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Session:
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5B - Electro-Optics II
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Date & Time:
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Tuesday August 8, 2:30 PM - 4:00 PM
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Paper Title:
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An Approximation Method For Finding Emissivity and Temperature of a Blackbody
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Speaker:
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Larry Paul, Photonucleonics Engineer
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CoAuthors:
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Klaus Jaeger
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Speaker Info
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Company:
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The Bionetics Corporation
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Department:
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Photonucleonics
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Address:
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813 Irving-Wick Drive West
Heath, OH, 43056, United States
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Phone:
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740-788-5403
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Fax:
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740-788-5404
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Email:
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lpaul@afmetcal.af.mil
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Abstract:
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Characterizing temperature sources is required for maintaining a temperature scale. The determination of a blackbody's emissivity and temperature can be found by comparing the measured spectral radiance of a test blackbody to the measured spectral radiance of a standard of known emissivity and temperature. Using Planck's law, calculating the temperature and emissivity of the blackbody can be accomplished by finding the temperature that minimizes the standard deviation of emissivity measurements. This can require specialized programming. An approximation method can be employed that uses simple statistical functions. The temperature and the emissivity of the standard blackbody are known within uncertainties. Spectral radiance measurements are taken of the test blackbody and standard blackbody at a number of wavelengths. The emissivity at each wavelength of the test item is the product of the emissivity of the standard, the standard to test theoretical radiance ratio, and the test to standard measured radiance ratio. The theoretical radiance of the test item is a function of the temperature of the test item according to Planck's law. We want to calculate the test temperature that minimizes the standard deviation of the test emissivities at different wavelengths. To find this temperature within a small uncertainty can require several iterations of calculations when employing an exact Newton method. This paper discusses a method to reduce the calculations by making some assumptions. The uncertainty of this approximation decreases for higher emissivities. The derivation of this method is presented. Results with different degrees of approximation are presented. These results are compared to the results obtained from the exact Newton method. This comparison shows that the method discussed yields good approximations. This method can be employed using simple statistical functions commonly found in spreadsheets without the need for writing specialized code to perform the exact Newton method. This method can also be used to provide a close initial guess for the exact method to reduce the number of iterations required to obtain a prescribed uncertainty.
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