IR equations

Infrared Thermal Testing IR Equations

My ASNT Level III Pre-Exam Preparatory Self Study Notes 20th April 2015

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Infrared Thermography

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Fion Zhang at Shanghai 20th May 2015

http://meilishouxihu.blog.163.com/

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http://greekhouseoffonts.com/

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IVONA TTS Capable.

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http://www.naturalreaders.com/

IR Equations

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Handbook of nondestructive evaluation

Constants

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 Planck's constant, h = 6.6256 x 10-34, and, the radiation frequency, ʋ cycles per second. (E = hʋ)  c = 2.9979 x 108 ms-1. If these photons traveled at the speed of light, then they must obey the theory of relativity, stating E2 = c2p2, and each photon must have the momentum p = E/c = h/ λ, The frequency can be found by dividing the speed of light by its particle wavelength ʋ = c/λ

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Heat Transfers

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Zeroth law of thermodynamics: If two systems are in thermal equilibrium respectively with a third system, they must be in thermal equilibrium with each other. This law helps define the notion of temperature.

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First law of thermodynamics The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems. The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but cannot be created or destroyed. The first law is often formulated by stating that the change in the internal energy of a closed system is equal to the amount of heat supplied to the system, minus the amount of work done by the system on its surroundings. Equivalently, perpetual motion machines of the first kind are impossible.

First law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out from a system, its internal energy changes in accord with the law of conservation of energy. Equivalently, perpetual motion machines of the first kind are impossible.

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https://en.wikipedia.org/wiki/First_law_of_thermodynamics

Second law of thermodynamics The second law of thermodynamics states that every natural thermodynamic process proceeds in the sense in which the sum of the entropies of all bodies taking part in the process is increased. In the limiting case, for reversible processes this sum remains unchanged.

The second law is an empirical finding that has been accepted as an axiom of thermodynamic theory. Statistical thermodynamics, classical or quantum, explains the law. The second law has been expressed in many ways. Its first formulation is credited to the French scientist Sadi Carnot in 1824 (see Timeline of thermodynamics).

In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases.

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https://en.wikipedia.org/wiki/Second_law_of_thermodynamics

Third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero.[2] With the exception of non-crystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero, and is equal to the log of the multiplicity of the quantum ground states.

The third law of thermodynamics is sometimes stated as follows, regarding the properties of systems in equilibrium at absolute zero temperature: The entropy of a perfect crystal at absolute zero is exactly equal to zero.

At absolute zero (zero kelvin), the system must be in a state with the minimum possible energy, and the above statement of the third law holds true provided that the perfect crystal has only one minimum energy state. Entropy is related to the number of accessible microstates, and for a system consisting of many particles, quantum mechanics indicates that there is only one unique state (called the ground state) with minimum energy.[1] If the system does not have a well-defined order (if its order is glassy, for example), then in practice there will remain some finite entropy as the system is brought to very low temperatures as the system becomes locked into a configuration with non-minimal energy. The constant value is called the residual entropy of the system.

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https://en.wikipedia.org/wiki/Third_law_of_thermodynamics

Kirchhoff's law of thermal radiation In thermodynamics, Kirchhoff's law of thermal radiation refers to wavelengthspecific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium.

A body at temperature T radiates electromagnetic energy. A perfect black body in thermodynamic equilibrium absorbs all light that strikes it, and radiates energy according to a unique law of radiative emissive power for temperature T, universal for all perfect black bodies. Kirchhoff's law states that: For a body of any arbitrary material, emitting and absorbing thermal electromagnetic radiation at every wavelength in thermodynamic equilibrium, the ratio of its emissive power to its dimensionless coefficient of absorption is equal to a universal function only of radiative wavelength and temperature.

That universal function describes the perfect black-body emissive power

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https://en.wikipedia.org/wiki/Kirchhoff%27s_law_of_thermal_radiation

Kirchhoff's circuit laws Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff.[1] This generalized the work of Georg Ohm and preceded the work of Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws.

Both of Kirchhoff's laws can be understood as corollaries of the Maxwell equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits.

The current entering any junction is equal to the current leaving that junction. i2 + i3 = i1 + i4

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https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws

Newton's law of cooling Newton's law of cooling states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings while under the effects of a breeze. As such, it is equivalent to a statement that the heat transfer coefficient, which mediates between heat losses and temperature differences, is a constant. This condition is generally true in thermal conduction (where it is guaranteed by Fourier's law), but it is often only approximately true in conditions of convective heat transfer, where a number of physical processes make effective heat transfer coefficients somewhat dependent on temperature differences. Finally, in the case of heat transfer by thermal radiation, Newton's law of cooling is not true. dQ/dt = hA∆T(t) Q is the thermal energy in joules H is the heat transfer coefficient (assumed independent of T here) (W/m2 K) A is the heat transfer surface area (m2) ∆T(t) is the time-dependent thermal gradient between environment and object

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https://en.wikipedia.org/wiki/Newton%27s_law_of_cooling

Fourier's law The law of heat conduction, also known as Fourier's law, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows. We can state this law in two equivalent forms: the integral form, in which we look at the amount of energy flowing into or out of a body as a whole, and the differential form, in which we look at the flow rates or fluxes of energy locally.

Newton's law of cooling is a discrete analog of Fourier's law, while Ohm's law is the electrical analogue of Fourier's law. →

q = K∇T

→ q = is the local heat flux density, W·m-2 K = is the material's conductivity, W·m-1· K-1 ∇T = is the temperature gradient, K·m-1.

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https://en.wikipedia.org/wiki/Thermal_conduction#Fourier.27s_law

∇

Del, or nabla, is an operator used in mathematics, in particular, in

vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a one-dimensional domain, it denotes its standard derivative as defined in calculus. When applied to a field (a function defined on a multi-dimensional domain), del may denote the gradient (locally steepest slope) of a scalar field (or sometimes of a vector field, as in the Navier–Stokes equations), the divergence of a vector field, or the curl (rotation) of a vector field, depending on the way it is applied.

Strictly speaking, del is not a specific operator, but rather a convenient mathematical notation for those three operators, that makes many equations easier to write and remember. The del symbol can be interpreted as a vector of partial derivative operators, and its three possible meanings—gradient, divergence, and curl—can be formally viewed as the product of scalars, dot product, and cross product, respectively, of the del "operator" with the field.

These formal products do not necessarily commute with other operators or products Charlie Chong/ Fion Zhang

https://en.wikipedia.org/wiki/Del

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NASA EDDY CURRENT TESTING RQA/M 1-5330 .17

Fourier’s law - The One Dimensional Heat Conduction Equation Heat conduction is one of the three modes of heat transfer. In 1822, a French physicist published a treatise giving a complete theory and mathematical model. Who was he, and which mathematical formulation is he most famously known for?

Introduction Heat conduction is transfer of heat from a warmer to a colder object by direct contact. A famous example is shown in A Christmas Story, where Ralphie dares his friend Flick to lick a frozen flagpole, and the latter subsequently gets his tongue stuck to it.

The mathematical model was first formulated by the French physicist Jean Baptiste Joseph Fourier, he of the eponymous Fourier Series. He found that heat flux is proportional to the magnitude of a temperature gradient. His equation is called Fourier's Law.

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NASA EDDY CURRENT TESTING RQA/M 1-5330 .17

Fourier's Law Of Heat Conduction (Joseph Fourier) In a one dimensional differential form, Fourier's Law is as follows: 1) The heat flux per unit area, q = Q/A = - kdT/dx.

The symbol q is the heat flux, which is the heat per unit area, and it is a vector.

Q is the heat rate. dT/dx is the thermal gradient in the direction of the flow.

The minus sign is to show that the flow of heat is from hotter to colder. If the temperature decreases with x, q will be positive and will flow in the direction of x. If the temperature increases with x, q will be negative, and will flow opposite to the direction of x. In the International System of Units SI, q is watts per meter squared (w/m2).

The constant k is the thermal conductivity, and is used to show that not all materials heat up or retain heat equally well. In SI units, k is W/m ∙ K, where W is watts, m is meters, and K is Kelvin. It may also be J/m ∙ s ∙ K, where J is joules and s is seconds. In the English system, it is Btu/h∙ft∙ºF, or British thermal units per horsepower∙ foot∙ Fahrenheit.

