International Journal of Thermophysics

, Volume 36, Issue 8, pp 1757–1765 | Cite as

Gray-Body Radiation Using a Blackbody Source and an Optical Chopper

  • H. Rodríguez-ArteagaEmail author
  • D. Cárdenas-García


The emissivity of most material surfaces that can be used as radiation sources is a function of wavelength. On the other hand, blackbody cavities with emissivities higher than 0.995 in a wide wavelength range are readily available in many laboratories. If it were possible to attenuate by a constant factor the radiation emitted by those blackbodies, then they could be used as gray-body radiators. A neutral density filter is not an option to attenuate the radiation from a blackbody source because its transmittance is wavelength dependent. Optical choppers, usually rotating disk shutters, are widely used to modulate the intensity of a light beam. The apparent transmittance of an optical chopper is defined in terms of the mark-to-space ratio. Most optical choppers have a 1:1 ratio which would be equivalent to 50 % transmittance. To attenuate the radiation coming from a blackbody, the optical chopper should have a stable rotating speed and a high chopping frequency so its mark-to-space cycle time is very short compared to a radiation thermometer response time. If this condition is fulfilled, the radiation thermometer would display a temperature reading as if it were aiming to a gray-body at the temperature of the blackbody and with an emissivity equal to the optical chopper transmittance. This method to obtain a gray-body radiator using a blackbody source and an optical chopper is discussed, and some measurements including its uncertainty analysis are reported.


Blackbody Emissivity Gray-body Radiance temperature Transmittance 

List of Symbols

\(\varepsilon _{\mathrm{GB}}\)

Spectral emissivity of a gray-body, having a constant value, independent of wavelength

\(\lambda \)

Wavelength (m)

\(L\, (\lambda ,T)\)

Spectral radiance of a surface at given wavelength \(\lambda \) and temperature \(T\) (\(\hbox {W}{\cdot }\hbox {m}^{-2}{\cdot }\upmu \hbox {m}^{-1}{\cdot }\hbox {sr}^{-1}\))

\(L_{\mathrm{b}}(\lambda ,T)\)

Spectral radiance of a blackbody at given wavelength \(\lambda \) and temperature \(T\), as defined by Planck’s radiation law (\(\hbox {W}{\cdot }\hbox {m}^{-2}{\cdot }\upmu \hbox {m}^{-1}{\cdot }\hbox {sr}^{-1}\))


Signal produced in the detector of a radiation thermometer, produced by that part of the radiation energy, emitted and/or reflected from the objects under measurement, that builds an image in the thermometer optical system, arbitrary units


Temperature of an object that could be a blackbody, a gray-body, the surface of a chopper disk, or the surroundings walls (K)

\(\tau _{\mathrm{CD}}\)

Transmittance of a chopper disk, defined by its mark-to-space ratio


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Thermometry DivisionCentro Nacional de MetrologíaEl MarquésMéxico

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