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By Sam Berman, HFIES

Senior Scientist Emeritus Lawrence Berkeley National Laboratory

and

Robert Clear, FIES

Staff Scientist (Retired) Lawrence Berkeley National Laboratory

#### Abstract:

During the past two decades, the lighting community has come to recognize that retinal photoreception extends beyond rods and cones, and includes a small number of intrinsically photosensitive retinal ganglion cells (ipRGCs) with their own unique spectral sensitivity. In this dialogue we provide a simple method for incorporating the metrological consequences of this sensitivity into lighting practice.

#### Background:

The total number of these ipRGC cells is estimated for humans to be between 4,000 and 8,000, compared to many millions of rods and cones [Liao et al 2016, Nasir-Ahmed et al 2017]. These cells are capable of responding to light even in the absence of rod or cone input because they contain the opsin photopigment known as melanopsin. They are specialized for responding to ambient levels of light (irradiance) for a wide variety of primarily non-image-forming light effects. These include synchronization of circadian clocks to light/dark cycles, regulation of pupil size, sleep propensity, pineal melatonin production, and scene brightness perception.

Present anatomical research studies show that these melanopsin cells are distributed across the retina with a slightly greater concentration from 2 degrees to 4 degrees of eccentricity than at higher eccentricities, while being essentially absent in the fovea [Dacey et al 2005, Nasir-Ahmed opt cit]. Although the ipRGCs are not present in the fovea, melanopsin is active at photopic light levels. The ipRGCs are also reported to be active even at scotopic levels [Sonoda et al 2018], albeit with a different spectral sensitivity than that of either the rods (scotopic sensitivity) or the cones (photopic sensitivity). The spectral response of melanopsin, M(λ), peaks in the bluish region at about 488 to 490 nm. This is shown in **Figure 1**, with the peak sensitivity normalized to unity [Lucas et al 2014, CIE 2018]. For visual comparison, the scotopic and photopic sensitivity functions are also shown in **Figure 1** normalized to unity at their peak wavelengths.

#### Some History:

Calibration of light meters is based on the photopic spectral sensitivity function, V(λ), which is normalized at its peak wavelength of 555 nm to the value of 683. This normalization, based on historical considerations, defines the psychophysical unit of the lumen as 683 lumens per watt of physical light power at 555 nm. The complete V(λ) function is determined by several psychophysical methods under conditions where the test lighting is confined to the central fovea, thus ensuring uniquely cone-receptor responses as there are no rod or melanopsin receptors in the fovea. On the other hand, especially at lower light levels (mesopic levels), natural visual scenes can be affected by rod receptor responses, whose inclusion is captured by the scotopic spectral sensitivity function. The traditional method for incorporating such spectral consequences is to retain the canonical definition of the lumen as above and include the scotopic spectral sensitivity by adjusting its normalization to have the defined value of 683 lumens at 555 nm. Because the peak of the scotopic sensitivity function occurs at the lower wavelength of 507 nm, the result of applying the canonical normalization is that the peak value of the scotopic sensitivity function at 507 nm becomes 1,700.

Thus, when characterizing spectral properties of light sources of varying spectral power distributions (SPDs) it should be noted that they will have both a photopic content (P) and a scotopic content (S). For those sources where the SPDs are intensity independent, it is especially useful to characterize such spectral properties in terms of the intensity-independent ratio S/P, which is a unique property of the SPD [Lighting Research Center 2009]. Catalogs of source properties often include S/P values among other spectral properties.

#### Melanopic Normalization:

Despite the fact that the definition of a lumen as a standard can be readily applied to other photoreceptor responses to radiant energy, such as the recently discovered melanopic response, we believe there are strong reasons that this photoreceptor spectral response should instead be quantified by *melanopic effective watts*. Melanopic effective watts are currently defined analogously to photopic lumens but with the substitution of V(λ) by the melanopic sensitivity function normalized to unity at its peak wavelength sensitivity of 490 nm. Melanopic effective watts are defined explicitly by **Equation 1**, where **S(λ)** is the SPD of the source and M(λ) is the melanopsin sensitivity function (see **Figure 1**):

M(S) = ∫S(λ)M(λ)dλ **(1)**

This approach is intuitive, and being based on a standard physical unit it has a number of other practical advantages. One comes from the fact that current estimates of the melanopic sensitivity function are based on a standard template employed to fit the data over a relatively small number of wavelengths [Govardoskii et al. 2000, Brainard et al. 2001, Thapan et al. 2001]. The accuracy of this procedure is likely to be far less at wavelengths where the relative sensitivity is low, than near the peak sensitivity. Any future changes in the estimated sensitivity function are therefore likely to have significantly larger effects on calculated melanopic-lumen values than on calculated effective-watt values [Berman/Clear 2019].

