While short times scale variations in spectrally resolved infrared radiances are dominated in most locations by changes in cloud height and fraction, and so are not strongly frequency dependent, long term changes forced by increases in infrared emissive gases are expected to produce changes in lapse rate and water vapor distribution that will produce radiative changes that vary strongly across the infrared spectrum. These expected changes, along with our ability to make precisely calibrated observations of such radiances from space, make a compelling case for the development of benchmark observations of infrared radiance. To qualify as benchmark observations, it must be demonstrated that such observations are free of aliasing errors. We show how the expected aliasing and sampling errors in means, variances and covariances of radiance depend on the number, orbit, and footprint of the satellite or satellites used to obtain radiance observations. In particular, we demonstrate the distinct advantage of using true polar (precessing) orbits for observations of annual mean radiances. For zonal mean observations, a single precessing, nadir-viewing satellite is sufficient to produce annual mean radiance observations accurate to 0.1 K in brightness temperature, while at least three sun-synchronous satellites are necessary for such accuracy.