Talk:Lambert's cosine law

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I corrected the statement that the radiance follows the cosine. I took out the telecommunications link and the section:

Contents

[edit] Sources

because it made no sense to me when I followed the link.

I am thinking this might cause a problem with some people's links, so if I did wrong, please fix it. I'm new to Wikipedia, so if I'm not following protocol, please let me know that too.

Paul Reiser 20:42, 30 Nov 2004 (UTC)

The protocol is be bold. Good job. For what it's worth, the link to Federal Standard 1037C is essentially a historical glitch. The original text of this page is from [1] (a sub-page of [2]. Frames suck). But it isn't especially relevant. Dbenbenn 02:54, 6 Jan 2005 (UTC)

[edit] Lambertian diffuse lighting model

The page Lambertian diffuse lighting model has a lot of the same information as this page. As far as I can tell, the Lambertian model simply posits the Lambertian cosine law. Should the pages be merged? Dbenbenn 02:06, 6 Jan 2005 (UTC)

I think they should, under "Lambert's cosine law". I will do that in a day or two, unless you do it first. Paul Reiser 04:06, 6 Jan 2005 (UTC)

I think the page Lambertian diffuse lighting model is quite a bit clearer than the Lambert's cosine law page. In the latter page, all that "flux", "total power", etc, makes things too complicated. "Apparent brightness" is so much easier to understand. Oleg Alexandrov 04:17, 6 Jan 2005 (UTC)

We could have the first paragraph be more intuitive, the second more technically precise with links to definitions. Maybe a diagram, too. --PAR.

I saw a nice explaination of Lambert's cosine law at this MIT class page. They do not talk at all about the observer's line of sight, as you do in the first paragraph of Lambert's cosine law. From that external link I think it follows that the power observed does not depend about the observer's line of sight, because light spreads in all directions equally. Does this contradict your first paragraph? I could be wrong, I don't know much about this. Oleg Alexandrov 19:25, 6 Jan 2005 (UTC)

Thats ok, I seem to have problems explaining this clearly. If I can write a page that you approve of, maybe we will have a good page. The problem is that there are two quantities, both of which have units of photons/sec/cm^2/sr or energy/sec/cm^2/sr. The emission from the Lambertian surface is measured in these units, and that emission varies as the cosine of the angle from the normal. The observer measures radiance, which is also in these units and that is independent of the angle from the normal. Some people say "intensity goes as the cosine of the angle" which is correct for the emitted intensity, while others say "intensity is constant" which is true for the observed intensity. The thing about the observed intensity, is that as you vary the angle, and keep the area you are looking at constant, the solid angle the observer sees for that area decreases as the cosine of the angle, as does the number of photons/sec received, and so the ratio of the photons emitted from the area divided by the solid angle that the observer sees for that area has the two cosines cancel, and the observed photons/sec per solid angle is constant. I'll try to draw a diagram that illustrates this.Paul Reiser 22:21, 6 Jan 2005 (UTC)

OK, I understand things now. I think for people in computer graphics, who use Lambert's cosine law a lot (maybe more than people in other disciplines), what matters is the observed intentsity, that is, what is in the eye of the beholder. Maybe the article should be split into two clearly delimited parts, one being what the observer sees, and the other being what happens at the surface itself when the light strikes. And maybe what the obverver sees should be given priority. Or maybe not. I don't know. I am looking forward to your changes to the article. Oleg Alexandrov 22:46, 6 Jan 2005 (UTC)
How about this: "The observed brightness at a point depends on the angle at which the light strikes that surface, but not on the angle of view. Specifically, the brightness is proportional to the cosine of the angle between the light source and the surface normal." Dbenbenn 23:10, 6 Jan 2005 (UTC)

This would be nice! One could also maybe add after your text: "Therefore, a point appears brightest if the light strickes "head on" at that point, and dimmer if the light strikes under an angle...." Just some thoughts. Oleg Alexandrov 23:18, 6 Jan 2005 (UTC)

Done. I ended up removing the following text. Perhaps some of it should go back in?

... is the statement that the total power observed from a "Lambertian" area element is directly proportional to the cosine of the angle θ made by the observer's line of sight and the line normal to the area.
This means that the area element will be just as bright no matter what angle it is viewed from. The total amount of power that an observer sees will be proportional to the brightness multiplied by the solid angle subtended by the area element. The area element will have a maximum solid angle subtended when it is viewed "head on" (i.e. θ=0) and will become smaller as the angle is increased until it is zero when θ=90 degrees. That means that the total power observed will be maximum when the area element is viewed head-on, and will drop to zero when viewed edge-on. The brightness (or power per unit solid angle) will be constant, however. The sun, for example, is almost a Lambertian radiator, and as a result the brightness of the sun is almost the same everywhere on an image of the solar disk.
When an area element is radiating as a result of being illuminated by an external source, the flux (energy/time/area) landing on that area element will be proportional to the cosine of the angle between the illuminating source and the normal. For a Lambertian reflector, the light reflected from this source will be the same in all directions, so the radiance seen by any observer will then be proportional that incident flux which will be proportional to the cosine of the incident (not the observing) angle.

