• DOI:10.1364/AO.16.001113
• Corpus ID: 38214919

Digital hologram reconstruction of radio telescope data.

@article{Kellman1977DigitalHR,
  title={Digital hologram reconstruction of radio telescope data.},
  author={Peter Kellman and Sklar Leonard and Eamon B. Barrett},
  journal={Applied optics},
  year={1977},
  volume={16 5},
  pages={
          1113-4
        }
}

• P. Kellman, S. Leonard, E. Barrett
• Published 1 May 1977
• Physics
• Applied optics

Fourier relations between antenna aperture distributions and their far fields are well known for coherent illumination. Less familiar are those for imaging incoherent sources. Such methods involve interferometry and are the basis for radio astronomy. Stated briefly, the radio star brightness distribution to be determined can be obtained from Fourier transforming measurements made of the complex visibility. The complex visibility is a measure of the complex correlation (or mutual coherence) of the received energy; and, therefore, it is not surprising that it should be a Fourier pair with the actual object intensity distribution. This is known as the well-celebrated Van Cittert-Zernike theorem. In the special case of radio astronomy, the 2-D correlation function is derived from a discretely spaced antenna array, where the vector spacing (measured by wavelengths) determines the spatial frequency. Many spatial frequencies are sampled as the earth rotates. The reconstruction of the source distribution from these samples is named rotational synthesis, which is the subject of this Letter. The Fourier transform relation that has been quoted may be exploited for this purpose, but it is important to note that other methods to estimate the source distribution do exist and may have better properties since such methods (maximum entropy, for instance) account for noise and other errors neglected in a simple analysis. The outstanding advantage of the Fourier method is in its directness and ease of implementation. This Letter will deal with two such implementations of the Fourier transform: optical and digital. The data used in our experiment consist of observations of the double radio source Cygnus-A gathered by the Stanford five-element array. The reconstruction steps are as follows: complex visibility measurements or correlations are recorded from each antenna pair and must be formatted to provide discrete samples of the 2-D complex spectrum of the radio source. Use of a discrete grid involves spatial quantization, which can be quite severe. The sampling grid in the spatial frequency domain is shown in Fig. 1. The digital reconstruction is simply derived from an FFT of the 2-D matrix of complex observations on this grid. The matrix size was 1024 × 1024. The resultant digital reconstruction is shown in Fig. 2. The reconstruction shows two point sources convolved with the synthetic aperture antenna pattern, which gives rise to the ring lobe structure. The experimental procedure for the optical Fourier transform used in this work required a film recording of the input data. Furthermore, since the film transparency has only real and positive transmittance, it was necessary to code the complex data prior to recording. There are several computer holographic methods of coding. In these experiments we used a binary coded phase detour kinoform (with phase quantization into eight bins). A real, positive matrix was recorded with a PDS microdensitometer in write mode. A positive transparency was then illuminated with coherent light from an argon laser, and the resultant spectral components were focused with a simple spherical lens onto film. The output plane recording is shown in Fig. 3. A qualitative comparison between the optical and digital methods shows that the relatively simple optical analog technique produced a reconstruction in which two sources are Fig. 1. Sampling grid in spatial frequency domain.