, produce a different spectral distribution and color perception compared to the older incandescent and halogen luminaires, prompting a need for the proper assessment of these new lamps [1]. However, at present, the Color Rendering Index (CRI) is the only metric widely used to determine the hue performance of electric light sources. This definition, proposed in 1974 and recognized by the Commission Internationale de l’Eclairage (CIE) [ 2 ], came about as a procedure for quantifying the color perception produced by fluorescent lamps. Its calculation is articulated around the assessment of eight low saturated color samples in the CIE diagram 1960 u,v. A light source reference with a theoretically perfect rendering is used to select the samples which are subsequently compared with those observed for the case of a studied lamp. The deviation of these samples in the color space determines the quantification of this metric. However, some deficiencies can be noted in the CRI calculation procedure, mostly the nonuniform color distribution of the color space [ 3 ], the limitations of the color sample [ 4 ], and the selection of the light source reference [5]. Taking the previous scenario into consideration, the CRI metric was reaffirmed in 1995 and subsequently updated in 1999, including six new illuminants [ 6 ]. However, despite improvements in Energies 2018,11, 2545; doi:10.3390/en11102545 www.mdpi.com/journal/energies Energies 2018,11, 2545 2 of 19 this definition, the scientific community was not fully satisfied with the results obtained with CRI and new metrics were developed to evaluate color rendering. In an attempt to improve the understanding of color perception provided by light sources, Rea et al. defined the Gamut Area Index (GAI) [ 7 ], which can be determined as the ratio between the areas bounded by the color samples of CRI for the light source studied and a reference. The authors concluded that GAI predicts a better color discrimination on the Farnsworth-Munsell 100 Hue Test than CRI [8]. In order to achieve an accurate calculation of color rendering for LED lamps, the Color Quality Scale (CQS) was proposed [ 9 ]. This metric established 15 new color samples—with a higher saturation than in CRI—an updated color space, and a new chromatic adaptation to CMCCAT2000. Subsequently, Smet et al. proposed a redefinition of CRI called CRI2012 [ 10 ]- based on 210 real reflectance samples and on the colorimetric color difference model CRI-CAM02UCS [ 11 ]. Although CRI2012 is still based on a color space, the results of this metric are more accurate than in the original definition. One of the most up-to-date methods is TM-30-15, developed by the Illuminating Engineering Society of North America (IESNA) [ 12 ]. This procedure analyzes 99 color samples and uses a continuous illuminant reference depending on the color temperature of the light source studied. At present, IESNA is encouraging the widespread use of this new metric among luminaire manufacturers [ 13 ]. Based on this metric, the CIE developed the Color Fidelity Index in 2017 (Rf) [ 14 ] to improve the results provided by CRI. This new concept does not address the need for color quality measures relating to perception other than fidelity, although it incorporates most of the improvements proposed by TM-30-15. Chromatic preference can vary depending on context, and the assessment of the color rendering can therefore be affected by the boundary conditions [ 15 ]. In keeping with this, Schanda et al. [ 16 ] studied the color fidelity for a picture gallery and finally selected a multilight-emitting diode for this particular case study. Most recently, Lin et al. [ 17 ] analyzed the color preference in a restaurant, a retail display, and a supermarket, obtaining different results in each case study. Other studies, such as that by Hegde et al. [ 18 ], demonstrate that the saturation of colors also varies depending on the age of the observer. The best method to determine the accuracy of color rendering metrics relies on the analysis of surveys. Houser et al. [ 19 ] analyzed 40 surveys to ascertain whiteness perception under different LED lamps. Jost-Boissard et al. [ 20 ] assessed the color quality of LED lamps, analyzing 9 warm light sources using 45 surveys and 8 cool luminaires based on the results of 36 observers. Dangol et al. [ 21 ] investigated the performance of CRI, CQS, and CRI2012, evaluating 20 surveys relating to 3 LED lamps with different color temperatures. The authors concluded that the three metrics had a high correlation with a noticeable difference in color temperature. Moreover, Chen et al. [ 22 ] demonstrated eight kinds of optimal white OLEDs spectra using a similar methodology. Gu et al. [ 23 ] analyzed different metrics using 10 surveys, concluding that the CAM02-UCS color space is one of the best for the assessment of the deviation of the color samples. The color quality of the environment also affects circadian rhythm [ 24 ], which determines the cycles between alertness and sleepiness, and thus affects the health and wellbeing of individuals [ 25 ]. Therefore, color rendering is also crucial to our health and performance. As deduced from this introduction, colorimetry definitions are constantly being updated, which means there are no solid, unified criteria regarding the color rendering of a light source. In addition, most of the new metrics attempting to quantify the color performance of a light source are based on a color space chart, which always depends on a subjective interpretation of the color distribution [ 26 ]. However, color rendering can also be determined analyzing the spectral power distribution (SPD) [ 27 ], which describes the power per unit wavelength of a light source, or using the subjective analysis of the color of familiar objects [ 28 ], such as the Memory Color Quality Index (Rm). Energies 2018,11, 2545 3 of 19 Finally, it must be highlighted that daylighting represents a perfect color rendering of our environment [ 29 ] and could be considered as a suitable reference to determine the color rendition of a light source. 1.2. Aim and Objectives The aim of this study is to assess a new metric which serves to quantify the affinity of electric light sources to daylighting. This new concept can be particularly interesting in those contexts where color perception must be close to that observed under natural light conditions, such as clothing stores, car dealers, galleries, or textile factories [30]. The new metric is based on a sole light source reference, regardless of the color temperature of the light source studied. This sole reference is daylighting, as its color rendering can be considered perfect [ 31 – 33 ]. Therefore, the calculation of this new concept relies on the comparison of the perceived spectral distributions provided both by daylighting and by the studied light source. Accordingly, the Daylight Spectrum Index is defined [ 34 ] in order to provide an objective definition to assess the affinity of the electric light source with the natural light. This new concept can serve to complement other current procedures, such as TM-30-15 or CIE 2017 [ 12 , 13 ], giving information about the fidelity of the studied light source with respect to daylighting. Once the new metric is determined, its accuracy is evaluated using a light source testing box. Although this methodology is similar to those proposed by other authors [ 8 , 28 ], it offers new nuances that highlight the innovative aspects of this study, as detailed below: • The accuracy of the new metric is evaluated by means of 80 surveys of the color performance of 7 different light sources. This study sample is larger than in previous research [ 8 , 19 – 21 , 23 ], providing considerable precision for the conclusions obtained. • Both the color rendering and the affinity to daylighting are assessed by means of the results observed in the surveys as well as the color saturation of the samples. • The new metric is contrasted with the results obtained using other color rendering metrics, such as the Color Rendering Index, the Color Quality Scale, the Gamut Area, and TM-30-15. 2. Calculation Procedure of Daylight Spectrum Index 2.1. Metric Definition The Daylight Spectrum Index (DSI) is defined as the ratio of the area bounded by the color perception of the SPD of a light source studied and that which is limited by daylight. In other words, the DSI represents the affinity of the light source perception to daylight according to its spectral distribution. 2.2. Calculation Procedure 2.2.1. Definition of Daylight Spectral Distribution Sky conditions are key in establishing a suitable reference to assess the color rendering of a light source. The typical sky conditions for calculating the DSI correspond to CIE D65 [ 35 ], considered the most common daylight spectrum for Northern Europe. However, it must be recognized that the boundary conditions can affect the color perception of our context, and therefore, the spectral distribution of the sky should be adjusted to the typical weather conditions of the location where the color rendering analysis is carried out. Accordingly, a study in a location with a predominant clear sky should choose an SPD close to CIE D75, while an assessment in an environment with a mainly cloudy sky must select a typical spectral distribution for an overcast sky, that is to say, CIE D50. Figure 1 shows the most frequent spectral distributions for daylighting. Energies 2018,11, 2545 4 of 19 Energies 2018, 11, x FOR PEER REVIEW 4 of 19 Figure 1. Daylight spectral power distribution (SPD) of the most common skies for Europe. CIE S 014-2/E:2006. 