Dbenbenn 00:25, 7 Jan 2005 (UTC)

[edit] Lambertian radiators?

The text I removed above talks about "Lambertian radiators", such as the sun. And some of the links to this page expect there to stuff about Lambertian radiators here. As far as I can tell, a Lambertian radiator is simply one that emits light uniformly in all directions. I don't see where the cosine comes into it. Dbenbenn 02:23, 7 Jan 2005 (UTC)

[edit] On the rewrite

Now I understand! I have just one problem with the article. The people in computer graphics I think use this law much more than anybody else. For them, the Lambert's law is:

"The brightness of a point on a surface is proportional to the cosine of the angle betwen the incident ray at that point and the surface normal at that point".

The way you wrote the article, this is an afterthought, put in the very last paragraph, and stated there as a conclussion of the very long theory you developed in this article. So, for phisisists your article will be interesting, for computer graphics people, it will be kind of not helpful. I don't know how to reconcile these. Oleg Alexandrov 05:33, 7 Jan 2005 (UTC)

The reflection law is a special case of the emission law, so thats why I did it that way, plus I have a physics bias. Putting the reflection part in the first section doesn't sound like a bad idea to me. Paul Reiser 16:25, 7 Jan 2005 (UTC)

[edit] Image:LambertCosineLaw.png

Hey Paul,

Would you consider splitting Image:LambertCosineLaw.png into two images (the top and bottom). Then if you remove the "Figure 1" and "Figure 2" captions, we can just put them in text, with code like

[[Image:LambertCosineLaw.png|thumb|right|411px|Figure 1: Emitted intensity]]

Dbenbenn 14:28, 7 Jan 2005 (UTC)

Ok, I will split it up and stick it in somewhere using the above format. I didn't like the captions anyway, and this gives more freedom to change. Paul Reiser 16:25, 7 Jan 2005 (UTC)

I split them, but do you know how to center the captions?Paul Reiser 17:11, 7 Jan 2005 (UTC)

Why do you want the caption centered to start with? I think left-aligned looks just fine. There is some info about captions at Wikipedia:Picture tutorial, but not what you want (at least I could not see centered captions).
Oh, if you really really want it, I think you can hard-code centered caption in html instead of using Wiki markup. Just look at the html source code of the page, and figure out where to insert a <center></center> thing. Oleg Alexandrov 17:54, 7 Jan 2005 (UTC)

Thanks, that worked fine. Its just that in scientific publications, single-line captions are centered, multi-line are not. I expanded the captions, so they stayed left-justified.

[edit] Terminology

I have adjusted the terminology used on this page to agree better with correct optics usage. Note that "brightness" is an ambiguous term, and should not be used in any scientific context, except when talking non-quantitatively about human perception of light. "Intensity" was also a problem here, since it is also ambiguous, and the sense in which it was used on the page conformed to none of the common standards. Intensity was used here to mean luminance and/or radiance. Intensity much more commonly means any one of luminous intensity, radiant intensity, irradiance, or illuminance. See also intensity (which is the same as irradiance). I am in the process of updating the definitions of some of the linked terms, so if the definitions are not clear right now they may be soon. --Srleffler 07:04, 15 November 2005 (UTC)

I strongly object to the use of the luminous terms - the article should not give the impression that this is a phenomenon which involves the response of the human eye for its validity or understanding. It should be done in radiance units, and every time the article offers an intuitive explanation in terms of a human observer, I think, with a little thought, it could be written so as to be technically correct, but not confusing to someone who doesn't understand the difference. I will do this soon, unless somebody agrees with me and does it sooner. PAR 17:57, 15 November 2005 (UTC)
Sounds fine to me. I used photometric units because I thought they lent themselves better to intuitive explanations, and also because, based on the date, I assumed Lambert originally formulated his law in photometric units. I did keep the radiometric units for the long example at the end. It is important to me that whatever units are used, the units and the explanation must be technically correct. Incorrect use of these units already leads to a lot of confusion.--Srleffler 04:39, 16 November 2005 (UTC)

[edit] Moon example

An anonymous editor altered the moon example today, completely reversing the sense of it. I have commented it out in the article for now, pending confirmation of one version or the other by someone with knowledge of this subject. The old text was:

For example, if the moon were a Lambertian reflector, one would expect to see its reflected brightness appreciably diminish towards the outer edge, or limb. The fact that it does not diminish illustrates that the moon is not a Lambertian reflector, and in fact tends to reflect more light into the oblique angles than a Lambertian reflector would.

and the new text is:

For example, if the moon were a Lambertian reflector, one would expect not to see its reflected brightness appreciably diminish towards the outer edge, or limb. The fact that it does not diminish illustrates that the moon is nearly a Lambertian reflector.