If the peak value as a function of wavelength of a visual sensitivity function is normalized to unity, then the values at the other wavelengths are directly a measure of their efficiency for the visual pathway in question. The integral over all visible wavelengths of the product of the sensitivity function, normalized in this manner, and the spectral power distribution of a given source yields the biologically effective wattage of the source.

This procedure has several advantages over methods based on lumens. It is by far the simplest procedure. It has an intrinsic meaning that makes for easier interpretation, in that the ratio of effective watts to input watts is a direct measure of relative biological efficiency. Because these ratios are actual efficiencies, the relative values for different sources are a direct measure of the efficiency of a given source in stimulating such a biological response. This is not possible using lumens and efficacies such as lm/w, because each of these quantities has a different maximum efficacy. Finally, effective watts do not reach extreme high values and they are not likely to be confused with photopic or scotopic measures.

In addition, note that the use of effective watts is not without precedent as it is used to quantify the stimuli for blue-light and ultraviolet (UV) hazards [Chaney/Sliney 2005, Olino 2011], and has been recommended by the CIE for nonvisual effects of ocular radiation [DIN 20015].

#### The Melanopic-Photopic Ratio (M/P):

For any SPD, and analogous to the spectral factor S/P, the ratio M/P is introduced here as the melanopic spectral factor associated with that SPD. The numerator M is given by Equation 1, and the denominator is the net lumens for the same SPD calculated by replacing M(λ) in Equation 1 with V(λ) normalized to the value 683 at 555nm. For most common sources S(λ) is provided in units of milliwatts per nanometer (nm) and thus by applying Equation 1 the quantity M/P will have the dimensions of effective milliwatts per lumen. For nominally white sources, this definition yields M/P ratios in the vicinity of 1. **Table 1** lists M/P values for a few well known sources based on known SPDs and the Lucas et al. and CIE values for M(λ).

**Table 1. Some Representative Source M/P (Effective Milliwatts per Lumen) Values Based on Lucas et al (2014) Values for M(λ).**

Source | CCT (K) | M/P |
---|---|---|

High Pressure Sodium | 1960 | 0.24 |

Incandescent Lamp, 100W | 2810 | 0.64 |

LED | 3855 | 0.82 |

Metal Halide | 4000 | 0.73 |

Sunlight | 4889 | 1.12 |

Equal Energy White | 5460 | 1.20 |

CIE Illuminant D65 | 6500 | 1.33 |

#### Understanding the M/P Value:

The M/P ratio, introduced here as effective milliwatts per photopic lumen, is numerically identical to the term *melanopic efficacy of luminous radiation* defined in CIE S 026:2018 and listed in Table A.1 in that document. However, we strongly object to defining that quantity as melanopic efficacy, because common engineering practice identifies photometric efficacies in terms of lumens. This misinterpretation can lead to measurements being erroneously labeled as “melanopic lux” that were determined by multiplying photopic lux by the factor M/P. Such a computation does not yield “melanopic lux.”

However, if “melanopic lux” is nevertheless desired, it can be computationally obtained by renormalizing the M(λ) of Figure 1 at the wavelength of 555 nm, given by CIE S 026 (2018) as 0.1621, to the value of 0.683 mW/lumen. In which case, computationally, “melanopic lux” = (0.683/0.1621) x melanopic effective milliwatts = 4.213 x melanopic effective milliwatts = 4.213 x (M/P) x photopic lux.

Note that M/P values for a wide range of sources can be estimated to within 3% of their actual value from their S/P values by employing **Equation 2** [Berman and Clear 2019]:

M/P = [(0.41212 x S/P + 0.45827) x S/P] – 0.07428 **(2)**

Table 1 lists some representative M/P values, and **Figure 2** shows that a rough M/P estimate for whitish sources can be made from their CCT values.

Note that the M/P value (in milliwatts per lumen) can be useful for providing an estimate of the relative melanopic efficiency at a fixed photopic output for a source, thus providing an immediate path for application in the absence of a melanopic meter.

#### Elementary Example of Using M/P:

If 2 sources S_{1} and S_{2} having different M/P values are required to produce the same melanopic output i.e. M_{1}=M_{2}, then it follows algebraically that the ratio of their respective photopic outputs P_{1}/P_{2}, is provided by:

P_{1}/P_{2} = [(M_{2}/P_{2})/(M_{1}/P_{1})] **(3)**

Because Equation 3 is based on ratios of M/P values, the resultant P_{1}/P_{2} value in Equation 3 is independent of the value at which M is normalized.

