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Spectral Response (Wavelength)
Every object with a temperature above absolute zero (0 Kelvin) radiates energy over a wide spectral
band. For example, if a significant part of this energy is within the band of 400–700 nm, we can see that
energy. This is the visible light band. This is the case with an electric stove burner at a temperature of
800 °C. The burner appears red or orange to the eye (red hot). That burner is also emitting energy at
other wavelengths, which we can not see. This includes wavelengths in the infrared portion of the
electromagnetic spectrum.
An example of an object emitting energy at wavelengths we can see is the sun. The sun's surface
temperature is about 5750 K. According to Wien's Displacement Law, see Equation 1, the peak
wavelength for this temperature is about 500 nm which happens to be in the visible light band. Thus the
eye detects wavelengths corresponding to the temperature of the Sun.
By the same respect, if we are measuring an object at room temperature, (23 °C or about 296 K), the
peak wavelength is 9.8 μ m which is inside the 8 μ m to 14 μ m band. In fact the temperature
corresponding to a peak wavelength at 8 μ m is 89 °C and the temperature corresponding to a peak
wavelength at 14 μ m is -66 °C. This is one of the reasons the 8 μ m to 14 μ m is widely used in handheld
IR thermometers.
IR thermometers take advantage of this peak wavelength phenomenon. They measure the amount of
energy radiating from an object and calculate temperature based on this measured energy. In most
handheld IR thermometers, the sensor and optical system measure IR energy in the 8 μ m to 14 μ m
band.
The mathematical equation describing the spectral power radiated by a perfect blackbody for a given
wavelength is Planck's Law. If Planck's Law, see Equation 2, is integrated over the entire electro-
magnetic spectrum, this gives us the Stefan-Boltzmann Law. This is the T to the 4th law (T
problem with the Stefan-Boltzmann Law, see Equation 3, is that it is not limited to a specific band. To
get the energy within a certain band, we would need to integrate Planck's Law for the limits of this
bandwidth. This integral cannot be solved analytically.
The mathematical equation describing the peak wavelength for a given temperature is Wien's
Displacement Law.
Equation 1: Wien's Displacement Law
Equation 2: Planck's Law
Basic Infrared Thermometry Theory - Relating to the use of the Product
λ
T =c
max
3
c
1L
L λ T
(
,
)
=
------------------------------------- -
c
1 –
2
λ
------ -
exp
λT
Precision Infrared Calibrator
). The
4
11
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