Abstract
This chapter introduces the subject of diffraction—the key mechanism that determines how light propagates through the atmosphere and comes to final focus in the telescope image plane. The origin and basis of the Fresnel-Kirchhoff diffraction formula is described; this formula derives directly from Maxwell’s equations. Solutions to the formula are given in three regions, all of which are used in the subsequent light propagation analysis: the geometrical optics region, the near-field Fresnel region and the far-field Fraunhofer region. The distribution of light energy in the Fraunhofer region describes the final image formed by the telescope. Optical system terminologies used to describe optical systems—telescopes in particular—are introduced (e.g., optical axis, telescope objective, central obstruction, and telescope pupil function). Ray terminologies are also introduced (e.g., principal ray, marginal ray). The amplitude and intensity point–spread functions of telescopes are defined. Linear superposition, convolution, isoplanaticity, and coherence are described for dealing with extended objects.
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Notes
- 1.
George Green (1793–1841) was a self-taught English mathematical physicist. In “An essay on the application of mathematical analysis to the theories of electricity and magnetism,” published in 1828, he introduced what are now referred to as Green’s functions and Green’s theorem (Born and Wolf 2003). His theory formed a crucial part of the foundation for later work on electromagnetic theory by James Clerk Maxwell.
- 2.
If a screen is placed at the location of a real image, the image will be seen by looking directly at the screen.
- 3.
Such telescopes do not include Schmidt–Cassegrain telescopes where the front aspheric corrector plate generally acts as the aperture stop.
- 4.
The Gaussian PDF is frequently assumed when calculating Strehl intensity from rms wavefront error (Malacara 1992). For general applications, it would be difficult to justify any other PDF choice.
- 5.
The complex coherence factor is also referred to sometimes as the complex degree of coherence when discussing illumination coherence properties.
- 6.
Occasional exceptions are conceivable but of doubtful practical significance. Large plasma-filled regions in space, if energized by a nearby star or other object, could possibly provide just the right conditions for amplifying stray light photons. Such regions act like giant, single-pass laser cavities, which could in principal produce powerful coherent laser beam pulses traveling in the same direction as the initial triggering photon.
- 7.
Rayleigh was only familiar with incoherent light sources.
- 8.
In 1856, more than one hundred years after Newton first proposed the remedy of “serene and quiet air … on the tops of the highest mountains” for seeing the stars more clearly through Earth’s atmosphere, Charles Piazzi Smyth (1819–1900), petitioned the Admiralty for a grant of £500 to take a telescope to the mountain tops of Tenerife and test whether Newton had been correct. The funding was granted and Smyth duly completed the mission (Piazzi Smyth, 1858). After moving to the Royal Observatory, Edinburgh in 1846 to take up his appointment as the second Astronomer Royal for Scotland, he was appalled by the poor observing conditions he found there. While nothing immediately came of his efforts, starting around the beginning of the twentieth century, the siting of large astronomical telescopes “on the tops of the highest mountains” has become standard practice.
- 9.
This certainly holds true for telescope aberrations of several waves or less and therefore holds for most large astronomical telescopes. It does not hold, however, for gross aberrations (cf., Sect. 11.4.10.3).
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McKechnie, T.S. (2022). Diffraction. In: General Theory of Light Propagation and Imaging Through the Atmosphere. Progress in Optical Science and Photonics, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-030-98828-9_4
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