A preliminary usefulness metric is defined. The metric is intended to characterize the energy efficiency of light sources in a more comprehensive way than the luminous efficacy of a source by taking selected spectral aspects of human centric lighting into consideration. The presented version of the metric is a combination of well-established measures of color quality, brightness and the circadian effect derived from the spectral power distribution of the light source. The metric includes a limited application dependence: it yields different values for interior and exterior applications, static and dynamic as well as relaxing and activating light source spectra. Light source categories (A-G) with preliminary category limits were also computed in the two-dimensional diagram associated with the metric. The metric should be considered as a basis for further discussions and not as a final solution.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Today’s lighting technology, especially the technology of the interior lighting of offices, industry halls, schools, hospitals, retail etc. undergoes a dynamic transition from conventional luminaire systems via luminaires with white LEDs of fixed spatial light intensity distributions and fixed correlated color temperature (CCT) towards flexible automatic and intelligent LED luminaires with sensor-based and time dependent (dynamic) lighting as well as feedback control systems. In the last decades, lighting designers, architects and luminaire developers used standalone individual descriptor quantities like the UGR (Unified Glare Rating) metric for glare, luminance, illuminance, homogeneity measures and the color rendering index in order to describe or optimize these lighting systems.
Today, to implement intelligent and integrative illuminating technology for application dependent and user dependent (individual) lighting, complex models are necessary. These models should consist of an appropriate combination of the different descriptors of the quality of human centric lighting (HCL) [1–8]. For successful HCL design, the physical properties of electromagnetic radiation, or, more specifically, the spectral, spatial and temporal light distributions of the lighting system have to be optimized  considering the most important HCL aspects [1, 2, 5, 8] and combining their descriptors appropriately depending on lighting application and the user’s characteristics as well as their expectations, see Fig. 1.
The design of spatial light properties (spatial radiance and irradiance distributions e.g. wall washing, diffuse or spot lighting, highlights and shadows, see e.g [6,9].) and temporal properties (for dynamic lighting e.g. changing correlated color temperatures during a working day, see e.g [10, 11].) are the subject of extensive lighting quality considerations for architectural design. In the present article, we will only deal with the spectral properties of lighting i.e. those properties that result from the spectral power distribution of the lighting system or, more specifically, the light source used in it. We are searching for an appropriate numeric quantity  that represents the most important HCL design aspects resulting from the spectrum of the light source. This quantity should express the usefulness  of the light source in a practicable way for general lighting applications. According to the definition of the present authors, a light source or a lighting system is considered useful if it exhibits optimal HCL properties in the sense of Fig. 1 by the use of as less electric energy as possible.
The aim of the present article is to define a possible numeric quantity that describes the usefulness of a light source in the above sense from its spectral power distribution and the input electric power (in W). As mentioned earlier  and as it was often pointed out in literature (see e.g [2, 5].), luminous efficacy of a source in lumens per watt units (which is still widely used today to this aim) is not an appropriate quantity (as “photometry is based on an incomplete description of the human visual system’s capabilities” ). The reason is that the V(λ) function represents only the linear combination of the long- (L-) and medium- (M-) wavelength sensitive cone photoreceptors neglecting the important signals of the short-wavelength sensitive (S-) cones, the rod photoreceptors (responsible for scotopic vision and co-working with the cones in mesopic vision) and the intrinsically photosensitive retinal ganglion cells (ipRGCs). Thus, instead of the luminous efficacy of a source, a combination of HCL relevant descriptor quantities should be used to characterize the light source  including a color rendition index as well as measures of brightness and the circadian effect.