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NASA EDDY CURRENT TESTING RQA/M 1-5330 .17

The thermal conductivity is larger for conductors than insulators. Silver is an excellent conductor at 428 W/m ∙ k, and so is copper with its value of 401 W/m*k. Air and wool are insulators and are poor conductors; they are 0.026 and 0.043 W/m ∙ k, respectively.

The heat transfer or conduction rate is a scalar and is 2) The total heat flow, Q = -kA ΔT/L, where L is the length of the slab. ΔT is the temperature difference between two different surfaces.

Equations 1 and 2 show that heat can be considered to be a flow. The flow of heat depends upon the thickness of the material, the area, and the conductivity, all of which combine to retard or resist this flow.

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NASA EDDY CURRENT TESTING RQA/M 1-5330 .17

Example A slab that is made from copper has a length of 10 cm and an area that is 90 cm2. The front side is heated to 150ยบC and the back to 10ยบC. Find the heat flux q and the heat flow rate Q in the slab once steady state is reached.

Assume dT/dx is constant.

From equation 1, we have q = -kA (Tback - Tfront) / L = - (401 W/m*K) * (10ยบC 150ยบC)/0.1 m = 5.6 x 105 W/m2. The heat rate is Q = qA = q(90 x 10-4 m2) = 5.1 x 103 watts or J/s.

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NASA EDDY CURRENT TESTING RQA/M 1-5330 .17

Fourier’s Law An empirical relationship between the conduction rate in a material and the temperature gradient in the direction of energy flow, first formulated by Fourier in 1822 [see Fourier (1955)] who concluded that "the heat flux resulting from thermal conduction is proportional to the magnitude of the temperature gradient and opposite to it in sign". For a unidirectional conduction process this observation may be expressed as: q = k∙dT/dx where the vector q is the heat flux (W/m2) in the positive x-direction, dT/dx is the (negative) temperature gradient (K/m) in the direction of heat flow (i.e., conduction occurs in the direction of decreasing temperature and the minus sign confirms this thermodynamic axiom) and the proportionality constant k is the Thermal Conductivity of the material (W/mK). Fourier's Law thus provides the definition of thermal conductivity and forms the basis of many methods of determining its value. Fourier's Law, as the basic rate equation of the conduction process, when combined with the principle of conservation of energy, also forms the basis for the analysis of most Conduction problems.

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http://thermopedia.com/content/781/

Convection Heat energy is transferred in fluids, either gases or liquids, by convection.

During this process, heat is transferred by conduction from one molecule to another and by the subsequent mixing of molecules. In natural convection, this mixing or diffusing of molecules is driven by the warmer (less dense) molecules’ tendency to rise and be replaced by more dense, cooler molecules.

Cool cream settling to the bottom of a cup of hot tea is a good example of natural convection. Forced convection is the result of fluid movement caused by external forces such as wind or moving air from a fan. Natural convection is quickly overcome by these forces, which dramatically affect the movement of the fluid. Figure 9-2 shows the typical, yet dramatic, pattern associated, in large part, with the cooling effect of convection on a person’s nose.

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FIGURE 9-2.

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Newton’s Law of Cooling describes the relationship between the various factors that influence convection: Q = h × A × ∆T where Q = heat energy h = coefficient of convective heat transfer A = area ∆T = Temperature difference The coefficient of convective heat transfer is often determined experimentally or by estimation from other test data for the surfaces and fluids involved. The exact value depends on a variety of factors, of which the most important are velocity, orientation, surface condition, geometry, and fluid viscosity.

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Changes in h can be significant due merely to a change in orientation. The topside of a horizontal surface can transfer over 50% more heat by natural convection than the underside of the same surface. In both natural and forced convection, a thin layer of relatively still fluid molecules adheres to the transfer surface. This boundary layer, or film coefficient, varies in thickness depending on several factors, the most important being the velocity of the fluid moving over the surface. The boundary layer has a measurable thermal resistance to conductive heat transfer. The thicker the layer, the greater the resistance. This, in turn, affects the convective transfer as well. At slow velocities, these boundary layers can build up significantly. At higher velocities, the thickness of this layer and its insulating effect are both diminished. Why should thermographers be concerned with convection? As forced convection, such as the wind, increases, heat transfer increases and can have a significant impact on the temperature of a heated or cooled surface. Regardless of velocity, this moving air has no affect on ambient surfaces (?) . Thermographers inspect a variety of components where an increase in temperature over ambient is an indication of a potential problem.

Forced convection is capable of masking these indications.

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Radiation In addition to heat energy being transferred by conduction and convection it can also be transferred by radiation. Thermal infrared radiation is a form of electromagnetic energy similar to light, radio waves, and x-rays. All forms of electromagnetic radiation travel at the speed of light, 186,000 miles/second (3 Ă— 108 meters/second).

All forms of electromagnetic radiation travel in a straight line as a waveform; they differ only in their wavelength. Infrared radiation that is detected with thermal imaging systems has wavelengths between approximately 2 and 15 microns (Οm). Electromagnetic radiation can also travel through a vacuum, as demonstrated by the sun’s warming effect from a distance of over 94 million miles of space. All objects above absolute zero radiate infrared radiation. The amount and the exact wavelengths radiated depend primarily on the temperature of the object. It is this phenomenon that allows us to see radiant surfaces with infrared sensing cameras.

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Thermal diffusivity In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure.[1] It measures the ability of a material to conduct thermal energy relative to its ability to store thermal energy. It has the SI unit of m²/s. Thermal diffusivity is usually denoted α but a, κ, K,and D are also used. The formula is:

α = k/(ρCp) Where: k = Heat conductivity ρ = density Cp = Specific heat The diffusivity determine how fast a material heat up or cool down.

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Thermal Conductivity Thermal conductivity k is the relative one dimensional capability of a material to transfer heat. It affects the speed (thus time, t) that a given quantity of heat applied to one point in a slab of material will travel a given distance within that material to another point cooler than the first. Thermal conductivity is high for metals and low for porous materials. It is logical. therefore. that heat will be conducted more rapidly in metals than in more porous materials. Although thermal conductivity varies slightly with temperature in solids and liquids and with temperature and pressure in gases, for practical purposes it can be considered a constant for a particular material. Table 2.1 is a list of thermal properties for several common materials.

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Heat Capacity (thermal capacitance) The heat capacity of a malerial or a structure describes its ability to store heat.

It is the product of the specific thermal energy Cp and the density ρ of the material. When thermal energy is stored in a structure and then the structure is placed in a cooler environment, the sections of the structure that have low heat capacity will change temperature more rapidly because less thermal energy is stored in them. Consequently, these sections will reach thermal equilibrium with their surroundings sooner than those sections with higher heat capacity. thermal capacitance (Volumetric heat capacity) J/(m³·K) = Cp x ρ where ρ is density kg/m³ Cp is specific heat capacity J/(kg·K)

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The term thermal capacitance is used to describe heat capacity in terms of an electrical analog. where loss of heat is analogous to loss of charge on a capacitor. Structures with low thermal capacitance reach equilibrium sooner when placed in a cooler environmcnt than those with high thermal capacitance. This phenomenon is exploited when performing unstimulated nondestructive testing of structures, specifically when locating water saturated sections on flat roofs. This is discussed in greater detail in Chapter 5,

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Thermal Diffusivity

As in emissivity ε. the heat conducting properties of materials may vary from sample to sample. depending on variables in the fabrication process and other factors.

Thermal diffusivity α is the 3D expansion of thermal conductivity in any given material sample. Diffusivily relates more to transient heat flow, whereas conductivity relates to steady state heat flow. It takes into account the thermal conductivity k of the sample, its specific heat Cp and its density ρ. Its equation is

α = k/(ρ∙Cp) cm2s-1. where α = Heat diffusivity m²/s ρ is density kg/m³ Cp is specific heat capacity J/(kg·K) k is thermal conductivity W/(m·K) Together, can be considered the volumetric heat capacity J/(m³·K). https://en.wikipedia.org/wiki/Thermal_diffusivity

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Because thermal diffusivity of a sample can be measured directly using infrared thermography, it is used extensively by the materials flaw evaluation community as an assessment of a test sample's ability to carry heat away, in all directions, from a heat injection site. Table 2.1 lists thermal diffusivities for several common materials in increasing order of thermal diffusivity. Several protocols for measuring the thermal diffusivity of a test sample are described by Maldague.

