Plank's Blackbody Distribution Law

The intensity of radiation emitted from an object is a function of its temperature, wavelength, and emissivity. A perfect emitter, also known as a blackbody, is a material that radiates 100% of the electromagnetic energy that is theoretically possible for a material at a specified temperature. Planck’s blackbody equation, developed by Max Planck in 1901, defines the intensity of radiation for a blackbody as a function of temperature and wavelength.

Each plot in Planck’s blackbody curve represents the energy distribution at a different temperature. As temperature increases, the intensity of radiation increases. Additionally, as the temperature of an object increases, the peak intensity moves to shorter wavelengths. The surface of the sun, at 6000°C, has its peak in the yellow region of the visible portion of the spectrum, and therefore, appears yellow.

We can also observe this phenomenon by slowly heating a piece of metal. At room temperature, the metal does not emit any light visible to the human eye. However, if we heat it to approximately 500°C, it begins to glow red. At 500°C, the metal emits visible light primarily in the red portion of the visible spectrum. As the temperature of the metal increases to approximately 1500°C, it begins to glow white. At 1500°C, the metal emits energy at all visible wavelengths. White light is the combination of all visible colors.

Objects that emit energy well also absorb energy well. Therefore, a perfect emitter is also a perfect absorber. The term blackbody arose because a perfect absorber absorbs all visible electromagnetic energy (light) and appears black. Blackbodies are useful as a reference to characterize the behavior of materials. The relationship between the intensity of energy emitted by a blackbody at various wavelengths as a function of temperature was discovered by Max Planck in 1900.

What is Emissivity

All objects and materials do not radiate infrared energy equally. Emissivity is a term describing the efficiency with which a material radiates infrared energy. A blackbody has an emissivity of 1.00 and no other material can radiate more thermal energy at a given temperature. An object with an emissivity of 0 emits no infrared energy. Real-world objects have emissivity values between 0 and 1.00. The lower emissivity of most real-world materials reduces the intensity of radiation from the theoretical predictions of Planck’s Law.

The temperature of an object and its emissivity define how much infrared energy an object will emit. The figure below shows that quartz emits less energy than a blackbody at the same temperature and therefore has an emissivity below 1.00.

Absorption, Transmission and Reflection

Infrared energy, when incident upon matter, be it solid, liquid or gas, will exhibit the properties of absorption, reflection, and transmission to varying degrees.

Absorption

Absorption is the degree to which infrared energy is absorbed by a material. Materials such as plastic, ceramic, and textiles are good absorbers. Infrared energy absorbed by real-world objects is generally retransferred to their surroundings by conduction, convection, or radiation.

Transmission

Transmission is the degree to which infrared energy passes through a material. There are few materials that transmit energy efficiently in the infrared region between 7 and 14µm. Germanium is one of the few good transmitters of infrared energy and thus it is used frequently as lens material in infrared cameras.

Reflection

Reflection is the degree to which infrared energy reflects off a material. Polished metals such as aluminum, gold and nickel are very good reflectors.

Conservation of Energy Equations

Conservation of energy implies that the amount of incident energy is equal to the sum of the absorbed, reflected, and transmitted energy.

(1) Incident Energy = Absorbed Energy + Transmitted Energy + Reflected Energy

Consider equation 1 for an object in a vacuum at a constant temperature. Because it is in a vacuum, there are no other sources of energy input to the object or output from the object. The absorbed energy by the object increases its thermal energy – the transmitted and reflected energy does not. In order for the temperature of the object to remain constant, the object must radiate the same amount of energy as it absorbs.

(2) Emitted Energy = Absorbed Energy

Therefore, objects that are good absorbers are good emitters and objects that are poor absorbers are poor emitters. Applying equation 2, Equation 1 can be restated as follows:

(3) Incident Energy = Emitted Energy + Transmitted Energy + Reflected Energy

Setting the incident energy equal to 100%, the equation 3 becomes:

(4) 100% = %Emitted Energy + %Transmitted Energy + %Reflected Energy

Because emissivity equals the efficiency with which a material radiates energy, equation 4 can be restated as follows:

(5) 100% = Emissivity + %Transmitted Energy + %Reflected Energy

Applying similar terms to %Transmitted Energy and %Reflected Energy,

(6) 100% = Emissivity + Transmissivity + Reflectivity

According to equation 6, there is a balance between emissivity, transmissivity, and reflectivity. Increasing the value of one of these parameters requires a decrease in the sum of the other two parameters. If the emissivity of an object increases, the sum of its transmissivity and reflectivity must decrease. Likewise, if the reflectivity of an object increases, the sum of its emissivity and transmissivity must decrease.

