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

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

I was looking at the curve of SLOG3 but didn't understand how light can be reflected more than a 100%? This indicates to me that 100% reflectance isn't really 100% and that instead it's in relation to some standard. Consequently, this would indicate that 18% gray reflectance isn't reflecting 18% of all light either. Could someone please explain what exactly is happening here? Thanks.

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

How about when a light source is in the frame?

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

Good point. Flew over my head for some reason. But how do you translate incident light sources into a reflectance %. And would this also mean anything above 100% reflectance is by definition an incident light source? Sorry if I sound like an absolute amateur. I'm still learning.

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Re: How can you have a scene linear reflectance greater than 100%?
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It might have something to do with diffuse vs. directed (specular) reflections.

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Fluorescence
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White paper often has a reflectance of well above 100%, the reason being that the reflectance is defined as the ratio of the visible light reflected to the visible light incident, measured in standard daylight. Optical brighteners are used to increase the reflectance because they convert incident UV light into reflected visible light and this accounts for the increase above 100%.

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Re: How can you have a scene linear reflectance greater than 100%?
4

J A C S wrote:

It might have something to do with diffuse vs. directed (specular) reflections.

Indeed. Those reference levels are for 18% and 100% diffuse reflections (from Lambertian surfaces). With such surfaces, as the name “diffuse” suggests, not all the light that lands on a given point from a given source is reflected in the direction of the camera. With specular reflections, it can be. See section 1.3 of BT.2390-9 for some discussion on this. This image from the first link is also a great illustration.

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Re: How can you have a scene linear reflectance greater than 100%?
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Mandem wrote:

Good point. Flew over my head for some reason. But how do you translate incident light sources into a reflectance %. And would this also mean anything above 100% reflectance is by definition an incident light source? Sorry if I sound like an absolute amateur. I'm still learning.

You can think of specularity as partial inclusion of the light source in the image.

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Inverse square law
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Mandem wrote:

I was looking at the curve of SLOG3 but didn't understand how light can be reflected more than a 100%? This indicates to me that 100% reflectance isn't really 100% and that instead it's in relation to some standard. Consequently, this would indicate that 18% gray reflectance isn't reflecting 18% of all light either. Could someone please explain what exactly is happening here? Thanks.

Mark, J A C S, Tom and Jim all make valid points.

Further to Mark's post it is not even necessary for a source of light to be in frame. It can simply be out of frame and off to one side.

You can have an ideal diffuse Lambertian surface, which reflects 100% of the incident light, and scatters it according to the Lambertian cosine rule. When illuminated by a distant light source, such as the sun, you will detect the same luminance from each part of the surface. It all appears uniformly bright.

When the illumination is oblique and from a nearby source, the illuminance (lumens per square metre) is higher for those parts of the surface which are closest to the source. These parts appear brighter because they are reflecting 100% of a high illuminance, while the more distant parts of the scene are reflecting 100% of a lower irradiance.

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Alan Robinson

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Re: Fluorescence

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

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

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

spider-mario wrote:

J A C S wrote:

It might have something to do with diffuse vs. directed (specular) reflections.

Indeed. Those reference levels are for 18% and 100% diffuse reflections (from Lambertian surfaces). With such surfaces, as the name “diffuse” suggests, not all the light that lands on a given point from a given source is reflected in the direction of the camera. With specular reflections, it can be. See section 1.3 of BT.2390-9 for some discussion on this. This image from the first link is also a great illustration.

So when we look at the graph where we start dealing with above 100% reflectance, is that just specular reflectance getting translated into it's equivalent in terms of diffuse reflectance. Which, in other words, means that 100% spectral reflectance is the true 100% reflectance of all the light, X, that was incident on the object whereas 100% diffuse reflectance is not?

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Reflector
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Mandem wrote:

Good point. Flew over my head for some reason. But how do you translate incident light sources into a reflectance %.

Assuming the reflector is a diffuse, Lambertian surface, like matte paint or unfinished wood, then a reflected metering will have a clear relationship with an incident metering, as the apparent brightness remains the same no matter what angle you view the surface. Otherwise you may have to take lots of measurements and integrate them.

And would this also mean anything above 100% reflectance is by definition an incident light source?

I wouldn’t say “incident” light source, but just a light source: more light is coming off of it than is falling on it.

What’s happening might be subtle. For example, ultraviolet light, which is normally not photographable, can cause materials to fluoresce, sometimes making them brighter than even 100%: in this case, it’s not mainly reflecting visible light, and it’s not necessarily *reflecting* ultraviolet light, but another process is going on. Or, an object in the scene might reflect the light source directly like a mirror, making it brighter than 100% as well. Or an object might be translucent, transmitting light from a hidden light source.

