Multiple telescope interferometry

What we learn in this chapter

Radio astronomers have learned to overcome the limitations of diffraction with interferometry, the use of two or more telescopes viewing the same source at the same time. The instantaneous beam of two telescopes is an interference fringe pattern on the sky. As the earth rotates, the pattern sweeps across a postulated point source yielding a time varying interference signal when the signals from the two telescopes are summed or multiplied. Simple examples show that two telescopes on the rotating earth can, in most cases, locate the position of a point source. Each brief two-telescope observation with a given baseline (telescope separation and relative orientation) can be described as a point on a two-dimensional plot (Fourier plane) of the x and y spatial frequencies. For each such point, the detected oscillatory signal yields a value of the complex visibility function V(b) which is one spatial Fourier component of the sky brightness distribution. Large arrays of telescopes making repeated observations as the earth rotates provide additional points in the Fourier plane and thus additional Fourier components. With sufficient coverage of the Fourier plane, the Fourier transform of V(b) yields a reasonable approximation of the true sky brightness function. This process is called aperture synthesis.

Interferometry dominates radio astronomy, e.g., the US VLA and the Australian AT arrays. The greatest antenna spacings yield the highest angular resolution. Very Long Baseline Interferometry (VLBI) with radio telescopes on different continents yields angular resolutions of <1 milliarcsecond (mas) and as low as 0.5 mas if one detector is in high earth orbit as is the Japanese HALCA satellite (space VLBI). Optical interferometry is likely to become important in the near future because new 8-m class optical observatories are being built with one or more pairs of telescopes in close proximity with —100 m spacings, potentially yielding resolutions of ~1 mas.

176 7 Multiple telescope interferometry 7.1 Introduction

Interferometry is an observational technique wherein the interference of electromagnetic waves is used to extract the highest possible angular resolution allowed by basic physical principles. We have seen in Section 5.5 how interference within a single telescope aperture due to atmospheric density fluctuations can lead to speckles from which one can construct, in principle, the image expected in the absence of such fluctuations. Speckle interferometry could also be called single-aperture interferometry.

Here we consider how interference between the signals received from two or more separate telescopes viewing the same object can yield extremely high angular resolution. This could be called multi-aperture interferometry but the usual name is long baseline interferometry. One can think of an array of telescopes viewing the same source as being several small segments of a huge hypothetical telescope of diameter comparable to the spacing between the outermost telescopes of the array. It turns out that one can attain, with some limitations, the higher angular resolution of the hypothetical single large telescope.

The simplest arrangement is two telescopes separated by the distance B known as the baseline. (We redefine the baseline as a vector B below.) In this case, the hypothetical large telescope would have a diameter B, and its angular resolution would be, from (5.8), 0min = 1.22X/B ~ X/B, where X is the wavelength of the radiation. If the separation B is large compared to the individual telescope diameters d, the potential angular resolution will be much better (smaller 0min) than that of one telescope alone with 0min ~ X/d. Because the two telescopes would make up only a small portion of the hypothetical large telescope, the image quality would be terrible. It is much better if more telescopes are used to fill the hypothetical aperture. Nevertheless, even in the two-telescope case, one can obtain information about the angular structure on the fine scale represented by 0min ~ X/B.

Interferometry is now carried out routinely at radio wavelengths. The long wavelengths of radio waves yield very poor angular resolutions for a single telescope because radio wavelengths are so large. The improvement of resolution obtained by interferometry is thus a necessity for radio astronomers.

Arrays of radio telescopes spreading over tens of kilometers yield angular resolutions less than 1". Telescopes on different continents working together routinely yield <0.001" resolution, and earth-bound telescopes working with a satellite can probe angular scales several times smaller than that. The latter two arrangements are called Very Long Baseline Interferometry (VLBI) and Space VLBI respectively. An array of telescopes will produce sky maps with imperfect point-source response functions because the telescopes do not form a complete large telescope. Nevertheless, high-quality maps are obtained through (i) a judicious spacing of the individual telescopes, (ii) the continuously changing orientation of the individual telescopes relative to the celestial source due to the rotation of the earth or the motion of a satellite, and (iii) sophisticated analysis techniques.

Long baseline interferometry at optical wavelengths is now coming into use with the construction of new modern telescopes in groups of two or four. Interferometry of x rays has just been demonstrated in the laboratory. In this chapter, we use radio interferometry as the basis of our discussion. The principles are the same at other (shorter) wavelengths, but the technical hurdles are greater.

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