References
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The brightness temperature of the sky is related to emitted power per unit wavelength interval via the Rayleigh-Jeans law, which is valid in the mm-wave frequency range, and justifies a linear relationship between emission intensity and temperature, even when dealing with a “grey body” like the atmosphere, rather than a black-body.
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Both S and R outputs contain a (generally large) constant contribution from internal mixer and amplifier noise in the receiver. For sensitivity to small variations in (S-R) this noise contribution must be as small as possible. In the present case, a cryogenically cooled mixer and preamplifier system was employed, with an overall single sideband noise tmperature of 1100 K and Δτz≃0.005 could be detected. The receiver noise contribution to apparent sky brightness temperature is omitted in Eq.'s A.2 and A.3, since it cancels in the difference equation A.4.
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de Zafra, R.L., Parrish, A., Solomon, P.M. et al. A quasi-continuous record of atmospheric opacity at λ = 1.1 mm over 34 days at Mauna Kea observatory. Int J Infrared Milli Waves 4, 757–765 (1983). https://doi.org/10.1007/BF01009694
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DOI: https://doi.org/10.1007/BF01009694