Spectral explorer

A colour number starts as a curve: how much light a surface returns at each wavelength. Choose one or two measured materials, a light and an observer, and watch that curve become a stimulus, then X, Y and Z, then L*a*b* — and see why two surfaces can sit close together under one light and further apart under another.

Samples, light and observer

First sampleSecond sampleIlluminant

Standard observer

1. What the surface reflects

Solid line — Green lawn grass. Selective: it reflects most in the green (500–570 nm), averaging 7.5%, and least in the violet and blue (400–490 nm), averaging 3.3%. The highest single band is 730 nm at 36.6%. Freshly picked lawn grass, probably Kentucky bluegrass, measured immediately after picking. Chlorophyll absorbs blue and red, leaving a modest green peak near 550 nm and a steep rise beyond 700 nm.
Dashed line — Light green plastic tarpaulin. Selective: it reflects most in the green (500–570 nm), averaging 29.6%, and least in the yellow to red (580–700 nm), averaging 10.8%. The highest single band is 520 nm at 39.9%. Light green rip-stop plastic tarpaulin. A pigmented green: a peak near 520 nm with low reflectance either side, and no vegetation-style rise in the far red.

2. What reaches the eye under Daylight, CIE D65

Dotted line: the light. Solid and dashed lines: the light multiplied, wavelength by wavelength, by the reflectance above. That product is the colour stimulus — the only thing the eye receives. A surface cannot return light the lamp did not supply, which is why the same sample gives a different stimulus under each illuminant.

Data table: reflectance and stimulus at each wavelength

Ten-nanometre band means, 380–730 nm. Light and stimulus are relative to the light’s strongest band = 100.
Wavelength	D65	Reflectance: Green lawn grass	Reflectance: Light green plastic tarpaulin	Stimulus: Green lawn grass	Stimulus: Light green plastic tarpaulin
380 nm	43.2	2.1%	5.9%	0.9	2.6
390 nm	48.3	2.2%	6.7%	1.1	3.2
400 nm	67.6	2.5%	7.2%	1.7	4.9
410 nm	77.0	2.8%	7.6%	2.1	5.9
420 nm	78.8	3.0%	8.0%	2.3	6.3
430 nm	76.2	3.1%	8.6%	2.3	6.5
440 nm	88.0	3.1%	9.4%	2.8	8.3
450 nm	98.2	3.5%	10.4%	3.4	10.3
460 nm	100.0	3.6%	11.6%	3.6	11.6
470 nm	98.3	3.6%	13.1%	3.6	12.8
480 nm	98.0	3.7%	15.6%	3.6	15.3
490 nm	93.6	3.7%	20.2%	3.5	18.9
500 nm	92.9	4.0%	28.0%	3.7	26.0
510 nm	91.8	4.7%	36.5%	4.3	33.5
520 nm	89.9	6.3%	39.9%	5.6	35.9
530 nm	91.1	8.3%	37.6%	7.5	34.2
540 nm	89.3	9.3%	32.4%	8.3	28.9
550 nm	88.3	9.7%	26.2%	8.5	23.1
560 nm	85.4	9.5%	20.2%	8.1	17.2
570 nm	82.5	8.5%	15.8%	7.0	13.0
580 nm	81.1	7.2%	13.2%	5.9	10.7
590 nm	76.6	6.6%	11.9%	5.1	9.1
600 nm	76.5	6.3%	10.8%	4.8	8.2
610 nm	76.2	6.0%	9.9%	4.6	7.6
620 nm	74.6	5.6%	9.6%	4.1	7.2
630 nm	71.5	5.3%	9.6%	3.8	6.8
640 nm	70.9	5.0%	9.7%	3.6	6.9
650 nm	68.7	4.5%	10.3%	3.1	7.1
660 nm	68.5	4.2%	11.3%	2.9	7.7
670 nm	69.5	3.9%	11.9%	2.7	8.2
680 nm	66.5	3.9%	11.7%	2.6	7.8
690 nm	60.6	4.7%	11.1%	2.8	6.7
700 nm	61.0	8.8%	10.1%	5.4	6.2
710 nm	61.9	16.1%	9.5%	9.9	5.9
720 nm	54.8	25.1%	9.9%	13.7	5.4
730 nm	58.9	36.6%	11.5%	21.6	6.8

3. The colour that results

Green lawn grass under D65 for the 10° observer: L* 31.7, a* -6.9, b* 17.2. Light green plastic tarpaulin under D65 for the 10° observer: L* 54.1, a* -40.8, b* 22.4. Each stimulus is weighted by the observer’s three colour-matching functions and summed to X, Y and Z; L*a*b* then expresses those relative to a perfect white under the same light.