2.2.2. Color Perception of the Sky Once the suitable SPD for the sky conditions is selected, the color perception must be taken into account. The responsivity spectra of a human being for color perception is based on three cone cells, called long (L), medium (M), and short (S). The sensitivity functions of the cone photoreceptors are described in Figure 2 [36]. Figure 2. Normalized responsivity spectra of human cone cells: short (S), medium (M), and long (L) types. According to the degree of sensitivity of human color perception, the SPD of the selected sky conditions can be modified by the color functions, as expressed in Equations (1) to (3): 𝑓𝐷(𝐿)= 𝑓(𝐿)· 𝑓(𝑆𝑘𝑦) (1) 𝑓𝐷(𝑀)= 𝑓(𝑀)· 𝑓(𝑆𝑘𝑦) (2) 𝑓𝐷(𝑆)= 𝑓(𝑆)· 𝑓(𝑆𝑘𝑦) (3) where f(L), f(M), and f(S) correspond to the color sensitivity functions and f(Sky) is equivalent to the SPD of the selected sky as a function of the wavelength. Figure 1. Daylight spectral power distribution (SPD) of the most common skies for Europe. CIE S 014-2/E:2006. 2.2.2. Color Perception of the Sky Once the suitable SPD for the sky conditions is selected, the color perception must be taken into account. The responsivity spectra of a human being for color perception is based on three cone cells, called long (L), medium (M), and short (S). The sensitivity functions of the cone photoreceptors are described in Figure 2[36]. Energies 2018, 11, x FOR PEER REVIEW 4 of 19 Figure 1. Daylight spectral power distribution (SPD) of the most common skies for Europe. CIE S 014-2/E:2006. 2.2.2. Color Perception of the Sky Once the suitable SPD for the sky conditions is selected, the color perception must be taken into account. The responsivity spectra of a human being for color perception is based on three cone cells, called long (L), medium (M), and short (S). The sensitivity functions of the cone photoreceptors are described in Figure 2 [36]. Figure 2. Normalized responsivity spectra of human cone cells: short (S), medium (M), and long (L) types. According to the degree of sensitivity of human color perception, the SPD of the selected sky conditions can be modified by the color functions, as expressed in Equations (1) to (3): 𝑓𝐷(𝐿)= 𝑓(𝐿)· 𝑓(𝑆𝑘𝑦) (1) 𝑓𝐷(𝑀)= 𝑓(𝑀)· 𝑓(𝑆𝑘𝑦) (2) 𝑓𝐷(𝑆)= 𝑓(𝑆)· 𝑓(𝑆𝑘𝑦) (3) where f(L), f(M), and f(S) correspond to the color sensitivity functions and f(Sky) is equivalent to the SPD of the selected sky as a function of the wavelength. Figure 2. Normalized responsivity spectra of human cone cells: short (S), medium (M), and long (L) types. According to the degree of sensitivity of human color perception, the SPD of the selected sky conditions can be modified by the color functions, as expressed in Equations (1) to (3): fD(L)=f(L)·f(Sky)(1) fD(M)=f(M)·f(Sky)(2) fD(S)=f(S)·f(Sky)(3) where f(L), f(M), and f(S) correspond to the color sensitivity functions and f(Sky) is equivalent to the SPD of the selected sky as a function of the wavelength. Energies 2018,11, 2545 5 of 19 Figure 3shows the SPD of the daylight conditions perceived by the human visual color system considering a typical daylight spectrum for Northern Europe, CIE D65. This spectral perception of natural light serves as a reference for the color rendering of the studied light source. Energies 2018, 11, x FOR PEER REVIEW 5 of 19 Figure 3 shows the SPD of the daylight conditions perceived by the human visual color system considering a typical daylight spectrum for Northern Europe, CIE D65. This spectral perception of natural light serves as a reference for the color rendering of the studied light source. Figure 3. SPD of the sky reference modified by color sensitivity functions f(L), f(M), and f(S). 2.2.3. Normalization of the Resulting SPD of the Sky After determining the human perception of the sky vault, the resulting function must be normalized. This normalization should be carried out as follows: 1. The specific total perceived power (Ts) is calculated by the integration of the area under the resulting function. 2. A scalar (P) is calculated according to the following Equation (4): 𝑃 = 𝑇𝑎 𝑇𝑠 (4) where Ta represents an arbitrary value used to scale the results. 3. Each value of the wavelength axis is multiplied by the scalar P in order to generate a normalized dataset. The previous process can be expressed as seen in Equations (5) to (7): 𝑓𝑁(𝐿)= 𝑓𝐷(𝐿)𝑇𝑎 ∫𝑓𝐷(𝐿)𝑑𝐿 730 380 (5) 𝑓𝑁(𝑀)= 𝑓𝐷(𝑀)𝑇𝑎 ∫𝑓𝐷(𝑀)𝑑𝑀 730 380 (6) 𝑓𝑁(𝑆)= 𝑓𝐷(𝑆)𝑇𝑎 ∫𝑓𝐷(𝑆)𝑑𝑆 730 380 (7) where fD(L), fD(M), and fD(S) are the SPD of the sky modified by the color responsivity functions, as seen in Equations (1) to (3), and Ta is the arbitrary value used to scale the results. This process helps determine a relative perception of daylighting, regardless of the luminance of the sky vault. Accordingly, the spectral distribution perceived from the light source studied can be compared with that defined by the daylight conditions, ignoring the difference of luminous flux. In accordance with Equations (5) to (7), Figure 4 shows the resulting SPD of the sky, modified by the color sensitivity functions and normalized for a scalar value of 10. Figure 3. SPD of the sky reference modified by color sensitivity functions f(L), f(M), and f(S). 