Most solid objects exhibit very low transmission of infrared energy – the majority of incident energy is either absorbed or reflected. By setting transmissivity equal to zero, equation 6 can be restated as follows:

(7) 100% = Emissivity + Reflectivity

For objects that do not transmit energy, there is a simple balance between emissivity and reflectivity. If emissivity increases, reflectivity must decrease. If reflectivity increases, emissivity must decrease. For example, a plastic material with emissivity = 0.92 has reflectivity = 0.08. A polished aluminum surface with emissivity = 0.12 has reflectivity = 0.88.

The emissive and reflective behavior of most materials is similar in the visible and infrared regions of the electromagnetic spectrum. Polished metals, for example, have low emissivity and high reflectivity in both the visible and infrared. It is important to understand, however, that some materials that are good absorbers, transmitters, or reflectors in the visible, may exhibit completely different characteristics in the infrared.

Effects of Emissivity

Infrared cameras detect and measure the sum of infrared energy over a range of wavelengths determined by the sensitivity of the camera’s detector. These cameras cannot discriminate energy at 7µm from energy at 14µm the way the human eye can distinguish various wavelengths of light as colors. They calculate the temperature objects by detecting and quantifying the emitted energy over the operational wavelength range of the detector. Temperature is then calculated by relating the measured energy to the temperature of a blackbody radiating an equivalent amount of energy according to Planck’s Blackbody Law.

Because the emissivity of an object affects how much energy an object emits, emissivity also influences a camera’s temperature calculation. Consider the case of two objects at the same temperature, one having high emissivity and the other low. Even though the two objects have the same temperature, the one with the low emissivity will radiate less energy. Consequently, the temperature calculated by the camera will be lower than that calculated for the high emissivity object.

Apparent Temperature

Infrared cameras cannot detect the emissivity of objects in order to calculate their true temperature. They can only calculate the “apparent” temperature of objects. The apparent temperature of an object is a function of both its temperature and emissivity. Given two objects with the same true temperature but different emissivity, a higher apparent temperature will be calculated for the object with higher emissivity (see figure below).

Given two objects with the same emissivity but different true temperature, a higher apparent temperature will be calculated for the object with higher true temperature. The apparent temperature of an object may be substantially different from its true temperature. Only when the emissivity of objects is known can thermal imagers compensate for emissivity and calculate true temperature.

Reflectivity

Objects with high reflectivity can reflect energy radiated by other objects. For example, polished aluminum reflects about 90% of the energy incident upon its surface. Just as infrared cameras cannot detect the emissivity of objects in order to calculate their true temperature, they also can’t detect the reflectivity of objects. Therefore, when calculating the apparent temperature of an object, thermal imagers detect and quantify energy emitted from the object, as well as, energy reflected from the surface of the object.

If an object reflects energy from another radiating source with a higher temperature, the apparent temperature that is calculated for the object will be higher than its true temperature. Likewise, if an object reflects energy from another radiating source with a lower temperature, the apparent temperature that is calculated for the object will be lower than its true temperature.

Given two objects with the same true temperature but different emissivity, a higher apparent temperature will be calculated for the object with higher emissivity (see figure below). Given two objects with the same emissivity but different true temperature, a higher apparent temperature will be calculated for the object with higher true temperature. The apparent temperature of an object may be substantially different from its true temperature. Only when the emissivity of objects is known can thermal imagers compensate for emissivity and calculate true temperature.

Emissivity Examples

A material’s emissivity can vary at different wavelengths. Most materials, however, have relatively uniform emissivity throughout the wavelength range in which thermal imagers operate. For example, the emissivity of most plastics, ceramics, and metals does not vary significantly throughout the wavelength range of 7 to 14µm. Different materials can have widely different emissivity values within the range of 0 to 1.00 (see table below).

Many common materials including plastics, ceramics, water, and organic materials have high emissivity. Uncoated metals may have very low emissivity. Polished stainless steel, for example, has an emissivity of approximately 0.1 and therefore emits only one tenth the amount of energy of a blackbody at the same temperature.

Note: The emissivity date in the table above are approximate values. The emissivity of a particular material depends on its specific chemical makeup and surface characteristics. Smooth, shiny surfaces, for example, tend to have higher reflectivity and thus, low emissivity.

Increasing Emissivity

The surface characteristics of a material determine its emissivity. To increase a material’s emissivity, it is necessary to increase the emissivity of its surface. Following are several methods of altering a material’s surface to increase its emissivity. For a given material, one or more of these approaches may be effective. Choose the method that is easiest to apply/remove and that has minimum affect on the temperature of the material. Apply coatings, treatments, liquids, tapes, or powders as thin as possible to prevent altering the thermal behavior of the original material.

• Apply thin masking tape

• Apply thin polyimide tape with silicone adhesive

• Apply a thin layer of paint

• Apply a permanent surface treatment such as anodizing

Determining Emissivity

Optotherm Thermalyze software has the ability to compensate for emissivity so that accurate temperature measurements can be made of materials with emissivity below 1.00. The accuracy of the measurement, however, is determined by the precision to which the emissivity value and ambient temperature are known. Additionally, the temperature of objects in the environment must be uniform. Radiance from objects that are hotter or colder than the surroundings can reflect off of the target and affect the accuracy of emissivity compensation.