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Radiation Principle of Blackbody

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Radiation Principles of a Black Body The radiation law by Planck shows the basic correlation for non-contact temperature measurements: It describes the spectral specific radiation Mλs of the black body into the half space depending on its temperature T and the wavelength λ. A blackbody doesn't emit equal amounts of radiation at all wavelengths; instead, most of the energy is radiated within a relatively narrow band of wavelengths. The location of that band varies with the body's temperature; for example: very cold gas in inter-stellar space 20K (radio) a live human being 310K (infrared) The exact amount of energy emitted at a particular wavelength λ is given by the Planck function: energy (Joules) emitted per second per unit wavelength

Where: c light speed, C1 3.74∙10-16 W m2, C2 1.44∙10-2 K∙m, h Planck‘s constant Charlie Chong/ Fion Zhang

http://spiff.rit.edu/classes/phys317/lectures/planck.html

Obviously, if one integrates from the shortest possible wavelength (lambda = 0) to the longest possible wavelength (lambda = infinity), and multiplies by (pi), one ought to end up with the same total energy emitted per second as given by the Stefan-Boltzmann Law: energy per second per square meter, R(T) = σT4 where σ is the Stephan-Boltzman constant (= 5.67×10-8 W/(m2·K4)) and T is the temperature of the surface in kelvin.

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http://spiff.rit.edu/classes/phys317/lectures/planck.html

The Sun’s Electromagnetic Spectrum The energy that reaches the Earth is known as solar radiation. Although the sun emits radiation at all wavelengths, approximately 44% falls within visible-light wavelengths. The region of the spectrum referred to as visible light (light our eyes can detect) is composed of relatively short wavelengths in the range 400 nanometers (nm), or 0.4 micrometers (μm), through 700 nm, or 0.7 μm.

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http://www.ces.fau.edu/nasa/module-2/radiation-sun.php

Infrared radiation that is detected with thermal imaging systems has wavelengths between approximately 2 and 15 microns (Îźm). (2 x 10 m ~15 x 10 -6

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-6

m)

Stephen-Boltzmann Law Is the wavelength independent rate of emission of radiant energy per unit area, given by; W = ε B T4 Planck Law Is the radiation intensity of the emittance at each particular differential wavelength, given by; W(λ) = 2πhc2/(λ5)∙(e hc/λkT – 1)-1 W(λ) = The rate of emission, radiant energy per unit energy as a function of wavelength λ = The wavelength of the emitted radiation h = Planck constant 6.625 x 10-34 J∙s c = Speed of light 2.998 x 108 m∙s-1 k = Boltzmann constant 1.380 x 10-23 J∙K-1 Charlie Chong/ Fion Zhang

Wien Law Wavelength of maximum emittance is given by the single temperature evaluation; λmax =b/T b = Wien displacement constant 2879 μm∙K-1

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Due to atmospheric absorption, significant transmission through air occurs in only two “windows” or wavebands: the short (2~6 μm) and long (8~15 μm) wavebands. Both can be used for many thermal applications. With some applications, one waveband may offer a distinct advantage or make certain applications feasible. These situations will be addressed in subsequent sections. The amount of energy emitted by a surface depends on several factors, as shown by the Stefan–Boltzmann formula: Q = σ × Ɛ × T4 absolute Where: Q = energy transmitted by radiation (per unit area?) σ = the Stefan–Boltzmann constant (0.1714 × 10-8 Btu/hr × ft2 × R4) Ɛ = the emissivity value of the surface T = the absolute temperature of the surface The rate of change of energy transmitted by radiation; ∆Q/ ∆t = σ × Ɛ × A x T4 absolute ？

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Thermal Radiation and Stefan-Boltzmann Equation

â– https://www.youtube.com/embed/93-_JhGNn1Y Charlie Chong/ Fion Zhang

https://www.youtube.com/watch?v=93-_JhGNn1Y

Due to atmospheric absorption, significant transmission through air occurs in only two “windows” or wavebands: the short (2~6 μm) and long (8~15 μm) wavebands. (1μm = 1x 10-6 m, 1nm= 1 x 10-9 m)

0.7 ~ 1.4 μm 1.4 ~ 3.0 μm 3.0 ~ 1.0 x 106 μm

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Due to atmospheric absorption, significant transmission through air occurs in only two “windows” or wavebands: the short (2~6 μm) and long (8~15 μm) wavebands. (1μm = 1x 10-6 m, 1nm= 1 x 10-9 m)

0.7 μm ~ 1 mm

Due to atmospheric absorption, significant transmission through air occurs in only two “windows” or wavebands: the short (2~6 μm) and long (8~15 μm) wavebands.

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When electromagnetic radiation interacts with a surface several events may occur. Thermal radiation may be reflected by the surface, just like light on a mirror. It can be absorbed by the surface, in which case it often causes a change in the temperature of the surface. In some cases, the radiation can also be transmitted through the surface; light passing through a window is a good example. The sum of these three components must equal the total amount of energy involved.

This relationship, known as the conservation of energy, is stated as follows: R+A+T=1 where R = Reflected energy A = Absorbed energy T = Transmitted energy

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Radiation is never perfectly transmitted, absorbed, or reflected by a material.

Two or three phenomena are occurring at once. For example, one can see through a window (transmission) and also see reflections in the window at the same time. It is also known that glass absorbs a small portion of the radiation because the sun can cause it to heat up. For a typical glass window, 92% of the light radiation is transmitted, 6% is reflected, and 2% is absorbed. One hundred percent of the radiation incident on the glass is accounted for.

Infrared radiation, like light and other forms of electromagnetic radiation, also behaves in this way. When a surface is viewed, not only radiation that has been absorbed may be seen, but also radiation that is being transmitted through the target and/or reflected by it. Neither the transmitted nor reflected radiation provides any information about the temperature of the surface.

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The combined radiation reflecting from a surface to the infrared system is called its radiosity. The job of the thermographer is to distinguish the emitted component from the others so that more about the target temperature can be understood. Only a few materials transmit infrared radiation very efficiently.

The lens material of the camera is one. Transmissive materials can be used as thermal windows, allowing viewing into enclosures. The atmosphere is also fairly transparent, at least in two wavebands. In the rest of the thermal spectrum, water vapor and carbon dioxide absorb most thermal radiation. As can be seen from Figure 9-3, radiation is transmitted quite readily in both the short (2–6 μm) and long (8–14 (15) μm) wavebands. Infrared systems have been optimized to one of these bands or the other. Broadband systems are also available and have some response in both wavebands.

A transmission curve for glass would show us that glass is somewhat transparent in the short waveband and opaque in the long waveband. It is surprising to try to look thermally through a window and not be able to see much of anything!

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FIGURE 9-3.

(6μm ~ 8μm)

The atmosphere is also fairly transparent, at least in two wavebands. In the rest of the thermal spectrum, water vapor and carbon dioxide absorb most thermal radiation. (6μm ~ 8 μm)

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Radiosity: The combined radiation reflecting from a surface to the infrared system is called its radiosity.

Radiosity (radiometry) In radiometry, radiosity is the radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area, and spectral radiosity is the radiosity of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength The SI unit of radiosity is the watt per square metre (W/m2), while that of spectral radiosity in frequency is the watt per square metre per hertz (W·m−2 ·Hz−1) and that of spectral radiosity in wavelength is the watt per square metre per metre (W·m−3) - commonly the watt per square metre per nanometre (W·m−2 ·nm−1). The CGS unit erg per square centimeter per second (erg·cm−2 ·s−1) is often used in astronomy. Radiosity is often called "intensity" in branches of physics other than radiometry, but in radiometry this usage leads to confusion with radiant intensity.

radiant intensity (radiometry) In radiometry, radiant intensity is the radiant flux emitted, reflected, transmitted or received, per unit solid angle, and spectral intensity is the radiant intensity per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. These are directional quantities. The SI unit of radiant intensity is the watt per steradian (W/sr), while that of spectral intensity in frequency is the watt per steradian per hertz (W·sr−1 ·Hz−1) and that of spectral intensity in wavelength is the watt per steradian per metre (W·sr−1 ·m−1) - commonly the watt per steradian per nanometre (W·sr−1 ·nm−1). Radiant intensity is distinct from irradiance and radiant exitance, which are often called intensity in branches of physics other than radiometry. In radio-frequency engineering, radiant intensity is sometimes called radiation intensity.

