Telescopes and their Aberrations


Ophthalmic Internship





Alvaro Cordova

Introduction:

The night sky has been a source of wonder since time immemorial. Many cultures through out the world have used the stars as a means of navigation or by the farmer as a window of time when to plant crops (Bennett, 1999, pp. 97, 104). However, the night sky would also be a source of fear. The occasional comet was almost always thought to precede a bad omen. Comets were described as a “Harbinger of Doom” or “Menace of the Universe.” (Goldman, 2005) The regularity in which the planets moved and the “perfect” circle shapes the moon and other night sky objects appeared to have, brought about one of the first models of the universe. Ptolemy put the earth at the center of the universe and the planets and sun would orbit the earth. This model was perhaps the first attempt to explain the apparent retrograde motion exhibited by the planets. The early Catholic church eventually adopted this view of the universe as doctrine as well as Aristotelean ideas (Bennett, 1999, pp. 108,147). Galileo Galilee challenged the church's earth centered view as well as its notion of perfection. Galileo believed the heliocentric model of the universe since a lot of the apparent problems with Ptolemy's theory cleared up. The church maintained that anything but a circle would be considered imperfect or flawed. Although Galileo is credited with inventing the telescope, it was more than likely Hans Lippershey who actually invented the telescope a year before (Bennett, 1999, pp. 147-148; Dickinson, 1998, p. 136; Gluck, 1964, p. 102). The telescope has since been one of the ideal methods of viewing the sky. This paper will cover the different types telescopes and their aberrations as well as some key advances in telescope design known as adaptive optics. Basic knowledge of lenses and mirrors as well and the images they form are assumed. Such famous telescopes as the Hubble telescope, have photographed breathtaking views of celestial objects that continue to inspire and awe the public. It is no coincidence that the telescope plays an important role in developing the first scientific discipline: astronomy. The importance of the inner workings of the telescope can not be understated since many amateur astronomers to this day contribute to the discovery of comets. Because of adaptive optics, astronomy is undergoing a new golden age.

Types of Telescopes:

There exists several types of telescopes and each has certain strengths and weaknesses. Generally, the optical elements of a telescope are enclosed in a tube to block out stray light. Telescopes are generally divided into two main divisions: refracting or reflecting (Bennett, 1999, p. 184; Consolmagno, 2000, p. 203; Cutnell, 1998, p. 817). The telescope that Galileo used is known as a refracting telescope. Refracting telescopes are made up of an objective lens and an eye piece. Refracting telescopes come in two varieties depending on the eyepiece used. An astronomical telescope has a plus powered eyepiece and a Galilean telescope would have a minus powered eyepiece (NAVEDTRA, 1997, p. 5-19). The objective lens is the first refractive surface light encounters in a telescope. The focal point will then lie between the objective lens and the eyepiece (Bennett, 1999, p.185; Cutnell, 1998, p. 815; Gluck, 1964, p. 108; Halliday, 1997, p. 889; Ogle, 1979, p. 123; Strong, 2004, p. 338). One of the important factors in determining a good refracting telescope is the size of the objective lens. The larger the lens the more light will reach the eyepiece and the clearer the image will be (Bennett, 1999, p. 186; Consolmagno, 2000, p. 203). It is important to note that the image of a refracting telescope will be inverted with the exception of the Galilean telescope. Sometimes another lens is placed in between the objective lens and eyepiece in order to erect the inverted image (Freeman, 1990, p. 199; NAVEDTRA, 1997, p. 5-19). The approximate length of a refracting telescope would be the sum total of focal lengths (Strong, 2004, p. 338). The largest refracting telescope in the world today has an objective lens that is one meter in diameter and a telescope tube nineteen and a half meters long (Bennett, 1999, p. 185).

Reflecting telescopes are more modern in origin and are more versatile. The reflecting telescope can come in a variety of dimensions and types such as the Dobsonian, Cassegrain and Maksutov. A reflecting telescope is comprised of a primary concave mirror and an eyepiece. The primary mirror is placed at the end of a tube facing the opening and reflects the light onto a secondary mirror, which is considerably smaller, and in turn reflects to an eyepiece. In this case, the primary mirror is the first object that light will hit with the exception of the Maksutov.

The Dobsonian telescope is also known as a Newtonian telescope. In Dobsonian telescopes, the primary mirror focuses the image onto a secondary flat mirror that is angled so that the reflected light ends up at the eyepiece that is on the side of the tube. Dobsonian telescopes are the most popular telescopes on the market. These telescopes provide a good value for the money but are bulkier than other types of reflector telescopes. (Consolmagno, 2000, p. 203; Dickinson, 1998, p. 68; NAVEDTRA, 1997, p. 5-16).