Sorry if I sound like an absolute amateur. I'm still learning.

No problem!

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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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100% of what?

Mandem wrote:

spider-mario wrote:

J A C S wrote:

It might have something to do with diffuse vs. directed (specular) reflections.

Indeed. Those reference levels are for 18% and 100% diffuse reflections (from Lambertian surfaces). With such surfaces, as the name “diffuse” suggests, not all the light that lands on a given point from a given source is reflected in the direction of the camera. With specular reflections, it can be. See section 1.3 of BT.2390-9 for some discussion on this. This image from the first link is also a great illustration.

So when we look at the graph where we start dealing with above 100% reflectance, is that just specular reflectance getting translated into it's equivalent in terms of diffuse reflectance. Which, in other words, means that 100% spectral reflectance is the true 100% reflectance of all the light, X, that was incident on the object whereas 100% diffuse reflectance is not?

It does not need to be specular reflectance. It could just be to handle parts of the scene which are more strongly illuminated than others.

A more extreme subject might be stained glass windows in a church interior.

I am not a video photographer, but surely the whole point of log gamma encoding to allow one to capture scenes which are not uniformly illuminated.

There may be a standard, but I suspect the reference point corresponding to 100% scene luminance is somewhat arbitrary, and chosen by the camera manufacturer or the photographer to accommodate scenes which include parts which are much brighter than the intended average.

Perhaps the "reflectance" tag in your screen shot is simply sloppy terminology - but for all I know, it could be accepted usage in the video community.

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Alan Robinson

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Re: 100% of what?
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alanr0 wrote:

[…]

There may be a standard, but I suspect the reference point corresponding to 100% scene luminance is somewhat arbitrary, and chosen by the camera manufacturer or the photographer to accommodate scenes which include parts which are much brighter than the intended average.

Perhaps the "reflectance" tag in your screen shot is simply sloppy terminology - but for all I know, it could be accepted usage in the video community.

As far as I know, the video community does generally use reflectance for reference levels. See for example page 6 of BT.2408-4:

It is important to know the reflectance of greyscale charts and white cards, to ensure that cameras are aligned to deliver the appropriate signal level and consistency in production.

An 18% grey card is commonly used for camera set-up in non-live workflows as it is the closest standard reflectance card to skin tones. It may also be useful when trying to match SDR and HDR cameras as the 18% grey should not be affected by any SDR camera “knee”.

A 75%HLG or 58%PQ marker on a waveform monitor, representing the reference level, will help the camera shader ensure that objects placed at the centre of interest within a scene are placed within the appropriate signal range, and that sufficient headroom is reserved for specular highlights.

And page 5:

The reference level, HDR Reference White, is defined in this Report as the nominal signal level obtained from an HDR camera and a 100% reflectance white card resulting in a nominal luminance of 203 cd/m² on a PQ display or on an HLG display that has a nominal peak luminance capability of 1000 cd/m². That is the signal level that would result from a 100% Lambertian reflector placed at the centre of interest within a scene under controlled lighting, commonly referred to as diffuse white¹. There may be brighter whites captured by the camera that are not at the centre of interest, and may therefore be brighter than the HDR Reference White.

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Re: 100% of what?

alanr0 wrote:

Mandem wrote:

spider-mario wrote:

J A C S wrote:

It might have something to do with diffuse vs. directed (specular) reflections.

Indeed. Those reference levels are for 18% and 100% diffuse reflections (from Lambertian surfaces). With such surfaces, as the name “diffuse” suggests, not all the light that lands on a given point from a given source is reflected in the direction of the camera. With specular reflections, it can be. See section 1.3 of BT.2390-9 for some discussion on this. This image from the first link is also a great illustration.

So when we look at the graph where we start dealing with above 100% reflectance, is that just specular reflectance getting translated into it's equivalent in terms of diffuse reflectance. Which, in other words, means that 100% spectral reflectance is the true 100% reflectance of all the light, X, that was incident on the object whereas 100% diffuse reflectance is not?

It does not need to be specular reflectance. It could just be to handle parts of the scene which are more strongly illuminated than others.

Does this not mean that there is some standard against which it is being measured? Perhaps the average illuminance of the scene? Say we have 2 areas in a frame, one significantly more illuminated than the other and both of these areas have an 18% middle gray card in them. Of course the 18% gray card in the strongly illuminated area will reflect in ABSOLUTE terms much more relative to the 18% gray card in the less illuminated area but proportionally they're both reflecting equal amounts. So how would we go about deciding which 1 is actually an 18% reflectance. This is getting quite messy and confusing the more I think about it.

