1.1. Effects of Tropospheric Fluctuations
 Radio signals propagating through the Earth's atmosphere have their phase corrupted by irregularities in the index of refraction. The contribution of charged particles in the ionosphere and interplanetary medium to the phase of the signal scales as ν−1, compared to ν+1 for the neutral troposphere (ν is the radio frequency). At frequencies above approximately 3–8 GHz, fluctuations of the density and the humidity in the neutral troposphere produce the dominant contributions to the total phase fluctuations.
 Two classes of precision phase measurements of radio signals propagating through the Earth's atmosphere will be limited in accuracy by these fluctuations. The first involves round trip propagation between a radio antenna on the ground and a spacecraft (round trip propagation avoids the phase impurity of a frequency standard on board the spacecraft). Low-frequency gravitational wave searches can be conducted in this manner [Tinto and Armstrong, 1998], and high phase precision is needed for a sensitive search.
 The second class of measurements is interferometry, involving simultaneous observations of a celestial radio source with two or more radio telescopes. In connected element interferometry (e.g., the Very Large Array in New Mexico), a single frequency standard is distributed to all the telescopes. In very long baseline interferometry (VLBI), separate high-stability frequency standards (e.g., hydrogen masers) are used at each telescope. In either case, the relative phase stability of oscillators at the different radio telescopes is sufficiently good that the coherence times of observations are limited by phase fluctuations in the local medium (the Earth's troposphere at high radio frequencies). The coherence time decreases rapidly toward higher observing frequency, and is often only 10–30 s at 86 GHz [Rogers et al., 1984]. Interferometric observations require that a source (either the target object or an angularly nearby calibrator) be detectable within one coherence time. The short coherence times at high frequencies result in poor sensitivity. The time variability of the atmospheric coherence time leads to poor calibration of visibility amplitudes, and poor imaging capability.
1.2. Calibration With Water Vapor Radiometers
 At radio frequencies, the refractivity of water vapor is roughly 20 times larger than for dry air [Hill et al., 1982; Owens, 1967]. Because of its high refractivity and inhomogeneous distribution in the atmosphere, water vapor is responsible for most of the tropospheric refractivity fluctuations.
 Water vapor radiometers (WVR) [Elgered, 1993] measure the thermal emission from tropospheric water vapor along a specific line of sight on the sky. The 22 GHz spectral line of water vapor has generally been used. The atmosphere is optically thin in this line under most conditions, so that brightness temperatures are approximately proportional to line-of-sight column densities. At least two spectral channels are used. The first is near 20.8 or 23.8 GHz, on a shoulder of the line. At these two frequencies, the emissivity is nearly independent of the effect of pressure broadening, minimizing the sensitivity of the brightness temperature to the height distribution of the water vapor. A second sensing channel is near 31 GHz, beyond the spectral line. The emission at this frequency is only weakly sensitive to water vapor, but is strongly sensitive to the presence of liquid water in the atmosphere. This high-frequency channel is thus useful for detection of clouds, which corrupt WVR determinations of water vapor.
 The refractivity of water vapor is nearly proportional to ρv/T, where ρv is the vapor density and T is the absolute temperature. Therefore, WVR brightness temperatures can be used to infer the time-variable delay in the same direction, potentially improving the accuracy of radio science measurements [Resch et al., 1984] and the coherence of high-frequency interferometry [Welch, 1999]. Knowledge of the temperature profile in the atmosphere improves the accuracy of the brightness temperature to path delay conversion.
 A high-performance WVR-based troposphere calibration system has been designed and built at the Jet Propulsion Laboratory (JPL), in support of radio science measurements on the link between NASA's Deep Space Network (DSN) and the Cassini spacecraft [Tanner, 1998; Keihm and Marsh, 1996]. As a test of the accuracy of this system, the level of phase fluctuations measured with radio interferometry over a 21 km baseline at Goldstone, California, was reduced after application of atmosphere calibration measurements [Naudet et al., 2000].
 The Cassini Troposphere Calibration System was designed to optimize calibration of fluctuations on timescales of 100–10,000 s, with performance at 1000–10,000 s given the highest priority. Because of the timescales of interest, the WVR in this system will be located on the ground, approximately 50 m from the axis of the radio telescope used for the link between Earth and Cassini.
 The offset location of the WVR causes its sampled troposphere volume to be different (little or no overlap) from the tropospheric volume traversed between the spacecraft and the radio telescope. As a result, accurate calibration of fluctuations on short timescales (<100 s) is not possible [Linfield and Wilcox, 1993]. A different WVR location is needed for calibration of short-timescale radio science measurements or millimeter-wavelength interferometry.
 The volume mismatch can be eliminated by integrating a WVR into a beam waveguide (BWG) antenna. Tests of such a configuration have been encouraging [Tanner, 2000]. However, there will be significant challenges in designing such a system, especially the difficulty of splitting the three WVR frequencies from the signals used for the spacecraft uplink and downlink. Such a splitting must be extremely stable, in terms of amplitude loss and added noise. In addition, a calibration capability is desired for non-BWG antennas. It is worthwhile considering other WVR configurations.
 Two WVR configurations were analyzed in this study. The first consists of a radiometer mounted on the back of a radio telescope subreflector, as illustrated schematically in Figure 1. The WVR would have a conical beam that is coaxial with the cylindrical near-field beam of the radio telescope. Because of the substantial overlap between the cylindrical and conical troposphere volumes sampled by the radio telescope and WVR, the volume mismatch can be much smaller than for an offset beam. As with an offset location, a radiometer on the back of a radio telescope subreflector can use a clear aperture reflector to minimize sidelobes. This location avoids two of the problems with an integrated BWG location: scattering off the radio telescope feed legs (causing time-variable ground pickup) and the complication of splitting the signal between the radio science and WVR frequencies.
 The drawbacks of this subreflector location are as follows: (1) It does not completely eliminate the volume mismatch problem, (2) the WVR must have low weight to avoid causing excess flexure of the feed legs, and (3) access to the WVR for maintenance is not as convenient as for an offset location. For reference, the weight of the radiometer in the Cassini Troposphere Calibration System is 150 lb. and the weight of its clear aperture, off-axis parabolic antenna is 60 lb. Minimizing the weight was not a primary consideration in the design of the system.
 The second configuration has an off-axis feed in the focal plane of the radio telescope. This feed samples a cylindrical tropospheric volume which is offset in angle from the source direction. The geometry is illustrated in Figure 2. Like the first configuration, this does not completely eliminate the volume mismatch problem. It has the additional problem of scattering (and time-dependent ground pickup) off the feed legs of the radio telescope. It has the advantage of not adding any weight to be supported by the feed legs. Furthermore, it is compatible with telescopes that have Cassegrain feed rings, such as the Very Large Array (VLA), Very Long Baseline Array (VLBA), and the proposed Atacama Large Millimeter Array (ALMA). This configuration has been proposed for the VLA (using a 22 GHz receiver) [Butler, 1999] and ALMA (using a 183 GHz receiver) [Hills and Richer, 2000; Gibb and Harris, 2000], as a means of improving coherence in high-frequency interferometry.