Interferometric Imaging from Space

— 17 — Interferometric imaging from space Andreas QuirrenbachI Abstract Astronomical interferometry, the coherent combination of light from two or more telescopes, can provide images of celestial objects with very high angular resolution. The van Cittert–Zernike theorem forms the theoretical foundation of interferometric measurements and for the reconstruction of images from interferometric data. The closure phase method and phase self-calibration techniques retain useful phase information even if the individual phases are corrupted by instrumen- tal errors. The introduction of a π phase shift in one of the interferometer arms leads to the rejection of on-axis light through destructive interference, enabling observations with extremely high contrast. The most critical technological requirements for space interferometry concern path length control, formation flying, fringe tracking, and specialized optical components. Concepts for space-borne interferometers have been developed covering a wide range of scientific applications and wavelength regimes. Introduction: Why interferometry, why in space? The angular resolution of optical systems with size d operated at a wavelength λ is limited by diffraction to λ/d. High resolution thus implies large optical systems; whenever the desired≈ resolution exceeds the limits of reasonably-sized monolithic telescopes, the entrance aperture has to be split into several smaller collectors, whose separate beams have to be combined coherently. Such systems are commonly called astronomical interferometers; the simplest concept of this kind is shown in Figure 17.1 and discussed in more detail in the following section. Interferometry at radio wavelengths was introduced in the 1950s and has become the dominant technique in radio astronomy today. Optical/near-infrared interferometry, in contrast, has remained more of a specialty employed to address selected astronomical problems, and to make a limited number of fundamental measurements. This is mainly due to the challenging requirement of measuring and con- trolling optical paths within the instrument with sub-wavelength precision, and in particular to the difficulties encountered when doing this on the ground through the Earth’s atmosphere. ILandessternwarte, Universität Heidelberg, Germany 293 294 17. Interferometric imaging from space Space offers a number of advantages, which together enable applications of interferometry that are inconceivable on the ground. The most important of these are: Absence of atmospheric turbulence and dispersion. Typical path length fluctuations for visible/near-IR light through the atmosphere have amplitudes of tens of micrometres and coherence time scales of milliseconds (the latter scaling with λ6/5). Fast servo loops are thus necessary to maintain coherence in ground-based interferometers; the need to measure the phase at a high rate limits the sensitivity. Furthermore, dispersion in air introduces a wavelength dependence of the path length, which needs to be compensated carefully. These requirements obviously do not exist in space. Thermally stable and vibration-free environment. In the absence of atmospheric fluctuations, vibrations and thermal drifts are the dominant sources of path length variations. These are much more easily controllable in space than on the ground. Access to the whole electromagnetic spectrum. Just like single telescopes, interferometers in space do not suffer from atmospheric extinction blocking access to parts of the electromagnetic spectrum. Low background. Above the atmosphere, there is little scattered light and no airglow. The whole interferometer can be cooled to reduce the thermal emission of the optics. This is even more important than cooling of monolithic telescopes, since interferometers usually have many more reflecting surfaces in the light path. Free choice of orientation. In interferometers that are tied to the rotating Earth, the observing geometry changes continuously. This necessitates the inclusion of long delay lines moving at the sidereal rate to compensate the unequal interferometer arm lengths. In space, the geometry can be held fixed for each target, and array layouts are possible in which all interferometer arms have equal lengths, obviating the necessity for long delay lines. On the other hand, measurement and control of the orientation of a telescope array in space is a major challenge, because of the lack of a natural stable platform. Space interferometry has three principal areas of application: precise astrometry, high-resolution imaging, and detection of faint objects near much brighter ones. While the first of these topics is covered in the preceding chapter (Lindegren 2010; see also Unwin et al 2008), the subject of this chapter is an overview of the second and third. The emphasis is on interferometry in the visible and near-infrared, but most of the principles are equally