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Re: 100% of what?
1

Mandem wrote:

alanr0 wrote:

Mandem wrote:

spider-mario wrote:

J A C S wrote:

It might have something to do with diffuse vs. directed (specular) reflections.

Indeed. Those reference levels are for 18% and 100% diffuse reflections (from Lambertian surfaces). With such surfaces, as the name “diffuse” suggests, not all the light that lands on a given point from a given source is reflected in the direction of the camera. With specular reflections, it can be. See section 1.3 of BT.2390-9 for some discussion on this. This image from the first link is also a great illustration.

So when we look at the graph where we start dealing with above 100% reflectance, is that just specular reflectance getting translated into it's equivalent in terms of diffuse reflectance. Which, in other words, means that 100% spectral reflectance is the true 100% reflectance of all the light, X, that was incident on the object whereas 100% diffuse reflectance is not?

It does not need to be specular reflectance. It could just be to handle parts of the scene which are more strongly illuminated than others.

Does this not mean that there is some standard against which it is being measured? Perhaps the average illuminance of the scene? Say we have 2 areas in a frame, one significantly more illuminated than the other and both of these areas have an 18% middle gray card in them. Of course the 18% gray card in the strongly illuminated area will reflect in ABSOLUTE terms much more relative to the 18% gray card in the less illuminated area but proportionally they're both reflecting equal amounts. So how would we go about deciding which 1 is actually an 18% reflectance. This is getting quite messy and confusing the more I think about it.

If you want absolute reflectance of a surface, you measure incident illuminance, and reflected luminance under controlled conditions.

As far as I can tell, video folk appear to use reflectance as a relative measure of image brightness.  For wide dynamic range formats, the levels corresponding to nominal reflectances of 18% grey and 100% grey are both considerably less than the peak image brightness.

spider-mario quoted from one set of recommendations - specifically ITU report BT.2408-4.

If I understand correctly, the calibration is for a signal which produces an output luminance of 203 cd/m² from a wide dynamic range display. This is intended to represent 100% diffuse reflectance from a surface with "nominal" illumination in the region of interest. The actual luminance at the subject will depend on the illumination employed, the camera gain and exposure settings, and the intent of the photographer.

The same section refers to a display with nominal peak luminance of 1000 cd/m², while the introduction discusses "ideal peak luminance" of 10000 cd/m².

Table 1 on page 6 (8 in the pdf) specifies display luminance values for both HLG and PQ formats.

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Alan Robinson

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White is white except when it ain’t
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Mandem wrote:

Does this not mean that there is some standard against which it is being measured? Perhaps the average illuminance of the scene? Say we have 2 areas in a frame, one significantly more illuminated than the other and both of these areas have an 18% middle gray card in them. Of course the 18% gray card in the strongly illuminated area will reflect in ABSOLUTE terms much more relative to the 18% gray card in the less illuminated area but proportionally they're both reflecting equal amounts. So how would we go about deciding which 1 is actually an 18% reflectance. This is getting quite messy and confusing the more I think about it.

There is a human physiological or psychological phenomenon called “lightness constancy”, which assigns an unvarying tone to our mental models of objects. A white object, in our mind’s eye, is always white and we always expect it to look white, and it almost always appears to be white, and are very surprised when it doesn’t.

An 18% gray card reflects 18% of the visible light falling on it, but how much light is falling on it? That varies, wildly. Direct sunlight might be a thousand times brighter than dim living room illumination at night.

Exposure and metering theory and standards typically *assumes* that the light falling on the scene is completely uniform, even if it isn’t.

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Re: White is white except when it ain’t

Mark Scott Abeln wrote:

Mandem wrote:

Does this not mean that there is some standard against which it is being measured? Perhaps the average illuminance of the scene? Say we have 2 areas in a frame, one significantly more illuminated than the other and both of these areas have an 18% middle gray card in them. Of course the 18% gray card in the strongly illuminated area will reflect in ABSOLUTE terms much more relative to the 18% gray card in the less illuminated area but proportionally they're both reflecting equal amounts. So how would we go about deciding which 1 is actually an 18% reflectance. This is getting quite messy and confusing the more I think about it.

There is a human physiological or psychological phenomenon called “lightness constancy”, which assigns an unvarying tone to our mental models of objects. A white object, in our mind’s eye, is always white and we always expect it to look white, and it almost always appears to be white, and are very surprised when it doesn’t.

An 18% gray card reflects 18% of the visible light falling on it, but how much light is falling on it? That varies, wildly. Direct sunlight might be a thousand times brighter than dim living room illumination at night.

Exposure and metering theory and standards typically *assumes* that the light falling on the scene is completely uniform, even if it isn’t.

