Fig. 2.24 The relationship between an object's spatial structure and the measured visibility function. An interferometer allows the visibility to be measured as a function of the length of the baseline. By adjusting one's model to fit the experimental points, one can then obtain the structure of the source by an inverse Fourier transform spaces that are being sampled point by point. To reconstruct a correct representation of the astronomical object, it is essential, if the second dimension is to be properly covered, to have several observational baselines (several separations between the telescopes) and, equally, several different orientations of these baselines relative to the plane of the sky. In practice, it is generally the rotation of the Earth that alters the orientation of the fixed baselines, as, in particular, it is with the VLTI. In the case of a space interferometer, several different distances between the telescopes need to be employed, as well as several different orientations of those baselines relative to the sky. (It needs to be possible to turn the interferometer or, at the very least, to change its orientation relative to the line of sight to the target.)
One of the difficulties of interferometry by measuring visibility (apart, as we have seen, from measuring the actual visibilities accurately), is the necessity for having precise models that allow for the study of the visibility and its variations, in particular as a function of the observational wavelength (chromatic models). While it is not necessary for there to be a systematic knowledge of the visibility in absolute terms, it is often useful, or even indispensable, to study the relative variations of this value as a function of wavelength (for the observation of gaps in protoplanetary disks, for example - see Chap. 7).
18.104.22.168 Detection of Planets via Modulation of the Visibility
A star and a planet in orbit may be considered as a combination of two mutually incoherent sources, with a high level of contrast. In this case, the visibility of this combination via interferometry is equal to the sum of the visibilities, weighted to account for the relative intensity of the sources. Mathematically, this visibility may be expressed by the equation (Borde, 2003):
i/2 V2 + V22 + 2 rVi V2cosy h I2 V 2 = -— (1+7)2-where r = + (237)
Vi and V2 are the visibilities of the individual objects, I1 and I2 their relative intensities and y denotes the angular position of the star/planet system relative to the interferometer's baseline. This visibility function is shown graphically in Fig. 2.25.
Detection of objects with very low luminosity (high contrast) therefore requires an extremely accurate measurement of visibility. The maximum accuracy over several observations is in the region of 10~3.
Cancellation interferometry, also known as dark fringe interferometry or interference coronagraphy, differs uniquely from the method just described in its recombination technique. A diagrammatic representation of such an interferometer is shown in Fig. 2.26.
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