Christopher S. Ruf
Department of Electrical Engineering
The Pennsylvania State University
I. Introduction
This report outlines the standard approach by which microwave/millimeter wave radiometers are absolutely calibrated. Common terminology is first defined, followed by a review of the steps involved in radiometer calibration. Modifications to the standard approach are also considered which are necessary to accommodate some of the new radiometer system designs. The standard approach assumes that the radiometer uses a real aperture antenna (typically a reflector, horn, or phased array) and that direct measurements are made of the power in selected linear polarization components of the incident electric field. Modifications to the standard approach are necessary for two new classes of radiometer designs: the "Stoke's" radiometer, which measures the third and/or fourth Stoke's parameters in addition to the standard measurements, which are the first two Stoke's parameters; and the synthetic aperture interferometric radiometer (SAIR), which images the standard polarization components indirectly by measuring the Fourier transform of the image.
II. Definitions
The definitions used here follow the conventions described in [1]-[3]. The temperature equivalent power detected by a radiometer (TRAD) can be decomposed into several sources. The first source is the brightness temperature (TB), defined as the beam averaged thermal emission incident on the radiometer antenna from the direction of its main beam. TB is itself a component of the antenna temperature (TA), which is the beam averaged thermal emission incident on the antenna from all directions. The relationship between TA and TRAD depends on the method used to calibrate the radiometer. If calibration is referenced to the input of the antenna (e.g. by surrounding it by warm or cold absorber loads), then they are equal. If calibration is achieved by switching the input to the radiometer from the antenna to separate warm or cold loads, then the reference point is the input to that switch. In the latter case, the contribution of TA to TRAD is reduced by hardware losses between the antenna and the switch, and an additional component of TRAD is contributed by thermal emission from the lossy hardware. Absolute calibration of a radiometer implies a conversion from measurements of TRAD to estimates of TB (TB is then the input to subsequent geophysical data processing and analysis). The conversion from TRAD to TB can be decomposed according to the sources of TRAD. TA calibration implies conversion from TRAD to TA. This step accounts for thermal emission by and losses due to the radiometer hardware, as noted above, and also corrects for non-ideal emission/reflection properties of the calibration loads. TB calibration implies conversion from TA to TB. This step is essentially an antenna deconvolution process, which typically involves an estimate of the relative sensitivity of the antenna within and outside of its main beam, together with an estimate of the thermal emission incident on the antenna outside of its main beam.
III. Calibration
TB calibration has been attempted in different ways. Direct measurements of the antenna pattern in all directions, together with a model for the mean thermal emission in the side lobes, have been used to predict the side lobe corrections a priori [1], [3]. Alternatively, modeled estimates of TB, together with measurements of TA, have been used to estimate the side lobe corrections from the data [4], [5]. Of particular concern in the latter case is the accuracy of the modeled TB. Clear sky and calm wind conditions over cold, open oceans are particularly amenable to accurate modeling of low TB values [4]-[6]. Selected regions of the Amazon rain forest with very low differential polarization signatures are also good candidates for accurate high TB values [5].
Calibration of a "Stoke's" radiometer is similar to the standard approach described above for the first two Stoke's parameters. One approach to TA calibration of the third and fourth Stoke's parameters, U and V, has been described in [7]. A pair of calibration loads, together with a polarizing grid, is assembled in a geometry which varies the U and V components of TA in a controlled way, thus allowing the necessary hardware calibration coefficients to be estimated. TB calibration of U and V can in principle be approached in either of the two ways discussed above. However, determination of the appropriate antenna patterns will require measurement of the cross-correlation between orthogonal linearly polarized components of the received fields. This is a somewhat non-standard antenna range measurement. The alternative approach to TB calibration requires that an estimate be made of the U and V components of TB during measurement of TA. This could, for example, be accomplished for a spacecraft radiometer using aircraft underflights by a "Stoke's" radiometer, similar to the approach used in [4] for a conventional radiometer.
Calibration of a SAIR requires that one step in the standard approach be modified. The role of TA is replaced by the visibility function, TVIS, which is closely related to the Fourier transform of the angular distribution of TB. The hardware calibration aspects of TA, in the standard approach, are replaced by TVIS calibration. TB calibration in the SAIR context implies a conversion from TVIS to TB, where TB is a function of look angle. This is commonly referred to as image reconstruction. This approach to SAIR calibration is described in [8]. Just as in the standard approach to TB calibration, image reconstruction can be accomplished a priori, using antenna range measurements, or inverted from modeled angular distributions of TB together with coincident measurements of TVIS.
REFERENCES
[1] P.N. Swanson and A.L. Riley, "The SeaSat Scanning Multichannel Microwave Radiometer (SMMR): Radiometric calibration algorithm development and performance," IEEE J. Ocean. Eng., 5(2), 116-124, 1980.
[2] C.S. Ruf, M.A. Janssen, and S.J. Keihm, "TOPEX/POSEIDON Microwave Radiometer (TMR): I. Instrument description and antenna temperature calibration," IEEE Trans. Geosci. Remote Sens., 33(1), 125-137, 1995
[3] M.A. Janssen, C.S. Ruf, and S.J. Keihm, "TOPEX/POSEIDON Microwave Radiometer (TMR): II. Antenna Pattern Correction and Brightness Temperature Algorithm," IEEE Trans. Geosci. Remote Sens., 33(1), 138-146, 1995.
[4] J.P. Hollinger, J.L. Pierce, and G.A. Poe, "SSM/I Instrument Evaluation," IEEE Trans. Geosci. Remote Sens., 28(5), 781-790, 1990.
[5] C.S. Ruf, S.J. Keihm, B. Subramanya, and M.A. Janssen, "TOPEX/POSEIDON Microwave Radiometer Performance and In-flight Calibration," J. Geophys. Res., 99(C12), 24915-24926, 1994.
[6] L.A. Klein and C.T. Swift "An improved model for the dielectric constant of sea water at microwave frequencies," IEEE J. Ocean. Eng., 2, 104-111, 1977.
[7] A.J. Gasiewski and D.B. Kunkee, "Calibration and Applications of Polarization-Correlating Radiometers," IEEE Trans. Geosci. Remote Sens., 41(5), 767-773, 1993.
[8] A.B. Tanner and C.T. Swift, "Calibration of a synthetic aperture radiometer," IEEE Trans. Geosci. Remote Sens., 31(1), 257-267, 1993.
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