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

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## Abstract

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.

## Keywords

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 (\(\hbox {W}{\cdot }\hbox {m}^{-2}{\cdot }\upmu \hbox {m}^{-1}{\cdot }\hbox {sr}^{-1}\))

- \(S(T)\)
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

- \(T\)
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

## References

- 1.D.P. DeWitt, F.P. Incropera, in
*Theory and Practice of Radiation Thermometry,*chap. 1, ed. by D.P. DeWitt, G.D. Nutter (Wiley, New York, 1989), pp. 21–89Google Scholar - 2.P. Saunders, Meas. Sci. Technol.
**20**, 025104 (2009)CrossRefGoogle Scholar - 3.F. Sakuma, S. Hattori, in
*Temperature: Its Measurement and Control in Science and Industry*, vol. 5, ed. by J.F. Schooley (AIP, New York, 1982), pp. 421–427Google Scholar - 4.P. Saunders, J. Fischer, M. Sadli, M. Battuello, C.W. Park, Z. Yuan, H. Yoon, W. Li, E. van der Ham, F. Sakuma, J. Ishii, M. Ballico, G. Machin, N. Fox, J. Hollandt, M. Matveyev, P. Bloembergen, S. Ugur, Int. J. Thermophys.
**29**, 1066 (2008)CrossRefADSGoogle Scholar - 5.ASTM Committee E20 on Temperature Measurement, E2758-10 (ASTM International, Conshohocken, PA, 2010)Google Scholar