Mathematically, there is a high number of possibilities to combine such HCL relevant descriptor quantities that result from the spectral power distribution of the light source and the electric power. In the present article, just a preliminary proposal of a possible computational method will be described. The aim is to compute a new usefulness measure (abbreviated by UM). By developing this method, the present authors kept the following principles in mind:
- 1. for the sake of a practicable and widely acceptable solution for the characterization of the light source, only a few HCL aspects were selected (from Fig. 1) which are essential for general interior and exterior lighting. This method can be discussed in a subsequent dialogue within the lighting community (lighting industry, lighting architects and facility managers);
- 2. the metrics to describe these HCL aspects were based on well-established and well-known work (e.g. widely-known publications or international standards) to be ready for instant world-wide industrial application;
- 3. in order to combine the selected metrics in a mathematically sound way, the correlations among these metrics were analyzed (in Section 2) for a representative set of 302 absolute spectra (i.e. absolute spectro-radiometric data including luminous efficacy of a source in lm/W) of today’s widely used light sources (obtained with the cordial help of METAS, Switzerland; these are all typical commercial products; see Table 4) to arrive at a two-dimensional concept consisting of a measure of color quality (abscissa) and a combination of a measure of brightness and a measure of the circadian effect (ordinate) of the spectrum of the light source;
- 4. the value of the proposed new usefulness measure (UM) should be application dependent. E.g. if the aim is concentrated work in an office then the UM value of a warm white light source should be very low  because although we input electric energy, the users who would like to work will not be satisfied as they rather need a cool white light source for concentrated working. But the same warm white light source should obtain a higher UM value if it is being used to illuminate a living room in the evening for relaxing . Additionally, the type of application (interior, exterior) and the luminance level in exterior lighting (type of street) as well as the possibility of dynamic lighting should also be considered.
2. Lighting quality metrics of the selected HCL aspects and their correlations
Table 1 shows the HCL aspects selected for the definition of the present, preliminary proposal of the usefulness metric (UM) and their numeric descriptors chosen to be included in the present version and also some other metrics, as possible alternatives. The reason of choosing CIE CRI Ra  as well as the alternative metrics in Table 1 are discussed in Section 5.
As can be seen from Table 1, the aspects brightness, color quality and the circadian effect were selected in the present version of the usefulness metric (UM) method. The concept of brightness shall be understood in the sense of spatial brightness [22, 23] to be described by the quantity Leq = Lv (S/V)0.24 according to Fotios and Levermore  if the light source should be used for interior lighting (Leq means equivalent luminance and Lv means luminance in cd/m2). Here, the symbol S represents the signal of the short-wavelength sensitive human photoreceptors (the so-called S-cones) computed by weighting the relative spectral power distribution of the light source with the spectral sensitivity of the S-cones (with Smith and Pokorny cone sensitivity data ) and integrating in the visible range. The quantity V (so-called V-signal) is obtained by weighting the relative spectral power distribution of the light source with the V(λ) function and integrating in the visible wavelength range.
If the light source should be used for exterior lighting then the quantity Lmes (the mesopic luminance of CIE Publ. 191:2010 ) comes into play instead of Lv (S/V)0.24. When computing the value of Lmes, either Lv = 3.0 cd/m2 (that represents M class streets ) or Lv = 0.3 cd/m2 (that represents P class streets  with 5 lx and with a luminance coefficient of the road of 0.06 cd/(m2 lx) is used as the luminance level in the computational method of CIE Publ. 191 . The reason of choosing Lmes  to describe exterior brightness is that although it was developed from visual performance data, this measure correlates well with brightness  (r2 = 0.86 according to Fig. 4 in ). The mesopic metric Lmes weights rod and cone signals at the characteristic lower (mesopic) luminance levels of exterior lighting while the Leq metric according to Fotios and Levermore  considers S-cones that have a more accentuated response at the characteristically higher (photopic) luminance levels of interior lighting than rods.
The circadian effect is characterized in the present version of the usefulness metric (UM) by the so-called melanopic factor amel computed from the relative spectral power distribution of the light source according to DIN SPEC 5031-100  in the following way: the relative spectral power distribution is weighted by the so-called smel(λ) function  (based on Lucas et al. ) and integrated in the visible wavelength range; and the result is divided by the above defined V-signal of the relative spectrum.
