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Published October 11, 2019 | Submitted
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Spatial Distribution of Thermal Radiation at Microwave Frequencies

Abstract

Theoretical and experimental radiation patterns are given in spectral form for the thermal radiation from thin slots or heated wires having dimensions of the order of the comparison wavelength. Maxwell's equations and noise theory form the basis of the analyses in which three independent methods are used to predict a spatial distribution which exhibits interference minima and maxima. In the first, the wave equation is solved for a noise-excited transmission line which is suddenly short- and open-circuited at alternate ends. By a study of the trapped noise currents, it is found that the radiation pattern has an interference structure which is smoothed as the loss is increased. Secondly, a formula is derived for the radiation pattern of a heated wire by a computation of its absorption in an isothermal enclosure and by an application of the principle of detailed balancing. Finally, the pattern of a long thin slot is computed directly using the Leontovich-Rytov distributed source generalization of Nyquist's noise formula. Fraunhofer pattern measurements are taken for a thin slot excited by a gaseous discharge at 10,100 ± 200°K. The pattern measuring apparatus is a Dicke radiometer having the following characteristics: frequency 9200 mc/s, bandwidth to the detector 16 mc/s, modulation frequency 1000 c/s, and residual noise level 0.3 rms°K. The theory and the experiment demonstrate an interference phenomenon even though the source excitation is spatially extended and uncorrelated in time and space. The patterns are not even approximately Lambertian, e.g., a thin slot of 9.5π radians length exhibits a pattern having nine relative maxima in 180° with the maximum emission at 63° from the normal.

Additional Information

Research supported by the U. S. Air Force Office of Scientific Research. The author wishes to express his indebtedness to his advisor, Professor C. H. Papas, for his helpful suggestions, his stimulating criticisms, and his encouragement throughout all phases of this investigation. The author wishes to acknowledge the following helpful discussions of specific topics. Mr. G. D. Boyd, on gaseous discharge tubes Mr. H. H. Kuehl, on antenna theory Professor R. V. Langmuir, on experimental techniques Professor T. Lauritsen, on thermal radiation Professor H. C. Martel, on noise theory Dr. G. F. Smith, on experimental techniques Dr. G. J. Stanley, on radiometer design Mr. C. H. Wilcox, on noise theory. Thanks are also extended to a colleague, H. Feiveson, who read the manuscript; Miss Benita von Klingspor, who prepared the figures; and Mrs. Ruth Stratton, who typed the text. The author is grateful for the generous financial support afforded him under the Howard Hughes Fellowship Program of the Hughes Aircraft Company.

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Created:
August 19, 2023
Modified:
January 14, 2024