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Many thin plastic films are transparent in varying degrees to infrared radiation.

A thin plastic bag may be useful as a camera cover in wet weather or dirty environments. Be aware, however, that all thin plastic films are not the same!

While they may look similar, it is important to test them for transparency and measure the degree of thermal attenuation. Depending on the exact atomic makeup of the plastic, they may absorb strongly in very narrow, specific wavebands. Therefore, to measure the temperature of a thin plastic film, a filter must be used to limit the radiation to those areas where absorption (and emission) occurs.

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The vast majority of materials are not transparent. Therefore, they are opaque to infrared radiation. This simplifies the task of looking at them thermally by leaving one less variable to deal with. This means that the only radiation we detect is that which is reflected and absorbed by the surface (R + A = 1).

If R = 1, the surface would be a perfect reflector. Although there are no such materials, the reflectivity of many polished shiny metals approaches this value.

They are like heat mirrors. Kirchhoff’s law says that for opaque surfaces the radiant energy that is absorbed must also be reemitted, or A = E. By substitution, it is concluded that the energy detected from an opaque surface is either reflected or emitted (R + E = 1). Only the emitted energy provides information about the temperature of the surface.

In other words, an efficient reflector is an inefficient emitter, and vice versa. For thermographers, this simple inverse relationship between reflectivity and emissivity forms the basis for interpretation of nearly all of that is seen. Emissive objects reveal a great deal about their temperature. Reflective surfaces do not. In fact, under certain conditions, very reflective surfaces typically hide their true thermal nature by reflecting the background and emitting very little of their own thermal energy.

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If E = 1, all energy is absorbed and reemitted. Such an object, which exists only in theory, is called a blackbody. Human skin with an emissivity of 0.98, is nearly a perfect blackbody, regardless of skin color. Emissivity is a characteristic of a material that indicates its relative efficiency in emitting infrared radiation. It is the ratio of thermal energy emitted by a surface to that energy emitted by a blackbody of the same temperature. Emissivity is a value between zero and one. Most nonmetals have emissivities above 0.8. Metals, on the other hand, especially shiny ones, typically have emissivities below 0.2.

Materials that are not blackbodies—in other words everything!—are called real bodies. Real bodies always emit less radiation than a blackbody at the same temperature. Exactly how much less depends on their emissivity.

Several factors can affect what the emissivity of a material is. Besides the material type, emissivity can also vary with surface condition, temperature, and wavelength. The emittance of an object can also vary with the angle of view.

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It is not difficult to characterize the emissivity of most materials that are not shiny metals. Many of them have already been characterized, and their values can be found in tables such as Table 9-2. These values should be used only as a guide. Because the exact emissivity of a material may vary from these values, skilled thermographers also need to understand how to measure the actual value. It is interesting to note that cracks, gaps, and holes emit thermal energy at a higher rate than the surfaces around them. The same is true for visible light. The pupil of your eye is black because it is a cavity, and the light that enters it is absorbed by it. When all light is absorbed by a surface, we say it is “black.� The emissivity of a cavity will approach 0.98 when it is seven times deeper than it is wide.

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NASA EDDY CURRENT TESTING RQA/M 1-5330 .17

From an expanded statement of the Stefan–Boltzmann law, the impact that reflection has on solving the temperature problem for opaque materials can be seen: Q = σ × Ɛ × T4 + (σ × (1 – Ɛ ) × T 4 background)

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The second part of the equation (in boldface) represents that portion of the radiosity that comes from the reflected energy. When using a radiometric system to make a measurement, it is important to characterize and account for the influence of the reflected background temperature. Consider these two possible scenarios: ď Ž When the object being viewed is very reflective, the temperature of the reflected background becomes quite significant. ď Ž When the background is at a temperature that is extremely different from the object being viewed, the influence of the background becomes more pronounced.

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It becomes clear that repeatable, accurate radiometric measurements can be made only when emissivities are high. This is a fundamental limitation within which all thermographers work. Generally, it is not recommended to make temperature measurements of surfaces with emissivities below approximately 0.50, in other words all shiny metals, except under tightly controlled laboratory conditions. However, with a strong understanding of how heat energy moves in materials and a working knowledge of radiation, the value of infrared thermography as a noncontact temperature measurement tool for nondestructive evaluation is remarkable.

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Fourier’s Law

■ https://www.youtube.com/embed/7U9tza1DaqI

Charlie Chong/ Fion Zhang

https://www.youtube.com/watch?v=7U9tza1DaqI

Stefan–Boltzmann formula: Q = σ × Ɛ × T4 absolute

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Stefan–Boltzmann law

■ https://vimeo.com/51844267 Charlie Chong/ Fion Zhang

Stefan–Boltzmann law

■ https://www.youtube.com/embed/8hJx2Kjtz0U Charlie Chong/ Fion Zhang

https://www.youtube.com/watch?v=8hJx2Kjtz0U

Thermal Radiation Principles The intensity of the emitted energy from an object varies with temperature and radiation wavelength. If the object is colder than about 500°C, emitted radiation lies completely within IR wavelengths. In addition to emitting radiation, an object reacts to incident radiation from its surroundings by absorbing and reflecting a portion of it, or allowing some of it to pass through (as through a lens). From this physical principle, the Total Radiation Law is derived, which can be stated with the following formula:

W = αW + ρW +τW, which can be simplified to: 1 = α+ ρ +τ , The coefficients a, r, and t describe the object’s incident energy absorbtion alpha (α), reflection Rho (ρ), and transmission Tau (τ ). Each coefficient can have a value from zero to one, depending on how well an object absorbs, reflects, or transmits incident radiation. For example, if ρ = 0, τ = 0, and α = 1, then there is no reflected or transmitted radiation, and 100% of incident radiation is absorbed. This is called a perfect blackbody. In the real world there are no objects that are perfect absorbers, reflectors, or transmitters, although some may come very close to one of these properties. Nonetheless, the concept of a perfect blackbody is very important in the science of thermography, because it is the foundation for relating IR radiation to an object’s temperature.

Charlie Chong/ Fion Zhang

http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

Keywords: Object’s incident energy:  absorbtion alpha (α),  reflection Rho (ρ),  transmission Tau (τ ),  emissivity epsilon (Ɛ).

Charlie Chong/ Fion Zhang

http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

Fundamentally, a perfect blackbody is a perfect absorber and emitter of radiant energy. This concept is stated mathematical as Kirchhoff’s Law. The radiative properties of a body are denoted by the symbol Ɛ, the emittance or emissivity of the body. Kirchhoff’s law states that α = Ɛ, and since both values vary with the radiation wavelength, the formula can take the form α(λ) = Ɛ(λ), where λ denotes the wavelength.

The total radiation law can thus take the mathematical form 1 = Ɛ + ρ + τ, which for an opaque body (τ = 0) can be simplified to 1 = Ɛ + ρ or ρ = 1 – Ɛ (i.e., reflection = 1 – emissivity). Since a perfect blackbody is a perfect absorber, ρ = 0 and Ɛ = 1. The radiative properties of a perfect blackbody can also be described mathematically by Planck’s Law. Since this has a complex mathematical formula, and is a function of temperature and radiation wavelength, a blackbody’s radiative properties are usually shown as a series of curves (Figure 3).

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http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

Figure 3. Illustration of Planck’s Law

W α T4

Charlie Chong/ Fion Zhang

http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

Wien’s displacement law These curves show the radiation per wavelength unit and area unit, called the spectral radiant emittance of the blackbody. The higher the temperature, the more intense the emitted radiation. However, each emittance curve has a distinct maximum value at a certain wavelength. This maximum can be calculated from Wien’s displacement law, λmax = 2898/T, or (λmax x T = 2.898 x 10-3 m.K) where T is the absolute temperature of the blackbody, measured in Kelvin (K), and λmax is the wavelength at the maximum intensity (in μm). Using blackbody emittance curves, one can find that an object at 30°C has a maximum near 10μm, whereas an object at 1000°C has a radiant intensity with a maximum of near 2.3μm. The latter has a maximum spectral radiant emittance about 1,400 times higher than a blackbody at 30°C, with a considerable portion of the radiation in the visible spectrum.