In the correlation analysis (according to principle No. 3 of Section 1), the values of the metrics to be used in UM (listed in the middle column of Table 1) were computed for the above mentioned 302 spectral power distributions. Pearson’s correlation coefficients between these values are listed in Table 2 and four selected relationships are shown in Fig. 2.
As can be seen from Table 2 and Fig. 2, the descriptors of brightness correlate with each other (r≥0.94) and also with the melanopic factor amel (r≥0.92) strongly while the quantity Ra exhibits negative correlation with these measures indicating that these two groups of descriptors (1st group: Ra and 2nd group: Lmes or (S/V)0.24 and amel) should be represented as two different dimensions in the definition of the usefulness measure UM, see Section 3. Latter correlation is negative because Ra prefers a broad spectral power distribution whereas the other measures are higher when the spectral power distribution is concentrated on the shorter-wavelength sensitive region according to the spectral sensitivity of the related retinal receptors. Therefore, the computational method of the usefulness measure should represent a trade-off relationship.
3. Computational method of the new, preliminary usefulness measure (UM)
According to the four principles described in Section 1 and the correlation analysis of Section 2, the new, preliminary usefulness measure (UM) is defined as follows. Input quantities of the computational method are the spectral power distribution of the light source, and the luminous flux (lm) and electric power (W) of the light source. According to the correlation analysis in Section 2, the new usefulness measure (UM) is defined as a two-dimensional quantity (i.e. consisting of a set of two values) to be represented as a point in a diagram with two orthogonal axes (see Fig. 6). A measure of color quality is on the abscissa (UM1). Because of its widespread use today, UM1 equals the conventional CIE color rendering index Ra  in the present version of the method (while in future modifications, CIE Rf  or CQS Qp  can also be considered, see the Discussion). This means that UM1 = Ra in the present version of the computational method.
Because of the low correlation between Ra (that strongly depends on longer wavelengths) and the measures of brightness and the circadian effect (latter two measures depend more on shorter wavelengths), a combined measure of brightness and the circadian effect (as an energy efficiency measure) of the light source appears on the ordinate (UM2) (see Fig. 6). The quantity UM2 is defined by Eq. (1).Eq. (1), Φv is the luminous flux (lm) of the light source and Pel is the electric power (W). As can be seen, energy efficiency is incorporated in this second component (UM2, Eq. (1) by multiplying the luminous efficacy of a source (Φv/Pel) by the compound modification term in the square brackets in Eq. (1). This modification term is explained below.
If the light source should be used for interior lighting then the quantity Leq represents the measure of scene brightness with Leq = Lv (S/V)0.24 according to Fotios and Levermore , and, if the light source should be used for exterior lighting then Leq = Lmes  (as already mentioned in Section 2). To be in favor of dynamic lighting, the value of α in Eq. (1) equals 1.00 if there is no dynamic lighting in the given application of the light source. The value of α equals 1.15 if there is dynamic lighting with correlated color temperatures in the range CCT = 5500 K – 6500 K. Data (relative spectrum, luminous flux and electric power) of the highest available CCT shall be used to carry out the computation in this case.
The factor α = 1.15 is a preliminary value estimated from a previous experiment in which significant positive effect of dynamic lighting on female permanent morning shift workers was found . The present authors calculated the absolute values of the differences of the logarithms of the mean characteristic values of sleep latency, subjective mood rating of anxiety/depression, arousal and heart rate variability between the dynamic and the static conditions from the data available in this publication . In average, the value of 15% was found as a characteristic benefit percentage of dynamic lighting hence the multiplicative factor of 1.15 is used. It should be noted that this is just a preliminary estimate and much more experimental data should be generated and analyzed to arrive at a final solution.