2.2.3. Normalization of the Resulting SPD of the Sky After determining the human perception of the sky vault, the resulting function must be normalized. This normalization should be carried out as follows: 1. The specific total perceived power (Ts) is calculated by the integration of the area under the resulting function. 2. A scalar (P) is calculated according to the following Equation (4): P=Ta Ts(4) where Ta represents an arbitrary value used to scale the results. 3. Each value of the wavelength axis is multiplied by the scalar Pin order to generate a normalized dataset. The previous process can be expressed as seen in Equations (5) to (7): fN(L)=fD(L)Ta R730 380 fD(L)dL (5) fN(M)=fD(M)Ta R730 380 fD(M)dM (6) fN(S)=fD(S)Ta R730 380 fD(S)dS (7) where f D (L), f D (M), and f D (S) are the SPD of the sky modified by the color responsivity functions, as seen in Equations (1) to (3), and Ta is the arbitrary value used to scale the results. This process helps determine a relative perception of daylighting, regardless of the luminance of the sky vault. Accordingly, the spectral distribution perceived from the light source studied can be compared with that defined by the daylight conditions, ignoring the difference of luminous flux. In accordance with Equations (5) to (7), Figure 4shows the resulting SPD of the sky, modified by the color sensitivity functions and normalized for a scalar value of 10. Energies 2018,11, 2545 6 of 19 Energies 2018, 11, x FOR PEER REVIEW 6 of 19 Figure 4. SPD of the sky reference modified by color sensitivity functions f(L), f(M), and f(S) and normalized for Ta = 10. 2.2.4. Color Perception of the Studied Light Source As described in the previous procedure, the color perception of the light source studied can be defined in accordance with color functions, as seen in Equations (8) to (10): 𝛿(𝐿)= 𝑓(𝐿)· 𝑓(𝐿𝑖𝑔ℎ𝑡) (8) 𝛿(𝑀)= 𝑓(𝑀)· 𝑓(𝐿𝑖𝑔ℎ𝑡) (9) 𝛿(𝑆)= 𝑓(𝑆)· 𝑓(𝐿𝑖𝑔ℎ𝑡) (10) where f(L), f(M), and f(S) correspond to the color sensitivity functions and f(Light) is equivalent to the SPD of the studied light source as a function of the wavelength. As an example, the color perception of the spectral distribution of an LED lamp, considering a correlated color temperature (CCT) of 6500 K, is shown in Figure 5. Figure 5. SPD of the studied light source modified by color sensitivity functions f(L), f(M), and f(S). Figure 4. SPD of the sky reference modified by color sensitivity functions f(L), f(M), and f(S) and normalized for Ta = 10. 2.2.4. Color Perception of the Studied Light Source As described in the previous procedure, the color perception of the light source studied can be defined in accordance with color functions, as seen in Equations (8) to (10): δ(L)=f(L)·f(Light)(8) δ(M)=f(M)·f(Light)(9) δ(S)=f(S)·f(Light)(10) where f(L), f(M), and f(S) correspond to the color sensitivity functions and f(Light) is equivalent to the SPD of the studied light source as a function of the wavelength. As an example, the color perception of the spectral distribution of an LED lamp, considering a correlated color temperature (CCT) of 6500 K, is shown in Figure 5. Energies 2018, 11, x FOR PEER REVIEW 6 of 19 Figure 4. SPD of the sky reference modified by color sensitivity functions f(L), f(M), and f(S) and normalized for Ta = 10. 2.2.4. Color Perception of the Studied Light Source As described in the previous procedure, the color perception of the light source studied can be defined in accordance with color functions, as seen in Equations (8) to (10): 𝛿(𝐿)= 𝑓(𝐿)· 𝑓(𝐿𝑖𝑔ℎ𝑡) (8) 𝛿(𝑀)= 𝑓(𝑀)· 𝑓(𝐿𝑖𝑔ℎ𝑡) (9) 𝛿(𝑆)= 𝑓(𝑆)· 𝑓(𝐿𝑖𝑔ℎ𝑡) (10) where f(L), f(M), and f(S) correspond to the color sensitivity functions and f(Light) is equivalent to the SPD of the studied light source as a function of the wavelength. As an example, the color perception of the spectral distribution of an LED lamp, considering a correlated color temperature (CCT) of 6500 K, is shown in Figure 5. Figure 5. SPD of the studied light source modified by color sensitivity functions f(L), f(M), and f(S). Figure 5. SPD of the studied light source modified by color sensitivity functions f(L), f(M), and f(S). Energies 2018,11, 2545 7 of 19 2.2.5. Normalization of the Resulting SPD of the Studied Light Source As described in the calculation process of daylight reference, the resulting SPD of the light source studied is normalized using the same scalar value as in the previous case and according to Equations (11) to (13): δN(L)=δ(L)Ta R730 380 δ(L)dL (11) δN(M)=δ(M)Ta R730 380 δ(M)dM (12) δN(S)=δ(S)Ta R730 380 δ(S)dS (13) where δ (L), δ (M), and δ (S) are the SPD of the light source studied multiplied by the color responsivity functions, as seen in Equations (8) to (10), and Ta is the scalar value defined in Equations (5) to (7). As in the calculation process of the perceived daylight, Figure 6shows the resulting SPD of the LED lamp analyzed, modified by the color sensitivity functions and normalized for the scalar value defined above. Energies 2018, 11, x FOR PEER REVIEW 7 of 19 2.2.5. Normalization of the Resulting SPD of the Studied Light Source As described in the