Charlie Chong/ Fion Zhang

http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

Wien’s displacement law These curves show the radiation per wavelength unit and area unit, called the spectral radiant emittance of the blackbody. The higher the temperature, the more intense the emitted radiation. However, each emittance curve has a distinct maximum value at a certain wavelength. This maximum can be calculated from Wien’s displacement law, λmax = 2898/T, or (λmax x T = 2.898 x 10-3 m.K) where T is the absolute temperature of the blackbody, measured in Kelvin (K), and λmax is the wavelength at the maximum intensity (in μm). Using blackbody emittance curves, one can find that an object at 30°C has a maximum near 10μm, whereas an object at 1000°C has a radiant intensity with a maximum of near 2.3μm. The latter has a maximum spectral radiant emittance about 1,400 times higher than a blackbody at 30°C, with a considerable portion of the radiation in the visible spectrum. λmax in meter, T in Kelvin.

Charlie Chong/ Fion Zhang

http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html

Wien's Displacement Law When the temperature of a blackbody radiator increases, the overall radiated energy increases and the peak of the radiation curve moves to shorter wavelengths. When the maximum is evaluated from the Planck radiation formula, the product of the peak wavelength and the temperature is found to be a constant.

Charlie Chong/ Fion Zhang

http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html#c3

This relationship is called Wien's displacement law and is useful for the determining the temperatures of hot radiant objects such as stars, and indeed for a determination of the temperature of any radiant object whose temperature is far above that of its surroundings.

It should be noted that the peak of the radiation curve in the Wien relationship is the peak only because the intensity is plotted as a function of wavelength. If frequency or some other variable is used on the horizontal axis, the peak will be at a different wavelength.

Charlie Chong/ Fion Zhang

http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html

Wien's displacement law states that the black body radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck radiation law which describes the spectral brightness of black body radiation as a function of wavelength at any given temperature. However it had been discovered by Wilhelm Wien several years before Max Planck developed that more general equation, and describes the entire shift of the spectrum of black body radiation toward shorter wavelengths as temperature increases. Formally, Wien's displacement law states that the spectral radiance of black body radiation per unit wavelength, peaks at the wavelength λmax given by:

λmax x T = b (2.898 x 10-3 m.K) where T is the absolute temperature in Kelvin. b is a constant of proportionality called Wien's displacement constant, equal to 2.8977721(26)×10−3 m K. If one is considering the peak of black body emission per unit frequency or per proportional bandwidth, one must use a different proportionality constant. However the form of the law remains the same: the peak wavelength is inversely proportional to temperature (or the peak frequency is directly proportional to temperature). Wien's displacement law may be referred to as "Wien's law", a term which is also used for the Wien approximation.

Charlie Chong/ Fion Zhang

http://en.wikipedia.org/wiki/Wien%27s_displacement_law

Stefan-Bolzmann law From Planck’s law, the total radiated energy W from a blackbody can be calculated. This is expressed by a formula known as the Stefan-Bolzmann law: W = σ ∙ T4 (W/m2), (here the emissivity Ɛ was assumed =1) where σ is the Stefan-Bolzmann’s constant (5.67 × 10–8 W/m2K4). As an example, a human being with a normal temperature (about 300 K) will radiate about 500W/ m2 of effective body surface. As a rule of thumb, the effective body surface is 1m2, and radiates about 0.5kW - a substantial heat loss. The equations described in this section provide important relationships between emitted radiation and temperature of a perfect blackbody. Since most objects of interest to thermographers are not perfect blackbodies, there needs to be some way for an IR camera to graph the temperature of a “normal” object.

Charlie Chong/ Fion Zhang

http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

Radiation Curves (Intensity Plot)

The wavelength of the peak of the blackbody radiation curve decreases in a linear fashion ? as the temperature is increased (Wien's displacement law).

This linear variation is not evident in this kind of plot since the intensity increases with the fourth power of the temperature (Stefan- Boltzmann law).

The nature of the peak wavelength change is made more evident by plotting the fourth root of the intensity.

Charlie Chong/ Fion Zhang

http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html

Radiation Curves (Intensity Plot)

Charlie Chong/ Fion Zhang

http://en.wikipedia.org/wiki/Wien%27s_displacement_law

Summarizing How a perfect black body changes with temperatures?  The λmax changes in a linear manner ? ( inversely proportionally) according to Wien's Displacement Law  The total total radiated energy W changes in a fourth power T4 proportionally according to Stefan-Bolzmann law

Charlie Chong/ Fion Zhang

http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html

Thermal Diffusivity As in emissivity Ɛ. the heat conducting properties of materials may vary from sample to sample. depending on variables in the fabrication process and other factors.

Thermal diffusivity α is the 3D expansion of thermal conductivity in any given material sample. Diffusivily relates more to transient heat flow, whereas conductivity relates to steady state heat flow. It takes into account the thermal conductivity k of the sample, its specific heat Cp, and its density ρ. Its equation is

α = k/ρ Cp cm2s-1.

Because thermal diffusivity of a sample can be measured directly using infrared thermography, it is used extensively by the materials flaw evaluation community as an assessment of a test sample's ability to carry heat away, in all directions, from a heat injection site. Table 2.1 lists thermal diffusivities for several common materials in increasing order of thermal diffusivity. Several protocols for measuring the thermal diffusivity of a test sample are described by Maldague.

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Emissivity ε, reflection ρ , transmission τ and absorption σ

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The Black Body A black body is a radiator, which absorbs all incoming radiation. It shows neither reflection nor transmissivity. α = ε = 1 (α absorption, ε emissivity) A black body radiates the maximum energy possible at each wavelength. The concentration of the radiation does not depend on angles. The black body is the basis for understanding the physical fundaments of non-contact temperature measurement and for calibrating the infrared thermometers.

Charlie Chong/ Fion Zhang

http://physics.unm.edu/Courses/Finley/p262/ThermalRad/ThermalRad.html

Drawing of a black body: 1 - ceramic conduit, 2 - heating, 3 - conduit made from Al2O3, 4 – aperture

Charlie Chong/ Fion Zhang

Cavity radiator——A hole, crack, scratch, or cavity that will have a higher emissivity that the surrounding surface because reflectivity is reduced. A cavity seven times deeper than wide will have an emissivity approaching 0.98.

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The following illustration shows the graphic description of the formula depending on 位 with different temperatures as parameters.

Spectral specific radiation M位s of the black body depending on the wavelength

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With rising temperatures the maximum of the spectral specific radiation shifts to shorter wavelengths. As the formula is very abstract it cannot be used for many practical applications. But, you may derive various correlations from it.

By integrating the spectral radiation intensity for all wavelengths from 0 to infinite you can obtain the emitted radiation value of the body as a whole. This correlation is called Stefan-Boltzmann-Law.

Ďƒ = 5,67∙10-8 WM-2K-4

Charlie Chong/ Fion Zhang

The entire emitted radiation of a black body within the overall wavelength range increases proportional to the fourth power of its absolute temperature.

The graphic illustration of Planck’s law also shows, that the wavelength, which is used to generate the maximum of the emitted radiation of a black body, shifts when temperatures change. Wien’s displacement law can be derived from Planck’s formula by differentiation.

The wavelength, showing the maximum of radiation, shifts with increasing temperature towards the range of short wavelengths.

Charlie Chong/ Fion Zhang

The Grey Body Only few bodies meet the ideal of the black body. Many bodies emit far less radiation at the same temperature. The emissivity ε defines the relation of the radiation value in real and of the black body. It is between zero and one. The infrared sensor receives the emitted radiation from the object surface, but also reflected radiation from the surroundings and perhaps penetrated infrared radiation from the measuring object: ε + ρ +τ = 1 ε emissivity ρ reflection τ transmissivity Most bodies do not show transmissivity in infrared, therefore the following applies: ε+ρ=1 This fact is very helpful as it is much easier to measure the reflection than to measure the emissivity.

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Infrared energy reflected at a body surface Hence emissivity is expressed as:Emissivity = Radiation emitted by an object at temperature T Radiation emitted by a Black Body at temperature T

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Emission, reflection and transmission

ρ τ ε

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Emissivity Setting 1. Where the temperature of the target object is higher than the ambient temperature (see heater shown) : ■ Excessively high emissivity settings result in excessively high temperature readings.

■ Excessively low emissivity settings result in excessively low temperature readings.

1. Where the temperature of the target object is lower than the ambient temperature (see door shown): ■ Excessively high emissivity settings result in excessively low temperature readings.

