# How can you have a scene linear reflectance greater than 100%?

Started 3 months ago | Questions thread
Clouds, Mie scatter and log gamma

Mandem wrote:

Interesting. So what about the claimed 90% reflectance for white paper? Also, why use optical brighteners to begin with?

So that the paper looks brighter. Some people like that.

It's just that it's so unintuitive having reflectance percentages greater than 100%(in this case going all the way up to 1400%-ish in the graph) as it doesn't really make sense(you can only reflect a 100% of light). Perhaps, as someone alluded above, it has to do with diffuse and spectral reflectances and even incident and reflectance all being considered together in 1 graph.

I' m gonna try and explain this conundrum with an example. Imagine we have a frame where we are OUTSIDE and we can see:

-The sun at noon(Incident)

-Clouds(reflects)

-A caucasian person(reflects)

-White Paper(reflects)

-18% middle gray card(reflects)

Now in many measurements the clouds(especially ones close to the sun) will have a reflectance % significantly above 100%, whereas white paper will be somewhere 90-100%

What makes you say that the clouds will have reflectance greater than 100%? As you point out, the total light scattered cannot exceed the total light incident.

It is true that the angular distribution of light scattered by individual water droplets is not Lambertian, but is predominantly in the forward direction.  Mie scattering dominates for typical droplet sizes in the 1-30 µm range.

Having said this, I would expect light scattered from clouds 30 degrees or more from the sun to be approximately Lambertian, but I don't have any hard data on this.

but the problem is they're both being lighted by the sun thus have the same amount of light falling on them. So if a sun is giving out an X amount of light it doesn't make sense that white paper will reflect 0.9X,18% gray will give 0.18X, whereas the clouds will be anywhere from 2X-30X(Just making up random numbers here) you can't reflect more than X itself(I.e above 100% reflectance) is what's tripping me up.

Have you compared the intensity reflected from clouds with the intensity reflected from a sheet of white paper in direct sunlight - perhaps using a camera in "spot metering" mode?

It may be simply that the clouds appear brighter against a blue sky background. Unfortunately, it is too overcast where I am at present for me to confirm this.

Hope I managed to explain myself. Perhaps the individual who made LUTCALC is using some standard that I'm unaware of.

You don't give sufficient information on what LUTCALC is trying to do, but one of the reasons for recording video with a logarithmic tone curve is to capture a wide dynamic range with a limited number of bits. For example you might wish to video someone sitting in the shade of a tree, and capture decent shadow detail at the same time as recording subjects in full sunlight without signal overload.

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Alan Robinson

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