Abstract
This chapter examines in detail the properties of cores and halos in star images. Strong cores emerge when \(\sigma / \lambda < 0.4\). In average astronomical seeing conditions, cores dominate the images at near-IR and longer wavelengths. In the other regime, \(\sigma / \lambda > 0.4\), halos instead dominate the images; in average seeing conditions images at visible wavelengths usually appear as halos. Halo shape closely replicates the shape of seeing-disc images often formed by large telescopes at visible wavelengths. Halos width is typically ~1 arcsec. In stark contrast, core shape is set by the telescope point-spread function. When cores dominate the images, extremely high resolution can be obtained. For large diffraction-limited instruments with circular apertures, resolution is given by \(1.22 \cdot \lambda / D \); at near-IR wavelengths resolution is typically ~ 0.1 arcsec. Though image cores generally appear over a wide range of wavelengths, one particular wavelength—referred to as the optimum wavelength—gives rise to maximum irradiance at core center. Such a wavelength has obvious significance to HEL weapon systems.
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- 1.
Angular jitter of the core refers to the random angular wanderings of these features in the image plane of the telescope.
- 2.
For many years, image cores were largely considered theoretical abstractions rather than practical vehicles for providing improved telescope resolution. Prior to about 1990, the lax optical specifications of large ground-based telescopes eliminated any possibility of obtaining diffraction-limited cores at visible wavelengths. Roger Griffin described the cores he saw directly by eye using the 200-in. Mt. Palomar and 100-in. Mt. Wilson telescopes (Appendix G) as significantly broader than the diffraction limit, a description consistent with the less than diffraction-limited optics used in these two venerable instruments.
- 3.
By considering only circularly symmetric telescope PSFs, we effectively restrict ourselves here to telescopes with circular apertures, circular central obstructions, and circularly symmetric aberrations (which include defocus and spherical aberration).
- 4.
A detailed study of the aberrations of the Mayall telescope, circa 1991, was conducted by Baldwin et al. (1992) prior to carrying out an optics upgrade program in 1992. Because the intensity envelopes shown in Fig. 10.8 for the aberrated telescope are based on a simplified set of aberration parameters, these envelopes only nominally describe the aberrated shapes of the image cores produced by the Mayall instrument at that time (shown at bottom in Fig. 10.9).
- 5.
The D 4 dependence assumes no increase in σ as the telescope diameter increases. Except for a limitingly small turbulence structure outer scale limit, at least some small σ increase is inevitable as D increases, which would have the effect of causing irradiance at core center to grow at a rate slower than D 4.
- 6.
Image quiver is another name for image wander. In this book, the latter term is generally used.
- 7.
The RGO site at Herstmonceux Castle is about 70 ft above sea level. Astronomical images obtained at this site do not therefore benefit from the significantly better seeing conditions found at high-altitude sites.
- 8.
Prior to that time, when the UKIRT IR-FPA camera was used in the “high-resolution” imaging mode, the angular subtense of the individual pixels was set at 0.65 arcsec, an angle so large that resolving ~0.1-arcsec IR image cores was entirely out of the question.
- 9.
- 10.
In 1896, the Royal Observatory, Edinburgh was moved two miles southwards from its old location in the center of the city on Calton Hill, to its present site on Blackford Hill (146 m altitude). The largest telescope at the observatory is a 36-in. Cassegrain reflector which was installed in 1930 but is now no longer operational. As a youth, the author lived close to the observatory at 10 Observatory Road. As a teenager, he constructed a 6-in. Newtonian reflector telescope, grinding two ship’s portholes together to make the primary mirror, faithfully following an early version of “How to make a telescope” by Texereau (1984). Disappointed by the blurry images, the author attributed the problem to figure errors of the paraboloidal primary mirror which, during fabrication, had been tested using a crude Foucault test, with the slit and knife-edge made from razor blades; the Foucault test was first described in 1858 by the French physicist, Jean Bernard Leon Foucault (1819–1868). However, in 1997—some thirty-five years after the construction of the instrument—after being urged to have it tested interferometrically by Mr. Garry Marions, a respected Optical Technician at the Developmental Optics Facility, US Air Force Research Laboratory (AFRL), Albuquerque, New Mexico, the instrument was finally tested this way. Somewhat taken aback, the authors discovered that the instrument was in fact diffraction-limited, the interferogram indicating a P-V wavefront error of about 0.2 waves (HeNe). While researching for this book—but now fifty years after the construction of the instrument—the author learned that more than a century earlier, the seeing conditions in Edinburgh had been described as “appalling” (Footnote 8, in Chap. 4, p. 92) by the second Astronomer Royal for Scotland, Charles Piazzi Smyth. The mystery of the blurry images was finally resolved.
- 11.
Strehl intensity usually refers to the intensity attained in the center of the star image. The brightest speckle can arise anywhere within the extent of the seeing disc area so that this speckle does not necessarily lie close to the image center. Also, the brightest speckle generally appears and disappears in the image in a random discontinuous manner, making it difficult to rationalize the precise properties of the final shifted and stacked image.
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McKechnie, T.S. (2016). Core and Halo Star Images Formed by Large Telescopes. In: General Theory of Light Propagation and Imaging Through the Atmosphere. Springer Series in Optical Sciences, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-319-18209-4_10
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