Theory of Lunar Occultation: New Methods of Estimating Brightness Distributions and Their Widths

Abstract

view Abstract Citations (3) References (11) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Theory of Lunar Occultation: New Methods of Estimating Brightness Distributions and Their Widths Lang, Kenneth R. Abstract In order to deduce new methods for determining brightness distributions and their widths, the formulae for the monochromatic radiation intensity at the Earth during the lunar occultation of a radio- frequency source are examined. It is shown that, when the source is sufficiently narrow, the oscillatory portion of the radiation intensity may be assigned an envelope amplitude and a phase for each value of time. Each complex number thus defined gives the amplitude and phase of one spatial Fourier component of the source brightness distribution. When the intensity is observed over a narrow band of frequencies, the oscillatory term of the monochromatic intensity is shown to be modified by multiplication with a certain function of frequency and bandwidth. In light of these derivations, a method is specified in this paper by which the Fourier components of the source brightness distribution may he obtained from the intensity observed as the source passes behind the Moon. Because only a finite number of data can be observed, spatial frequencies higher than a certain cutoff value are not available. An estimated bright- ness distribution, obtained by taking a Fourier transform of the available Fourier components of the source brightness distribution, is a convolution of the true brightness distribution with a function whose width depends on the number of data used. The Scheuer method of restoration results in a distribution that is the convolution of this estimated distribution with a Gaussian function Both methods of deter- mining brightness distributions have a resolution which depends an the number of useful data, and this number is shown to be a function of antenna aperture, source width, bandwidth, and noise. When source width is all that is required, only the inner part of the envelope of the intensity need be determined. Source widths obtained by directly comparing observed envelopes with theoretical ones compare well with scintillation observations Publication: The Astrophysical Journal Pub Date: December 1969 DOI: 10.1086/150278 Bibcode: 1969ApJ...158.1189L full text sources ADS |