mathematics

Kreft's dichromaticity index

Kreft's dichromaticity index is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Kreft's dichromaticity index rather than just read about it. In short: Kreft's dichromaticity index (DI) is a measure for quantification of dichromatism. It is defined as the difference in hue angle (Δhab) between the color of the sample at the dilution, where the chroma (color saturation) is maximal, and the color of four times more diluted (or thinner) and four times more concentrated (or thicker) sample.

Key takeaways

Kreft's dichromaticity index belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Kreft's dichromaticity index to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Kreft's dichromaticity index from memory before moving on to harder problems.

Reference excerpt

Kreft's dichromaticity index (DI) is a measure for quantification of dichromatism. It is defined as the difference in hue angle (Δhab) between the color of the sample at the dilution, where the chroma (color saturation) is maximal, and the color of four times more diluted (or thinner) and four times more concentrated (or thicker) sample. The two hue angle differences are called the dichromaticity index towards lighter (Kreft's DIL) and dichromaticity index towards darker (Kreft's DID) respectively. Kreft's dichromaticity indexes DIL and DID for pumpkin seed oil, which is one of the most dichromatic substances, are −9 and −44, respectively. This means, that pumpkin seed oil changes its color from green-yellow to orange-red (for 44 degrees in Lab color space) when the thickness of the observed layer is increased from cca 0.5 mm to 2 mm; and it changes slightly towards green (for 9 degrees) if its thickness is reduced for four-fold. The color of pumpkin oil at increasing thickness or concentration presented in CIELAB colorspace diagram. Straight lines are vectors showing hue (angle) and chroma (length) of the color at maximal chroma (toward the square mark), and the colors of four-fold less or more diluted or thick pumpkin oil (DIL and DID). Note that DID is −44.1 degrees and DIL corresponds to −8.97 degrees. Dichromaticity (DIL and DID) of selected substances, calculated from their VIS absorption spectra by the computer algorithm “Dichromaticity index calculator”:

Maximal chroma: chroma at concentration (thickness) where the color of the substance has maximal chroma (saturation). Angle at maximal chroma: the hue, which is represented by the angle of the vector to the color with maximal chroma in the CIELAB colorspace diagram.

References

External links Free Dichromaticity Index Calculator software

Illustrations

Worked examples

Example 1 — a first encounter with Kreft's dichromaticity index

Start with the simplest possible case. Write down what Kreft's dichromaticity index claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Kreft's dichromaticity index before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Kreft's dichromaticity index ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Kreft's dichromaticity index

In research: Kreft's dichromaticity index appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Kreft's dichromaticity index in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Kreft's dichromaticity index is common in secondary-school and first-year university syllabi. It links to neighbouring topics Color, Index numbers, Optics, so understanding it makes those chapters shorter.
In everyday life: Look for Kreft's dichromaticity index outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Kreft's dichromaticity index in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Kreft's dichromaticity index means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Kreft's dichromaticity index out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Kreft's dichromaticity index in simple terms?

Why does Kreft's dichromaticity index matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Kreft's dichromaticity index?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Kreft's dichromaticity index.