In the present version of the method, the circadian effect of the light source (represented by the value of C in Eq. (1) is not taken into consideration if the light source is used for exterior lighting and this is expressed by setting the so-called decision factor β to zero in case of exterior lighting applications. For interior lighting, β equals 1. For interior lighting, the descriptor of the circadian effect (C) is considered (by the present authors) activating in case of CCT≥3800 K, relaxing for CCT≤3200 K and neither activating nor relaxing for 3200 K<CCT<3800 K. For an activating light source, Eq. (2) shows how to compute the value of the descriptor of the circadian effect (C).Equation (2) means that more activating light sources get a higher C value in the range of CCT≥3800 K (i.e. the neutral white – cool white light sources). In Eq. (2), amel is computed from the relative spectral power distribution of the light source while the symbol amel,0 means the melanopic factor of the reference light source which is defined as a phase of daylight, a blackbody radiator or a mixture of the two. This reference light source is determined (for any CCT) according to the method of CIE Publ. 224:2017  from the relative spectral power distribution of the light source to be evaluated (as a test light source). This method includes “a smooth, linear transition from a Planckian reference to a daylight reference such that at 4 000 K and below it is purely Planckian, at 4500 K it is a 50:50 mix of the two, and at 5000 K and above it is purely a daylight reference.” Eq. (3); unlike Eq. (2) in which amel,0 appears in the denominator. Thus, more relaxing light sources (i.e. warmer white tones) obtain a higher value of C in the range of CCT≤3200 K. Finally, in case of neither activating nor relaxing light sources (3200 K<CCT<3800 K), Eq. (4) shows the way of computing the value of C by mixing Eq. (2) and Eq. (3).Figure 3 shows the values of amel and amel,0 as a function of CCT for the sample set of 302 light sources.
As can be seen from Fig. 3, for most light sources in this sample set amel < amel,0. This means that the light sources exhibit in tendency less circadian effect (in terms of amel) than their reference illuminant. Seven fluorescent lamp spectra between 4000 K and 5000 K (with about amel = 0.9) have a high amount of radiation inside the maximum of the smel(λ) function and they constitute a conspicuous cluster in Fig. 3. Figure 4 shows the value of C for the same sample set as a function of CCT.
As can be seen from Fig. 4, warm white light sources obtain (in tendency) a greater (and positive) C value than neutral or cool white light sources (which tend to have negative C values). The reason is that, in Eq. (3), the quantity amel,0 (the melanopic factor of the reference light source which is in tendency greater than amel) is in the numerator unlike neutral and cool white as in Eq. (2), amel,0 appears in the denominator. A negative C value indicates that the circadian effect of the light source is less than the circadian effect of its reference illuminant thus the light source should obtain a negative circadian evaluation.
Figure 5 shows the descriptor of brightness (Leq/Lv) = (S/V)0.24 and also the modification term in the square brackets in Eq. (1) i.e. the quantity [(Leq/Lv) + C] as a function of CCT for the sample set of 302 light sources. In the example of Fig. 5, interior lighting with no dynamic lighting is assumed i.e. α = β = 1.
As can be seen from Fig. 5, the value of the term [(Leq/Lv) + C] increases in tendency with increasing CCT. It can also be seen that, in the present version of the method, the brightness term (Leq/Lv) prevails but the value of this brightness term is modified (increased for warm white and decreased for neutral and cool white) by the quantity C that represents the circadian effect in comparison with the reference illuminant. The value of C tends to be positive for warm white sources because amel<amel,0 usually holds in case of the present set of 302 light sources (see Fig. 3). Therefore, according to Eq. (3) (for warm white or relaxing spectra), C >0 (see Fig. 4). Thus, by adding the value of C, we get a better score than with the (Leq / Lv) term alone. The reason is that it is advantageous if a warm white light source has less amel than its reference source as the aim is to provide a relaxing environment. But the value of C tends to be negative for neutral and cool white spectra because amel<amel,0 generally holds in case of the present set of 302 light sources (see Fig. 3) and, according to Eq. (2), C<0 (see Fig. 4). This means that we obtain less circadian effect for the present set of 302 light sources (as none of them was circadian-optimized) than it would be possible by conscious circadian optimization. Hence, by adding C (small grey rectangles in Fig. 5), we obtain a worse score in case of CCT>3800 K than with the (Leq / Lv) term alone (see the open circles in Fig. 5).