applicable at other wavelengths. Principles of interferometry and aperture synthesis The following sections give a brief introduction to the principles of interferometry and aperture synthesis. For more complete treatments of the subject see 295 the reviews by Shao and Colavita (1992), Quirrenbach (2001), Monnier (2003) and Cunha et al (2007), and the books by Thompson et al (1986) and by Cassen et al (2006). Visibility measurements The most important components of an astronomical interferometer are shown schematically in Figure 17.1: two telescopes or siderostats, delay lines that can be moved to equalize the optical path length in the two interferometer arms, a beam combiner, and detectors. When the delay difference Dext Dint between the two 1 − interferometer arms is exactly zero, the observed signal Iout is the sum of signals from the two arms I1, I2, plus an interference term: I = I + I +2 I I (V (u, v)) . (17.1) out 1 2 1 2 ℜ Here the visibility V (u, v) is a complexp number with modulus V 1, which depends on the coordinates (u = x/λ , v = y/λ) of the baseline B =| (|x, ≤ y) between the two telescopes, and on the sky brightness distribution, i.e., the structure of the source being observed (see the following section for details). By introducing phase shifts of 0, π/2, π, and 3 π/2, one can determine the visibility amplitude V and phase φ = arg(V ). This can either be done simultaneously, by splitting the| | light into four channels, or sequentially, by varying Dint in steps of λ/4 and counting the photons at each step.2 In Michelson arrays with N telescopes the N(N 1)/2 visibilities can either be measured by pairwise beam combination, or by bringing− the light from all telescopes together on one detector. In the latter “all-on-one” techniques, the fringes from the different baselines have to be encoded either spatially (by using a non-redundant output pupil) or temporally (by using different dither frequencies for the beams from individual telescopes). It should be noted here that the signal-to-noise ratio (SNR) of all interferometric 2 observables depends not only on the photon count Np, but on NpV for the photon- noise limited regime and on NpV for the background-limited regime, and that the SNR drops precipitously in the photon-starved regime (see Shao and Colavita 1992 for details). The very drastic loss of sensitivity with source extension may come as a nasty surprise if observations are not planned carefully: even for a modestly resolved star one may find that V =0.1 and thus lose 5 magnitudes of sensitivity compared to a point source. The van Cittert–Zernike theorem For a more formal treatment of the interferometer response, it is useful to introduce the source coherence function defined as γ(ξ , ξ , τ)= E(ξ ,t)E∗(ξ ,t τ) , (17.2) 1 2 h 1 2 − i 1For simplicity, we will mostly ignore the complications brought about by dispersion for con- verting between delay, optical path length, and fringe phase. 2Note that the there is already a phase shift of π between the two detectors shown in Figure 17.1 due to the additional reflection at the beam combiner for one of them. Thus the sum of the intensities measured by them is independent of V and Dint, as required by conservation of energy. 296 17. Interferometric imaging from space v × Dext =Bs Baseline B Telescope 1Detector Telescope 2 Detector D1 D2 Delay Line 1 Delay Line 2 Figure 17.1: Schematic drawing of the light path through a two-element interferometer. The external delay Dext = B · sˆ is compensated by the two delay lines, here B is the baseline vector and sˆ the unit vector in the direction of the source. The path lengths D1, D2 through the delay lines are monitored with laser interferometers. The zero-order interference maximum occurs when the delay line positions are such that the internal delay Dint = D2 D1 is equal to Dext. The beams from the two telescopes are combined with a plate− that has a relative transmission of 50 % and a reflectivity of 50 %. The architecture shown is a Michelson interferometer with co-axial beam combination in the pupil plane (cf., Page 301). 297 where E is the radiation field, ξ the (two-dimensional) direction cosine on the sky, 3 and τ the temporal delay. For ξ1 = ξ2 = ξ, γ is the time autocorrelation function of the radiation from direction ξ; for τ = 0, this is the time-averaged brightness from that direction B(ξ)= E(ξ) 2 . An extended source is called spatially incoherent4 if γ = 0 for ξ = ξ ; in| this case| 1 6 2 γ(ξ , ξ , τ)= γ(ξ , τ) · δ(ξ ξ ) . (17.3) 1 2 1 1 − 2 The electric field of radiation from a source located at position ξ received by a · telescope at position u has a phase term e−2 π i ξ u. To compute the interference term between two telescopes located at positions u1, u2, one has to integrate the correlations between all pairs of sky positions ξ1, ξ2 with the appropriate phase terms: ∞ ∞ · · −2 π i(ξ1 u1−ξ2 u2) Γ(u1, u2, τ)= γ(ξ1, ξ2, τ)e dξ1dξ2 .

Load more