Color basics - whiteness calculation - Huaqiang Electronic Network

Whiteness is a visual attribute characterized by high reflectance and low color saturation. In the context of color science, white is considered a group of colors within the wavelength range of approximately 470–570 nm. Generally, it has a brightness value (Y) greater than 70 and an excitation purity (Pe) less than 0.1. Although white is not a single monochromatic color, observers can often distinguish differences in whiteness based on spectral reflectance, excitation purity, and dominant wavelength. However, the perception of whiteness varies among individuals, and different evaluation methods may yield different results. Additionally, personal preferences play a role—some people prefer white with a red tint, others with blue or green, and these preferences can influence their perception of whiteness.

The evaluation of whiteness also depends heavily on the lighting conditions under which the sample is viewed. For example, the same sample may appear differently under varying brightness levels or different light sources with distinct spectral power distributions. In practical applications, two common methods are used to evaluate whiteness: one involves comparing the sample to a known standard using a colorimeter, while the other uses a dedicated whiteness measuring instrument.

Many instruments come preloaded with various whiteness calculation formulas. During measurement, the device automatically applies the selected formula and displays the calculated whiteness value. This method is objective since it relies on standardized conditions, ensuring consistent and reliable results.

Whiteness Calculation Formulas Based on Ideal White

These formulas essentially calculate the difference between the sample’s color and that of an ideal white reference. One of the most commonly used is the Hunter whiteness formula.

Hunter Whiteness Formula

This formula defines the whiteness of a fully reflective diffuser as 100. It evaluates the sample by calculating the color difference relative to this ideal white. The formula is expressed as:

Where L, a, b represent the lightness and chromaticity values of the sample in the CIELAB color space. k₁ is a constant, typically set to 1. The values aₚ and bₚ represent the ideal whiteness coordinates in the CIELAB system. For non-fluorescent samples, aₚ = 0.00 and bₚ = 0.00. For fluorescent samples, aₚ = 3.50 and bₚ = -15.87.

CIE1982 Whiteness Evaluation Formula (Gantz Whiteness Formula)

Recommended by the International Commission on Illumination (CIE), the Gantz formula is widely used for evaluating whiteness. It has three variations depending on the preferred white tone:

1. Blue preference:

2. Red preference:

3. Neutral preference:

In this formula, x₀ and y₀ represent the chromaticity coordinates of ideal white in the 2° field of view, Y, x, y are the brightness and chromaticity values of the sample, W represents the whiteness value, and T_w indicates the tone offset. A positive T_w suggests a greenish tone, while a negative value indicates a reddish tone.

Whiteness Determination Based on Reflectance

Single-Band Whiteness Formula

Some formulas use the reflectance of a specific wavelength region to determine whiteness. For instance:

1. Using green light reflectance (G) to indicate whiteness.

2. Using blue light reflectance (R₄₅₇) to indicate whiteness.

The ISO standard defines the whiteness of paper using the reflectance at 457.0 nm ± 0.5 nm, referred to as ISO whiteness or blue light whiteness.

Multi-Band Whiteness Formula

Another approach involves combining reflectances from multiple wavelengths. Two examples include:

1. The Taube formula: W = 4B – 3G, where B is the blue reflectance and G is the green reflectance.

2. Using the yellowness index to express whiteness:

These formulas have their own strengths and limitations. While some are more accurate for non-fluorescent samples, others are better suited for materials with fluorescent whitening agents.

Modern instruments such as the precision colorimeter series (CS-200, CS-210, CS-220) and spectrophotometer series (CS-580, CS-600, CS-610, CS-660) offer advanced capabilities for measuring and displaying both Hunter and Gantz whiteness values, making them essential tools in quality control and product development.