This is weird.
I got a program for clipping colours in an arbitrary space to a spectral locus
last night. Now, this isn’t quite what you are after, but I might as well chip
in my bit…
If you take an equal unit of each wavelength in SI units
400nm Yxy = 108.728 cd/m2 0.17334 0.00480
410nm Yxy = 332.225 cd/m2 0.17258 0.00480
420nm Yxy = 1098.26 cd/m2 0.17141 0.00510
430nm Yxy = 3184.97 cd/m2 0.16888 0.00690
440nm Yxy = 6315.02 cd/m2 0.16441 0.01086
450nm Yxy = 10433.5 cd/m2 0.15664 0.01770
460nm Yxy = 16474.0 cd/m2 0.14396 0.02970
470nm Yxy = 24980.0 cd/m2 0.12412 0.05780
480nm Yxy = 38170.2 cd/m2 0.09129 0.13270
490nm Yxy = 57115.2 cd/m2 0.04539 0.29498
500nm Yxy = 88684.8 cd/m2 0.00817 0.53842
510nm Yxy = 138107. cd/m2 0.01387 0.75019
520nm Yxy = 194942. cd/m2 0.07430 0.83380
530nm Yxy = 236676. cd/m2 0.15472 0.80586
540nm Yxy = 261936. cd/m2 0.22962 0.75433
550nm Yxy = 273179. cd/m2 0.30160 0.69231
560nm Yxy = 273193. cd/m2 0.37310 0.62445
570nm Yxy = 261387. cd/m2 0.44406 0.55471
580nm Yxy = 238872. cd/m2 0.51249 0.48659
590nm Yxy = 207846. cd/m2 0.57515 0.42423
600nm Yxy = 173251. cd/m2 0.62704 0.37249
610nm Yxy = 138107. cd/m2 0.66576 0.33401
620nm Yxy = 104610. cd/m2 0.69150 0.30834
630nm Yxy = 72760.0 cd/m2 0.70792 0.29203
640nm Yxy = 48049.0 cd/m2 0.71903 0.28093
650nm Yxy = 29378.6 cd/m2 0.72599 0.27401
660nm Yxy = 16748.5 cd/m2 0.72997 0.27003
670nm Yxy = 8786.11 cd/m2 0.73199 0.26801
680nm Yxy = 4667.62 cd/m2 0.73342 0.26658
690nm Yxy = 2254.19 cd/m2 0.73439 0.26561
700nm Yxy = 1126.27 cd/m2 0.73469 0.26531
You can see this peaks at 555 nm as it should. However, the Y value is not a
great measure of how bright it appears to you. Also the contrast is huge so
your 430 nm violet will be hard to see.
Another problem is the standard tables of the CIE values give the weights as
ASCII numbers, so they lose precision when the numbers get very small.
I imagine you are mentally drawing Iines between your 430nm point and your
white point in an (x,y) diagram, and seeing where it intercepts the locus.
Let me suggest a very different route for plotting a spectrum. This may not be
what you want to do, but bear with me for now…
I remember seeing what someone claimed to be an accurate representation of the
spectrum in CMYK and not being very impressed with it. Too much yellow, too
much cyan, as I recall. You phrased your question in terms of RGB so I am going
to assume you have an RGB projector and you can scale your RGB values to vary
the brightness. If you are printing in CMYK then you can add K to vary the
brightness.
Suppose you are looking at your colour gamut down the luminance axis. The most
saturated colours you can get will be bounded by the colour corners of your RGB
cube. The most saturated colours you can get will be somewhere on the
R-Y-G-C-B-M circuit. Some of the B_M_R segment won’t be on the spectrum, but
all the spectral colours will be approximated in there somewhere.
This circuit has a brightness that goes up and down, as you go from 1 to 2
primaries. The saturation also goes in and out. You will also probably want to
shape the intensity so the extreme reds and violets go to black. You way not
want to do this exactly according to the CIE Y weights as this will make the
blues very dark.
Suppose you start off with a 1-D set of RGB values that cover the R-Y-G-C-B-M
circuit.
Calculate the hue angle out from white, do that, and replace everything that is
outside your wavelength range with black.
Do a 1D convolution of these values with some smooth function such as a
Gaussian with a half-height width of (say) 40nm. This will smooth out much of
the discontinuity at the R-Y-G-C-B-M corners. This will reduce the saturation
of colours such as the primary green, but this is a good thing as they were
sticking out too far anyhow. I don’t think you want to reduce everything to a
perfect circle in (x,y) but a bit of rounding off won’t hurt.
You will now have a smooth set of points that will lie on your spectrum, except…
- the wavelength scale is unknown.
- the brightness is arbitrary.
The wavelength scale is probably not far off uniform, if you remember the
geometry when projecting to the white point. Perhaps imagine it in u’v’ instead
as that is less distorted (though the result should be the same).
The spectrum will go dark at either extreme in a realistic manner. It won’t be
an exact match to the CIE standard, but an exact match would depend on your
white and the reference spectrum you are trying to simulate. And, for the
violets, the difference between D65 and 6500K blackbody will be big. And your
projector colours are probably a long way away from the spectral locus, so
there is a lot of leverage in your (x,y) plot geometry.
If this spectrum doesn’t look right to you, then at least we reduced things
from a 3D problem to a 1D one, so you might be able to tweak it from there.
Okay, that’s not what you asked fr, and I know it. But if you can follow these
steps, you can perhaps see why there is not necessarily a single answer to
“What is the RGB for 430nm light?”.
Or you could get your projector to project a white line, and use a diffraction
grating...
Hope this helps a bit.
Cheers
Richard Kirk