calculation process of daylight reference, the resulting SPD of the light source studied is normalized using the same scalar value as in the previous case and according to Equations (11) to (13): 𝛿𝑁(𝐿)= 𝛿(𝐿)𝑇𝑎 ∫𝛿(𝐿)𝑑𝐿 730 380 (11) 𝛿𝑁(𝑀)= 𝛿(𝑀)𝑇𝑎 ∫𝛿(𝑀)𝑑𝑀 730 380 (12) 𝛿𝑁(𝑆)= 𝛿(𝑆)𝑇𝑎 ∫𝛿(𝑆)𝑑𝑆 730 380 (13) where δ(L), δ(M), and δ(S) are the SPD of the light source studied multiplied by the color responsivity functions, as seen in Equations (8) to (10), and Ta is the scalar value defined in Equations (5) to (7). As in the calculation process of the perceived daylight, Figure 6 shows the resulting SPD of the LED lamp analyzed, modified by the color sensitivity functions and normalized for the scalar value defined above. Figure 6. SPD of the light source modified by color sensitivity functions f(L), f(M), and f(S) and normalized for Ta = 10. 2.2.6. Ratio of the Resulting Areas As expressed before, the DSI is defined as the ratio of the normalized area bounded by the color perception of the SPD of a light source studied and that which is limited by daylight. This statement can be expressed as seen in Equations (14) to (16), depending on the color sensitivity functions described above: 𝐷𝑆𝐼𝑅 (%)=100 ·∫𝑀𝑖𝑛(𝛿𝑁(𝐿), 𝑓𝑁(𝐿)) 𝑑𝐿 730 380 ∫𝑓𝑁(𝐿) 𝑑𝐿 730 380 (14) 𝐷𝑆𝐼𝐺 (%)=100 ·∫𝑀𝑖𝑛(𝛿𝑁(𝑀), 𝑓𝑁(𝑀)) 𝑑𝑀 730 380 ∫𝑓𝑁(𝑀) 𝑑𝑀 730 380 (15) 𝐷𝑆𝐼𝐵 (%)=100 ·∫𝑀𝑖𝑛(𝛿𝑁(𝑆), 𝑓𝑁(𝑆)) 𝑑𝑆 730 380 ∫𝑓𝑁(𝑆) 𝑑𝑆 730 380 (16) Figure 6. SPD of the light source modified by color sensitivity functions f(L), f(M), and f(S) and normalized for Ta = 10. 2.2.6. Ratio of the Resulting Areas As expressed before, the DSI is defined as the ratio of the normalized area bounded by the color perception of the SPD of a light source studied and that which is limited by daylight. This statement can be expressed as seen in Equations (14) to (16), depending on the color sensitivity functions described above: DSIR(%)=100·R730 380 Min(δN(L),fN(L))dL R730 380 fN(L)dL (14) DSIG(%)=100·R730 380 Min(δN(M),fN(M))dM R730 380 fN(M)dM (15) DSIB(%)=100·R730 380 Min(δN(S),fN(S))dS R730 380 fN(S)dS (16) Energies 2018,11, 2545 8 of 19 where δN (L), δN (M), and δN (S) correspond to the normalized functions of the light source studied according to the color perception and f N (L), f N (M), and f N (S) are the same functions for the daylight reference. As expressed in Equations (14) to (16), the color affinity of a light source with daylighting can be calculated depending on the color range defined by the cone photoreceptors. Therefore, DSI R determines the color affinity for red hues, while DSI G and DSI B conclude the similarity for green and blue hues, respectively. The overall score for DSI can be defined as the average value between the results observed for each cone photoreceptor, that is to say, the mean value of Equations (14) to (16). As deduced from Equations (14) to (16), the DSI for the analyzed LED lamp with a CCT of 6500 K in comparison with a daylight spectrum CIE D65 is shown in Figure 7, obtaining a DSI value equal to 83%, which corresponds to the area limited under both functions for each photoreceptor. Energies 2018, 11, x FOR PEER REVIEW 8 of 19 where δN(L), δN(M), and δN(S) correspond to the normalized functions of the light source studied according to the color perception and fN(L), fN(M), and fN(S) are the same functions for the daylight reference. As expressed in Equations (14) to (16), the color affinity of a light source with daylighting can be calculated depending on the color range defined by the cone photoreceptors. Therefore, DSIR determines the color affinity for red hues, while DSIG and DSIB conclude the similarity for green and blue hues, respectively. The overall score for DSI can be defined as the average value between the results observed for each cone photoreceptor, that is to say, the mean value of Equations (14) to (16). As deduced from Equations (14) to (16), the DSI for the analyzed LED lamp with a CCT of 6500 K in comparison with a daylight spectrum CIE D65 is shown in Figure 7, obtaining a DSI value equal to 83%, which corresponds to the area limited under both functions for each photoreceptor. Figure 7. Daylight spectrum index (DSI) for an LED lamp with correlated color temperature (CCT) 6500 K compared with a daylight spectrum CIE D65. As can be deduced from the previous procedure, the calculation of DSI is a way to assess the affinity of a light source to the spectral distribution of daylight conditions, although it can also be useful to determine the color rendering of a studied lamp, since natural light represents a perfect color rendering for the human being. 