4. Definition of usefulness categories (A-G). Evaluation of the new usefulness measure for a set of 302 practical light sources
Figure 6 shows the result of a computation of the UM method (i.e. the values of UM1 and UM2) for the above mentioned set of 302 light sources with the preliminary UM category limit values listed in Table 3 and with α = 1 (no dynamic lighting) and β = 1 (interior lighting) in this example. As a last step of the UM method, a usefulness category (A: best; down to G: worst) is determined from the values of UM1 and UM2 of the light source in the UM1 - UM2 diagram by the use of the preliminary category limit values in Table 3.
A light source belongs to the category „A“ if both UM1 and UM2 are greater than the limiting value of the category “A” in Table 3. This means that, in order to satisfy the “A” criterion, both UM1 >UM1(limit,A) and UM2 > UM2(limit,A) shall be true. Such light sources are depicted by dark green empty circles in Fig. 6. The quantities UM1(limit,A) and UM2(limit,A) represent the limits for the category “A” (“best usefulness”) in the present two-dimensional UM concept. This corresponds to a rectangular domain (domain “A”) in the top right corner of the UM1 - UM2 diagram of Fig. 6. The following domains (B-G) are L-shaped areas to the left of and below domain “A”. Light sources of the sample set in domains B-G are depicted by light green, yellowish green, yellow, orange, red and black symbols, respectively. To belong to the category “B”, both UM1 >UM1(limit,B) and UM2 > UM2(limit,B) shall be true but the light source should not belong to domain “A”, etc.
It is important to emphasize that the new usefulness measure UM (Fig. 6) is two-dimensional: every light source obtains two values (UM1 and UM2). The reason is (as mentioned above) that these two measures (UM1 and UM2) do not correlate with each other, and, therefore, two evaluation dimensions are necessary. The UM categories A-G are determined based on this two-dimensional representation. Mathematically, it would be false to use a one-dimensional quantity as a basis of usefulness evaluation and the determination of the categories within this concept.
Figure 7 shows the same 302 light sources with the same category symbols according to the UM method as in Fig. 6 but, in Fig. 7, the ordinate of Fig. 6 was replaced by luminous efficacy of a source (lm/W) values.
As can be seen from Fig. 7, the order of the symbols according to Fig. 6 is disrupted by replacing the UM2 axis by the conventional quantity luminous efficacy of a source (in lm/W) i.e. by disregarding the modification term [α(Leq/Lv) + βC] (with α = β = 1 in this example) in Fig. 7. Light sources of the same category scatter widely in the direction of the ordinate. The reason is that the conventional quantity luminous efficacy of a source is based on the V(λ) function and this function ignores the blue-wavelength sensitive retinal mechanisms (S-cones and ipRGCs in this example) contributing to the brightness response and the circadian response.
Table 4 shows the distribution of the 302 light sources of the example according to light source type and UM category computed with the preliminary category limit values of Table 3. By changing the values in Table 3 (in the computer program developed by one of the authors, QTV), the distribution of the light sources in Figs. 6 and 7 and Table 4 changes. The present UM category limit values shall be the subject of international discussions if such a method is considered in the future for industrial and commercial applications.
As can be seen from Table 4, conventional incandescent lamps are in the category G, compact fluorescent lamps in the categories F and G while the other fluorescent light sources (semi-compact and tube-shaped) obtained a broad range of category assignments between B and G with one tube-shaped fluorescent lamp in the category B. Finally, 14 high-quality LED light sources reached “category A” evaluation. The preliminary UM category limit values in Table 3 were determined computationally to get the predefined percentage values in each category shown in the last row of Table 4. The use of predefined percentage values represents just one possible decision strategy. This strategy and the percentage values themselves should be discussed in the future.
In this Section, the advantages and limitations of the new usefulness measure and the possible use of alternative metrics are discussed. Concerning the general advantages of the method, it should be noted that the increase of electric energy efficiency of lighting is a very important issue today. To quantify energy efficiency, today’s accepted metric is luminous efficacy of a source (lm/W), a quantity which is the result of weighting the spectral radiant flux of the light source by the V(λ) function. But, as mentioned in the Introduction, the V(λ) function over-weights the spectral power distribution of the light source in the range around 555 nm compared to its benefit  for human users.
