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.
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:
for lighter/thinner and darker/thicker directions respectively.
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. Its spectral-to-perceptual translation follows standard color-science practice rather than direct wavelength labeling.
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.
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.
Relationships to Other Abstractions¶
Current abstraction Kreft’s Dichromaticity Index Domain-specific
Parents (1) — more general patterns this builds on
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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 (94th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (1565 abstractions)
Nearest neighbors
- Color Quality Scale — 0.82
- Tint, shade and tone — 0.79
- Color Solid — 0.77
- Artificial Sunlight — 0.76
- Transmittance — 0.76
Computed from structural-signature embeddings · 2026-09-08