■ Excessively low emissivity settings result in excessively high temperature readings .

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Spectral Transmission

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Charlie Chong/ Fion Zhang

Charlie Chong/ Fion Zhang

Recalling: FIGURE 9-3.

(2–6 μm)

(6μm ~ 8μm)

(8–14 (15) μm)

The atmosphere is also fairly transparent, at least in two wavebands. In the rest of the thermal spectrum, water vapor and carbon dioxide absorb most thermal radiation. (6μm ~ 8μm)

Charlie Chong/ Fion Zhang

Not Used

Mid IR

Not Used

Long IR (Used for Thermography)

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Spectral emissivity of some materials & measurement techniques

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Spectral emissivity of some materials: 1 - Enamel, 2 - Plaster, 3 - Concrete, 4 - Chamotte

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Spectral emissivity of metallic materials: 1 - Silver, 2 - Gold, 3 - Platin, 4 - Rhodium, 5 - Chrome, 6 - Tantalum, 7 - Molybdenum This may result in varying measuring results. Consequently, already the choice of the infrared thermometer depends on the wavelength and temperature range, in which metallic materials show a relatively high emissivity. For metallic materials the shortest possible wavelength should be used, as the measuring error increases in correlation to the wavelength. The optimal wavelength for metals ranges with 0.8 to 1.0μm for high temperatures at the limit of the visible area. Additionally, wavelengths of 1.6 μm, 2.2 μm and 3.9 μm are possible.

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Temperature Measurement of Plastics Transmissivities of plastics vary with the wavelength. They react inversely proportional to the thickness, whereas thin materials are more transmissive than thick plastics. Optimal measurements can be carried out with wavelengths, where transmissivity is almost zero independent from the thickness.

■ Polyethylene, polypropylen, nylon and polystyrene are non- ransmissive at 3.43 μm ■ Polyester, polyurethane, teflon, FEP and polyamide are non-transmissive at 7.9 μm.

For thicker and pigmented films wavelengths between 8 and 14 μm will do.

The manufacturer of infrared thermometers can determine the optimal spectral range for the temperature measurement by testing the plastics material. The reflection is between 5 and 10 % for almost all plastics.

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Spectral permeability of plastics made from polethylene PE.

Spectral transmissivity of plastic layers made of polyester

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Plastics Transmission Spectra

Wave number = 1/位 = 1/(3.33 x 10-4) = 3000 cm-1

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http://www.globalspec.com/reference/50771/203279/Chapter-3-Plastics-Transmission-Spectra

Temperature Measurement of Glass If you measure temperatures of glass it implies that you take care of reflection and transmissivity. A careful selection of the wavelength facilitates measurements of the glass surface as well as of the deeper layers of the glass. Wavelengths of 1.0μm, 2.2μm or 3.9μm are appropriate for measuring deeper layers whereas 5 μm are recommended for surface measurements. If temperatures are low, you should use wavelengths between 8 and 14μm in combination with an emissivity of 0.85 in order to compensate reflection. For this purpose a thermometer with short response time should be used as glass is a bad heat conductor and can change its surface temperature quickly.

Charlie Chong/ Fion Zhang

Spectral transmissivity of glass

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Spectral transmissivity of : Optical Glass (N-BK7 and others)

Charlie Chong/ Fion Zhang

http://www.crystran.co.uk/optical-materials/optical-glass-n-bk7-and-others

Transmissivity of typical infrared materials (1 mm thick) 1 - Glass, 2 - Germanium, 3 - Amorphous Silicon, 4 - KRS5

Charlie Chong/ Fion Zhang

http://www.crystran.co.uk/optical-materials/optical-glass-n-bk7-and-others

Transmissivity of typical infrared materials

Charlie Chong/ Fion Zhang

http://www.crystran.co.uk/optical-materials/optical-glass-n-bk7-and-others

Synthetic Quartz Glass, UV-Grade Fused Silica, Transmission

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http://www.pgo-online.com/intl/katalog/curves/quartz_glass_transmission.html

Reflection Ď , Spectral & Diffuse

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Reflections off Specular and Diffuse Surfaces

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Reflections off Specular and Diffuse Surfaces

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Reflections off Specular and Diffuse Surfaces

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Lambert radiator A Lambert radiator is an object that reflects incident radiation with the optimum diffusion; in other words the incident radiation is reflected with equal strength in all directions. You can measure the temperature of the reflected radiation on a Lambert radiator using the thermal imager.

Charlie Chong/ Fion Zhang

FOV, IFOV calculations

Charlie Chong/ Fion Zhang

geometric

, IFOV

measured

-

FOV (field of view) Field of view of the thermal imager. It is specified as an angle (e.g. 32째) and defines the area that can be seen with the thermal imager. The field of view is dependent on the detector in the thermal imager and on the lens used. Widengle lenses have a large field of view for the same detector.

Charlie Chong/ Fion Zhang

IFOVgeo (Instantaneous Field of View) Geometric resolution (spatial resolution). Measure of the ability of a detector, in conjunction with the lens, to resolve details. The geometric resolution is specified in mrad (= milliradian) and defines the smallest object that, depending on the measuring distance, can still be depicted on the thermal image. On the thermal image, the size of this object corresponds to one pixel.

IFOVmeas (Measurement Instantaneous Field of View) Designation of the smallest object for which the temperature can be accurately measured by the thermal imager. It is 2 to 3 times larger than the smallest identifiable object (IFOV geo). The following rule of thumb applies: IFOVmeas ≈ 3 x IFOVgeo. IFOV meas is also known as the measuring spot.

Charlie Chong/ Fion Zhang

Field of View (FOV) A field of view (FOV) is a specification that defines the size of what is seen in the thermal image. The lens has the greatest influence on what the FOV will be, regardless of the size of the array. Large arrays, however, provide greater detail, regardless of the lens used, compared to narrow arrays. For some applications, such as work in outdoor substations or inside a building, a large FOV is useful. While smaller arrays may provide sufficient detail in a building, more detail is important in substation work. See Figure 4-7.

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Figure 4-7. The field of view (FOV) is a specification that defines the area that is seen in the thermal image when using a specific lens.

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What is IFOV? A measure of the spatial resolution of a remote sensing imaging system.

Defined as the angle subtended by a single detector element on the axis of the optical system. IFOV has the following attributes: â– Solid angle through which a detector is sensitive to radiation. â– The IFOV and the distance from the target determines the spatial resolution.

A low altitude imaging instrument will have a higher spatial resolution than a higher altitude instrument with the same IFOV

Charlie Chong/ Fion Zhang

http://www.ssec.wisc.edu/sose/tutor/ifov/define.html

What is IFOV? IFOV (instantaneous field of view) – smallest object detectable The IFOV (instantaneous field of view), also known as IFOVgeo (geometric resolution), is the measure of the ability of the detector to resolve detail in conjunction with the objective. Geometric resolution is represented by mrad and defines the smallest object that can be represented in the image of the display, depending on the measuring distance. The thermography, the size of this object corresponds to a pixel. The value represented by mrad corresponds to the size of the visible point [mm] a pixel at a distance of 1 m.

Charlie Chong/ Fion Zhang

http://www.academiatesto.com.ar/cms/?q=ifov

Instantaneous Field of View (IFOV) An instantaneous field of view (IFOV) is a specification used to describe the capability of a thermal imager to resolve spatial detail (spatial resolution). The IFOV is typically specified as an angle in milliradians (mRad). When projected from the detector through the lens, the IFOV gives the size of an object that can be seen at a given distance. An IFOV measurement is the measurement resolution of a thermal imager that describes the smallest size object that can be measured at a given distance. See Figure 4-8. It is specified as an angle (in mRad) but is typically larger by a factor of three than the IFOV. This is due to the fact that the imager requires more information about the radiation of a target to measure it than it does to detect it. It is vital to understand and work within the spatial and measurement resolution specific to each system.

Failure to do so can lead to inaccurate data or overlooked findings.

IFOV, θ in milli-radian H in mm = D∙ θ

Charlie Chong/ Fion Zhang

D in meter

H

Figure 4-8. An IFOV measurement is the measurement resolution of a thermal imager that describes the smallest size object that can be measured at a given distance. IFOV is similar to seeing a sign in the distance while IFOV measurement is similar to reading the sign, either because it is closer or larger.