--Srleffler 05:48, 6 February 2006 (UTC)

Yes the anon edit was wrong. The increased angle of incidence near the limb will cause a decreased amount of light/area falling on the surface at the limb for any kind of reflector. For a lambertian reflector, that decreased amount of light will have the same brightness when viewed from any angle, but its still decreased from the larger light/area falling on the surface normal to the sun (i.e. away from the limb). The fact that the decrease in brightness is less than expected means the moon is not a perfect lambertian reflector. PAR 20:10, 6 February 2006 (UTC)


Despite the discussion above, I think the text on the page is still wrong. The light falling on the moon's surface per square metre must fall continuously to zero as you approach the terminator (the border between the illuminated and the dark parts of the moon's surface). Therefore the apparent brightness (however you define it) must also fall to zero continuously. The fact that the terminator appears to be a discontinuity must be because of the non-linearity of human perception.
When the moon is full, the terminator coincides with the limb. Therefore the apparent brightness must fall smoothly to zero as you approach the limb.
I am not sure that the moon is a good example at all. --194.81.223.66 13:22, 19 December 2006 (UTC)

[edit] shorter is btter

I prefer shorter articles. So I prefer not merging.

[edit] Examples

I came here looking for information -- and didn't find it. As far as I can tell, laser light is non-lambertian on account of the photons being in phase. I'm interested to know if there are other sources (perhaps LEDs? electric arcs?). While it's an interesting definition, it should be possible to know what it distinguishes between. If all the known light in the universe is Lambertian, then it's not a useful distinction ... sittingduck 21:06, 1 Mar 2006 (UTC)

Yes, laser light is not lambertian. Nor is a flashlight. Lots of other sources of light are not lambertian, and most surfaces are not pure lambertian reflectors. Pure lambertian light is not all that common, but is widely used as an approximate model for diffuse reflection and emission of light. Combining some lambertian reflection with some specular reflection creates a good model for many surfaces. This approach is used in computer graphics, etc.--Srleffler 23:21, 1 March 2006 (UTC)


[edit] First WIKI edit ever

I dunno what I am doing with this WIKI thing... I guess this is the right way to add a comment to the bottom here.

Anyway, I am a computer graphics guy and would like to comment on this discussion. I see what apears to me to be a gaping hole in the definitions offered here. First Diffusion is a reflective property of a surface normal. Scattered reflectivity of a kind defined by the shader being used. Radience seems different. Radience would be more along the lines of luminosity - although it may be a superset that includes various reflective properties in some sciences. Luminous or radient properties are defined by rays which originate from the calculated normal for a smoothed surface. Diffusion is calculated from a light source. For example Lambertian Diffuse is basically the just the cosine of the angle between the surface and the light.

The gaping hole I mentioned is for a solid deffinition of Diffuse or Diffusion as it applies to Computer Graphics. The algo being used to "scatter" the reflected light is not important to this general definition. But I think should be included in any of the definitions of diffuse shading models such as Phong, Lambert, Minnaert, OrenNayer, Generic Occlusion Shaders, Generic Translucency shaders (where the diffusion is of refracted light and not reflected light), And likewise Sub Surface Scattering which is also a kind of "Diffuse" property.

My email address for further disscussion or whatever is Tesselator@gmail.com and my name is James Dean Prentice III. You can also reach me during the day at the Kyoto Institute Of Science and Technology in the Computer Science Department by just asking for Jim sensei. :)

Welcome! Yes, this is the right way to add a comment. Only one change: add four tildes ("~~~~") at the end of your comment. The software will replace this with your ip address or username and a timestamp, to make it easier to see which comments are from whom.
I think you may be confused because you're looking for information on computer graphics, and you have ended up at an article on physics. This article deals with the physics of diffuse reflection from an idealized "Lambertian" surface. The companion article on Lambertian reflectance talks a bit about computer graphics applications. These articles are still "under construction", and may end up getting merged into a single article eventually. There are also articles on the Phong reflection model and Phong shading. Some of the material you are looking for may be summarized at 3D computer graphics.--Srleffler 21:24, 4 May 2006 (UTC)