Emissivity in Infrared Measurement

Emissivity is a fundamental property in infrared temperature measurement that defines how efficiently an object emits infrared radiation compared to an ideal blackbody. The emissivity value quantifies a material’s ability to emit thermal radiation compared to an ideal blackbody, with values ranging from 0 to 1. The emittance is a surface’s actual radiative energy output, influenced by temperature and material-dependent emissivity.

A blackbody is an idealized object that absorbs all incident radiation without reflection or transmission and emits the maximum possible energy at every wavelength. Its radiation distribution is independent of direction. However, real materials rarely meet this ideal. Gray bodies emit significantly less radiation at the same temperature. A material is considered a “gray” body if its emissivity remains constant across all wavelengths, though this does not occur in nature.

Emissivity is categorized based on its spectral and directional characteristics:

• Total hemispherical emissivity [math]\varepsilon[/math]: Integrated emissivity over the entire spectrum.
• Monochromatic emissivity [math]\varepsilon_\lambda[/math]: Emissivity at a specific wavelength.
• Hemispherical emissivity [math]\varepsilon_h[/math]: Emissivity averaged over all directions.
• Directional emissivity [math]\varepsilon_d[/math]: Emissivity measured in a specific direction.

Scientifically, the hemispherical emissivity [math]\varepsilon_h[/math] is the ratio between the radiant exitance of that surface [math]M_\lambda(\lambda,T)[/math] and the radiant exitance [math]Mλ°(λ,T)[/math] of a black body at the same temperature and emissivity [math]\epsilon=1[/math] . Emissivity can be specified for a particular wavelength, direction, and polarization. [1]

[math]\epsilon_{h}\left(\lambda,T\right)=\frac{M_{\lambda}\left(\lambda,T\right)}{M°_{\lambda}\left(\lambda,T\right)}[/math]

Hemispherical emissivity is determined by integrating directional emissivity over the entire hemisphere. Its relationship with normal directional emissivity is governed by the refractive index, making it possible to calculate one from the other. This approximation remains valid even for non-smooth dielectric surfaces, as surface roughness has minimal influence on emissivity. While diffuse surfaces exhibit directional emissivity values similar to their hemispherical counterparts, specular surfaces tend to show a decrease in emissivity at higher angles.

Directional emissivity is the relevant parameter for infrared temperature measurement since infrared cameras and pyrometers capture thermal radiation from a specific direction rather than from all angles. These devices typically assume emissivity values at or near normal incidence, meaning measurements taken perpendicular to the surface provide the most accurate results. When measurements must be taken at an angle, adjustments may be required to account for changes in emissivity with viewing angle.

Kirchhoff’s Law of Thermal Radiation states that for a body in thermal equilibrium, the emissivity of a surface is equal to its absorptivity at a given wavelength. Since the total incident radiation on a surface must be either emitted, transmitted, or reflected, the relationship is expressed as the following equation, where [math]\tau[/math] is the transmissivity, [math]\rho[/math] is the reflectivity per wavelength.

[math]\varepsilon\ =\ 1\ -\ \tau\ -\ \rho[/math]

For opaque materials with significant thickness so that no light passes through the material, the emissivity is simplified to the following [2]:

[math]\varepsilon\ =\ 1\ -\ \rho[/math]

Like other optical properties, emissivity is influenced by a material’s chemical composition and geometric structure. It can be evaluated using optical parameters such as the material’s refractive index and extinction coefficient. The extinction coefficient represents light attenuation due to scattering and absorption per unit volume. Emissivity is governed by equations that describe the behavior of its two distinct linear polarization components. These polarization directions—S-polarized (perpendicular to the plane of incidence) and P-polarized (parallel to it)—define how an incident wave interacts with a surface. Any polarization state can be decomposed into these orthogonal linear components [1,3].

In the following, the complex refractive index of the second material must be considered, which is [math]n=n_{2}+ik[/math] , while [math]n_{1}[/math] simplifies to 1. In the following equations, the emissivity power is obtained, depending on the polarization direction. Fresnel-based formulas only apply to smooth surfaces.

[math]\epsilon_{p}=1-\parallel\frac{n.\cos\left(\phi\right)-\sqrt{1-\frac{\sin^{2}\left(\phi\right)}{n^{2}}}}{n\cos\left(\phi\right)+\sqrt{1-\frac{\sin^{2}\left(\phi\right)}{n^{2}}}}\parallel^{2}[/math]

[math]\epsilon_{s}=1-\parallel\frac{\cos\left(\phi\right)-n.\sqrt{1-\frac{\sin^{2}\left(\phi\right)}{n^{2}}}}{\cos\left(\phi\right)+n.\sqrt{1-\frac{\sin^{2}\left(\phi\right)}{n^{2}}}}\parallel^{2}[/math]

Most practical applications emphasize unpolarized infrared emission. This signifies an equal power distribution in the s and p polarizations, meaning that the material’s effective emissivity is essentially the average of the two polarization directions.

[math]\varepsilon=\ \frac{1}{2}\left(\varepsilon_s\ +\ \varepsilon_p\right)[/math]

In the case of normal emission, perpendicular to the surface, there is no distinction between s and p polarization. Thus, the directional normal emissivity simplifies to the following equation.