The new usefulness measure (UM), however, considers all useful wavelengths by the inclusion of a color quality measure (the CIE CRI Ra in the present version) which is in favor of a balanced spectrum with ample yellow, orange and red content; and also the measures of brightness and the circadian effect thus supporting shorter wavelengths. Therefore, if the spectrum of the light source is characterized and then categorized by the aid of the UM method then the efficiency of the conversion of electric energy into electromagnetic radiation is represented in a more comprehensive way than provided by the conventional concept of luminous efficacy of a source. The benefits described by the luminous flux (in lm) of the light source (e.g. visual acuity) remain included via the term Φv in Eq. (1).
Also, the UM efficiency concept includes a possible, preliminary dependence on lighting application (interior or exterior lighting) including a possible way of considering the availability of dynamic lighting. E.g. for “relaxing” applications, the circadian component is in favor of warm white tones and this fosters relaxation and reduces sleep latency in the evening. The labelling of a light source by the new UM categories fosters the productivity of working hours and the satisfaction and life quality of the light source user if a new evaluating system based on the present new usefulness measure (UM) or its modification gains momentum on the consumer market. The way of communicating the UM method for the labelling of lighting products for non-experts and the subsequent legislative procedure are difficult tasks. A diagram like Fig. 6 is surely not appropriate to this purpose and a huge amount of additional committee work is required.
As seen from Table 1, the descriptor quantities of the following HCL aspects were combined in the usefulness metric (UM): brightness, the circadian effect and color quality; and, implicitly, via the term Φv in Eq. (1), also a further aspect, visual acuity. As mentioned in the Introduction, only some selected aspects were considered in the present version and only those aspects that can be described based on the spectral power distribution of the light source. The presence or absence of disturbing tints (e.g. greenish or purplish shades) in the perceived white tone of the light source , for example, was not included in the method because manufacturers tend to avoid such white tones especially by the use of appropriately tight LED chromaticity regions (so-called “bins”) in recent times. The present UM also ignores the issue of (intercultural) white tone preference (see e.g .).
Concerning the alternative metrics (see the last column of Table 1), Berman’s metric  i.e. Leq = Lv (R/V)0.5 (with R being the rod signal to be computed by weighting the relative spectral power distribution of the light source by the scotopic luminous efficiency function) was not used because (unlike Lmes of CIE 191:2010 ) this metric (a forerunner of Lmes) does not weight rod and cone contributions at different mesopic levels differently. To compute brightness in the photopic range, the Fotios and Levermore  metric was chosen because it is experimentally well-established and also due to recent experimental evidence about the appropriateness of the S-cone signal to describe another important attribute, visual clarity , in the photopic range. The present authors did not use the CIE Leq metric  because its accuracy was problematic when predicting their own recent visual brightness experiment results (this issue will be dealt with in another article to be published later).
To characterize the circadian effect, the melanopic factor amel  was used. In future possible modifications of the present, preliminary version of the UM method, the circadian stimulus (CS) [21,30–32] is the most important alternative. The CS scale was tested and verified in recent field studies . CS accounts for the interactions of the rod and cone signals with the signals of the intrinsically photosensitive retinal ganglion cells (ipRGCs) and also for spectral non-additivities. The melanopic factor amel does not take the neurophysiology and neuroanatomy of the retina nor the operating characteristics of the circadian system into account . Despite this known deficiency, amel was chosen in the present version due to its simplicity; this is important for practical lighting design and illumination planning. Figure 8 compares the two measures (amel and CS) in case of the sample set of 302 light source data. To compute the data of Fig. 8, seven different illuminance levels between 10 lx and 1000 lx were considered and CS and log10(amel Ev) were computed for each one of the 302 light source spectra and for each illuminance level.
