Date: October 9, 2010
Title: A Primer on High End Refractor Telescope Optics. Part 2
Podcaster: Edgardo Molina
Organization: Pleiades. Research and Astronomical Studies A.C. www.pleiades.org.mx (web site soon to be presented also in English)
Description: Part 2 of a 3-part series on High End Refractor Optics, explaining the physics behind the elements that conform the beloved (and sometimes not), refractor telescopes.
Bio: Edgardo Molina. B.S. in Mechanical Engineering from the Anahuac University in Mexico City. Post graduate studies in IT Engineering and a Masters Degree in IT Engineering. Working for IPTEL, an IT firm delivering solutions to enterprises since 1998. Space exploration enthusiast who participated in several Mexican space related activities. Licensed amateur radio operator with call sign XE1XUS. Amateur astronomer since childhood and actual founder and president of the Pleiades. Research and Astronomical Studies A.C. in Mexico City, Mexico. Avid visual observer and astrophotography fan. Public reach through education in exact sciences, engineering and astronomy. Lectures and teaching in several universities since 1993.
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Transcript:
High End Refractor Telescope Optics
Hello again. This is Edgardo Molina, from Pleiades. Research and Astronomical Studies in Mexico City, Mexico. Today I am your host for this episode of the 365 Days of Astronomy Podcast.
This is part 2 of 3 related to our series titled High End Refractor Optics. I hope you enjoy the physics behind the elements that conform the beloved (and sometimes not), refractor telescopes.
A refractor optical telescope is a telescope which is used to gather and focus light mainly from the visible part of the electromagnetic spectrum for directly viewing a magnified image for making a photograph, or collecting data through electronic image sensors.
A telescope’s light gathering power is directly related to the diameter (or aperture) of the objective lens. The larger the lens is, the more light the telescope can collect. What is commonly described as a telescope’s power, its magnification, is a function of both the objective’s focal length and that of the eyepiece.
The basic scheme is that the primary light-gathering element the objective, focuses that light from the distant object to a focal plane where it forms a real image. This image may be recorded or viewed through an eyepiece which acts like a magnifying glass. The eye then sees an inverted magnified virtual image of the object.
Angular resolution
Ignoring blurring of the image by turbulence in the atmosphere (atmospheric seeing) and optical imperfections of the telescope, the angular resolution of an optical telescope is determined by the diameter of the objective, termed its “aperture” (the primary lens.)
The equation governing angular resolution shows that, all else being equal, the larger the aperture, the better the angular resolution. The resolution is not given by the maximum magnification (or “power”) of a telescope. Telescopes marketed by giving high values of the maximum power often deliver poor images.
For large ground-based telescopes, the resolution is limited by atmospheric seeing. This limit can be overcome by placing the telescopes above the atmosphere, e.g., on the summits of high mountains, on balloon and high-flying airplanes, or in space. Resolution limits can also be overcome by adaptive optics, speckle imaging or lucky imaging for ground-based telescopes.
Focal length and f-ratio
The focal length determines how wide an angle the telescope can view with a given eyepiece or size of a CCD detector or photographic plate. The f-ratio (or focal ratio, or f- number) of a telescope is the ratio between the focal length and the aperture (i.e., diameter) of the objective. Thus, for a given aperture (light-gathering power), low f-ratios indicate wide fields of view. Wide-field telescopes (such as astrographs) are used to track satellites and asteroids, for cosmic-ray research, and for astronomical surveys of the sky. It is more difficult to reduce optical aberrations in telescopes with low f-ratio than in telescopes with larger f-ratio.
The light-gathering power (or light grasp) of an optical telescope is directly related to the square of the diameter (or aperture) of the objective lens or mirror. Note that the area of a circle is proportional to the square of the radius. A telescope with a lens which has a diameter three times that of another will have nine times the light-gathering power. Larger objectives gather more light, and more sensitive imaging equipment can produce better images from less light.
No telescope can form a perfect image. Even if a refracting telescope could have a perfect lens, the effects of aperture diffraction are unavoidable. In reality, perfect mirrors and perfect lenses do not exist, so image aberrations in addition to aperture diffraction must be taken into account. Image aberrations can be broken down into two main classes, monochromatic, and polychromatic. In 1857, Philipp Ludwig von Seidel decomposed the first order monochromatic aberrations into five constituent aberrations. They are now commonly referred to as the five Seidel Aberrations.