The Cassegrain has a primary mirror with a hole in the center. The primary mirror focuses the image on to a secondary mirror, which is slightly convex. The secondary mirror reflects it back toward a third mirror located behind the primary mirror through the center. The third mirror reflects the oncoming light into the eyepiece. Cassegrains are notably smaller than the Dobsonian and are usually more expensive (Consolmagno, 2000, p. 203; Dickinson, 1998, p. 68).

The Maksutov reflector is also known as a catadioptic reflector. It is similar in design to the Cassegrain and has a corrective plate that does some of the work that the primary mirror would have done. The other difference to the Cassegrain reflector is that the secondary mirror in the Maksutov is flat. This allows the tube to be especially compact. These telescopes are also more expensive than the Dobsonian (Consolmagno, 2000, p. 203; Dickinson, 1998, pp. 69 – 72; NAVEDTRA, 1997, p. 5-16).

Eyepieces:

Eyepieces are responsible for magnifying the image made by the objective mirror or lens with the exception of the Galilean telescope. In the case of the Galilean telescope, the lens attempts to make the converging light parallel by diverging it with a minus lens. In the other types of telescopes the eyepiece is a plus lens that converges divergent light. (Gluck, 1964, p. 109).

Telescope Capabilities:

The telescope has three very important qualities. It's ability to magnify, the quality or resolution of the image, and the amount of image called the field of view impact the price and quality of the telescope.

The objective lens, mirror and eye piece form a relationship, one of which, is magnification. Angular magnification is equal to the focal length of the objective lens divided by the focal length of the eyepiece. For example, a 100mm focal length lens with an eye piece whose focal length is 25mm, the telescope will provide 4x the amount of magnification (angular magnification = (focal length of primary mirror or objective lens) / (focal length of eyepiece)) (Consolmagno, 2000, p. 203; Freeman, 1990, p. 197; Gluck, 1964, p. 109).

Resolution deals with the quality of the image. There is a theoretical limit to resolution that is dependent upon the primary mirror or objective lens. The larger the primary mirror or objective lens the greater the theoretical limit for resolution. Resolution is measured in arc seconds, which are divisions of a circle. A circle contains 360 degrees. Each degree is then divided into 60 minutes and each minute into 60 seconds. A working approximation of resolution would be to divide 120 arc seconds by the aperture in millimeters. The aperture in the case of a telescope would be the objective lens or primary mirror. So, a 100mm objective lens would have 1.2 arc seconds of resolution. (resolution = (120 arc seconds) / (aperture of telescope)) (Bennett, 1999, p. 188; Consolmagno, 2000, p. 203).

Another quality important to amateur and professional astronomers alike is the field of view. Field of view is the amount of sky one can possibly see given a specific amount of magnification. The field of view is measured by the apparent field, which is the approximate angle the eye piece makes when up to your eye divided by the magnification. The apparent field is usually between 35 - 40 degrees. So given a telescope with a magnification of 4x one can see about 10 arc seconds of view (field of view = (40 degrees or apparent field) / magnification) (Consolmagno, 2000, pp. 203, 204).

Telescope Aberrations:

Telescopes, as with any optical system, can contain aberrations that will hinder the clarity of what is being viewed. The aberrations encountered with telescopes are chromatic aberration, spherical aberration, coma, astigmatism, distortion, and curvature of field.

Chromatic aberrations are primarily the problem of refracting telescopes and eyepieces. White light consists of several wavelengths of light. Each wavelength converges at different focal lengths, if the light is incident to the refractive element, given the same medium. Chromatic aberrations come in two varieties: axial and lateral. Axial chromatic aberration is a series of focal lengths along the axis of the lens. Lateral chromatic aberrations are the differing image sizes that are produced by the wavelengths. So in the case of crown glass, the blue and violet wavelengths will converge before the red wavelength. This is due to the fact that the lens can bend the smallest wavelength for a longer duration than a larger wavelength. Lateral chromatic aberration is the more common complaint. What the individual sees is an unclear image. If the dispersion is significant it is actually possible to see the different colors. This aberration can usually be corrected by choosing a lens that has a lower dispersion value. An achromatic lens may be used as well. An achromatic lens attempts to converge more than one wavelength using lenses of differing compositions into a compound lens. A lens with high dispersion will disperse the colors enough so that the secondary element, usually crown glass, focuses all of them to a point. A good telescope will usually have an achromatic lens and will be considerably more in price (Abramowitz, 2005; Cutnell, 1998, p. 818; Brooks, 1996, pp. 502-503; Lester, 2004).

