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A pair that never matched under D65 is not metameric, it is wrong. The two faults have different remedies.
Worst Metamerism Index
—dE
Across the test illuminants, net of the reference mismatch
Indices & Margins
Index under Illuminant A
—dE
Index under F11
—dE
Margin under A
—dE
Margin under F11
—dE
Worst Margin
—dE
Illuminants Failing
—nos
Worst Total Difference
—dE
Shift Relative to Reference Match
—x
Margin on the Reference Match
—dE
This is the additive correction of the special index, which subtracts the reference mismatch from the test difference; CIE 15 also describes a multiplicative correction, and the two agree closely while the reference mismatch is small and diverge once it is not. Where the D65 difference is a substantial fraction of the tolerance, correct the match first and re-measure rather than trusting either correction to see through it. The index is a property of the PAIR, not of the sample: a batch can be metameric against a dyed standard and acceptable against a pigment-printed one, or vice versa, because metamerism arises from the difference in spectral curves rather than from either curve alone. That is also why the remedy is a change of dye combination - typically replacing one component with a dye whose absorption band sits where the one in the standard sits - and why it must be settled at lab-dip stage, since no production correction reaches it. Illuminant A and F11 are the conventional pair because they bracket the practical failure modes, tungsten warmth and narrow-band fluorescent spikes, but a buyer with LED store lighting is testing under something this pair does not represent well, and an LED spectrum should be added where that is the selling environment.
Using this calculator
About the Special Index of Metamerism Across Illuminants
The formula
This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.
The special index, additive formM(test) = dE(test) - dE(reference)
Taking out the residual mismatch under D65 leaves only the part that is genuinely illuminant-dependent.
The illuminant that decides the complaintM(worst) = max( M(A), M(F11) )
A pair is judged by its worst light, not its average one, because that is the light it will be rejected under.
How much of the fault is metamerismratio = M(worst) / dE(reference)
A large ratio says the pair matches well and travels badly, which is a dye selection problem rather than a dyeing one.
Symbols used above
Symbol
Stands for
Unit
deltaEReference
Difference under D65
dE
matchTolerance
Match Tolerance
dE
deltaETestA
Difference under Illuminant A
dE
deltaETestF11
Difference under F11
dE
metamerismLimit
Metamerism Limit
dE
worstIndex
Worst Metamerism Index
dE
metamerismIndexA
Index under Illuminant A
dE
metamerismIndexF11
Index under F11
dE
marginA
Margin under A
dE
marginF11
Margin under F11
dE
worstMargin
Worst Margin
dE
illuminantsFailing
Illuminants Failing
nos
worstTotalDifference
Worst Total Difference
dE
shadeShiftRatio
Shift Relative to Reference Match
x
referenceMargin
Margin on the Reference Match
dE
How the result is derived
Step by step, from the values you type to the figure on screen.
The 5 inputs are read from the form on every keystroke: Difference under D65, Match Tolerance, Difference under Illuminant A, Difference under F11 and Metamerism Limit.
Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
The validated values are substituted into the expression above, which resolves Worst Metamerism Index together with every supporting figure in one pass — no value is carried over from a previous entry.
The supporting outputs — Index under Illuminant A, Index under F11, Margin under A, Margin under F11, Worst Margin, Illuminants Failing, Worst Total Difference, Shift Relative to Reference Match and Margin on the Reference Match — come from the same pass, so they always describe the same case as the headline figure.
Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.
What each input means
Where to read each value on the floor, the unit it must be in, and the range the tool accepts.
Input
Unit
Accepted range
Default
What it means
Difference under D65
dE
0 to 10 dE
0.35
Match Tolerance
dE
0.05 to 5 dE
0.8
Difference under Illuminant A
dE
0 to 10 dE
1.62
Tungsten. The classic shop-window failure
Difference under F11
dE
0 to 10 dE
1.15
Narrow-band fluorescent, the usual store lighting
Metamerism Limit
dE
0.1 to 5 dE
1
What the tool returns
The headline figure and every supporting value it is built from.
Output
Unit
What it tells you
Worst Metamerism Index (headline result)
dE
Across the test illuminants, net of the reference mismatch
Index under Illuminant A
dE
Index under F11
dE
Margin under A
dE
Margin under F11
dE
Worst Margin
dE
Illuminants Failing
nos
Worst Total Difference
dE
Shift Relative to Reference Match
x
Margin on the Reference Match
dE
Worked example
Given
Difference under D65
0.35 dE
Match Tolerance
0.8 dE
Difference under Illuminant A
1.62 dE
Difference under F11
1.15 dE
Metamerism Limit
1 dE
The tool loads with this case already solved — the Worst Metamerism Index shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.
