Cycles, unit of light energy ATTN: Brecht

Thought I’d try and dust this godforsaken answer off once and for all.

Q: What is the unit of measurement of light energy in Cycles?

This has been asked of me far too many times, and a quick Google search reveals even more. Couple that with completely confused folks conflating watts with electrical watts, and photometric units that are completely wrong, I thought I’d step up as formal idiot and try to get a clear answer. I believe @brecht is the only person who can answer this conclusively.

To the best of my knowledge, we divide “energy” up into four classes, only two of which are relevant to a path tracer:

  1. Radiance
  2. Irradiance
  3. Luminance
  4. Illuminance

First, the difference between the terms and their “ir” counterparts. The “ir” prefix typically refers to exitant values. The non-“ir” values are incident. That is, in layperson’s terms, outgoing versus incoming in relation to a surface.

Second, Luminance and Illuminance are photometric units, meaning they are psychophysical and wound up with more complex ideas of spectra. Therefore, the terms and concepts are not relevant to this discussion.

That leaves us with radiance in Cycles. In the documentation, the unit of measurement is listed as watts per square meter, which I believe cannot be the appropriate definition as it would be missing the geometry aspect to calculate the energy. I believe the correct unit here is watts per square meter per steradian, which is the traditional unit of measurement for radiance by all accounts.

So, once and for all, is the base unit of light energy indeed the radiance based watt per square meter per steradian @brecht?

Thanks so much.

Additional Question: Given there are different classes of lights, it also stands to reason that the units of energy vary between them. Is this the case?

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It’s indeed Watts per square meter per steradian.

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I love you. Thanks so much.

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Note that most lights in Cycles use Watts, since what is specified is the total energy emitted over the entire area of the light in all directions. The total energy does not change if you scale the light. It is however modulated by color and shaders so the effective Watts will be typically be lower unless that’s purely (1,1,1).

It’s W/(m^2) for sun light and W/(m^2 . sr) for emission values in (surface) materials.

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So for spot lights it is the total energy that would be emitted if it were not limited by the spot angle? I can see why it makes sense to have them match point lights, and the trade off is that the number of W set to be emitted is not the number of W actually emitted. Is that the case?

Yes, that’s how it works for spot lights.

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I find that when discussing radiometric energy, it’s wise to think in terms of “flow” and “area”, much like electricity has “amps” and “volts”; two interrelated mechanics.

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I am a bit confused about the sun unit being Radiance. It really looks like it’s Irradiance (Watts/m2) otherwise we would be using 15.4 MW to get any light from it.

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Brecht confirmed the units above, clearly.

Well, I was going off my memory, I’d have to dive into the code to double check.

Is it the same for the world environment (the 360 degree environment) Background node?

I have worked on adding physical light units in my add-on and from all my tests and conversions, it really looks like sun strength is in irradiance.

The rest is in radiance. And I added an advanced power unit that does support the angle of emission, so people have the choice to use it or not.

It would seem challenging to evaluate anything in Blender based on numbers given there is no correlation to ISO via 12232:2019 expressed anywhere, so any evaluation is missing a critical ground truth. It would also lead to a discontinuity in units given there is only one input area.

At any rate, unless @brecht explicitly states differently, these discussions loop in circles.

Without talking about absolute radiance (which can be compared with other softwares that do follow ISO standards), it’s very possible to compare the brightness of a point light of which the radiant flux is known with a sunlight.

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I’m pretty sure it is the opposite for Irradiance: it is the power received per unit area of surface as explained here https://en.wikipedia.org/wiki/Irradiance. So it is an incident quantity, not an exitant one (also the case for Illuminance). The exitant equivalent of Irradiance is Radiosity as described here: https://en.wikipedia.org/wiki/Radiosity_(radiometry). Irradiance can be expressed as incident Radiance integrated over the hemisphere, while Radiosity is expressed from integrating Radiance over the hemisphere.

Wikipedia gives a quite comprehensive table of radiometry units: https://en.wikipedia.org/wiki/Radiometry.

Also the PBRT book gives a good explanation of the quantities mostly used in rendering: http://www.pbr-book.org/3ed-2018/Color_and_Radiometry/Radiometry.html

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It was likely a tad of an oversimplification on my part regarding the “i” components. Radiance is essentially the flux density per unit solid viewing angle. Irradiance is per unit area.