How does the CIE L relate to either the "whiteness" or "brightness" number.

[mearussi]

I'm trying to compare different paper/canvas manufacturers white levels and keep coming across these three different standards of measurement and was wondering how they relate to each other. Any ideas? 

[digitaldog]

Brightness is a perceptual (human) phenomena while Luminance (Luminosity) is a measure of the total radiant energy from a body. It has nothing to do with what a human perceives but rather describes the total radiant energy, such as watts/second of a source (the surface of a radiating object like a display).
 
"Lightness" is a scaled value relative to the dynamic range of a system. In the CIE L*a*b* system L is "Lightness." Lightness is the perception of color without the chromaticity component and is scaled to a particular media or scene, such as a display, a print, or a real natural scene. L50 is perceptually halfway between the white and black of a system. L50 may be 100 cd/m^2 or 1000 cd/m^2 you don’t know unless you also know luminance of white and black. Analogy: 50 paces would be a unit perceptually similar to both an ant and a human.

As for "Whiteness":
https://en.wikipedia.org/wiki/Whiteness_(colorimetry)

[Ernst Dinkla]

I'm trying to compare different paper/canvas manufacturers white levels and keep coming across these three different standards of measurement and was wondering how they relate to each other. Any ideas?

Search Xerox Paper Brightness and you will find a pdf that explains it well. There is a link on my SpectrumViz page too.

Ernst, getypt op de lei.

[mearussi]

Thank you both, that helps.

[MfAlab]

It's all calculation.

L* is from CIELAB color space, calculated from Y in the CIEXYZ. It is trying to match how lightness in human eyes. Luminous efficiency function V(λ) is be used.
Whiteness is also calculated from CIEXYZ, but yellow/blue tints are considered. It presents how white is a paper. Bluish papers have higher whiteness than yellowish papers.
Brightness's purpose is something like Whiteness, but using a spectral distribution function to calculate it. Brightness mainly considers reflection around 460 nm, OBAs will make huge influence.

There is no simple formula to convert from each other. But you can get your own L*/Whiteness/Brightness from spectral reflectance distribution of a paper white.