[math]\varepsilon_n(\phi=0°)=(4 n_1 n_2)/((n_1+n_2 )^2+k^2 )[/math]

Due to its intrinsic optical and physical properties, each material exhibits a unique emissivity behavior across different wavelengths. For real materials, emissivity often varies with the emission angle, meaning they do not behave as Lambertian surfaces (which emit radiation uniformly in all directions). Still, the difference between conducting and dielectric materials needs to be made.

Emissivity decreases when measured at oblique angles for dielectric materials. A dielectric material is an electrical insulator that can store and support an electrostatic field while minimizing energy loss. Figure 1 shows, as an example, the directional emissivity over the angle of exposure for a dielectric material. This typical curve shape can also be transferred to non-conducting materials, such as glass, plastics, or organic materials. The only factor influencing the emissivity of a smooth dielectric interface is its real-valued refractive index. It can be derived that emissivity is constant up to angles of 60° and then drops due to Lambert’s cosine law and can, therefore, be considered Lambertian within this domain.
Moreover, Figure 1 illustrates exemplarily the relationship of the conductor material. Interestingly, the directional emissivity for conductors can even increase at other angles and then drops due to Lambert’s cosine law. Still, the emissivity remains almost constant for angles up to 60°, although on a lower level.

Emissivity depends on direction and varies with wavelength, a property known as spectral emissivity. This variation occurs because materials interact differently with infrared radiation at different wavelengths due to their atomic and molecular structures. The absorption and emission of thermal radiation are governed by electronic transitions, vibrational modes, and lattice interactions, which are wavelength-dependent. Due to their high reflectivity, conductors, such as metal, tend to have lower emissivity at longer infrared wavelengths. In contrast, dielectrics, such as ceramics or oxides, exhibit higher emissivity in specific spectral bands where their molecular vibrations strongly absorb and re-emit energy. As seen in Figure 2, this dependency is particularly relevant in infrared temperature measurement, as selecting the appropriate spectral range ensures accurate readings, especially for materials with varying emissivity across the infrared spectrum.

When a material’s surface is roughened, its emissivity increases due to the multiple reflections and scattering of thermal radiation within the microstructures of the rough surface. Roughness has a large effect on low-emissivity metals but a smaller relative effect on already high-emissivity dielectrics. A smooth surface reflects more incident radiation, reducing the amount absorbed and emitted. In contrast, a rough surface creates numerous microscopic cavities that trap radiation, increasing absorption and re-emission. This effect is particularly pronounced in metals, where polished surfaces have low emissivity due to high reflectivity. As roughness increases, the effective surface area for emission grows, allowing more energy to be radiated. Additionally, surface irregularities disrupt specular reflection, converting it into diffuse reflection, which enhances energy absorption and reduces loss due to external reflections. At microscopic scales, rough surfaces can also alter the material’s optical properties, affecting how it interacts with infrared radiation. This combination of enhanced absorption, multiple internal reflections, and increased surface area results in a higher overall emissivity. The following equation shows the relationship between the roughness R_a, which quantifies the deviation of a surface profile from its mean line and the spectral emissivity between two surface conditions with the same material [4,5,6].

[math]\varepsilon=\ \left(1\ +\ \left(\frac{1}{\varepsilon_0}\ -\ 1\right)\frac{R_a}{R_0}\right)^{-1}[/math]

In the equation [math]\varepsilon_0[/math] is the emissivity of the smooth surface and [math]R_{0}[/math] refers to the initial roughness. This equation expresses how emissivity increases asymptotically with roughness. Surface roughness varies by treatment, with mirror-polished metals at 0.01–0.1 µm, machined metals at 0.1–5 µm, and shot-blasted surfaces reaching 5–50 µm. Coated or oxidized surfaces range from 0.5 to 10 µm, while cast or corroded metals typically exceed 50 µm.

Emissivity is also temperature-dependent, as the intrinsic optical properties of a material can change with thermal excitation. At higher temperatures, alterations in the electron density, lattice vibrations, and phase transitions influence the material’s ability to emit thermal radiation. In metals, increased temperature can lead to a rise in free electron scattering, which may increase emissivity at specific wavelengths. Dielectrics and ceramics often exhibit increased emissivity at elevated temperatures due to enhanced phonon activity and changes in bandgap absorption. Additionally, surface oxidation or structural transformations at high temperatures can modify emissivity by altering the material’s reflectivity and absorption characteristics. Figure 4 shows the total emissivity changes for well-known materials that change emissivity over temperature.

When a material is semitransparent, its emissivity is influenced by both its optical properties and its thickness due to partial transmission and internal reflections of infrared radiation. In very thin films, a significant portion of the radiation can pass through the material, reducing its effective emissivity. As the thickness increases, absorption becomes more dominant, leading to higher emissivity values. However, interference effects can also occur, where certain wavelengths experience constructive or destructive interference within the film, further altering the emissivity in a wavelength-dependent manner. Figure 5 illustrates this behavior for a thin plastic film, demonstrating how variations in thickness impact the material’s ability to emit infrared radiation.