Instantaneous field of view (spatial resolution)/ IFOV measurement (measurement of resolution)

Charlie Chong/ Fion Zhang

Discussion Subject: Answer this web queries from: http://www.thesnellgroup.com/community/ir-talk/f/9/p/1402/5433.aspx wonder if anyone can help me here. I am studying for my employer's Level 2 certification exam and I am using the ASNT supplement booklet to help. They ask a few question about IFOV and spot size calculation and I do not quite understand how they get the answers. basically it is not the answer I want but how they got to the answers.

Question #1: A camera has an IFOV of 1.9 mRad. What is it's theoretical minimum spot size at a distance of 100 cm? Answer is: 0.19 cm (What formula is used for this and are there any units conversion like mm to cm or mRad to something else?)

Question #2: The IFOV measurement of a radiometric system is 1.2 mRad. What is the maximum size object this system can accurately measure at a distance of 25 m? Answer is: 3 cm (now clearly there are unit conversions going on here from meters to cm. So how is it done?)

Question #3: You are looking at an electrical connection 20 m in the air. What IFOV measurement is required to accurately measure the temperature on the 2.54 cm (1 in.) head of a bolt? Answer is: 1.25 mRad (I know it's just a matter of transposing the formula, but again there is units changes and I do not know the formula to apply) Last question: Using an IR system with an IFOV measurement ratio of 180:1. What is the smallest size object you can accurately measure at a distance of 3m (3.3 ft)? Answer is: 16.6 mm or (0.65 in).

NOW this one I kind of figured out using: 1/180 = 0.0055 & 3 m = 3000mm therefore 0.0055 x 3000 = 16.5 Let me know if you all know how to do these problems. I think all I need is the formula and an understanding when and which units to convert.

Charlie Chong/ Fion Zhang

Answer: D= σ•d, IFOV ration= 1/σ = d/D Question #1: A camera has an IFOV of 1.9 mRad. What is it's theoretical minimum spot size at a distance of 100 cm? Answer is: 0.19 cm (What formula is used for this and are there any units conversion like mm to cm or mRad to something else?)

Calculation: D= 1.9 x 1 = 1.9mm or 0.19cm, (100cm = 1m) Question #2: The IFOV measurement of a radiometric system is 1.2 mRad. What is the maximum size object this system can accurately measure at a distance of 25 m? Answer is: 3 cm (now clearly there are unit conversions going on here from meters to cm. So how is it done?)

Calculation: D= 1.2 x 25m = 30mm = 3cm

Charlie Chong/ Fion Zhang

Question #3: You are looking at an electrical connection 20 m in the air. What IFOV measurement is required to accurately measure the temperature on the 2.54 cm (1 in.) head of a bolt? Answer is: 1.25 mRad (I know it's just a matter of transposing the formula, but again there is units changes and I do not know the formula to apply) Calculation: 25.4 = σ x 20, σ = 1.27mRad Last question: Using an IR system with an IFOV measurement ratio of 180:1.

What is the smallest size object you can accurately measure at a distance of 3m (3.3 ft)? Answer is: 16.6 mm or (0.65 in).

Calculation: 1/ σ = d/D = 180, σ = 1/180, D = σ∙d, D = 1/180 x 3 = 0.01667m = 16.7mm (when calculating IFOV ratio, good to use the same unit for all inputs)

Charlie Chong/ Fion Zhang

FOV-Field of view The field of view (FOV) of the thermal imager describes the area visible with the thermal imager (See Fig. 1.3). It is determined by the lens used (e.g. 32째 wide-angle lens or 9째 telephoto lens

Charlie Chong/ Fion Zhang

http://www.testo.in/knowledge-base/online-training/thermography/measuring-spot-measuring-distance/index.jsp

IFOV- Instantaneous Field of View (Smallest measurable object) This defines the size of a pixel according to the distance. With a spatial resolution of the lens of 3.5 mrad and a measuring distance of 1 m, the IFOVgeometric has an edge length of 3.5 mm and is shown on the display as a pixel (See Fig. 1.4).

IFOVgeo = Distance x θ To obtain a precise measurement, the measuring object should be 2~3 times larger than the smallest identifiable object (IFOVgeo).

The following rule of thumb therefore applies to the smallest measurable object (IFOVmeasured ): IFOVmeas ≈ 3 x IFOVgeo

Charlie Chong/ Fion Zhang

http://www.testo.in/knowledge-base/online-training/thermography/measuring-spot-measuring-distance/index.jsp

IFOV- Instantaneous Field of view

IFOVmeas ≈ 3 x IFOVgeo

Charlie Chong/ Fion Zhang

http://www.testo.in/knowledge-base/online-training/thermography/measuring-spot-measuring-distance/index.jsp

Figure 3.8: Instrument field-of-view determination

Charlie Chong/ Fion Zhang

More Reading: IFOVmeas: Measurement Spot Size The one specification related to IFOV and Spatial resolution but perhaps of more practical importance to quantitative thermographers than the IFOV angle, and unfortunately continues to be missing from many imager data sheets, is “Measurement Spot Size“. Defined as the size of the area from which radiometric measurement data are derived, it is used to determine the minimum size of the measurement area where accurate measurements can be made for a given target / distance. As mentioned before, the measurement spot size is not a single IFOV footprint.

Measurement spot size is intrinsically dependent on the IFOV footprint size, but usually consists of several single IFOV footprint elements. Measurement Spot Size is not easily derived from IFOV because imager software algorithms typically rely on several pixels to derive the measurement value, even if ultimately only one pixel is used for the measurement. Without knowing how many pixels are used in the algorithm, or the effect of adjacent pixels on the one the data is taken from, it is impossible to use IFOV alone to calculate an accurate, real world spot size.

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http://www.irinfo.org/11-01-2012-swirnow/

How many pixels (IFOV footprints) are needed for an accurate measurement and in what orientation is the manufacturer’s trade secret? Some manufacturers imply the measurement is made from a 3 x 3 array of pixels or 9 pixels total. Although this does not appear to be an absolute number, no other information is given. Some manufacturers have Field of View calculators on their websites; these will calculate the IFOV value for a given camera, lens and distance, but still give spot size as an IFOV value of a single footprint which then needs to be multiplied by some number of pixels.

There is a term “MFOV” which stands for the “Measurement FOV”, also known as IFOVmeas, and it defines the resolution of the imager for measuring temperature. It is also expressed as an angle in mRad and because multiple IFOV elements are required to make a measurement, it is always larger than the IFOV value and is more representative of the actual spot size required for an accurate measurement.

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http://www.irinfo.org/11-01-2012-swirnow/

There are a couple of ways to determine the measurement spot size. As previously stated, most manufacturers have a spot size measurement calculator which will allow you to approximate the measurement spot size.

However, the best way to measure it is using your camera / lens combination with a procedure such as the one detailed in the standard for measuring distant / target size values for infrared imaging radiometers. This standard is available from Infraspection Institute.

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http://www.irinfo.org/11-01-2012-swirnow/

NETD (Noise Equivalent Temperature Difference) Key figure for the smallest possible temperature difference that can be resolved by the imager. The smaller this value, the better the measuring resolution of the thermal imager.

MRTD - Minimum Resolvable Temperature Difference Minimum Resolvable Temperature Difference is a test developed by the Department of Defense (ASTM Standard E1213) and used to measure the performance of a infrared cameras ability discern the minimum level of thermal sensitivity that a operator of the camera can see. The test involves selecting the smallest test pattern (4 bars with a 7:1 length to width aspect ratio) that can be clearly distinguished by the operator as viewed on a display.

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http://www.prothermographer.com/training/IRBasics/qualitative_thermography/mrtd_minimum_resolvable_temperature_difference.htm

MRTD - Minimum Resolvable Temperature Difference ASTM Standard E1213

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http://www.prothermographer.com/training/IRBasics/qualitative_thermography/mrtd_minimum_resolvable_temperature_difference.htm

Thermal Detectors

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Figure 1.2. Examples of detector materials and their spectral responses relative to IR mid wave (MW) and long wave (LW) bands

InSb, InGaAs, PtSi, HgCdTe (MCT), and layered GaAs/AlGaAs for QWIP (Quantum Well Infrared Photon) detectors.

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http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

SWS- Short Wave System Short-wave systems in particular are susceptible to attenuation by the atmosphere (SWIR/MWIR) Shortwave systems are particularly sensitive to problems with solar glint or excessive solar reflection.

