ColorWorkDesk: A Guide to Colour Formulation in Colourimetry

Colour Formulation

Numerous industries rely on colourimetry to consistently achieve the correct colour: from fashion and design to the chemical and automotive sectors, colour formulation is a crucial process.

Yet, finding a formula capable of reproducing exactly the desired colour can be extremely complex without the help of specialised software, especially for those with little experience in the field.

Fortunately, the use of advanced numerical systems and their graphical representation can greatly simplify this task, making it more accessible even to those less familiar with the process.

Colour formulation, in fact, is a process that uses mathematical models to predict and create specific colours by combining various pigments and materials. These models take into account the type of material used and its optical properties to accurately predict the final colour.

Colourists can thus calculate and achieve the exact shade of colour desired, using advanced tools and scientific methods.

But it’s not just about mixing colours randomly—a formula consists of a series of ingredients, including dyes, pigments, and concentrated pastes, carefully selected among available options and combined in the correct proportions.

For example, mixing blue and yellow pigments yields a green pigment, but the final result also depends on how the material absorbs and diffuses light. This means the process is not merely visual but involves complex mathematical models.

Diffusion and Absorption

To better understand how colour formulation works, it’s essential to know two key concepts: diffusion and absorption.

Imagine light hitting an object. What happens to that light?

Some materials diffuse light, causing it to bounce within the material and preventing it from exiting easily. When a material diffuses a lot of light, it appears more opaque and covering, like a painted wall.

On the other hand, some materials selectively absorb light. This means they retain certain wavelengths of light and reflect others. Absorption is what gives materials their specific colour.

For example, a red object absorbs all wavelengths of light except red, which is reflected to our eyes.

If diffusion is high, we see more reflectance (i.e., the material reflects light), whereas if diffusion is low, the material will be more transparent and allow light to pass through, resulting in transmittance.

For more on reflectance and transmittance, see “ColorWorkDesk: How Spectrophotometers Work.”

The Kubelka-Munk Model: Predicting Pigment Behavior

The Kubelka-Munk model is a mathematical model used by colourists to predict the behavior of pigments and materials when mixed together.

This model allows for the calculation of two fundamental parameters for each ingredient:

• K, representing the material’s selective absorption
• S, representing the material’s selective diffusion

By knowing these two parameters, we can predict how a material will reflect light and, therefore, what colour we will see.

Imagine having a blue pigment: by measuring the values of K and S for this pigment at a particular light wavelength—say, 420 nm—we can understand how this colour will behave when mixed with other pigments. This allows us to determine reflectance for that specific point on the spectrum.

If we know the K and S values at 1% concentration of the blue pigment, we can easily calculate its behavior at higher concentrations, such as 10% or 20%, by simply multiplying K and S by the amount used.

Properties of K and S: Proportionality and Linear Combinations

The parameters K and S are proportional to the amount of pigment used.

This means that if we double the amount of pigment, K and S will also double. This property enables colourists to predict how the colour will change by increasing or decreasing the concentration of a pigment.

Additionally, K and S can be combined linearly: this means we can sum the K and S values of different pigments to determine the overall behavior of the mixture.

For example, if we have 20% of a blue pigment and 10% of a yellow pigment, we can multiply each pigment’s K and S values by their respective percentages and then sum them together.

This allows us to predict the final colour of the mixture without the need for physical experimentation.

The Colour Formulation Process

The colour formulation process is based on reflectance curves, which represent how a material reflects light at different wavelengths.

For each material, pigment, or concentrated paste, the K and S values are calculated in advance and stored in a colourant file containing all the necessary information to formulate a specific colour.

When a colourist needs to reproduce a colour, they compare the reflectance spectrum of the desired colour with that of a mixture of pigments in the colourant file.

Using the K and S values from the colourant file, the colourist can calculate the necessary mixture to achieve a colour as close as possible to the standard, reproducing a reflectance curve nearly identical to the standard.

To formulate a colour instrumentally, a colourant file and a reflection curve of the standard are required.

Tools and Software for Colour Formulation

To formulate colours, colourists use specialized software with two main objectives:

• Correctly selecting the materials and pigments needed for a specific formulation based on the chromaticity to be treated.
• Calculating the exact proportions of materials to achieve the best possible match to the standard.

However, this is not always an easy task.

For example, a typical formulation process involves using four pigments in a formula and quickly calculating pigment combinations. But when considering a set of 12 pigments, there are 495 combinations to analyse, each requiring much more complex calculations and significant execution time.

The real challenge is identifying the right pigments and calculating their exact proportions to achieve the desired colour.

Verifying the Final Result

After theoretically formulating a colour, it is crucial to verify that the result is correct by physically reproducing the formula.

Colourists compare the reflectance spectrum of the physically reproduced colour with that of the desired standard or analyze the differences using the L, a*, and b* parameters, which represent the coordinates of the colour in the CIELab 3D colour space.

For more on the CIELab colour space, see “ColorWorkDesk: How Spectrophotometers Work.”

If there are significant differences between the formulated spectrum and the standard spectrum, the colourist knows the formulation is not yet perfect and must adjust the mixture to get closer to the standard.

Today and Tomorrow: The Future of Colourimetry

Colour formulation is a sophisticated and scientific process that requires a deep understanding of light physics and the interaction between materials and pigments.

Today, thanks to mathematical models like Kubelka-Munk and advanced software, colourists can precisely predict the final colour and achieve it through accurate calculations.

Colourimetry, blending science and creativity, enables the creation of colours that meet both aesthetic and functional requirements in industries where colour precision is vital, such as textiles, automotive, and paints.

However, technologies for colour formulation are continuously evolving, and in the future, we may see even more sophisticated algorithms and tools that make the formulation process even more efficient and precise.

ColorWorkDesk: The Best Technologies for Colour Formulation on the Market Today

The ColorWorkDesk technology combines cutting-edge tools, such as portable and benchtop spectrophotometers (CWD), deep knowledge of colour physics and its properties, and mathematical modeling performed via centralised servers and advanced software.

These elements position it as an ideal and innovative solution for effective and efficient colourimetry across a wide range of industrial sectors.