Handling of melanopic quantities

Part 2 - calculating back and forth

Last week, in part 1 of this brief series of posts I have introduced you to melanopic equivalent daylight illuminance MEDI and the melanopic daylight efficacy ratio MDER which characterizes different light sources relating to their potential to elicit melanopic effects on humans.

But in your daily practice, you will not always find exactly those data values which you need for your plannings or for evaluations of light.

Therefore I am posting three little tables today, which will allow you to calculate back and forth from and to MEDI, MDER, or other quantities used in this context. In addition to MEDI and MDER, there is the melanopic action factor a???,? which is not based on the photometric scale of illuminance, but on the energy-related scale of irradiance, and other quantities, which are mainly used in US publications and in older scientific papers. Latter two are the well known “melanopic lux” and the M/P ratio, also abbreviated as MR.

For starting, please read some comments on these quantities.?Please note, that writing with subscripts as index is not supported by the LinkedIn editor. I have used a workaround-tool, which is not really perfect. What looks strange in the written text is meant as index. I have added the tables as image files for the accurate writing.

a)??????E? is the illuminance, measured at the eye of an observer. It is the standard photopic illuminance, which is calculated by weighting the spectrum with the V(λ) function, what gives the irradiance and multiplying the result (the irradiance) with the luminous efficacy of radiation 683?lm/W. This is well-known standard. For non-visual effects, it is important to measure at the user’s eye, and therefore E? is usually the vertical illuminance in a room. The unit for E? is lux, abbreviated lx.

b)?????MEDI is the melanopic equivalent daylight (D65) illuminance. The correct symbol is E?,???,????. The unit for MEDI is also lx. MEDI of any light source S at a specific illuminance level E?,? is equal to the illuminance E?,???,???? of daylight D65 which would create the same melanopic irradiance at the user’s eye as the light source S at E?,?.

Mathematically the melanopic irradiance is achieved by weighting the spectrum with the s???(λ) function. Multiplying the melanopic irradiance with the melanopic daylight equivalent of 754.03 lm/W gives the value of MEDI.

754.03 lm/W is the reciprocal of the melanopic efficacy of luminous radiation of daylight D65, which is 1.3262?W/m2.

c)?????MDER?is called the melanopic daylight efficacy ratio and is defined as the ratio of MEDI to E?. The symbol is ?????,?,????. MDER has no unit, as two quantities each having the unit lx are divided by each other. So the unit gets reduced. For daylight D65, MDER is 1.0.

d)?????The melanopic action factor a???,? is the ratio of melanopic irradiance to photopic irradiance.

Irradiance is measured on an energy scale in W/m2. By the division the unit is reduced and thus a???,? has no unit. For Daylight D65 the value of a???,? is 0.906.

e)?????The unit “melanopic lux” was introduced in 2013 and adopted quite quickly by scientists and practitioners. There was a need for measurement and assessment of melanopic quantities.

In the framework of standardization, it turned out that melanopic lux is not compliant to the SI system and to other metrics as defined by CIE. Therefore MEDI (melanopic EDI) has been introduced and melanopic lux was dropped. Mainly the formal reason that the SI system does not allow the definition of new units was responsible for this; not any scientific or other severe error.

It still continues to be used with a decreasing level of usage and relevance. The need to calculate from melanopic lux to MEDI is persistent, because many of the publications on non-visual effects of light from 2013 to 2019 have used melanopic lux.

Melanopic lux is achieved by first calculating the melanopic irradiance in the same way as described in b) by weighting the spectrum against the s???(λ)-function. The value of the ?irradiance (in W/m2) ?is multiplied by a factor of 832.1. Both without using a unit. Melanopic lux has no unit. The reason for a different factor as used in b) is the fact that for melanopic lux, an equi-energy spectrum has been used as reference spectrum, while for MEDI, the daylight D65 spectrum is used. Melanopic lux is 1103.75 at an illuminance of 1000 lx with daylight D65. Use MEDI and avoid melanopic lux in your own work.

Recently the abbreviation MEEI has come to use. It stands for melanopic equivalent equi-energy illuminance. If the hypothetical equi-energy spectrum with the same spectral irradiance at any wavelength is used as reference spectrum instead of daylight D65, the same calculation procedure as for MEDI can be applied and MEEI gets the same value as melanopic lux. This allows to save old documents which used “melanopic lux”. In my opinion a “quick and dirty trick”, which I don't recommended even if it is compliant with CIE S 026, because it may create additional chaos among practitioners. In principle you could define a melanopic equivalent illuminance, based on any existing illuminant as reference spectrum. But it would be chaotic for the user to understand the meaning of it, how to calculate it and the reason why not daylight is being used. You may end up with ten or more different MEXI, where X stands for an illuminant.

f)???????The M/P ratio, often used in the US, abbreviated MP or MR is used in most cases as the ratio of melanopic lux to photopic illuminance E?. Regarding the function, it is corresponding to MDER, while not using MEDI, but melanopic lux. In the following tables I have used this definition.

Unfortunately there is no standard which defines exactly what the M/P-ratio is. Sometimes MP is calculated differently on an energy scale by dividing melanopic by photopic irradiance. Then MP is equal to a???,?.

There are even other definitions in use for MP. Better avoid using it, because of lack of a clear definition in a standard and instead use MDER.

In a similar trick as mentioned in e), the abbreviation MEER has been introduced for melanopic equi-energy efficacy ratio. It is the ratio of MEEI to E?.

For using the tables, you simply look in the left column to the quantity which should be the outcome of your calculation. In the middle or right hand column you look for the quantity which is available to you.

The numbers in the tables are showing the results under the assumption that an illuminance of 500 lx is effective at the eye of an observer. The different illuminants are two LED sources as used in the LEDVANCE BIOLUX system for warm-white (2700 K) and cold-white light (6500 K), the CIE LED-illuminant B3 with a CCT of 4100 K, as defined in CIE 15 - 4th edition, and standard illuminant D65, also with a CCT of 6500 K.

Table 1 is if you have E? or MEDI available

Table 2 is if you have MDER or a???,? available

Table 3 is if you have melanopic lux or MP available.

Table 1: from E? or MEDI to other melanopic quantities

?Table 2: from MDER or a???,? to other melanopic quantities

Table 3: from “melanopic lux” or MR to other melanopic quantities