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

Started 3 months ago | Questions thread
alanr0 Senior Member • Posts: 2,484
Reflectance & scatter - why solid angles matter

Mandem wrote:

alanr0 wrote:


There is no mysterious physical process. It is simply a way to describe how the video signal represents different brightness levels.

So i'm guessing it is indeed "sloppy terminology" and a misnomer when they say "reflectance" . That would make sense as the formula for Reflectance=Reflected Light /Incident Light just doesn't work in any scenario as, like I said previously, it can't go past a 100% unless brighteners are involved.

It can make sense if you clarify what we mean by "reflected light" and "incident light". One source of confusion is failing to account for the directional properties of the incident and reflected light.

The SI system defines a whole zoo of different units used in photometry. The trick is to choose appropriate metrics for the situation you are analysing.

Instead of luminance, or illuminance, think in terms of the luminous flux (measured in lumen) reaching a defined area of the surface. If all of the incident photons are reflected in whatever direction, the ratio reflected flux / incident flux is 100%. If half the light is absorbed, and half reflected we have 50% reflectance.

Ignoring oddities such as fluorescence, this works for any surface.

The talk about diffuse reflectance and specular reflectance is starting to make more sense in the context of the intensity of light(what we'd call candelas/m2 or nits) hitting the sensor and that THIS IS what the "reflectance"(confusing misnomer) of the x-axis is actually referring to that gets converted into a digital code value(The ADC conversion process )

To make an example(and please correct me if I'm wrong. God I hope I'm not wrong... ), say we have a camera outside in an open field, at noon, facing head on a 100% diffuse reflective white paper and a mirror right next to it. Both the paper and mirror have incident light from the sun hitting them. Consequently, both are reflecting a 100% of the light incident on them. The fundamental difference arises in the fact that the diffuse reflective paper is scattering the light everywhere hence resulting in significantly less light intensity hitting the sensor as opposed to the mirror where the light rays are all directional towards the sensor thus a much stronger intensity of light is landing on the sensor.

OK, let's plug in some numbers:

Seen through the atmosphere at noon, the luminance of the sun is around 1.6·10⁹ cd/m².

The angle subtended by the sun is roughly 0.53 degrees. For a circular disk, this corresponds to a solid angle of 0.000067 steradian (67 µsr).

The illuminance reaching our surface is: Ev = Lv Ω = 108000 lm/m²

For an ideal diffuse reflector (reflectance R=1), the incident light is scattered into solid angle 2π steradian. When we take into account the cosine inclination factor, the surface luminance, Ls = R Ev / π = 34000 cd/m² (lm/sr/m²).

In contrast, with 100% specular reflection, if the camera is in the reflected beam, it sees the full 1.6·10⁹ cd/m² of the sun's surface, which is around 47000 times brighter.

In practice, it can be useful to measure specular and diffuse reflections from the same surface independently. Suppose we replace our diffuse reflector with white gloss paint.

We have specular reflection of 4% from the glossy surface.

The remaining 96% of incident light is transmitted and suffers 90% diffuse reflection by the white pigment.

Of the incident light, 9.6% is absorbed, net diffuse reflectance is 86.4%, with 4% specular reflection.

In noon sunlight, we have 29400 cd/m² diffuse emittance, and 65000000 cd/m² in a narrow specular reflection beam 0.53 degrees wide - now only 2200 times brighter.

Which finally brings me to the formula:

"Reflectance" = Object Reflected or Incident Light Intensity / 100% diffuse reflected white paper Light Intensity.

Edit:perhaps instead of saying "Light Intensity" it would be more clarifying just to say Luminance (Candela/m2)

Thus, in cases where the light intensity is greater than 100% diffuse white reflector we get above 100% "reflectance" (again awful misnomer) values.

Calculate using any of

  • reflected / incident luminous flux (lm)
  • reflected / incident luminous energy (lm.s)
  • ratio of reflected luminous excitance / incident irradiance (lm/m²).

and you are good to go.

Luminous intensity (cd = lm/sr) and luminance (cd/m² = lm/sr/m²) can be used for specular reflections, but not when the angular spread of the incident light is different for the reflected light.

Am I correct? Even if I'm not. I'd still like to thank all of you for taking the time and effort for trying to teach me. It just means something isn't really clicking for me. But I'll still try get to the end of this. If anyone has some other way of looking at it or explaining it. I'm all ears. Thanks

Hope this helps.

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Alan Robinson

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