Abstract
The theoretical resolution limits of large ground-based telescopes are examined. Optical tolerance specifications are set out for large telescopes. Lax tolerances can be adopted if halo-only images are considered adequate; tighter tolerances are required to exploit the much higher resolution levels provided by image cores. Telescope resolution is measured by the instrument’s ability to resolve binary stars. The Rayleigh resolution criterion employed to meet the broad-ranging requirements of this chapter—where images can be influenced by atmospheric turbulence, telescope aberrations, central obstructions, AO, etc.—is the version where a binary object is considered just-resolved when the intensity in the center of the image is 23.5 % less than the value attained in the peaks (i.e., 1.22 λ / D for diffraction-limited telescopes with circular apertures). Computer-generated and actual star images are shown for the Keck II instrument. Computer-generated binary star images are also shown for the future 40 m E-ELT instrument for various wavelengths in the range, 0.5–10 μm, with <10 mass resolution anticipated routinely in the optimum wavelength region.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Rayleigh’s first resolution criterion, devised in 1879, referred to spectroscopes (Strutt 1979). For the slit-based instruments considered in that paper, two wavelengths are considered just-resolved when the center of the (diffraction pattern) light distribution for one wavelength exactly overlies the first dark line of the light distribution for the other. In this case, the diffraction patterns are described by functions of the form, \((\sin (x)/x)^{2}\). The just-resolved interval, \(x = \pi\), is therefore slightly different than that obtained for the Airy pattern form, \((2 \cdot J_{1} (x)/x)^{2}\), which applies to circular apertures where the first dark ring occurs at \(x = 3.832\).
- 2.
The just-resolved separations given by these two versions of Rayleigh’s criterion agree to within 0.01 %.
- 3.
The rms wavefront error of the Mayall 3.8-m telescope around 1990 was about 0.40λ (HeNe). The rms wavefront error of the UKIRT 3.8-m telescope which at that time was incapable of delivering useful image cores at 2.2 µm must have been >0.50λ (HeNe).
- 4.
Active optics correction of telescope optics may be considered as a subset of adaptive optics in which only slow corrections are made to the imaging wavefronts, with timescales of the order of minutes. Such slow corrections are capable of correcting the fixed wavefront errors of the telescope but are not capable of correcting the more rapidly varying atmospherically induced wavefront errors.
- 5.
The Mayall telescope, where \(d = 1.65\,\text{m}\) and \(D = 3.8\,\text{m}\), has an exceptionally large central obstruction. Ignoring the instrument’s aberrations, for binary stars with equally bright components such a central obstruction would offer prospect of a 15 % resolution improvement.
- 6.
- 7.
In 1856, Pogson noted that in the stellar magnitude system introduced by the Greek astronomer Hipparchus, a first magnitude star is about 100 times brighter than a sixth magnitude star and suggested that this might be used as a standard. Thus, a first magnitude star is 1001/5 (or about 2.5119) times as bright as a second magnitude star.
- 8.
While an analytic solution would have been more convenient, the Author was unable to find such a solution.
- 9.
If \(w_{{o{\text{AO}}}} \approx w_{o}\), resolution offered by the halo improves in proportion to \(\sigma_{\text{AO}} /\sigma\). However, as discussed previously in Sect. 13.2.3, this relation does not hold generally since w oAO is not necessarily the same as w o .
- 10.
Scintillation refers to the amplitude fluctuation of the waves arriving at the telescope. Unlike phase fluctuation, the amplitude fluctuation can be seen directly by eye as twinkling.
- 11.
Scintillation structure size is inversely proportional to the scatter angle of the light arriving at the telescope.
- 12.
To justify this assumption, the average size of the scintillation structures must be at least several times smaller than the telescope diameter.
- 13.
The limitations are akin to those that apply to the Fried parameter, r o , discussed in Appendix I. A single parameter like this cannot adequately describe the most general type of core and halo image.
- 14.
This method of specifying telescope optical performance has now fallen into disuse. In effect, it places an angular limit on the gradients associated with the wavefront errors of the telescope. However, because this specification method takes no account of the lateral distances over which the wavefront gradients are subtended, it provides no information about either the P-V or rms wavefront errors introduced by the telescope; such information is of course essential if diffraction-limited instruments are to be constructed.
- 15.
Other attendees at the September 26, 1989, Seminar: G. Loos and B. Venet (AFRL), and B. Haddock (Lentec Corp.).
- 16.
To justify addition in quadrature in this kind of application merely requires that the wavefront error contributions made by the various optical components are either uncorrelated or statistically independent.
- 17.
The primary mirrors of the two 10-m Keck telescopes each consist of eighteen hexagonal-shaped mirror segments, each measuring about 1.8 m across.
- 18.
On Hawaii, seismic vibrations are caused by local volcanic activity. In California, at the 100-in. telescope on Mt. Wilson, seismic vibrations can be detected from waves breaking on the Pacific Ocean shore some 30 miles to the southwest.
- 19.
The 0.8 factor used here should not be confused with the absolute Strehl intensity which, for substantially diffraction-limited images, is indeed 0.8. In the present context, the factor 0.8 represents an additional Strehl intensity pull-down factor. For example, for a perfectly focused halo image where the absolute Strehl intensity might typically be only about 0.01, after the 0.8 pull-down caused by the just-allowable amount of defocus, Strehl intensity would decrease to the absolute value 0.008.
- 20.
Whereas the Keck instruments do not currently deliver diffraction-limited images at visible wavelengths, there is no reason why such images cannot be delivered in the future, given improvements in AO technology.
