minor error in CIE colorimetry

[MfAlab]

I build an excel to calculate some errors cause by source data in CIE colorimetry. First of all, the errors from spectral range. CIE recommend all rigorous calculations be calculated in the full range of wavelengths, 360 nm to 830 nm. In practical, we didn't use a spectrometer has that wavelength range. X-Rite i1 pro 2 is 380 ~ 730 nm, barbieri Spectro LFP S3 is 380 ~ 780 nm.

I calculated ΔE2000 at different spectral range, the result shows very small errors. CIE practical suggestion is 380 ~ 780 nm, the error causing by spectral range is only 0.0003 in average at D50, 2°. Analyze errors at different CMFs. In short wavelength, error significantly increases when wavelength be cut from 380 ~ 400 nm. Lack of long wavelength data, the errors double every 10 nm cutoff stably at 700 ~ 800 nm.

Focus on no errors wavelength range at 4 dp. D50 illuminant, 1931 2° CMF is 370 ~ 770 nm, 1964 10° CMF is 380 ~ 770 nm, new CIE fundamental CMF is 390 ~ 770 nm. CIE A illuminant, 1931 2° CMF is 370 ~ 780 nm, 1964 10° CMF is 380 ~ 780 nm, new CIE fundamental CMF is 390 ~ 780 nm. CIE practical suggestion calculating range 380 ~ 780 nm is reliable.

I also calculated other error causes, e.g, spectral interval, spectral resolution, interpolation function, significant figures. Anyone interested?

[Doug Gray]

This is consistent with what I see too.

There is an elephant in the room though. If I look at the M2 spectral responses of a paper with large amounts of OBAs with the I1Pro2 and iSis XL 2, the largest differences are at the shorter wavelengths.

This appears to be due to the illuminant differences. The I1Pro 2 measures M2 by taking two measurements. One with M0 (incandescent with about 2/3 M1 levels of uV). The other with uV only using uV leds. It appears to subtract the measurements from the uV passto come up with an estimate of what a uV cut illuminant (M2) would produce. But this is indirect at best.

OTOH, the iSis and ColorMunki read uV cut (M2) by default. BUT they do so with an illuminant spectra that peaks at about 440nm and has virtual no energy below 400nm. So they extrapolate those below 400nm. And, because of the spectral bump of the "white" led they use there are also odd differences between about 440nm and 500nm. Above 500nm the two spectros have similar responses.

This causes the white point of high OBA paper to differ a bit (1 to 2 dE 76) between the two spectros reading M2.

The iSis and CM are much closer with low OBA paper though the iSis still extrapolates (creates out of thin air) spectral readings at or below 400nm. However, with only these differences, the white points of low OBA paper are less than 1 dE.

Not that these are all that different in a practical sense. I'm actually surprised the two techniques are as close as they are with high OBA paper.