The five Seidel aberrations
Spherical aberration
The difference in focal length between paraxial rays and marginal rays, proportional to the square of the aperture.
Coma
A most objectionable defect by which points are imaged as comet-like asymmetrical patches of light with tails, which makes measurement very imprecise. Its magnitude is usually deduced from the optical sine theorem.
Astigmatism
The image of a point forms focal lines at the sagittal and tangental foci and in between (in the absence of coma) an elliptical shape.
Curvature of Field
The Petzval curvature means that the image instead of lying in a plane actually lies on a curved surface which is described as hollow or round. This causes problems when a flat imaging device is used e.g. a photographic plate or CCD image sensor.
Distortion
Either barrel or pincushion, a radial distortion which must be corrected for if multiple images are to be combined (similar to stitching multiple photos into a panoramic photo).
They are always listed in the above order since this expresses their interdependence as first order aberrations via moves of the exit/entrance pupils. The first Seidel aberration, Spherical Aberration, is independent of the position of the exit pupil (as it is the same for axial and extra-axial pencils). The second, coma, changes as a function of pupil distance and spherical aberration, hence the well-known result that it is impossible to correct the coma in a lens free of spherical aberration by simply moving the pupil. Similar dependencies affect the remaining aberrations in the list.
The chromatic aberrations
Longitudinal chromatic aberration: As with spherical aberration this is the same for axial and oblique pencils.
Transverse chromatic aberration (chromatic aberration of magnification)
Initially the detector used in telescopes was the human eye. Later, the sensitized photographic plate took its place, and the spectrograph was introduced, allowing the gathering of spectral information. After the photographic plate, successive generations of electronic detectors, such as the charge-coupled device (CCDs), have been perfected, each with more sensitivity and resolution, and often with a wider wavelength coverage.
Current research telescopes have several instruments to choose from such as: imagers, of different spectral responses and spectrographs, useful in different regions of the spectrum.
In recent years, a number of technologies to overcome the distortions caused by atmosphere on ground-based telescopes have been developed, with good results. See adaptive optics, Apochromatism
Apochromat, or apochromatic lens (apo),is a lens that has better correction of chromatic and spherical aberration than the much more common achromat lenses.
Chromatic aberration is the phenomenon of different colors focusing at different distances from a lens. In photography, chromatic aberration produces soft overall images, and color fringing at high-contrast edges, like an edge between black and white. Astronomers face similar problems, particularly with telescopes that use lenses rather than mirrors.
Achromatic lenses are corrected to bring two wavelengths (typically red and blue) into focus in the same plane. Apochromatic lenses are designed to bring three wavelengths (typically red, green, and blue) into focus in the same plane. The residual color error (secondary spectrum) can be up to an order of magnitude less than for an achromatic lens of equivalent aperture and focal length. Apochromats are also corrected for spherical aberration at two wavelengths, rather than one as in an achromat.
Astronomical objectives for wide-band digital imaging must have apochromatic correction, as the optical sensitivity of typical CCD imaging arrays can extend from the ultraviolet through the visible spectrum and into the near infrared wavelength range. Apochromatic lenses for astrophotography in the 60-150 mm aperture range have been developed and marketed by several different firms, with focal ratios ranging from f/5 to f/7. Focused and guided properly during the exposure, these apochromatic objectives are capable of producing the sharpest wide-field astrophotographs optically possible for the given aperture sizes.
Apochromatic designs require optical glasses with special dispersive properties to achieve three color crossings. This is usually achieved using costly fluoro-crown glasses, abnormal flint glasses, and even optically transparent liquids with highly unusual dispersive properties in the thin spaces between glass elements. The temperature dependence of glass and liquid index of refraction and dispersion must be accounted for during apochromat design to assure good optical performance over reasonable temperature ranges with only slight re-focusing. In some cases, apochromatic designs without anomalous dispersion glasses are possible.
For the 365 Days of Astronomy Podcast. This is Edgardo Molina. From Pleiades. Research and Astronomical Studies in Mexico City, Mexico wishing you Clear Skies.
Thank you for listening.
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