Calibration of radio interferometric observations becomes increasingly difficult towards lower frequencies. Below ~300 MHz, spatially variant refractions and propagation delays of radio waves traveling through the ionosphere cause phase rotations that can vary significantly with time, viewing direction and antenna location. In this article we present a description and first results of SPAM (Source Peeling and Atmospheric Modeling), a new calibration method that attempts to iteratively solve and correct for ionospheric phase errors. To model the ionosphere, we construct a time-variant, 2-dimensional phase screen at fixed height above the Earth's surface. Spatial variations are described by a truncated set of discrete Karhunen-Loeve base functions, optimized for an assumed power-law spectral density of free electrons density fluctuations, and a given configuration of calibrator sources and antenna locations. The model is constrained using antenna-based gain phases from individual self-calibrations on the available bright sources in the field-of-view. Application of SPAM on three test cases, a simulated visibility data set and two selected 74 MHz VLA data sets, yields significant improvements in image background noise (5-75 percent reduction) and source peak fluxes (up to 25 percent increase) as compared to the existing self-calibration and field-based calibration methods, which indicates a significant improvement in ionospheric phase calibration accuracy.
Deep Dive into Ionospheric Calibration of Low Frequency Radio Interferometric Observations using the Peeling Scheme: I. Method Description and First Results.
Calibration of radio interferometric observations becomes increasingly difficult towards lower frequencies. Below ~300 MHz, spatially variant refractions and propagation delays of radio waves traveling through the ionosphere cause phase rotations that can vary significantly with time, viewing direction and antenna location. In this article we present a description and first results of SPAM (Source Peeling and Atmospheric Modeling), a new calibration method that attempts to iteratively solve and correct for ionospheric phase errors. To model the ionosphere, we construct a time-variant, 2-dimensional phase screen at fixed height above the Earth’s surface. Spatial variations are described by a truncated set of discrete Karhunen-Loeve base functions, optimized for an assumed power-law spectral density of free electrons density fluctuations, and a given configuration of calibrator sources and antenna locations. The model is constrained using antenna-based gain phases from individual self-ca
Radio waves of cosmic origin are influenced by the Earth's atmosphere before detection at ground level. At low frequencies (LF; 300 MHz), the dominant effects are refraction, propagation delay and Faraday rotation caused by the ionosphere (e.g., Thompson, Moran & Swenson 2001; TMS2001 from here on). For a ground-based interferometer (array from here on) observing a LF cosmic source, the ionosphere is the main source of phase errors in the visibilities. Amplitude errors may also arise under severe ionospheric conditions due to diffraction or focussing (e.g., Jacobson & Erickson 1992).
The ionosphere causes propagation delay differences between array elements, resulting in phase errors in the visibilities. The delay per array element (antenna from here on) depends on the line-of-sight (LoS) through the ionosphere, and therefore on antenna position and viewing direction. The calibration of LF observations requires phase corrections that vary over the field-of-view (FoV) of each antenna. Calibration methods that determine just one phase correction for the full FoV of each antenna (like self-calibration; e.g., see Pearson & Readhead 1984) are therefore insufficient.
Ionospheric effects on LF interferometric observations have usually been ignored for several reasons: (i) the resolution and sensitivity of the existing arrays were generally too poor to be affected, (ii) existing calibration algorithms (e.g., self-calibration) appeared to give reasonable results most of the time, and (iii) a lack of computing power made the needed calculations prohibitly expensive. During the last 15 years, two large and more sensitive LF arrays have become operational: the VLA at 74 MHz (Kassim et al. 2007) and the GMRT at 153 and 235 MHz (Swarup 1991). Observations with these arrays have demonstrated that ionospheric phase errors are one of the main limiting factors for reaching the theoretical image noise level.
For optimal performance of these and future large arrays with LF capabilities (such as LOFAR, LWA and SKA), it is crucial to use calibration algorithms that can properly model and remove ionospheric contributions from the visibilities. Field-based calibration (Cotton et al. 2004) is the single existing ionospheric calibration & imaging method that incorporates direction-dependent phase calibration. This technique has been succesfully applied to many VLA 74 MHz data sets, but is limited by design for use with relatively compact arrays.
In Section 2, we discuss ionospheric calibration in more detail. In Section 3, we present a detailed description of SPAM, a new ionospheric calibration method that is appli-cable to LF observations with relatively larger arrays. In Section 4, we present the first results of SPAM calibration on simulated and real VLA 74 MHz observations and compare these with results from self-calibration and field-based calibration. A discussion and conclusions are presented in Section 5.
In this Section, we describe some physical properties of the ionosphere, the phase effects on radio interferometric observations and requirements for ionospheric phase calibration.
The ionosphere is a partially ionised layer of gas between ∼ 50 and 1000 km altitude over the Earth’s surface (e.g., Davies 1990). It is a dynamic, inhomogeneous medium, with electron density varying as a function of position and time. The state of ionization is mainly influenced by the Sun through photo-ionization at UV and short X-ray wavelengths and through injection of charged particles from the solar wind. Ionization during the day is balanced by recombination at night. The peak of the free electron density is located at a height around 300 km. The free electron column density along a LoS through the ionosphere is generally referred to as total electron content, or TEC. The TEC unit (TECU) is 10 16 m -2 which is a typically observed value at zenith during nighttime.
The refraction and propagation delay are caused by a varying refractive index n of the ionospheric plasma along the wave trajectory. For a cold, collisionless plasma without magnetic field, n is a function of the free electron density n e and is defined by (e.g., TMS2001)
with ν the radio frequency and ν p the plasma frequency, given by
with e the electron charge, m the electron mass, ǫ 0 the vacuum permittivity. Typically, for the ionosphere, ν p ranges from 1-10 MHz, but may locally rise up to ∼ 200 MHz in the presence of sporadic E-layers (clouds of unusually high free electron density). Cosmic radio waves with frequencies below the plasma frequency are reflected by the ionosphere and do not reach the Earth’s surface. For higher frequencies, the spatial variations in electron density cause local refractions of the wave (Snell’s Law) as it travels through the ionosphere, thereby modifying the wave’s trajectory. The total propagation delay, integrated along the LoS, results in a phase rotation given by
with c the speed of light in vacuum. For frequencies ν ≫ ν p , this
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