LWS- Long Wave System Long-wave systems, on the other hand, are generally more susceptible to error when used to measure temperatures of very low-emissive surfaces.(LWIR)

operate at 8 to 12Îźm operate at 2 to 6Îźm

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Thermal Detector

QWIP

Thermopile detector (non imaging?)

Quantum detectors are made from materials such as InSb, InGaAs, PtSi, HgCdTe (MCT), and layered GaAs/AlGaAs for QWIP (Quantum Well Infrared Photon) detectors. The operation of a quantum detector is based on the change of state of electrons in a crystal structure reacting to incident photons.

Pyroelectrical detector (non imaging?)

Thermal Imaging detector: Microbolometer: The detectors respond to radiant energy in a way that causes a change of state in the bulk material (e.g., resistance or capacitance, impedance, voltage, current ).

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http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

Figure 2.2. Detectivity (D*) curves for different detector materials

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http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

Table 2.1. Detector types and materials commonly used in IR cameras.

The Kelvin is a unit of measure for temperature based upon an absolute scale. It is one of the seven base units in the International System of Units (SI) and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The Kelvin is defined as the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C or 32.018 °F). In other words, it is defined such that the triple point of water or approximately 0ºC is exactly 273.16 K

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http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

Figure 1.2. Examples of detector materials and their spectral responses relative to IR mid wave (MW) and long wave (LW) bands

InSb, InGaAs, PtSi, HgCdTe (MCT), and layered GaAs/AlGaAs for QWIP (Quantum Well Infrared Photon) detectors.

Charlie Chong/ Fion Zhang

http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

Charlie Chong/ Fion Zhang

http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

Figure 4. Atmospheric attenuation (white areas) with a chart of the gases and water vapor causing most of it. The areas under the curve represent the highest IR transmission.

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http://www.universe-galaxies-stars.com/infrared.html

Figure 4. Atmospheric attenuation (white areas) with a chart of the gases and water vapor causing most of it. The areas under the curve represent the highest IR transmission.

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http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

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Figure 2.13. Relative response curves for a number of IR cameras

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http://www.flirmedia.com/MMC/THG/Brochures/T559243/T559243_EN.pdf

Figure 1.6: Typical blackbody distribution curves and basic radiation laws Stefan-Boltzmann Law Radiant Flux per Unit Area In W/cm2

W= σεT4 ε = emissivity (unity for a blackbody target) σ = Stefan-Boltzmann constant = 5.673 x I0-8 W/m-2∙K-4 T = absolute temperature of target (K)

Wien's Displacement Law λmax = b/T where: λmax = peak wavelength (μm) b = Wien's displacement constant (2897 or 3000 approximately)

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The Fourier conduction Law ( One dimension heat flow) The mathematical relationship that describes heat transfer as a function of the material that heat is conducting through is known as Fourier's law and is given below.

Fourier’s Law: q = k∙A∙(TH-TC)∙L-1 Where: q A k L

= heat transfer per unit time (W) = heat transfer area (m2) = thermal conductivity of material (W/m∙K) = material thickness (m)

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Figure 1.8: Spectral distribution of a blackbody, graybody and nongraybody

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Figure 1.11: Transmission, absorption and reflectance characteristics of glass

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Figure 1.12: Transmission curves of various infrared transmitting material

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Figure 1.12: Transmission curves of various infrared transmitting material

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Figure 3.2: Response Curves of Various Infrared Detectors

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qualitative thermographic

Performance parameters of instruments, therefore, do not include temperature accuracy, temperature repeatability and

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measurement spatial resolution.

Transformation of Infrared Radiation into an Electrical Signal

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Transformation of Infrared Radiation into an Electrical Signal and Calculation of the Object Temperature As per the Stefan-Boltzmann law the electric signal of the detector is as follows:

U~ εT4obj As the reflected ambient radiation and the self radiation of the infrared thermometer is to be considered as well, the formula is as follows:

U detector signal Tobj object temperature Tamb temperature of background radiation Tpyr temperature of the device C device specific constant Charlie Chong/ Fion Zhang

ρ = 1−ε Reflection of the object

http://www.luchsinger.it/pdf/BasicsInfrared.pdf

As infrared thermometers do not cover the wavelength range as a whole, the exponent n depends on the wavelength 位. At wavelengths ranging from 1 to 14 渭m n is between 17 and 2 (at long wavelengths between 2 and 3 and at short wavelengths between 15 and 17).

Thus the object temperature is determined as follows:

The results of these calculations for all temperatures are stored as curve band in the EEPROM of the infrared thermometer. Thus a quick access to the data as well as a fast calculation of the temperature are guaranteed.

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http://www.luchsinger.it/pdf/BasicsInfrared.pdf

Fourier Transform Infrared Spectrometry

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Fourier Transform Infrared Spectrometry FT-IR stands for Fourier Transform InfraRed, the preferred method of infrared spectroscopy. In infrared spectroscopy, IR radiation is passed through a sample. Some of the infrared radiation is absorbed by the sample and some of it is passed through (transmitted). The resulting spectrum represents the molecular absorption and transmission, creating a molecular fingerprint of the sample. Like a fingerprint no two unique molecular structures produce the same infrared spectrum. This makes infrared spectroscopy useful for several types of analysis.

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http://mmrc.caltech.edu/FTIR/FTIRintro.pdf

Fourier Transform Infrared Spectrometry

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http://mmrc.caltech.edu/FTIR/FTIRintro.pdf

Fourier Transformations

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Fourier transformation/ (inverse)/ Fourier synthesis The Fourier transform decomposes a function of time (a signal) into the frequencies that make it up, similarly to how a musical chord can be expressed as the amplitude (or loudness) of its constituent notes. The Fourier transform of a function of time itself is a complex-valued function of frequency, whose absolute value represents the amount of that frequency present in the original function, and whose complex argument is the phase offset of the basic sinusoid in that frequency.

The Fourier transform is called the frequency domain representation of the original signal. The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of time. The Fourier transform is not limited to functions of time, but in order to have a unified language, the domain of the original function is commonly referred to as the time domain.

For many functions of practical interest one can define an operation that reverses this: the inverse Fourier transformation, also called Fourier synthesis, of a frequency domain representation combines the contributions of all the different frequencies to recover the original function of time.

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In the first frames of the animation, a function f is resolved into Fourier series: a linear combination of sines and cosines (in blue). The component frequencies of these sines and cosines spread across the frequency spectrum, are represented as peaks in the frequency domain (actually Dirac delta functions, shown in the last frames of the animation https://en.wikipedia.org/wiki/Dirac_delta_function ). The frequency domain representation of the function,f, is the collection of these peaks at the frequencies that appear in this resolution of the function.

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https://upload.wikimedia.org/wikipedia/commons/7/72/Fourier_transform_time_and_frequency_domains_%28small%29.gif

Fourier transformation

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https://ranabasheer.wordpress.com/2014/03/16/why-do-we-use-fourier-transform/

IRT Applications

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Range: The temperature range defines the maximum to minimum temperature measurement capability of an infrared camera. Many infrared cameras have several ranges, similar to the ranges in a volt-ohm meter. If your target has a temperature higher or lower than the limits of your temperature range, temperature measurement will be impossible. Once an image is saved, its range is locked and cannot be changed with software.

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Span: is the part within the temperature range that we can see on the screen, from black to white. It is a subset of the range and can be adjusted in the camera as well as post analysis computer software. By adjusting the span controls we can make the span larger for less contrast, or smaller to improve contrast. Note how the thermal image changes.

Level: is the middle point of the Span. Level can also be changed in the computer. We can think of Span as thermal contrast and Level as thermal brightness. Adjusting the level allows us to change the thermal brightness of the image. Again note how the thermal image changes as we do this.

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End Of Reading

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Charlie Chong/ Fion Zhang

Terms & Definitions: http://www.infraredtraininginstitute.com/thermography-terms-definitions/ More Reading: http://www.testo.in/knowledge-base/onlinetraining/thermography/measurements-of-glass-and-metal-and-specularreflection/index.jsp

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Good Luck

Charlie Chong/ Fion Zhang

Good Luck

Charlie Chong/ Fion Zhang

https://www.yumpu.com/en/browse/user/charliechong Charlie Chong/ Fion Zhang