Abstract
In the last chapter, we discussed telescopes as optical devices able to form images in a way that could be explained by geometrical optics, at least to first order in the light intensity distribution. The wave nature of electromagnetic radiation produces diffraction effects that modify this distribution and introduce a fundamental limitation on the angular resolution of telescopes. Since astronomers always want to obtain images containing more and more detail, it is essential to come to grips with these effects, whose amplitude is directly related to the wavelength of the radiation. Using the notion of coherence discussed in Chap. 3 (see Sect. 3.2), we begin by examining the process by which images are formed in the presence of diffraction, and translate the results in terms of spatial frequency filtering.
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Notes
- 1.
The Italian physicist and astronomer Riccardo Giacconi, born in 1931, who later adopted US nationality, launched the first sounding rockets which discovered this radiation. For this work, he shared the 2002 Nobel Prize for Physics with Raymond Davis Jr. and Masatoshi Koshiba.
- 2.
Armand Hippolyte Fizeau (1819–1896) was one of the great French physicists of the nineteenth century who demonstrated the power of the wave model of light. Apart from his paper in 1868, which serves as a foundation for astronomical interferometry, he is also famous for measuring the speed of light, and for discovering the spectral shift effect so often attributed only to Doppler.
- 3.
Albert Abraham Michelson was an American physicist (1852–1931) and brilliant experimentalist who devised the interferometer now named after him which is used in spectroscopy (see Sect. 8.3).
- 4.
The Dutch physicist Frederik Zernike (1888–1966) won the Nobel Prize for Physics in 1953 for his invention of the phase contrast microscope. The Dutch mathematician Van Cittert also discovered this theorem in 1931.
- 5.
The German physicist Gustav Kirchhoff (1824–1887) founded spectral analysis in astronomy.
- 6.
Detailed demonstrations of the results given here can be found in Born M., Wolf E., Principles of Optics, Pergamon (1980), and also Françon M., Optique, and Hecht E., Optique, Pearson (2005).
- 7.
The French physicist Augustin Fresnel (1788–1827) was one of the founders of wave optics.
- 8.
The German optician Joseph-Franz Fraunhofer (1727–1826) built the first spectroscope. With this instrument he was able to study the Sun’s spectrum, where he discovered the absorption lines that carry his name.
- 9.
Sir George Biddell Airy (1801–1892) was a British astronomer and physicist.
- 10.
John Strutt (Lord Rayleigh, 1842–1919) was awarded the Nobel Prize for Physics in 1904 for the discovery of argon.
- 11.
We understand here that only almost pointlike sources will scintillate. According to the phase screen approximation, each point of an extended source produces its own diffraction pattern, with intensity variations. The patterns produced by the different points after passing through different non-uniformities will tend to balance out to yield an almost constant intensity over time.
- 12.
The American optician D.L. Fried developed the theory of light propagation in random media in the 1960s.
- 13.
The French astronomer Antoine Labeyrie, born in 1944, pioneered many developments in high angular resolution visible and infrared observation over the last decades of the twentieth century. The ‘bunch of grapes’ structure of star images had already been noted in the 1940s by the French astronomer Jean Rösch (1915–1999) at the Pic-du-Midi Observatory (France), but without drawing any particular conclusions about its significance.
- 14.
See Labeyrie A., Stellar interferometry methods, ARAA 16, 77, 1978.
- 15.
See, for example, Alloin D. & Mariotti J.M. (Eds.), Diffraction-limited imaging with large telescopes, Kluwer, 1989.
- 16.
The website www.ctio.noao.edu/atokovin/tutorial/ maintained by A. Tokovinin contains an excellent and detailed analysis of the ideas presented somewhat succinctly here, translated in several languages.
- 17.
Some beautiful examples can be found at the website of the National Solar Observatories (NSO) in the US, at the address www.nso.edu.
- 18.
The Falcon project, developed at the Paris Observatory and going into operation on the VLT in 2007, can be used to observe 15 galaxies at the same time, with spectral resolution \(\mathcal{R}\geq 600\). See www.onera.fr/dota/publications.php.
- 19.