3. Assessment of the Accuracy of DSI 3.1. Light Source Testing Box The analysis of the accuracy of the proposed metric was argued in the assessment of 80 colorimetry surveys, where respondents answered questions on the color rendering, color temperature, saturation, and chromatic perception of different samples inside a light source testing box. The survey sample was made up of 47 men and 33 women aged between 20 and 31 years old. Given that most of these respondents were students at the School of Architecture of Seville, a particular sensitivity to color perception was assumed. Prior to questions about colorimetry, the survey included questions on visual impairments, confirming that all respondents had suitably clear eyesight to perceive the objects inside the testing box. To ensure there were no respondents suffering from color blindness, each survey included a random Ishihara test [37], so all the surveys assessed have been completed by respondents with an appropriate color perception. The light source testing box, shown in Figure 8, was 60 cm wide by 60 cm deep by 60 cm high and was made of medium-density fiberboard (MDF) painted white. The white paint has a constant reflectance of 90%, except in the wavelength interval between 380 and 400 nm, where the average reflectance is 50%. Six electric light sources were located in the top of the box, hidden by a white panel. The lamps ran along a lane in order to ensure the light source studied was situated exactly in the center of the testing box. The lamps projected light through an opal diffuser, thus making it Figure 7. Daylight spectrum index (DSI) for an LED lamp with correlated color temperature (CCT) 6500 K compared with a daylight spectrum CIE D65. As can be deduced from the previous procedure, the calculation of DSI is a way to assess the affinity of a light source to the spectral distribution of daylight conditions, although it can also be useful to determine the color rendering of a studied lamp, since natural light represents a perfect color rendering for the human being. 3. Assessment of the Accuracy of DSI 3.1. Light Source Testing Box The analysis of the accuracy of the proposed metric was argued in the assessment of 80 colorimetry surveys, where respondents answered questions on the color rendering, color temperature, saturation, and chromatic perception of different samples inside a light source testing box. The survey sample was made up of 47 men and 33 women aged between 20 and 31 years old. Given that most of these respondents were students at the School of Architecture of Seville, a particular sensitivity to color perception was assumed. Prior to questions about colorimetry, the survey included questions on visual impairments, confirming that all respondents had suitably clear eyesight to perceive the objects inside the testing box. To ensure there were no respondents suffering from color blindness, each survey included a random Ishihara test [ 37 ], so all the surveys assessed have been completed by respondents with an appropriate color perception. The light source testing box, shown in Figure 8, was 60 cm wide by 60 cm deep by 60 cm high and was made of medium-density fiberboard (MDF) painted white. The white paint has a constant reflectance of 90%, except in the wavelength interval between 380 and 400 nm, where the average reflectance is 50%. Six electric light sources were located in the top of the box, hidden by a white panel. The lamps ran along a lane in order to ensure the light source studied was situated exactly in the center of the testing box. The lamps projected light through an opal diffuser, thus making it impossible for Energies 2018,11, 2545 9 of 19 respondents to identify the light source. Accordingly, a single-blind test could be carried out to prevent any potential prejudices on the part of the students surveyed. Energies 2018, 11, x FOR PEER REVIEW 9 of 19 impossible for respondents to identify the light source. Accordingly, a single-blind test could be carried out to prevent any potential prejudices on the part of the students surveyed. Figure 8. Analysis of color rendering of a warm and cool LED lamp in the light source testing box. 3.2. Light Sources Analyzed In addition to natural light, six lamps were evaluated by the respondents. In order to assess a wide range of luminaire types, three typical LED lamps—with a warm, neutral, and cool color temperature—were evaluated in the testing box as well as an incandescent lamp and two compact fluorescent lamps with cool and warm color temperatures. Multilight-emitting diodes, high-pressure sodium lamps, and metal halide luminaires were not assessed in the testing box due to the constraints of the box dimensions and their less frequent application to indoor architecture. The main color characteristics of the light sources studied, as well as the color rendering for most of the widespread metrics, are shown in Table 1. Table 1. Main colorimetric characteristics of the light sources studied in the testing box. Source 1 2 3 4 5 6 7 Abbreviation DL L27 L40 L65 IN FL65 FL25 Description Daylight CIE D65 LED 2700 K LED 4000 K LED 6500 K Incandescent Fluorescent 6500 K Fluorescent 2500 K CCT 6500 K 2754 K 4199 K 5692 K 2538 K 6307 K 2406 K CRI Ra 100 83 84 83 99 87 84 GAI CRI 100 91 86 87 97 106 112 CQS 100 84 84 81 99 86 78 TM-30-15 Rf 100 83 82 81 99 