Noise in Maps of the Sun at Radio Wavelengths I: Theoretical Considerations

The Sun is a powerful source of radio emissions, so much so that, unlike most celestial sources, this emission can dominate the system noise of radio telescopes. We outline the theory of noise in maps formed by Fourier synthesis techniques at radio wavelengths, with a focus on self-noise: that is, noise due to the source itself. As a means of developing intuition we consider noise for the case of a single dish, a two-element interferometer, and an $n$ -element array for simple limiting cases. We then turn to the question of the distribution of noise on a map of an arbitrary source observed at radio wavelengths by an $n$ -element interferometric array. We consider the implications of self-noise for observations of the Sun in a companion paper.