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PH507 Lecture 3 Professor Michael Smith 1 MULTIMEDIA ASTRONOMY Taught in Spring Term PH512 Kent Credits 15 at Level H Resolution: please read Chapter 1 (pdf file on Module page) Definition of parsec: One arcsecond of angular resolution sweeps out 1 Astronomical Unit of spatial resolution at a distance of 1 parsec. 1 AU = 1.5 1011 metres Angular resolution Ignoring blurring of the image by turbulence in the atmosphere (atmospheric seeing) and optical imperfections of the telescope, the angular resolution of an optical telescope is determined by the width of the objective, termed its "aperture" (the primary mirror, or lens.) The Rayleigh criterion for the resolution limit αR (in radians) is given by αR = 1.22λ / D, The angular diameter of the` Airy Disk, to the first dark diffraction ring is αAiry = 2.44/ D, where λ is the wavelength and D is the aperture. The factor 1.22 is derived from a calculation of the position of the first dark ring surrounding the central Airy disc of the diffraction pattern. If one considers diffraction through a circular aperture, then the calculation involves a Bessel function -- 1.220 is approximately the first zero of the Bessel function of the first kind, of order one (i.e. J1), divided by π (3.14159). This factor is used to approximate the ability of the human eye to distinguish two PH507 Lecture 3 Professor Michael Smith 2 separate point sources depending on the overlap of their Airy discs: For visible light (λ = 550 nm), this equation can be rewritten: αR = 138 / D. Here, αR denotes the resolution limit in arcseconds and D is in millimeters. In the ideal case, the two components of double stars can be split even if separated by slightly less than αR. This is taken into account by the Dawes limit αD = 116 / D. Essentially: the larger the aperture, the better the angular resolution PH507 Lecture 3 Professor Michael Smith 3 It should be noted that the resolution is NOT given by the maximum magnification (or "power") of a telescope. Telescopes marketed by giving high values of the maximum power often deliver poor images. For large ground-based telescopes, the resolution is limited by atmospheric seeing. This limit can be overcome by placing the telescopes above the atmosphere, e.g., on the summits of high mountains, on balloon and high-flying airplanes, or in space. Resolution limits can also be overcome by adaptive optics or speckle imaging for ground-based telescopes. Recently, it has become practical to perform aperture synthesis with arrays of optical telescopes. Very high resolution images can be obtained with groups of widely-spaced smaller telescopes, linked together by carefully controlled optical paths, but these interferometers can only be used for imaging bright objects such as stars or measuring the bright cores of active galaxies. PH507 Lecture 3 Professor Michael Smith 4