# Talk:Planckian locus

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## Approximation - some questions

I have some questions about the approximation equations.

1. The referenced page ( http://www.vendian.org/mncharity/dir3/blackbody/UnstableURLs/bbr_color.html ) gives a list of black body sRGB coordinates for various temperatures. There is no information on how the sRGB coordinates were converted to xy coordinates, there is no information as to the fitting procedure used. We need a reference for these fitting coefficients.
1. this is somewhat explained at http://www.vendian.org/mncharity/dir3/blackbody/, and there is Perl sources used to compute that, with links to CMFs and spectrum data he used. (on the 2nd note, http://www.vendian.org/mncharity/dir3/blackbody/parameters.html shows 10deg and 2deg CMFs integration curves plotted together, which is kind of obscures the fact they are different coordinates, I wonder if the author even realizes that). 91.124.93.184
2. What does the phrase "fitting 1" and "fitting 0.9996" mean?

PAR 13:23, 11 May 2006 (UTC)

The equations for x(T) at the bottom of the page display a major discontinuity at T=4000K. The equation for T(1000-4000) gives x(4000)=.3262 The equation for T(4000-8000) gives x(4000)=.5960

Is there a typo in the coefficients? J. Barry Krasner doctorjay@mailforce.net

Those equations are garbage and the person who put them there is not responding. I have removed them. PAR 22:13, 21 August 2006 (UTC)

## iso/cie 10526:1991(e)

I happen to have a hard copy of this std, and it says there in 5.1 (where source A is discussed) that spectrum for A is calculated as lambda^-5 (exp(c2/(lambda*T)) -1)^-1 with c2=1.4388x10^-2 m*K and T = a temperature in K * 1.4388/1.4350 because of change of c2 value. What this mean in relation to this article is that if you will integrate CMFs x spectrum computed with any other constants (no matter how good they are), your results in XYZ will be shifted; in particular, A will likely be outside of planckian locus. 91.124.93.184

[Stricken in response to edit comment of original poster, "killing my incorrect interpretation". Please do not delete material from talk page discussions. If you made a comment you no longer feel is correct, just write that on the page and/or strike out the incorrect statements.]--Srleffler 05:53, 17 January 2007 (UTC)

that's just clutters the page, anyway, what that thing said is that A source temperature is re-defined that way to match spectrum calculated before, it does not apply to all temperature range. 195.137.203.137

## PI or no PI ?

I have said what I have to here. Could someone else (besides me and PAR) please look into this? 195.137.203.137

The best way to get others to discuss an issue is to hold the discussion on the talk page for the article.--Srleffler 05:55, 17 January 2007 (UTC)

Looking over the page, and the discussion on PAR's talk page, it seems that you two are converging on a common understanding. I'm not an expert on this area, so I don't have much to add, but I do have an observation: I really don't like the use (on PAR's page) of the term "intensity" to refer to $I(\lambda,T)$, which seems (from PAR's comments) to have dimensions of power per unit area per unit solid angle per unit wavelength. "Spectral intensity" is better, leaving "intensity" in this case to mean merely power per unit area per unit solid angle, but I still have a problem with that. Intensity is already a highly overloaded word in physics, and optics in particular. This usage of the term, though, is not (as far as I know) common in physics. The only field I know of that uses intensity this way is astrophysics. The proper optics term for a quantity with dimensions of power per unit area per unit solid angle is radiance. $I(\lambda,T)$ would then be a spectral radiance.

Now, I don't know what terminology is used in the CIE color field. If "intensity" is really the correct term, keep it in the article but explain it and give the dimensions explicitly. A link to radiance would also be advisable, to clarify the meaning. If it is not clear in citable sources that "intensity" is the correct term, call $I(\lambda,T)$ the spectral radiance.

The way it is now is not really better: "where I(λ) is the spectral intensity... The black body spectral radiance is given by" prompts for qn like "why do I need radiance, when there's intensity in formulas above? 195.137.203.137

All of the quantities should probably have clearly specified units or dimensions, since these formulas can get confusing.--Srleffler 06:18, 17 January 2007 (UTC)

PS. to the anonymous editor: Welcome! Great to see a new editor working in this field.
PPS. You'll find in general, that when comparing different sources (including Wikipedia) you have to be really careful to look at how variables are defined in equations. Different authors often define similar-looking variables in different ways, which can lead to confusion if you don't watch for it.--Srleffler 06:23, 17 January 2007 (UTC)
the bad thing about this color thingie that there are loads of let's say incorrect information on the net that comes either from misunderstandings or carelessness of authors. then, there are that ISO/CIE standards, by they are hardly of any help, they assume you already know everything (if I were you, I wouldn't pay a buck for single page of that). so, I came here in a hope that people who work with this stuff shared their knowledge in some nice linear walkthrough manner, but what I've found is rather messy articles. Some are labeled "color project", some are "physics article". Some are linked both ways, some are one way. The worst thing is that there is no any index-like "start here" page, where a newcomer could get a clear picture (or if there is, I could not find it (couldn't it be done in some sort of template)). I'm not saying it's someone's fault, I realize that this place is a mess by design, but - let's say it - I just have to express my disappointment somewhere. 195.137.203.137
oh yeah, this is the nice spot to put such an index, or to link to such an index. as it is, it was not useful at all. 195.137.203.137
You are right - I missed that reference to intensity so I never changed it to radiance. I have fixed it now. As a result of your questions the article has been improved. Thanks. Sorry it's not a finished product yet. I will also take a look at this. PAR 14:35, 18 January 2007 (UTC)