If exposure and metering theory assumes uniform light throughout the scene then the only thing I can understand causing more than a 100% reflectance is like you said previously the conversion of non-visible light into visible light through whatever subtle process. Where can I learn more specifically about this? As most sources online barely ever even mention scene linear reflectance when discussing about dynamic range.

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Re: 100% of what?

alanr0 wrote:

[…]

As far as I can tell, video folk appear to use reflectance as a relative measure of image brightness. For wide dynamic range formats, the levels corresponding to nominal reflectances of 18% grey and 100% grey are both considerably less than the peak image brightness.

spider-mario quoted from one set of recommendations - specifically ITU report BT.2408-4.

If I understand correctly, the calibration is for a signal which produces an output luminance of 203 cd/m² from a wide dynamic range display. This is intended to represent 100% diffuse reflectance from a surface with "nominal" illumination in the region of interest. The actual luminance at the subject will depend on the illumination employed, the camera gain and exposure settings, and the intent of the photographer.

That matches my understanding as well.

The same section refers to a display with nominal peak luminance of 1000 cd/m², while the introduction discusses "ideal peak luminance" of 10000 cd/m².

Table 1 on page 6 (8 in the pdf) specifies display luminance values for both HLG and PQ formats.

To give more context: PQ is absolute and display-referred. Signals represent an absolute output luminance on a 10 000 cd/m² display. Thus, a PQ signal of 58% intrinsically means an output luminance of 203 cd/m².

HLG is different: it is relative and scene-referred. A 75% HLG signal represents approximately 26.5% of the maximum scene luminance that can be captured, to which the OOTF (opto-optical transfer function) still needs to be applied to get to display light. For HLG, that OOTF takes the form of a gamma function applied to luminance, and the gamma value happens to be 1.2 for a peak display luminance of 1000 cd/m² in a reference surround luminance of 5 cd/m². It was decided that it would be on such a “reference” HLG display that the output luminance of the reference white would coincide between PQ and HLG (see “Conversion between PQ and HLG” page 24 of that report: “There is currently an industry consensus that this common peak luminance should be 1000 cd/m²”), and indeed, we have 1000 × 0.265^1.2 ≈ 203 cd/m².

On a 500 cd/m² HLG display, the gamma would instead be 1.2 × 1.111^log₂(500 / 1000) ≈ 1.08, and therefore reference white would be output at 500 × 0.265^1.08 ≈ 119 cd/m². On a 500 cd/m² PQ display, it would likely stay closer to 203 cd/m² depending on how the tone mapping is done.

Conversely, on a 2000 cd/m² HLG display, reference white would brighten to ~340 cd/m².

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Words - why white is white except when it ain’t
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Mandem wrote:

Mark Scott Abeln wrote:

Mandem wrote:

Does this not mean that there is some standard against which it is being measured? Perhaps the average illuminance of the scene? Say we have 2 areas in a frame, one significantly more illuminated than the other and both of these areas have an 18% middle gray card in them. Of course the 18% gray card in the strongly illuminated area will reflect in ABSOLUTE terms much more relative to the 18% gray card in the less illuminated area but proportionally they're both reflecting equal amounts. So how would we go about deciding which 1 is actually an 18% reflectance. This is getting quite messy and confusing the more I think about it.

There is a human physiological or psychological phenomenon called “lightness constancy”, which assigns an unvarying tone to our mental models of objects. A white object, in our mind’s eye, is always white and we always expect it to look white, and it almost always appears to be white, and are very surprised when it doesn’t.

An 18% gray card reflects 18% of the visible light falling on it, but how much light is falling on it? That varies, wildly. Direct sunlight might be a thousand times brighter than dim living room illumination at night.

Exposure and metering theory and standards typically *assumes* that the light falling on the scene is completely uniform, even if it isn’t.

If exposure and metering theory assumes uniform light throughout the scene then the only thing I can understand causing more than a 100% reflectance is like you said previously the conversion of non-visible light into visible light through whatever subtle process. Where can I learn more specifically about this? As most sources online barely ever even mention scene linear reflectance when discussing about dynamic range.

Uniform illumination throughout the scene is a sometimes convenient fiction, which generally will not apply to log gamma encoding and wide dynamic range displays.

In the real world, surfaces with greater than 100% reflectance are uncommon. What does occur is non-Lambertian directional scattering (in particular specular reflection) and especially non-uniform illumination.

Whiter than white objects are possible, but rarely amplify by a factor of 5 or more, unless there is an awful lot of ultra-violet light present.

The various video tone curve standards specify how changes in recorded signal are converted to intensity by a display device. The numbers correspond to relative changes in luminance referred to the maximum output of the display. For reasons best known to themselves, the video community describe these brightness changes in terms of reflectance, even though most variation will arise from changes in subject illumination.

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

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