Small changes in an object’s emissivity can result in noticeable affects on measured temperature. A 0.02 reduction in emissivity, for example, can decrease the measured temperature of an object at 100°C by approximately 2°C. Likewise, variations in the ambient temperature can affect measured temperature. An increase in ambient temperature of 5°C, for example, can increase measure temperature of an object at 40°C with emissivity of 0.80 by approximately 1°C.

In order to compensate for the emissivity of an object, its emissivity must first be determined. There are two basic approaches to determining surface emissivity; surface treatment or material heating. Surface treatment involves applying a treatment that is of a known high emissivity (usually tape or paint) to the surface of the object and then heating the surface. Material heating involves uniformly heating the object to a known steady-state temperature that is above ambient temperature.

During both procedures, best results are achieved when the object is heated to a temperature close to the temperature at which measurements are to be taken during testing. If performed properly, correct emissivity values can be obtained using either approach. The chosen method will depend on the characteristics of the surface and size or shape of the object.

Surface Treatment

This method should be employed when the object’s size and shape facilitates applying a small section of masking tape. Masking tape is the preferred surface treatment for object temperatures below 100°C due to its uniform emissivity (0.95) and thickness.

Alternatively, a thin dab of paint or white-out can be used on objects with small or uneven surfaces where tape cannot be applied. The disadvantages of using paint or white-out are the possibility of deviations in coating emissivity and thermal diffusion due to variations in application thickness. If care is taken during the application of the coating, however, uniform results can be obtained.

To determine an object’s emissivity using the surface treatment method, follow these steps:

1. Apply a small section of masking tape to the area of interest making sure to leave a section of the original surface exposed.

2. Heat the surface to a temperature that is below 100°C. Heating can be accomplished by different methods including powering the device or heating the surface using a heating plate or hot air g.

3. Capture a thermal image of the heated surface. Note: Make sure that the heating source is not reflecting off of the exposed surface when the image is captured.

4. Draw a small region enclosing the tape and a second small region enclosing the exposed surface.

5. Set the emissivity of the region enclosing the tape to 0.95.

6. Adjust the emissivity of the region enclosing the exposed surface until the temperatures within both regions are equal. Record the emissivity of the obj.

Material Heating

This method should be employed when tape or paint cannot be applied to the surface due to an object’s small size or surface characteristics. Material heating can also be used to determine the emissivity of different materials comprising a complex object with many different surfaces.

To determine an object’s emissivity using the material heating method, follow these steps:

1. Heat the object to a known uniform steady-state temperature. One of the most common methods of heating small and thin objects, such as semiconductors chips, is using a heating plate. A thermal chamber can also be used provided there is an opening or infrared window on the chamber through which to image the object.

2. Measure the steady-state temperature of the object by measuring the temperature of a high emissivity area in the thermal image or by using a contact temperature probe.

3. Draw a small region enclosing each different surface to be measured.

4. Adjust the emissivity of each region until the temperatures within the regions are equal to the temperature of the object measured in step 2. Record the emissivity of each different surface.

A Note about Contact Temperature Probes

If used in appropriate situations and applied correctly, contact temperature probes such as thermocouples, thermistors, and RTDs can be used to accurately measure surface temperature. Small objects and thin surfaces, however, may not contain enough thermal mass to accurately measure using these devices. In these cases, contact probes can act as heat sinks and lower the temperature of the material, creating erroneous readings.

Also, a good thermal bond must exist between the material and contact probe in order to transfer sufficient thermal energy to heat the probe to the same temperature as the material. In many cases, poor thermal bonding results in erroneous temperature measurements that are much lower than true temperature. Measurement errors due to low thermal mass and poor thermal bonding can result in errors as great 10, 20, or even 30°C when measuring an object at 60°C.

Emissivity Values

Emissivity is a measure of a material’s radiating efficiency. An emissivity of 1.00 implies that the material is 100% efficient at radiating energy. An emissivity of 0.20 implies that the material radiates only 20% of that which it is capable of radiating.

Tables of emissivity values are only approximated values for real materials. A range of emissivity values is usually given for many materials whose emissivity can be affected by surface roughness or finish. Additionally, thin sheets of material such as plastics may be semi-transparent in the infrared and therefore have reduced emissivity.

To optimize the surface temperature measurement of a material:

• Avoid reflections by shielding the material from surrounding high temperature objects.

• For semi-transparent materials such as plastic film, assure that the background is uniform and lower in temperature than the material.

• Conduct the measurement perpendicular to the material’s surface whenever the emissivity is less than approximately 0.90. In all cases, do not exceed angles greater than 30 degrees from perpendicular.

Note: Applicable for material temperatures from 0 to 250°C