As can be seen from Fig. 8, although the quantity log10(amel Ev) is able to describe the tendency of the CS data in case of this set of 302 light source spectra (r2 = 0.95), in some cases, deviations from the mean tendency in the order of max ΔCS = 0.08 occur (latter error value can cause a significant error in the applications ).
Concerning color quality, CIE CRI Ra  is used in the present version of the UM method due to its worldwide acceptance and universal implementation today. In the future, the CIE 2017 color fidelity index (CIE Rf)  can be considered instead. This index is intended only for “scientific use” at the moment, therefore it was not included in the present (application oriented) version of the UM method. To incorporate color preference characteristics which are more relevant for general lighting than color fidelity and deviate from the color fidelity framework (see e.g [8, 19, 33].), the color quality scale metric CQS Qp  can be applied as an alternative metric in the future to replace Ra because Qp performed reasonably well in recent visual color preference experiments .
Unfortunately, CQS Qp (which correlates better with visual color preference characteristics than CQS Qa) is not so well known and it is not incorporated in international standards. Although the measures of color gamut (IES Rg  and CQS Qg ) do not correlate well with the other considered color quality metrics (this was shown in an additional computation in case of the 302 light sources) thus representing a possible third “usefulness” dimension, a gamut measure was not included in the UM method because a (standalone) color gamut metric is in favour of oversaturating the colored objects of the lit scene and this is not preferred by the users in general lighting applications .
A new, preliminary usefulness metric (UM) was defined to characterize the energy efficiency of light sources instead of the conventional quantity of luminous efficacy of a source (in lm/W units) by taking some selected aspects of human centric lighting (HCL) into consideration. In the present preliminary version of the usefulness metric, only some selected spectral properties of the light source were taken into account. Thus, UM should be considered as a basis for further discussions and not as a final solution. The new UM is a two-dimensional metric with two orthogonal components, UM1 and UM2. According to a correlation analysis of selected well-known light quality metrics for a representative set of widely used light source spectra (see Section 2), two basic types of metrics were found; those that (also) depend on longer wavelength components (color quality metrics) and those that (primarily) depend on shorter wavelength components (metrics of brightness and the circadian effect).
The first component, UM1 (which is the conventional CIE color rendering index CRI Ra in the present version of the method due to its widespread use today) describes the color quality of the light source. As it is assumed that (above a certain illuminance level) color quality does not depend on the amount of electric energy consumed, UM1 does not depend on input electric power (Pel). The second component (UM2) is an application dependent combination of a descriptor of brightness (from Fotios and Levermore  for interior lighting and CIE Lmes  for exterior lighting) and a descriptor of the circadian effect (the so-called DIN melanopic factor ). The dependence on luminous flux was preserved in Eq. (1) in order to retain a correlate of the spectral dependence of visual acuity. Application dependence means (in the present version) that the value of UM2 supports warm white light source spectra for more relaxing applications while it supports neutral and cool white spectra for activating applications. It is very important to extend the application dependence of the present version of UM in the future in order to account for a broader range of possible lighting applications.
The definition of the UM categories (A-G) that characterize the usefulness related to electric energy consumption is intrinsically two-dimensional; according to the above mentioned correlation analysis. Mathematically, the use of a one-dimensional quantity to determine the UM category limits is pointless because there are (at least) two dimensions underlying the usefulness of light sources. Finally, it should be mentioned that the way of communicating the new usefulness measure towards non-experts is a difficult procedure and this is out of the scope of the present article. Here, only an application-oriented scientific viewpoint is described. This can be discussed and modified by the use of alternative metrics, more application dependence, other category limit values and a user-friendly product labelling diagram in the future. For the experimental validation of UM, we need the results from extensive long-term field studies in different lighting applications about the long-term circadian effect combined with short-term user acceptance data.
Federal Ministry for the Environment, Nature Conservation and Nuclear Safety (Germany) represented by the Federal Environmental Agency, Germany (UBA) Project 37EV 16 123 0.
Authors would like to acknowledge the kind help of Dr. Peter Blattner (METAS, Switzerland) for sharing the data set of 302 light sources.
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