## Blackbody coordinates reference at vendian.org

The data look quite strange. For example, for 6500K it has 0.316/0.327 xy (or 0.314/0.325 at 10°), while it is widely pointed out for 0.313/0.329 (0.314/0.331), as in Wikipedia or any authentic color application. You can also check another popular values like 5000, 5500, 7500, 9300. May this file be as trashy, as the early given (and later removed) equations for estimating Planckian locus? But this is not the only file with “non-canonical” data I have seen. Are there different true data sets for black body? If so, how could a calculation of distance between CCT and T be made, while the source data for T may be ve-e-ery different? —The preceding unsigned comment was added by 213.234.235.82 (talk) 13:40, 30 March 2007 (UTC). (Small addition: to estimate how unperfect is this file, just look at the 5400 K that should be 0.333/0.333.)

you can always re-compute black body xyz using linked CMFs and spectrum formula from article. 195.137.203.137
Well, and how about mentioned “it is typically faster to compute these using polynomial approximations”? Those for CCT produce great results with simple formulae, so why the reverse approximation is hard to find? 213.234.235.82 15:57, 6 April 2007 (UTC)

## Integration from zero to infinity or in the visible spectrum?

for the exact calculation of "The Planckian locus in the XYZ color space". Is it really necessary (and why) to integrate from zero to infinity? I would guess it is totally sufficient to integrate in the visible spectrum from 380 to 780 nm. The other wavelengths are not visible and thus shouldn't play a role. And the values of X(lambda), Y(lambda) and Z(lambda) should also be zero for any invisible wavelength.--TeakHoken193.187.211.118 (talk) 12:59, 18 March 2009 (UTC)

I like to add something: the widest table for the color matching functions I ever found is from 360 to 830 nm in a 1nm step. The integral can be calculated for values of a availably table only.--TeakHoken193.187.211.118 (talk) 13:56, 18 March 2009 (UTC)

Of course, when you integrate, you can skip any interval where the integrand is zero. The XYZ functions are zero wherever light is invisible, so you could make the integral just go over the defined nonzero range of those, if you find a good source for their defined nonzero range. Dicklyon (talk) 16:52, 18 March 2009 (UTC)

## "SPD" ?

The article uses "SPD" twice, but doesn't explain what that refers to. smurfix (talk) 20:13, 25 April 2012 (UTC)

Spectral power distribution. –jacobolus (t) 21:22, 25 April 2012 (UTC)

## CCT calculation

from this article: 'The mathematical procedure for determining the correlated color temperature involves finding the closest point to the light source's white point on the Planckian locus'. The intention was probably 'the light source's tristimulus value', and not white point.

Similarly on the color temperature article it says 'The color temperature of a light source is the temperature of an ideal black body radiator that radiates light of comparable hue to that of the light source'. Hue has little to do with it - I imagine the intention was also the tristimulus value. — Preceding unsigned comment added by 82.81.32.236 (talk) 21:57, 3 July 2012 (UTC)

Your changes seem reasonable to me, though I am no expert. Why don’t you make it so, and then see if anyone complains? Vadmium (talk, contribs) 06:00, 5 July 2012 (UTC).

## The seemingly endless PI – no-PI debate

Over the years, there seems to have been constant confusion about whether to add or not add PI to the formula describing Planck’s law. There was a debate about that in 2007 here on this talk page, and as recently as this year User:HumblePiero "corrected" the formula by removing PI from it. So I want to clear up a few points:

1. There is not only one correct way to describe Planck’s law, there are several valid variants. The version used in this article is correct with PI as well as without PI. The variant with PI calculates the spectral radiant exitance of the black body, the variant without PI calculates the spectral radiance of the black body. Both describe Planck’s law perfectly well. But note that in any case, the letter I (capital i) is incorrect; this letter would describe the spectral intensity. The correct letters would be L for spectral radiance and M for spectral radiant exitance.
2. Even if the formula for spectral radiance is used, PI is usually not omitted but rather balanced by a second PI in the denominator. The reason is that 2 * PI * h * c^2 is the first radiation constant (c1), which is usually left untouched. (h * c / k is the second radiation constant, so the formula can be expressed more easily using c1 and c2.)
3. The funny point is that for the context of this article, PI or no PI doesn’t matter at all, because the whole 2 * h * c^2 (= c1) constant is irrelevant for the calculation and might as well be omitted. While this constant obviously influences the absolute values of XYZ, XYZ is always normalized at the end (to Y = 1, or by converting to xy, as in this article), so the absolute values don’t matter. So to avoid this confusion, it would be best to simply omit 2 * h * c^2 (with or without PI …) from the formula.

Is someone currently maintaining this article? If so, s/he might want to edit it accordingly. If not, I could do it myself, but since English isn’t my mother tongue, I would prefer a native speaker to do this. --Uli Zappe (talk) 06:11, 18 September 2014 (UTC)

Since nobody seemed to care, I have updated the article myself. Please correct any English deficiencies I might have introduced. Uli Zappe (talk) 06:29, 12 February 2015 (UTC)