Talk:Lambert's cosine law

message: I corrected the statement that the radiance follows the cosine. I took out the telecommunications link and the
section:
Sources
* Federal Standard 1037C
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)
replies: text: 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  (a sub-page of .  Frames suck).  But it isn't especially relevant.  Dbenbenn 02:54, 6 Jan 2005 (UTC)
thread_title: No caption given

message: 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)
thread_title:  Lambertian radiators? 

message: 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)
thread_title: On the rewrite

message: 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)
replies: text: 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)
replies: text: 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)

text: It seems that the term "radiance" is used improperly here. If you consider the radiance definition, you will see that the radiance of a Lambertian reflector is equal in all directions (because it already takes into account the cosine between the surface normal and the observer line of view). This contradicts with the sentence "In mathematical terms, the radiance along the normal is I photons/(s·cm2·sr) and the number of photons per second emitted into the vertical wedge is I dΩ dA. The number of photons per second emitted into the wedge at angle θ is I cos(θ) dΩ dA." Midnighter84 (talk) 23:12, 17 March 2011 (UTC)
thread_title: Terminology

message: 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)
replies: text: 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)
thread_title:  Examples 

message: 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)
thread_title:  First WIKI edit ever 

message: What is the difference between photons vs energy in this context, for thinking about the distribution of light output vs angle?
Please add a linear plot of angle vs photons/energy/light emitted.
What is the half-power angle for Lambertian sources?  This would be good material to add to the article, because this is the way many current light sources are rated.
It seems like the article should reference/link to LED SSL devices, since Lambertian is often mentioned for some high-power LED emitters.
-96.237.10.106 (talk) 12:40, 3 June 2009 (UTC)
replies: text: In this case it seems like the half-power angle would be 60 degrees, since cosine of that angle is one half. Personally, I donät know why they are making a difference between energy and photons, since a photon basically is energy quantized, i.e. one photon of a certain frequency v contains an energy E that is given by the Planck relation (or the Planck–Einstein equation) E = hv. Maybe they just prefer to keep a unitless number and instead try to obtain the probability distribution for the reflection angle of the photon. --Kri (talk) 01:11, 7 February 2011 (UTC)
thread_title:  photons vs energy 

message: In figure 1 and the associated paragraph d-Omega is variously referred to as both an angle and a solid angle. The result is it's not clear in Figure 1 if the segments are of equal angle or equal solid angle. In a 3-dimensional situation it doesn't make much sense that they would be both equal angles and equal solid angles, because the solid angle of a band around the hemisphere, of equal angle, increases as you approach the horizontal. I'd be very grateful if someone could clear up the confusion.
Araphid (talk) 10:34, 19 March 2014 (UTC)
thread_title:  disambiguate angle and solid angle ? 

message: There is no true photo of light scattered from a surface that obeys Lambert's cosine law. 
The mean backscattering from the full moon is directed back to the sun because the scattering dipoles on the moon oscillate in a plane perpendicular to the coming sunlight.
Any calculation that does not take the direction of the polarizing dipoles into account will not be correct.
Backscattering yields a uniform moon image, as well as the earth's image and the images of all the planets and their moons.
Back-scattering from any surface will not depend on the surface inclination angle to the coming light, and a curved surface will look uniform. It is, therefore, not surprising that true images, that obey Lambert's cosine law, are difficult to find.
In the calculation of Lambert's cosine law, there is a hidden assumption that the scattering dipoles oscillate in all random directions in space. This is not the case with the moon, and probably with other examples.
Urila (talk) 13:07, 29 October 2018 (UTC)
thread_title:  Backscattering yields a uniform full moon image.  

message: The opposition surge, the significant increase of 180 degrees backscattered light, is a well-established and well-documented phenomenon. See "Opposition surge" in Wikipedia, and the references therein. On the other hand, there is no single true photo that obeys Lambert's Cosine law, "Lambert's cosine law" in Wikipedia. 
The first figure in the article, "Lambert's cosine law" in Wikipedia, is an erroneous artist view.
Urila (talk) 09:12, 9 October 2020 (UTC)
thread_title:  The opposition surge and Lambert's Cosine Law 

message: In optics, Lambert's cosine law says that the radiant intensity or luminous intensity observed from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the direction of the incident light and the surface normal; I = I0cos(θ).[1][2] 2409:4042:2C1E:5C14:C0C4:2FFF:7ADA:503E (talk) 08:12, 29 May 2022 (UTC)
thread_title:  R 

message: In the interesting "Details of equal brightness effect" section Radiance (a certain number of photons/s per meter squared per steradian) is shown with the symbol I and Io.  This is confusing because with SI conventions I is used for intensity (e.g. photons/s per steradian). The correct symbol for radiance/luminance is L. Jack Hogan (talk) 08:47, 3 March 2023 (UTC)
thread_title:  The Symbol for radiance/luminance is L 

message: "When an area element is radiating as a result of being illuminated by an external source, the irradiance (energy or photons /time/area) landing on that area element will be proportional to the cosine of the angle between the illuminating source and the normal"
This is only true for a directional light source, like a light bulb.  Is it true on the peak of a mountain range with an overcast sky, for instance? Of course not.  
The point is that while the input to a Lambertian reflector can be from any random direction, its output is omnidirectional in the hemisphere above it in the proportion suggested by the cosine law.  What matters for the input is the number of photons/s that fall onto the surface of interest, regardless of where they came from.  And for that irradiance/illuminance the output is predetermined by the cosine law. Jack Hogan (talk) 09:15, 3 March 2023 (UTC)
thread_title:  Lambertian Scatterers section Inaccurate