- 21.
For this test, it makes little difference whether resolved or unresolved stars are used.
References
Allen, L., Angel, R., Mangus, J. D., Rodney, G. A., Shannon, R. R., & Spoelhof, C. (NASA-TM-103443, 1990, November). The Hubble Space Telescope optical systems failure report. NASA.
Born, M., & Wolf, E. (2003). Principles of optics (7th ed., revised). Cambridge: Cambridge University Press.
Cho, M. K., Stepp, L., & Kim, S. (2001). Wind buffeting effects on the Gemini 8m primary mirrors. Gemini Preprint #75. 950 N. Cherry Ave., Tucson, AZ 85721: Gemini Observatory.
den Dekker, A., & van den Bos, A. (1997). Resolution: A survey. Journal of the Optical Society of America A: Optics, Image Science, and Vision, 14(3), 547–557.
Forbes, F. F. (1991). Private communication. NOAO.
Goodman, J. W. (1990). Statistical optics. San Francisco: McMillan.
Griffin, R. F. (1990, May). Giant telescopes, tiny images. Sky & Telescope, 469.
Liu, M. (2011, March 21). Brown Dwarf Duo: William Keck observatory picture gallery. Retrieved January 16, 2013, from http://keckobservatory.org/gallery/detail/milky_way/7
Malacara, D. (1992). Optical shop testing. New York: Wiley.
Martin, B., Hill, J. M., & Angel, R. (1991). The new ground-based optical telescopes. Physics Today, March, 22–30.
McCarthy, D. W., Jr., McLeod, B., & Barlow, D. J. (1990). Infrared array camera for interferometry with the cophased multiple mirror telescope. In SPIE, V. 1236, Symposium on Astronomical Telescopes and Instrumentation for the 21st Century, 11–17 February. Tucson, AZ.
McKechnie, T. S. (1989, September 26). Seminar: Obtaining Diffraction Limited Images at Near Infrared Wavelengths Using Large Ground Based Telescopes. (Attendees: D. W. McCarthy, Jr., K. Hege, Steward Observatory, Tucson, G. Loos, B. Venet, AFRL, R. Haddock, Lentec Corp.) Albuquerque, New Mexico, USA.
McKechnie, T. S. (1990). Diffraction limited imaging using large ground-based telescopes. In Proceedings of SPIE, V. 1236, Symposium on Astronomical Telescopes and Instrumentation for the 21st Century, 11–17 February (pp. 164–178).
McKechnie, T. S. (1991). Light Propagation through the atmosphere and the properties of images formed by large ground-based telescopes. JOSA A, 8, 346–365.
McKechnie, T. S. (2010). Interferometric test method for testing convex aspheric mirror surfaces. In Proceedings of SPIE, Symposium on Telescopes and Systems, June 27–July 2, SPIE, V. 7739_31. San Diego, CA.
Neal, D. R., Copland, J., & Neal, D. A. (2002). Shack-Hartmann wave front sensor precision and accuracy. SPIE (Vol. 4779). Bellingham, WA.
Nelson, J., Mast, T., & Faber, S. (1985). The design of the Keck observatory and telescope. In J. E. Nelson, T. S. Mast, & S. M. Faber (Eds.), Keck observatory report 90. Kamuela, HI: Keck Observatory.
Ninneman, R. R., Sydney, P. F., Reamy, P. C., Lanier, T. V., Carter, S. E., & Olives, M. L. (1987). Ambient vibration test results of proposed RME LSS site at the Air Force Maui Optical Station (AMOS). Albuquerque: Air Force Weapons Laboratory, Kirtland AFB, N.M.
Ronchi, V. (1961). Resolving power of calculated and detected images. Journal of the Optical Society of America, 51, 458–460.
Sparrow, C. M. (1916). On spectroscopic resolving power. Astrophysical Journal, 44, 76–86.
Strutt, J. (1880). On the resolving power of telescopes. Philosophical Magazine X, 116–119.
Strutt, J. (1902). Collected papers, 3. Cambridge: Cambridge University Press.
Strutt, J. W. (1979). Investigations in optics, with special reference to the spectroscope. Philosophical Magazine, VIII.
Tollestrup, E. V., & Tokunaga, A. T. (2010). New phase compensating secondary mirrors for the NASA infrared telescope facility. In Proceedings of SPIE, V.7733, Ground-Based and Airborne Telescopes III, August 04. Bellingham, WA.
Ulich, R. L. (1982). Performance of the multi-mirror telescope (MMT) V: Pointing and tracking of the MMT. In L. D. Barr & G. Burbidge (Eds.), Proceedings of SPIE V. 332, Advanced technology optical telescopes (pp. 33–41).
Ulich, R. L. (1988). Overview of acquisition, tracking, and pointing system technologies. In J. E. Kimbrell (Ed.), Proceedings of SPIE (Vol. 887), Acquisition, tracking, and pointing II (pp. 40–63).
Welford, W. T. (1960). On the limiting sensitivity of the star test for optical instruments. Journal of the Optical Society of America, 50, 21.
Welford, W. T. (1962). Geometrical optics. Amsterdam: North-Holland Publishing Co.
Wilson, R. N. (2003, September). The history and development of the ESO active optics system. The Messenger, 113. ESO.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
McKechnie, T.S. (2016). Telescope Resolution and Optical Tolerance Specifications. 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_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-18209-4_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18208-7
Online ISBN: 978-3-319-18209-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)