84 68 DSI 100 80 85 84 83 72 55 The spectral distribution of the sky vault oscillates between CIE D65 and CIE D75, according to the typical sky conditions of spring and summer in Seville (southern Spain), the location where the trial was carried out. Both SPDs produce a perfect color rendering and can be compared with the results observed for the electric light sources studied. The SPD of the sky was checked before each battery of surveys with a Konica Minolta CL-70F spectrometer. All surveys were developed under daylight conditions avoiding direct solar incidence inside the testing box as well as a cloudy sky. The SPDs of the electric light sources evaluated in the testing box are shown in Figure 9 and correspond to the color temperature values defined in Table 1. Figure 8. Analysis of color rendering of a warm and cool LED lamp in the light source testing box. 3.2. Light Sources Analyzed In addition to natural light, six lamps were evaluated by the respondents. In order to assess a wide range of luminaire types, three typical LED lamps—with a warm, neutral, and cool color temperature—were evaluated in the testing box as well as an incandescent lamp and two compact fluorescent lamps with cool and warm color temperatures. Multilight-emitting diodes, high-pressure sodium lamps, and metal halide luminaires were not assessed in the testing box due to the constraints of the box dimensions and their less frequent application to indoor architecture. The main color characteristics of the light sources studied, as well as the color rendering for most of the widespread metrics, are shown in Table 1. Table 1. Main colorimetric characteristics of the light sources studied in the testing box. Source 1 2 3 4 5 6 7 Abbreviation DL L27 L40 L65 IN FL65 FL25 Description Daylight CIE D65 LED 2700 K LED 4000 K LED 6500 K Incandescent Fluorescent 6500 K Fluorescent 2500 K CCT 6500 K 2754 K 4199 K 5692 K 2538 K 6307 K 2406 K CRI Ra 100 83 84 83 99 87 84 GAI CRI 100 91 86 87 97 106 112 CQS 100 84 84 81 99 86 78 TM-30-15 Rf 100 83 82 81 99 84 68 DSI 100 80 85 84 83 72 55 The spectral distribution of the sky vault oscillates between CIE D65 and CIE D75, according to the typical sky conditions of spring and summer in Seville (southern Spain), the location where the trial was carried out. Both SPDs produce a perfect color rendering and can be compared with the results observed for the electric light sources studied. The SPD of the sky was checked before each battery of surveys with a Konica Minolta CL-70F spectrometer. All surveys were developed under daylight conditions avoiding direct solar incidence inside the testing box as well as a cloudy sky. The SPDs of the electric light sources evaluated in the testing box are shown in Figure 9and correspond to the color temperature values defined in Table 1. Energies 2018,11, 2545 16 of 19 results, reaching a divergence of 11% with respect to the surveys assessed. The accuracy of DSI is lower for fluorescent lamps, although this metric can be used in addition to other useful procedures, such as TM-30-15. It is worth noting that, as stated in the calculation procedure of DSI, this new metric solely focuses on the affinity of the perceived spectrum of the light source analyzed with regard to daylighting, avoiding any chromatic adaptation formulae, color space, or subjective interpretation of results. Therefore, in addition to offering accurate color rendering calculation, it is also easy to determine. Moreover, as described in the aim of this study, DSI can serve to complement other current procedures, such as TM-30-15 or CIE 2017, providing information about the fidelity of the studied light source with respect to daylighting. Moreover, it should also be noted that LED lamps provide the best color performance of all luminaires, as can be deduced from the surveys assessed. Specifically, LED lamps with a CCT between 4000 and 6500 K produce a better rendering than the rest of light sources tested in this research. Therefore, this type of luminaire not only allows the best energy efficiency but also provides higher chromatic perception, thus highlighting the obsolescence of incandescent and fluorescent lamps. It should also be recognized that the analysis of the SPD of the light source studied is key in determining the color performance, as it can provide more information about the color rendering than other procedures. In the specific case of color saturation, it can be concluded that the dominant spectrum generated by the lamp determines the hue range where saturation is higher. In addition, it is observed that light sources which provide a better color rendering have a balanced saturation for all hues. Finally, a clear relationship between color rendering and affinity with daylight conditions can be confirmed. In fact, the lamps that are more similar to the spectral perception of natural light also demonstrate the best color rendering, according to the surveys evaluated. Therefore, daylight