无线电干涉测量中的电离层功率谱层析成像
Ionospheric Power-Spectrum Tomography in Radio Interferometry
摘要：
本文描述了一种层析成像方法，根据二维平面阵列的无线电干涉观测，对电离层电子密度起伏的三维功率谱进行量化。该方法对一阶玻恩近似是有效的，并可能适用于校正由于全三维电离层的印记而引起的相位变化的观测vitrium。结果表明，在干涉测量中，电离层电子密度分布不是建模的主要结构，而其自相关函数或等效功率谱是建模的主要结构。一个精确的数学表达式推导出，提供了三维功率谱的电离层电子密度波动直接从一个重新缩放的散射强度场和入射强度场卷积与一个复杂的单位相量，取决于W-项，并定义在全天空光瞳平面。在小视场的限制下，该方法简化为单相屏近似。层析成像自校准在使用宽场天线干涉仪进行低射频高动态范围观测时可能变得很重要，因为三维电离层会引起天空的空间变化卷积，而单一相位屏幕会导致空间不变卷积。因此，在不引入校准过程中的误差的情况下，不能用单相屏来近似厚电离层。通过应用Radon投影和傅立叶投影切片定理，证明了在三维空间中的相屏法与层析法是一致的。最后，我们认为，由于短积分中不可校正的电离层相位波动，残余散斑可能会在源周围引起漫射强度晕，这可能会对长积分图像的动态范围造成根本限制。
英文摘要：
A tomographic method is described to quantify the three-dimensional power-spectrum of the ionospheric electron-density fluctuations based on radio-interferometric observations by a two-dimensional planar array. The method is valid to first-order Born approximation and might be applicable to correct observed visibilities for phase variations due to the imprint of the full three-dimensional ionosphere. It is shown that not the ionospheric electron density distribution is the primary structure to model in interferometry, but its autocorrelation function or equivalent its power-spectrum. An exact mathematical expression is derived that provides the three dimensional power-spectrum of the ionospheric electron-density fluctuations directly from a rescaled scattered intensity field and an incident intensity field convolved with a complex unit phasor that depends on the w-term and is defined on the full sky pupil plane. In the limit of a small field of view, the method reduces to the single phase screen approximation. Tomographic self-calibration can become important in high-dynamic range observations at low radio frequencies with wide-field antenna interferometers, because a three-dimensional ionosphere causes a spatially varying convolution of the sky, whereas a single phase screen results in a spatially invariant convolution. A thick ionosphere can therefore not be approximated by a single phase screen without introducing errors in the calibration process. By applying a Radon projection and the Fourier projection-slice theorem, it is shown that the phase-screen approach in three dimensions is identical to the tomographic method. Finally we suggest that residual speckle can cause a diffuse intensity halo around sources, due to uncorrectable ionospheric phase fluctuations in the short integrations, which could pose a fundamental limit on the dynamic range in long-integration images.
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