How to use it
Work through the input groups in order — Reference Illuminant and Test Illuminants. The defaults are a realistic case, so you can change one value at a time and watch what moves.
There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
Read Worst Metamerism Index in the dark results panel — that is the headline figure, expressed in dE.
Check the supporting rows underneath (Index under Illuminant A, Index under F11, Margin under A, Margin under F11, Worst Margin, Illuminants Failing, Worst Total Difference, Shift Relative to Reference Match and Margin on the Reference Match) before acting on the headline — they are where an implausible input usually shows itself first.
Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.
Where this is used
Process planning — establishing Worst Metamerism Index before a trial is booked, so machine time and material in Dyeing, Printing, Color Management & Chemical Control are committed against a calculated figure rather than an estimate.
Costing and quotation — Worst Metamerism Index is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Difference under D65) shows how much of the gap in Worst Metamerism Index each variable explains.
Teaching and study — the accepted ranges bracket normal Dyeing, Printing, Color Management & Chemical Control practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.
Assumptions and limits
This is the additive correction of the special index, which subtracts the reference mismatch from the test difference; CIE 15 also describes a multiplicative correction, and the two agree closely while the reference mismatch is small and diverge once it is not. Where the D65 difference is a substantial fraction of the tolerance, correct the match first and re-measure rather than trusting either correction to see through it. The index is a property of the PAIR, not of the sample: a batch can be metameric against a dyed standard and acceptable against a pigment-printed one, or vice versa, because metamerism arises from the difference in spectral curves rather than from either curve alone. That is also why the remedy is a change of dye combination - typically replacing one component with a dye whose absorption band sits where the one in the standard sits - and why it must be settled at lab-dip stage, since no production correction reaches it. Illuminant A and F11 are the conventional pair because they bracket the practical failure modes, tungsten warmth and narrow-band fluorescent spikes, but a buyer with LED store lighting is testing under something this pair does not represent well, and an LED spectrum should be added where that is the selling environment.
Every input is bounded to the range normal practice occupies (Difference under D65 0 to 10 dE, Match Tolerance 0.05 to 5 dE and Difference under Illuminant A 0 to 10 dE, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.
Questions people ask
What do I need to know before using the Special Index of Metamerism Across Illuminants?
Have these to hand: Difference under D65, Match Tolerance, Difference under Illuminant A, Difference under F11 and Metamerism Limit. With those entered, the tool returns Worst Metamerism Index immediately.
What exactly is Worst Metamerism Index?
Across the test illuminants, net of the reference mismatch. It is reported in dE. It is derived from Difference under D65, Match Tolerance, Difference under Illuminant A, Difference under F11 and Metamerism Limit, and is the figure the rest of the Dyeing, Printing, Color Management & Chemical Control calculation is built around.
Which units does this calculator expect?
Enter Difference under D65 in dE, Match Tolerance in dE, Difference under Illuminant A in dE, Difference under F11 in dE and Metamerism Limit in dE. Mixing unit systems is the most common cause of a result that looks an order of magnitude wrong — convert before typing, not after reading.
What are the other figures under the main result?
They are the intermediate quantities the calculation passes through: Index under Illuminant A, Index under F11, Margin under A, Margin under F11, Worst Margin, Illuminants Failing, Worst Total Difference, Shift Relative to Reference Match and Margin on the Reference Match. They are shown because a headline number nobody can trace is a number nobody trusts — checking them against your own expectation is the fastest way to confirm the inputs were read as you intended.
Can I rely on this for a production decision?
This is the additive correction of the special index, which subtracts the reference mismatch from the test difference; CIE 15 also describes a multiplicative correction, and the two agree closely while the reference mismatch is small and diverge once it is not. Where the D65 difference is a substantial fraction of the tolerance, correct the match first and re-measure rather than trusting either correction to see through it. The index is a property of the PAIR, not of the sample: a batch can be metameric against a dyed standard and acceptable against a pigment-printed one, or vice versa, because metamerism arises from the difference in spectral curves rather than from either curve alone. That is also why the remedy is a change of dye combination - typically replacing one component with a dye whose absorption band sits where the one in the standard sits - and why it must be settled at lab-dip stage, since no production correction reaches it. Illuminant A and F11 are the conventional pair because they bracket the practical failure modes, tungsten warmth and narrow-band fluorescent spikes, but a buyer with LED store lighting is testing under something this pair does not represent well, and an LED spectrum should be added where that is the selling environment. Treat the output as an engineering estimate that narrows the trial window, not as a substitute for the trial.
