Convertion from nanometers to CIELAB values

Sodious

25th July 2006 - 10:10 PM

Hi everyone,
I do not know if this is the right section for a question like this .
My name is Marinos and i would like some help to convert spectral data from a reflectance spectrometer to CIELAb values. Does someone know how to do it?
Thanks in advance

rpenner

26th July 2006 - 12:10 AM

It's a simple matter of integration.

1) Get CIELAB data from a study of human vision (My Taxi is here or I'd give you a URL)
2) Get your data tabluated at even intervals of 20 or 10 or 5 nm.
3) Multiply the two columns (you might need to interpolate if one of the two tables is tabulated via some other interval)
4) sum the products
5) normalize the sum (for some CIELAB data this is already done, unless you have interpolated....)

The result is an absolute X, Y and Z. Sometimes these are normalized by dividing by the sum of X, Y and Z.

rpenner

26th July 2006 - 01:59 AM

Oops, I found some errors I made in my haste. I told you how to make "Tristimulus Values" X, Y and Z, not CIELAB. The CIELAB is a transformed version of the X, Y, and Z relative to a "White Point" -- XYZ are about photons going into your eye and what color you see. Colored lights are best discussed in XYZ. CIELAB is about photons hitting a color surface and then your eye. CIE LAB is best for colors of paint, fabrics and fruit.
The variables are (L* (0-100), a* (-500..+500), and b* (-200..+200))

http://www.cie.co.at/cie/ (The CIE)
http://www.math.ucla.edu/~jimc/xcolor/color.txt (Some untrustworthy information)
http://www.cie.co.at/publ/abst/15-2004.html (A URL where you can get Standard Observer Data from the CIE -- in France, the comma is used as the decimal point)

Step 1, choose your CIE Standard Observer (1931, or 1964) depending on the viewing conditions you which to match colors for.

QUOTE

The delineation of the three color-matching response functions of the human observer is called the 1931 CIE Standard Observer (also known as the 2° Observer). This international standard can also be shown as a table of weighting factors from which a specification of color by CIE X, Y, Z tristimulus values can be derived. The 2° Observer is intended to be used when viewing smaller samples (typical of printed materials) that create an angle of view at the eye between about 1° and less than about 4°.

Using the 10° Observer (1964) is recommended whenever the pairs of specimens being viewed create an angle subtended at the eye greater than about 4°.

Step 2, get your CIE standard observer data tabulated at regular intervals

Step 3, get your data at regular intervals

Step 4, get reference data for "white" from a source. You usually can't fake this well, but if you are doing software simulation, the second CIE link above also points to "Standard Illuminants" or in the worse case, just find the bigest number in your data and say "white" is a sample that gives that value at all wavelengths.

Step 5, multiply and sum both your data (getting X, Y, and Z) and your white data (geting X_n, Y_n, and Z_n) with one of the standard observers.

Step 6, compute CIE L*a*b* from the correct formula at http://en.wikipedia.org/wiki/Lab_color_space