Spherical aberrations are incident parallel rays in the periphery of the lens or mirror that do not converge where the paraxial rays converge. This aberration becomes apparent in larger objective lenses and primary mirrors. The solution, in the case of the reflector, is to have a mirror that is slightly parabolic. The refracting telescope can use a system similar to the one needed in chromatic aberration or can use lenses that are aspheric. Aspheric lenses taper off in curvature toward the periphery allowing the light to converge at the focal point (Abramowitz, 2005; Brooks, 1996, p. 505; Lester, 2004).

Coma is an aberration in which a point of light is distorted into an almost comet like appearance. This aberration is caused by off axis rays that pass through different zones of a lens or mirror. These different areas will have different magnifications which overlap giving the object a comet like appearance. The solution for this aberration is to have a lens system similar to the correction for spherical aberration in the case of the refractor. A lens system that corrects spherical aberration and coma are called aplanatic For the reflecting telescope, a simple glass plate can be used that provides negligible amounts of chromatic aberration. Another way to address coma in the reflecting telescope is to make the primary mirror less parabolic and the secondary mirror slightly hyperbolic (Abramowitz, 2005; Brooks, 1996, p. 505; Lester, 2004).

Astigmatism is an aberration that contains two different foci between the sagittal and tangential planes; horizontal and vertical respectively. Astigmatism is made apparent when off axis rays strike the surface of the spherical lens or mirror. This is generally corrected using a lens system and in the case of mirrors, a plate (Abramowitz, 2005; Brooks, 1996, p. 505,506; Lester, 2004).

Distortion has the appearance of a barrel or pincushion. This aberration is caused by the uneven magnification across the lens or mirror system. This defect is found in compound systems in which there are many elements that correct for other aberrations. The image is no longer truly represented even though it may be sharp. Distortion may be corrected by making adjustments in the optical system, but may still be present to some degree (Abramowitz, 2005; Brooks, 1996, p. 508; Lester, 2004).

Lastly, curvature of field is an aberration that becomes apparent after other aberrations have been corrected. This aberration makes an image have curvature instead of focusing on a plane. This is corrected using a plate before the primary mirror. The plate will flatten the image back to a plane eliminating the aberration. This aberration is inherent because of the use of lenses which are themselves curved (Abramowitz, 2005; Brooks, 1996, p. 508; Lester, 2004).

Adaptive Optics:

The Hubble telescope was launched into space with the hope of escaping the optical problems inherent in an atmosphere. Although the topic of adaptive optics does not address an optical aberration per se, it has been a significant advance in terrestrial based telescopes. The atmosphere contains many small perturbations caused by temperature differences naturally in the atmosphere. Adaptive optics attempts to circumvent these issues (National Optical Astronomy Observatories, 2000; University of California Regents, 2002).

Adaptive optics systems attempt to cancel out a distorted wavefront. A beacon, which is generally a laser, is sent into the sky in order to detect the incoming wavefronts. After detection, the wavefront is analyzed. In order to cancel out the offending perturbation a deformable mirror is used. The deformable mirror effectively does the “opposite” of what the distortion is doing. The deformable mirror is made up of several smaller mirrors in a honeycomb arrangement. Each mirror is hooked up to a machine which allows it to move in whatever way the analyzing element determines will cancel out the distortion. There are only a handful of telescopes that have this technology in place such as the WIYN telescope in Kitt Peak, Arizona (Bennett, 1999, p. 194; European Southern Observatory, 2000; National Optical Astronomy Observatories, 2000; University of California Regents, 2002, 2004).

Conclusion:

Hubble Telescope will be retired in late 2007 and will be replaced by the James Webb Space telescope by 2010. The pictures and science provided by the new telescope should be no less amazing than that of Hubble. This new telescope will assist in answering the deeper questions about the origins of our universe. On earth, the birth of adaptive optics hopes to revitalize current telescopes with better image processing that may even surpass what Hubble can do now. Without the telescope, astronomy is simply not possible. The furthest reaches of the universe may come into full view in less than a decade and may usher in another golden age of astronomy and amateur astronomers will continue to scan the skies with telescopes in awe of this glorious universe.

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Copyright 2005 Alvaro Cordova