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1. Introduction

The performance of radio interferometers, particularly those operating at millimeter and submillimeter wavelengths, is often limited by fluctuations in the refractive index of the earth's atmosphere caused by water vapor. There is currently an active effort to correct for these fluctuations by using the techniques of water vapor radiometry (e.g. Welch 1994; Bremer 1995) and fast switching between the target and calibrator objects (Holdaway 1992; Holdaway & Owen 1995).

The refractivity of water vapor is dominated by contributions from strong lines in the far infrared part of the spectrum. The refractivity of water vapor is therefore almost constant from radio to submillimeter wavelengths, and is substantially lower in the optical, where temperature variations become the dominating factor. The broad distribution of water vapor in the atmosphere falls off with altitude and has a scale height of approximately 2 km. The fluctuations, however, arise from an irregular distribution of water vapor generated by turbulent mixing.

A comprehensive treatment of the theory of wave propagation in random media is given by Tatarskii (1961, 1971). More recent developments can be found in Tatarskii et al. (1992). Treuhaft & Lanyi (1987) made numerical integrations to model the effect of a turbulent layer of finite thickness, applying the results to VLBI observations. Most discussions of the theory of atmospheric turbulence concentrate on the structure function of the fluctuations, which describes how the phase difference between two points in space varies as a function of their separation. Simple theory (see next section) predicts that the structure function follows a power law, and there have been several measurements using radio interferometers to test this relationship (e.g. Armstrong & Sramek 1982; Sramek 1990; Coulman & Vernin 1991, all using the Very Large Array; Wright & Welch 1990, using Berkeley-Illinois-Maryland Association Millimeter Array; Olmi & Downes 1992, using the millimeter interferometer of the Institut de Radioastronomie Millimétrique). There is a wide scatter in the measured power law indices, some of which is due to the difficulties in measuring the phase fluctuations over sufficiently long time intervals (see Sect. 4.6 (click here)).

An alternative approach is to use an instrument dedicated to observing atmospheric phase fluctuations; existing phase monitors are interferometers that observe a tone of tex2html_wrap_inline128112 GHz from a geosynchronous communications satellite. The phase monitor at the summit of Mauna Kea (Masson 1993) and at the Nobeyama Radio Observatory (Ishiguro et al. 1990) have been operating the longest. These have since been joined by similar instruments at the Owens Valley Radio Observatory (OVRO), the Very Long Baseline Array station on Mauna Kea, and two in Chile which are being used to conduct site tests for the National Radio Astronomy Observatory's proposed Millimeter Array and the Japanese Large Millimeter and Submillimeter Array.

This paper focuses on the temporal power spectrum of atmospheric phase fluctuations measured with the OVRO phase monitor. This analysis is particularly useful for assessing the timescales over which the fluctuations are important, and will be used as the basis for a companion paper that studies phase calibration schemes, both with and without correction from water vapor radiometry. The primary aim of this paper is to develop the tools needed to understand phase monitor power spectra; it is not to make a detailed investigation of the properties of the atmosphere.

The next section describes how simple theory is used to form a model of phase fluctuations which includes the effects of a finite thickness of the turbulent layer, the orientation of the baseline with respect to the wind, and the elevation of the observations. Following this is a brief description of the OVRO phase monitor, the data processing, and an analysis of an illustrative sample of data (Sect. 3). There is then a discussion of the issues and implications of this work, including how to extrapolate data measured by a phase monitor to interferometers with different baselines observing at arbitrary elevation.


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