This remarkable observation is mentioned by Moran, Ann. Rev. Astron. Astroph., 2001. Much here is borrowed from this excellent reference.
- 20.
The British astronomer Martin Ryle (1918–1984) won the Nobel Prize for Physics with Anthony Hewish in 1974 for his work on radiofrequency interferometry.
- 21.
The American physicist and astronomer Charles Townes, born in 1915, received the Nobel Prize for Physics in 1988 for his work on maser pumping, the maser being a precursor of the laser.
- 22.
See, for example, Townes C.H., in Optical and Infrared Telescopes for the 1990s, A. Hewitt (Ed.), Kitt Peak National Observatory, 1980.
- 23.
The British physicist and astronomer Robert Hanbury-Brown (1916–2002) invented intensity interferometry with the Indian-born British mathematician Richard Twiss (1920–2005), developing their idea in Australia.
- 24.
A very complete description is given in Hanbury-Brown R., The intensity interferometer, ARAA 6, 13, 1968.
- 25.
See in particular Bracewell R., Computer image processing, ARAA 17, 113, 1979, and Pearson T., Readhead A., Image formation by self-calibration in astronomy, ARAA 22, 130, 1984.
- 26.
Schwarz U.J., Astron. Astrophys. 65, 345, 1978.
- 27.
K.I. Kellermann, J.M. Moran, The development of high resolution imaging in radioastronomy, ARAA 39, 457–509 (2001).
- 28.
Hale, D.D. et al., The Berkeley infrared spatial interferometer: A heterodyne stellar interferometer for the mid-infrared, Ap. J. 537, 998–1012 (2000).
- 29.
Pedretti, E., Labeyrie, A., Arnold, L., Thureau, N., Lardière, O., Boccaletti, A., Riaud, P., First images on the sky from a hypertelescope, Astron. Astrophys. Suppl. 147, 385, 2000.
- 30.
The British optician and astronomer Roger Angel, born in 1941, is professor at the Stewart Observatory, Tucson, where he had the idea of the LBT.
- 31.
Perrin, G. et al., Interferometric coupling of the Keck telescopes with single-mode fibers, Science 311, 194, 2006.
- 32.
See the detailed description and updates on the Space Interferometry Mission (SIM) at the website of the Jet Propulsion Laboratory (JPL) in California: planetquest.jpl.nasa.gov/SIM/.
- 33.
The complexity and cost of the mission must be balanced against its extraordinary aim, namely the detection of life on extrasolar planets. This is why, in 2007, it was once again proposed to the European Space Agency (ESA).
- 34.
The site maxim.gsfc.nasa.gov/docs/pathfinder/pathfinder.html describes the various aspects of the MAXIM mission.
- 35.
- 36.
The French astronomer Bernard Lyot (1897–1952) used images taken at the Pic-du-Midi observatory to produce a magnificent film entitled Flammes du Soleil, which showed the public the coronal activity of the Sun.
- 37.
Pierre Jacquinot (1910–2002) was a French optician whose work led to the Fourier transform spectrometer (see Sect. 8.3).
- 38.
François Roddier, born in 1936, and Claude Roddier, born in 1938, are French astronomers and opticians
- 39.
Daniel Rouan is a French astronomer born in 1950
- 40.
This idea could evolve toward a very compact device called the CIAXE. To carry out the required task, this makes judicious use of reflections on the optical interfaces of two thick lenses. However, such an optical system is very difficult to realise and has not yet seen the light of day at the time of writing (2007).
- 41.
The Australian-born radioastronomer Ronald Bracewell (1921–2007), professor at Stanford University in California, made many remarkable contributions to radiofrequency interferometry and signal processing.
- 42.
The Prouhet–Thué–Morse sequence is defined by the recurrence relations t 0 = 0, t 2k = t k , and t 2k + 1 = 1 − t k , and begins 01101001100101101001011001101001…
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Léna, P., Rouan, D., Lebrun, F., Mignard, F., Pelat, D. (2012). Diffraction and Image Formation. In: Observational Astrophysics. Astronomy and Astrophysics Library. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21815-6_6
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