Lumasense-technologies MCS640 Manual Bedienungsanleitung PDF herunterladen (Seite 17)

Section 4 Principles of Thermal Imaging

4.3 Blackbody Radiation

The emissivity of a body is dened formally by the equation below as the ratio of

the radiant energy emitted by the body to the radiation, which would be emitted by a

blackbody at the same temperature.

Where,

o = total radiant energy emitted by a body at a given temperature T.

Wbb = total radiant energy emitted by a blackbody at the same temperature T.

If all energy falling on an object were absorbed (no transmission or reection), the

absorptivity would equal to 1. At a steady temperature, all the energy absorbed could be

re-radiated (emitted) so that the emissivity of such a body would equal 1. Therefore in a

blackbody,

absorptivity = emissivity = 1

Practical real life objects do not behave exactly as this ideal, but as described with

transmissivity and reectivity,

absorptivity + transmissivity + reectivity = 1

Energy radiated from the blackbody is described as follows [“Planck’s Law”.]

(1)

In order to obtain total radiant emittance of the blackbody, integrate the equation (1)

through all wavelengths (0 to innity). The result is as follows and is called “Stefan-

Bolzmann equation.”

(2)

The temperature of blackbody can be obtained directly from the radiant energy of the

blackbody by this equation. In order to nd out the wavelength on the maximum spectral

radiant emittance, differentiate Planck’s law and take the value to 0.

(3)

This equation is called “Wien’s displacement law”.

Note:

A blackbody is a theoreti-

cal surface, which absorbs

and re-radiates all the IR

energy it receives. It does

not reect or transmit any

IR energy. Perfect black-

body surfaces do not exist

in nature.

Planck’s Law

Stefan Bolzmann’s equation

Wien’s displacement law

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Lumasense-technologies MCS640 Manual Bedienungsanleitung Seite 17