#### Fundamental Concerns about CIE S 026:2018:

The CIE devotes several sections and two appendices of this document to the calculation of what they referred to as the α-opic equivalent daylight (D65) illuminance (or luminance), where *α-opic* stands for any of the five photoreceptor responses, including that of melanopsin [CIE S 026:2018]. This “equivalent” illuminance is the photopic illuminance of a reference D65 source that has the same melanopic output as a test source. This output is treated as an illuminance and “expressed in lux,” but this quantity is not a lux value in the standard sense—i.e., the source spectral power distribution weighted and integrated against the photopic sensitivity function. This discrepancy is readily seen in that one watt/m^{2} of 555-nm radiation is by definition 683 lux. The “equivalent lux” is defined as the as melanopic effective radiation at this wavelength divided by the melanopic D65 efficacy ratio. The melanopic equivalent lux can be computed from Table 2 of CIE S 026 2018 as 162 W/m^{2}, and the melanopic D65 efficacy ratio is listed in Section 3.10 (and in Table 1, above) as approximately 1.33. This yields 162/1.33 = 122 melanopic equivalent lux for D65. This is clearly not a traditional illuminance.

Historically, the use of reference sources was needed for direct visual comparison in the development of photopic illuminances, and as well the photopic sensitivity function. However, present day technology has eliminated the need for a reference source in the determination of the melanopic and other sensitivity functions. It is the biological sensitivity function and not a reference source that is the fundamental quantity. The calculation of equivalent illuminances adds unneeded complexity and—given that it is not actually a luminous flux with units of lux—confusion. Sources can easily be matched in biological effectiveness, and evaluated in terms of efficiency in providing standard photopic illuminances (Equation 3) without a need to compute equivalent D65 illuminances. In the interest of simplicity, we strongly suggest avoiding the calculation of equivalent D65 lux as a standard practice.

#### Additional Examples Employing M/P:

Another application for the use of M/P values is provided when the visual outcome depends on both melanopic effects and photopic light levels. For example, it has been shown that the factor (M/P)^{n} as a multiplier of the photopic light level can provide excellent correlation with the data on both pupil size variation and scene brightness perception over a wide range of photopic conditions [Schlesselman et al. 2015, Berman 2008, Berman and Clear, 2019]. In these correlations, the exponent *n* depends on both the visual effect and the viewing conditions. For example, it is well known that the perception of scene brightness for whitish lighting, i.e., the brightness perception of a large space rather than a specific object, will depend on both the spectrum and the photopic light level of the ambient light [Levermore 1994]. This is because, at the same photopic illuminance level, ambient lighting with a more bluish tint will appear brighter due to the influence of melanopsin signals. Recent studies have shown that using the quantity P(M/P)^{0.33} in place of P alone provides an excellent correlation to the experimental data [Schlesselman et al. 2005]. The multiplicative factor (M/P)^{0.33} takes into account the melanopsin effect that comes into play when spatial brightness perception is observed across different spectra, even at the same photopic illuminance. This effect can be significant when comparing sources such as HPS with cooler-toned LED sources. For instance, based on the values in Table 1 (above), 3 lux of HPS will be perceived as about the same brightness as 2 lux of the listed LED (3 x 0.24^{0.33} = 1.87 = 2 x 0.82^{0.33}).

Light-driven pupil size variations are also known to be influenced by both photopic and melanopic factors [Berman et al. 1992, Tsujimura et al. 2010, Vienot et al. 2010, Adhikari et al. 2015]. As mentioned above, the combined influences can be correlated by the factor P (M/P)^{n} , where in this case the exponent *n* depends on the field of view exposed to the test lighting conditions. For two conditions studied, namely a full-field exposure or a full field excluding the fovea, the exponent n has the values 0.609 ± 0.003 and 0.788 ± 0.004, respectively [Berman and Clear 2019]. The larger exponent for the fovea-less condition is consistent with a more dominant melanopsin contribution, compared to cone receptors, as a consequence of the presumed absence of melanopsin in the retinal fovea.

Smaller pupils generally provide better acuity. Since the exponent for pupil size is larger than that for brightness, the light level differences between sources become even more significant when acuity is a consideration. A warehouse lit to 212 vertical lux of HPS gives the same pupil size as the same warehouse lit to 100 lux with the LED source from Table 1 (212 x 0.24^{0.609}) = 89 = (100 x 0.82^{0.609}), and is thus nearly equivalent in terms of acuity.

More details and discussion on these applications as well as further amplifications on the topics discussed here can be found in Berman and Clear 2019.

#### Conclusion:

The discovery of melanopsin receptors was a truly revolutionary event in our understanding of the visual system. In this posting we have articulated how employing effective melanopic mW/lumen, and the spectral factor M/P, as a means for quantifying melanopic source efficacy and melanopically related visual experiences integrates this new knowledge into lighting practice in a straightforward and successful manner.

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