Tristimulus values, chromaticity and CIELAB for each sample under Daylight, CIE D65, CIE 1964 10° observer
Sample	Screen approximation	X, Y, Z	x, y	L, a, b*	C*, h
Green lawn grass	#46502f	5.96, 6.97, 3.69	0.3586, 0.4192	31.7, -6.9, 17.2	18.6, 112°
Light green plastic tarpaulin	#1d945c	13.57, 22.10, 12.82	0.2798, 0.4557	54.1, -40.8, 22.4	46.5, 151°

The swatch is an sRGB approximation for an eye adapted to the light, always calculated with the 2° observer because sRGB is defined with it. It is clipped where the colour falls outside sRGB, your screen is probably uncalibrated, and no three-channel display can reproduce a spectrum. Trust the numbers, not the swatch.

4. The same spectrum through the 2° and 10° observers

CIELAB values of each sample under Daylight, CIE D65 for the 2° and 10° observers, and the size of the shift between them
Sample	2°: L, a, b*	10°: L, a, b*	Shift (ΔE00)
Green lawn grass	32.3, -10.5, 17.9	31.7, -6.9, 17.2	3.08
Light green plastic tarpaulin	54.3, -45.1, 21.0	54.1, -40.8, 22.4	1.92

Nothing about the sample or the light changed between the two columns — only the colour-matching functions. Green lawn grass moves by ΔE00 3.08: a large amount, because its reflectance is concentrated where the two observers' functions differ most. The shift is not a colour difference anyone sees; it is the size of the error made by comparing a 2° number with a 10° one.

5. The pair under every light

The pair is closest under FL2 with the 2° observer (ΔE00 21.2) and furthest apart under LED-RGB1 with the 10° observer (ΔE00 28.7). These never match, but the size of the gap depends on the light: each illuminant puts its power at different wavelengths, so it weights the places where the two curves disagree differently.

CIEDE2000 colour difference between Green lawn grass and Light green plastic tarpaulin under each illuminant, for the 2° and 10° observers
Illuminant	ΔE00, 2°	ΔE00, 10°	Reading (10°)
Daylight, CIE D65	25.8	26.6	Clearly different
Daylight, CIE D50 (graphic arts viewing)	25.5	26.2	Clearly different
Incandescent tungsten, CIE A	23.5	24.0	Clearly different
Cool-white fluorescent, CIE FL2	21.2	21.7	Clearly different
Narrow-band tri-phosphor fluorescent, CIE FL11	21.7	21.7	Clearly different
Phosphor-converted white LED, CIE LED-B3	23.7	24.2	Clearly different
Red-green-blue mixed LED, CIE LED-RGB1	28.4	28.7	Clearly different

Each ΔE00 compares L*a*b* values calculated relative to that light’s own white, as an instrument reports them. The reading labels are a rough guide for large samples side by side, not a tolerance.

What this calculation assumes

Every curve is reduced to 36 ten-nanometre band means from 380 to 730 nm. Standards prefer 5 nm or finer over 380–780 nm; the missing 740–780 nm tail carries very little weight but is not zero. See from spectrum to tristimulus values.
Reflectance only. A fluorescent surface also emits light it absorbed in the ultraviolet, by an amount that depends on the lamp. None of that is modelled here; see fluorescence and the UV component.
The measured curves come from the U.S. Geological Survey’s spectral library, made for remote sensing. The geometry is not the d/8° or 45°/0° of a colour instrument, so the L*a*b* values describe these specimens as USGS measured them, not what a paint-shop spectrophotometer would report. See reading a reflectance curve.
The 2° and 10° observers are averages. How much they disagree for a given spectrum is covered in how far 2° and 10° results differ, and the ways a mismatch between lights is scored in metamerism indices.

