Mie scattering coloration

Introduction

Colors in the visible light spectrum are characterized by different wavelengths ranging from 380 nm (violet/blue) to 780 nm (red color). Such a split can be observed by passing white light (superposition of lights of different wavelengths) through a prism or simply by observing rainbows (Fig. 1). While considering light-matter interactions, all wavelengths might not behave similarly. Depending on the physical/chemical nature of the materials, specific wavelengths can be either transmitted, either absorbed, either reflected. The deflection of the light (refraction) appears to be as well wavelength dependent. These optical effects lead to the understanding of coloration processes as described here below.

Generally speaking, it is necessary to distinguish between the colors that depend on the chemical nature of an object and those that do not.

The first case considers the selective absorption of light. When striking an object, certain range of wavelengths are absorbed by specific molecules, e.g. pigments or dyes. The origin of the perceived color in this context arises from the collection of the radiation that is not absorbed but instead reflected by the object.

In the second case, independently of the chemical nature, physical phenomena such as refraction, interference and scattering of light are responsible for the observed colors, known as structural coloration. In this specific case, colors are produced when a material is formed of one or more parallel thin layers, or otherwise composed of nano/microstructures on the scale of the color’s wavelength. The latter case is the origin of Mie scattering coloration.

Mie scattering

The coloration produced by Mie scattering arises from the scattering of the light by homogenous sphere sized from few nanometers to hundreds micrometers. The underlying physical process consists in the absorption of light by nano/micro spheres followed by its re-emission in different directions with different intensity. In nature, Mie scattering takes place in the lower 4.5 km of the atmosphere, where there may be many essentially spherical particles present with diameters approximately equal to 1 to 10 µm. For instance, cloud droplets scatter all wavelengths of the visible light creating the white appearance of the cloud.

Depending on the size, density, distribution of the spheres, the incidence angle of the light, the refractive index of the sphere and the distance to the observer, the intensity of the scattered light will be different for each wavelengths. This phenomena is illustrated here below by the render in Fig. 2 with gold/silver nanoparticles of variable size immersed (10nm to 100 nm) in liquid (colloidal solution). Depending on the particle size, it can be seen that the colorimetry will be different from one colloidal solution to another.

Mie scattering is part of the OceanTM rendering tool box and allows to play on a large set of relevant parameters in the simulation: sphere refractive index, sphere distribution, sphere size, …. In order to illustrate the use of this theory, several examples are presented here below.

1. Mixed fluids

The optically important elements in milk include vitamin B2, fat globules and proteins. The host medium is water in which many different components are dissolved. The component exhibiting the most significant absorption in the visible range is vitamin B2. The optical contribution of each elements is displayed in Fig. 3 through the renders made by OceanTM. The Mie scattering occurs when adding in the composition the protein and the fat globules. It can be seen that the protein are more likely to diffuse blue hue while fat globules diffuse white opaque colors. This is due to the size of the fat globules which are much bigger than the proteins. As the fat globules concentration is much higher than the protein’s one, the milk appears white. Moreover, the greater the concentration of fat globules, the more diffusive is the milk as it can be seen on Fig. 3 while considering skimmed milk, regular milk, and whole milk.

2. Alga and minerals concentration in the sea

The concentration of alga and minerals in the sea is not the same everywhere in the world. As a consequence, the Mie scattering caused by those elements is not the same, causing a difference in the perception of subsea components. As an illustration, submarine view renders from different sea is displayed in Fig. 4. It can be seen that depending on the concentration of alga both the diffusion and the colorimetry of the water is affected. As a result, the water will appears either clear, either troubled with a color either blueish, either greenish.

3. Colored minerals

In order to illustrate the impact of both the refractive index and the size of the particles, renders of metallic sphere with variable size in glass medium were realized (Fig. 5). From left to right : 40 nm silver spheres, high density of 40 nm silver spheres, 60 nm gold sphere, cranberry glass (mixed of molten glass and gold sphere). The caustics , which are the envelope  of light rays reflected or refracted  by a curved surface or object, can be observed on the render. This latter topic will described in another article. Moreover, bichromic behavior of the minerals can be observed. This feature corresponds to specific optical effects for which the absorbed and scattered light can lead to complementary color. It can be especially observed for the 60nm gold sphere for which transmitted light is mainly blue/green, while the scattered light is primarily red in color.

Conclusion

As we have seen, the diffusion of Mie is a omnipresent mechanism with a strong impact on appearance. In fact, being able to predict the optical properties of such materials is a real technical advantage: Indeed, thin films or solutions based on nanoparticles (ZrO2, TiO2, …) are increasingly used in industry for their innovative optical properties. Whether for aesthetic or technical use. In both cases, the appearance of these films or their interactions with other (composite) materials can be finely predicted.

In addition, these diffusion/absorption mechanisms may also have a role in the environment, as in the example of seawater. But atmospheric conditions such as snow, pollution or fog are just as many cases that fall within the scope of Mie’s theory. In fact, simulating these conditions and phenomena with precision provides a high degree of reliability to the simulations.

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