acts as the main light source reference for determining the color perception of individuals. Author Contributions: Conceptualization, I.A.; methodology, I.A., J.L. and P.B.; formal analysis, J.L.; investigation, I.A., J.L. and P.B.; data curation, J.L.; writing—original draft preparation, I.A., J.L. and P.B.; writing—review and editing, J.L. and P.B.; supervision, J.L. and P.B.; funding acquisition, I.A. Funding: This research was founded by the government of Spain through the research project: Efficient design for biodynamic lighting to promote the circadian rhythm in shift work centers (Ref BIA2017-86997-R). The authors wish to express their gratitude for all the technical and financial support provided. Acknowledgments: The authors are especially grateful to all those who participated as respondents in this study. Conflicts of Interest: The authors declare no conflict of interest. Abbreviations Glossary CRI Color Rendering Index CQS Color Quality Scale DSI Daylight Spectrum Index SPD Spectral Power Distribution Appendix A. Survey Form The survey form used for the trial described is shown below. As stated in the methodology, the respondents answered questions on their physiological response to the color perception, as well as others relating to the subjective perception of luminosity, color rendering, color temperature, saturation of different hues and the chromatic perception of the samples observed in the light source testing box. Each light source tested has its own survey box where respondents can assess the color qualities of the specific lamp. As described above, six electric light sources, in addition to natural light, were evaluated by 80 respondents. Energies 2018,11, 2545 17 of 19 Energies 2018, 11, x FOR PEER REVIEW 17 of 19 qualities of the specific lamp. As described above, six electric light sources, in addition to natural light, were evaluated by 80 respondents. PHYSIOLOGICAL CHARACTERISTICS RESPONDENT DATA Gender Age Reference Do you have any visual impairment? Which? Corrected? ISHIHARA TEST Fill in the boxes with the number that appears in the images: LIGHT SOURCE SKY CONDITIONS SKY CONDITIONS OVERCAST ALMOST CLOUDY INTERMEDIATE ALMOST CLEAR CLEAR Rate the sky conditions. OVERALL COLOR PERCEPTION LUMINOSITY VERY DARK DARK SUITABLE BRIGHT VERY BRIGHT Rate the color perception of the sample. COLOR RENDERING INSUFFICIENT SUFFICIENT GOOD VERY GOOD PERFECT Rate the color rendering. DAYLIGHT AFFINITY VERY FAR FAR INTERMEDIATE CLOSE VERY CLOSE Rate the daylight affinity. COLOR TEMPERATURE VERY WARM WARM NEUTRAL COOL VERY COOL Rate the color temperature of the sample. SATURATION OF COLOR NON SATURATED LOW SATURATED SUITABLE SATURATED VERY SATURATED Rate the orange and red hues. Rate the green and yellow hues. Rate the blue and violet hues. CHROMATIC PERCEPTION VERY POOR POOR REGULAR GOOD VERY GOOD Rate the perception of the fruit sample. Rate the perception of the paintings sample. References [1] Sandor, N.; Schanda, J. Visual colour rendering based on colour difference evaluations. Light. Res. Technol. 2006, 38, 225–239, doi:10.1191/1365782806lrt168oa. [2] Barbrow, L.E. International lighting vocabulary. J. SMPTE 1964, 73, 331–332. [3] MacAdam, D.L. Visual sensitivities to color differences in daylight. J. Opt. Soc. Am. 1942, 32, 247–274. [4] Schanda, J. A combined colour preference-colour rendering index. Light. Res. Technol. 1985, 17, 31–34. Y N Y N Energies 2018, 11, x FOR PEER REVIEW 17 of 19 qualities of the specific lamp. As described above, six electric light sources, in addition to natural light, were evaluated by 80 respondents. PHYSIOLOGICAL CHARACTERISTICS RESPONDENT DATA Gender Age Reference Do you have any visual impairment? Which? Corrected? ISHIHARA TEST Fill in the boxes with the number that appears in the images: LIGHT SOURCE SKY CONDITIONS SKY CONDITIONS OVERCAST ALMOST CLOUDY INTERMEDIATE ALMOST CLEAR CLEAR Rate the sky conditions. OVERALL COLOR PERCEPTION LUMINOSITY VERY DARK DARK SUITABLE BRIGHT VERY BRIGHT Rate the color perception of the sample. COLOR RENDERING INSUFFICIENT SUFFICIENT GOOD VERY GOOD PERFECT Rate the color rendering. DAYLIGHT AFFINITY VERY FAR FAR INTERMEDIATE CLOSE VERY CLOSE Rate the daylight affinity. COLOR TEMPERATURE VERY WARM WARM NEUTRAL COOL VERY COOL Rate the color temperature of the sample. SATURATION OF COLOR NON SATURATED LOW SATURATED SUITABLE SATURATED VERY SATURATED Rate the orange and red hues. Rate the green and yellow hues. Rate the blue and violet hues. CHROMATIC PERCEPTION VERY POOR POOR REGULAR GOOD VERY GOOD Rate the perception of the fruit sample. Rate the perception of the paintings sample. References [1] Sandor, N.; Schanda, J. Visual colour rendering based on colour difference evaluations. Light. Res. Technol. 2006, 38, 225–239, doi:10.1191/1365782806lrt168oa. [2] Barbrow, L.E. International lighting vocabulary. J. SMPTE 1964, 73, 331–332. [3] MacAdam, D.L. 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