First sample: USGS spectrum “Lawn_Grass GDS91 (Green) W1R1Ba AREF”, splib05a record 11208, Beckman 5270 laboratory spectrometer. Second sample: USGS spectrum “Plastic_Tarp GDS339 Green W1R1Fa AREF”, splib05a record 10440, ASD FieldSpec portable spectrometer. U.S. Geological Survey data are in the public domain.

How this works

Reflectance curves are measured spectra from the U.S. Geological Survey's Digital Spectral Library splib05a, reduced to 10 nm band means from 380 to 730 nm. Nothing is smoothed or fitted.
Illuminants and the CIE 1931 2° and 1964 10° colour-matching functions are the CIE's own published 1 nm tables, reduced to the same band means.
The CIE tables are © CIE, published under CC BY-SA 4.0, and are used here as 10 nm band means made by Colourwise; the datasets, their DOIs and what the licence covers are listed on the licensing page.
X, Y and Z are the sums of light × reflectance × each colour-matching function, scaled so a perfect white has Y = 100. L*a*b* is calculated relative to the chosen light's own white for the chosen observer, with no chromatic adaptation transform, and pairs are compared with CIEDE2000.
The optional 'constructed metamer' is the first sample's curve plus a spectral variation calculated to leave X, Y and Z unchanged under D65 for the 2° observer. It is arithmetic, not a measurement, and is labelled wherever it appears.
Metamerism index for a pair of samples. Both specimens' tristimulus values are calculated under the reference and the test illuminant for the chosen observer. The second specimen's X, Y and Z under the test illuminant are each multiplied by the ratio of the first specimen's to the second's under the reference illuminant, which makes the pair an exact match there. The index is the CIELAB difference ΔE*ab between the first specimen and the corrected second specimen under the test illuminant; the same corrected difference is also given by CIEDE2000, and the uncorrected ΔE*ab beside it. Calculated by Colourwise from the two reflectance spectra supplied and the CIE illuminant and observer tables in its spectral dataset. A derived figure, not a value any standard or instrument publishes for the pair. It is the colour difference a pair shows under the test illuminant, given that it matches under the reference. It is meaningful only when the uncorrected difference under the reference illuminant is small: a pair that is simply two different colours has no metamerism index worth quoting. A larger index means a match that holds less well when the light changes; whether a given value is acceptable is for the parties' own tolerance to decide.

Limitations

Ten-nanometre data over 380–730 nm is coarser and shorter than the 5 nm or finer over 380–780 nm that colorimetry standards prefer; results can differ slightly from a full-resolution calculation.
Only reflection is modelled. Fluorescence — light absorbed in the ultraviolet and re-emitted as visible — is not, so brightened papers, textiles and fluorescent colours cannot be represented.
The USGS spectra were measured for remote sensing in geometries unlike a colour instrument's, on one specimen each. They show how real materials behave; they are not reference colours for those materials.
The swatches are sRGB approximations, clipped to gamut, on a screen that is probably uncalibrated. A display cannot reproduce a spectrum.
Metamerism index. The multiplicative correction is Colourwise's choice. Standardised indices (DIN 6172, ISO 18314-4) define their own correction for the same purpose, and this figure does not claim to reproduce either. It is calculated from 10 nm band-averaged spectra and illuminant tables, so it will not agree to the last decimal with software working at finer intervals. It describes one pair, one pair of illuminants and one standard observer; it says nothing about another light or about how an individual viewer sees the pair.

Spectral explorer

1. What the surface reflects

2. What reaches the eye under Daylight, CIE D65

3. The colour that results

4. The same spectrum through the 2° and 10° observers

5. The pair under every light

What this calculation assumes

How this works

Limitations

Read next

Spectral explorer

1. What the surface reflects

2. What reaches the eye under Daylight, CIE D65

3. The colour that results

4. The same spectrum through the 2° and 10° observers

5. The pair under every light

What this calculation assumes

How this works

Limitations

Read next