Kreft’s Dichromaticity Index¶

A paired CIELAB hue-shift measure comparing a transparent sample's maximal-chroma state with fourfold lighter/thinner and darker/thicker states to quantify dichromatism.

Version: v2 · 2026-09-06 · History
Domain-specific #: 2144
Origin domain: physics
Subdomain: colorimetry
Aliases: Kreft dichromaticity index, DI L and DI D

Core Idea¶

Kreft’s dichromaticity index quantifies dichromatism: a transparent material's change in perceived hue as optical path length or concentration changes. A transmission spectrum is converted to CIELAB coordinates across a dilution or thickness series. The reference state is the concentration–path-length product \(x_*\) at which chroma \(C^*_{ab}\) is maximal. Two signed hue differences are then computed:

\[ DI_L=\Delta h_{ab}(x_*,x_*/4),\qquad DI_D=\Delta h_{ab}(x_*,4x_*), \]

for lighter/thinner and darker/thicker directions respectively.^[1]

The ordered pair preserves directional asymmetry: a material can shift differently on dilution and concentration. Sign depends on the declared shortest signed hue-angle convention.

The recognition invariant is spectral series + CIELAB conversion + maximal-chroma anchor + fixed fourfold perturbations + two signed hue-angle changes.

Structural Signature¶

A transparent or transmitting colored sample.
Spectral transmittance or absorbance over visible wavelengths.
Declared illuminant and standard observer.
Conversion to CIE tristimulus values and CIELAB coordinates.
Chroma \(C^*_{ab}=\sqrt{a^{*2}+b^{*2}}\).
Hue angle \(h_{ab}=\operatorname{atan2}(b^*,a^*)\).
A concentration or optical-thickness series.
The series point of maximal chroma.
Fourfold lighter/thinner and darker/thicker comparison states.
Signed circular hue differences \(DI_L\) and \(DI_D\).
Controlled angular wrapping and interpolation.

What It Is Not¶

The index is not ordinary total color difference \(\Delta E^*_{ab}\), which includes lightness and chroma changes. It is not a single hue angle, absorbance maximum, visual color name, or discrete comparator scale. It specifically measures hue trajectory around a maximal-chroma anchor.

It is also not the biological use of “dichromatic” for two-channel color vision. Here dichromatism concerns thickness- or concentration-dependent color of a material.

Scope of Application¶

The measure applies to dyes, pigments in transparent media, oils, biological chromophores, and other samples whose visible spectra yield systematic hue change with optical density. Pumpkin seed oil is a canonical high-dichromatism example.^[1] Its spectral-to-perceptual translation follows standard color-science practice rather than direct wavelength labeling.^[2]

Application assumes reproducible spectral data and meaningful CIELAB conversion. Scattering, fluorescence, chemical change across dilution, aggregation, or departure from the optical model can mix other phenomena into the result.^[3]

Clarity¶

Report sample preparation, solvent, temperature, path length or concentration, spectral instrument, illuminant, observer, white reference, CIELAB convention, interpolation method, maximal-chroma estimate, hue unwrapping, and sign orientation. Publish both \(DI_L\) and \(DI_D\); a single unsigned magnitude loses information.

Manages Complexity¶

The paired index reduces a full spectral and color trajectory to two interpretable angular displacements while anchoring comparisons at the sample's most saturated state. Fixed fourfold changes support reproducibility across samples whose absolute concentration scales differ.

Abstract Reasoning¶

Measure or model visible spectra across a sufficient optical-density range.
Convert each spectrum under fixed colorimetric conditions.
Compute chroma and circular hue angle.
Locate or interpolate the maximal-chroma state \(x_*\).
Evaluate colors at \(x_*/4\) and \(4x_*\).
Compute signed shortest hue differences with consistent wrapping.
Preserve the lighter and darker components separately.
Quantify sensitivity to spectral noise, interpolation, and colorimetric settings.
Check that chemistry and scattering remain stable across the series.

Knowledge Transfer¶

The portable pattern is anchor a nonlinear trajectory at its maximum salience, perturb the controlling scale symmetrically in log space, and retain directional response. It transfers to paired sensitivity indices, hysteresis-free path summaries, dose–response characterization, and multiscale feature change. The proposed immediate parent is Measurement.

Examples¶

Pumpkin seed oil. Increasing optical thickness shifts the observed color from green-yellow toward orange-red, giving a large dark-direction index relative to the light-direction index.^[1]

Non-dichromatic absorber. A substance whose normalized spectral shape stays constant as optical density changes follows nearly one hue direction and yields small indices, even though lightness changes strongly.

Circular pitfall. Hue angles near \(359°\) and \(1°\) differ by \(2°\), not \(358°\); unwrapped subtraction is essential.

Structural Tensions¶

Compact index versus full spectral trajectory.
Perceptual color space versus physical absorption.
Fixed fourfold comparison versus measurement range.
Signed direction versus circular angle ambiguity.
Maximal-chroma anchoring versus noisy interpolation.
Optical dilution versus chemical-state change.

Structural–Framed Character¶

Anchoring, scale perturbation, directional difference, and dimensional compression are structural. Spectral transmittance, CIELAB, hue, chroma, and dichromatism provide the constitutive optical frame.

Structural Core vs. Domain Accent¶

The portable core is a paired directional response about a maximum-salience reference on a multiplicative scale. The domain accent is CIELAB hue change derived from visible transmission spectra under fixed colorimetric conditions.

Measurement is the proposed immediate parent. Index, Normalization, Scaling and Scale Dependence, Color, Difference, Sensitivity, and Reference Frame are related. CIE standards fix the tristimulus and CIELAB framework on which the index depends.^[4]

The prospective queue contains one strict edge to prime:measurement. No live DAG mutation is authorized.

Relationships to Other Abstractions¶

Current abstraction Kreft’s Dichromaticity Index Domain-specific

Parents (1) — more general patterns this builds on

Kreft’s Dichromaticity Index is a kind of Measurement Prime

Measurement is the proposed immediate parent.

Hierarchy path (1) — routes to 1 parentless root

Kreft’s Dichromaticity Index → Measurement

Neighborhood in Abstraction Space¶

Kreft’s Dichromaticity Index sits in a sparse region of the domain-specific corpus (94^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (1565 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08

Not to Be Confused With¶

Total CIELAB color difference.
Hue angle alone.
Absorbance or optical density.
Standard Reference Method beer color.
Pleochroism.
Dichromatic color vision.
Two-color palette index.
Any unsigned before/after hue difference.

References¶

[1] Samo Kreft and Marko Kreft, “Quantification of Dichromatism: A Characteristic of Color in Transparent Materials,” Journal of the Optical Society of America A 26, no. 7 (2009): 1576–1581, doi:10.1364/JOSAA.26.001576. registry ↩a ↩b ↩c

[2] Günter Wyszecki and W. S. Stiles, Color Science, 2^nd ed. (Wiley, 1982), sections on spectral colorimetry and uniform color spaces. registry ↩

[3] Mark D. Fairchild, Color Appearance Models, 3^rd ed. (Wiley, 2013), chapters on colorimetry, viewing conditions, and CIELAB. registry ↩

[4] CIE, Colorimetry, 4^th ed., CIE 015:2018 (International Commission on Illumination, 2018), doi:10.25039/TR.015.2018. registry ↩