ASTR 130 (O'Connell) Lecture Notes

Summit of Mauna Kea, Hawaii, world's largest astronomical observing complex

A. THE HUMAN EYE

• The eye operates like a camera, with a lens, an iris, and a retina.

• The refractive lens is filled with fluid, and its shape can be adjusted by the surrounding muscles so that a sharp ("in focus") image is produced on the retina over a range of distances to objects being viewed. Limitations in the ability to adjust the lens produce the phenomena of "near-sightedness" and "far-sightedness." The resolution of the lens-plus-detector system of the eye is typically 1-2 minutes of arc.

• The iris automatically adjusts the eye's input aperture diameter according to the prevailing light level. This provides a "focal-ratio" for the eye in the range f/3 to f/8 (approximately). The largest aperture size, under very dark conditions, is about 5-7mm.

• The retina is a complex photo-detection system. Light falling on retinal cells triggers chemical changes that produce an electrical signal which is sent down the optic nerve to the brain. There are two kinds of photo-receptor cells in the retina: rods and cones. The cones are less numerous and operate only at high light levels, where they provide information on color as well as the brightness of scenes. The rods are more sensitive, so operate best at low light levels, but they produce only a "grey-scale" image without elements of color.

• Under the very low light conditions you will typically encounter when observing faint sources through a telescope, the rods slowly become more sensitive. It takes over 20 minutes to achieve highest sensitivity, or "full dark adaptation," but reasonable sensitivity occurs in about 3 minutes. You must avoid looking at bright lights to become dark-adapted. Using a red flashlight helps preserve night vision.

• The rods are preferentially distributed toward the edge of the retina, which is therefore more sensitive to faint sources. This is the basis for the "averted vision" technique, where you stare at a point about 20 degrees away from the object of interest but focus your attention on the target.

• Dynamic range: in a given scene, the eye can distinguish levels of illumination that have a brightness range of about 100:1, so it is said to have a dynamic range of 100. The maximum range of brightnesses detectable by the eye, after adjustments such as dark adaptation, is a remarkable 1,000,000:1.

• Integration time: the eye automatically adjusts the time interval during which it accumulates light energy before sending an image to the brain. This interval is called the "integration time" and is typically 0.1 sec; it increases to perhaps 0.2 sec for low-light levels. The reason that astronomical photographs show so much more detail than you can see with your eye is mainly due to the fact that cameras can have very long integration times, up to hours if necessary.

B. THE ELECTROMAGNETIC SPECTRUM

• Wavelengths of optical light are conventionally measured in units of "Ångstroms" (where 1 Å = 10^-8 cm).

• The optical band extends roughly from wavelengths of 4000 Å in the deep violet to 7000 Å in the deep red. Green light has a wavelength around 5000 Å, or about 0.0005 mm---far smaller than sizes encountered in everyday life.

• Because the wavelength of optical light is so small, we are not conscious of light's wavelike character.

C. TELESCOPES: GENERAL

• Invented: 1608 (Lippershey, Holland). [Note: microscope invented 1654, also in Holland.]

• First astronomical use: 1610, by (Galileo, Italy). Utterly transformed astronomy.

Purposes

• Collect more light from source
  This is the most important attribute of a telescope (because most astronomical sources are so faint)

• Magnify source
  "Magnify" means to make the source appear larger in angular size

• Resolve more detail in source
  "Resolution" is distinct from magnification. A higher resolution image looks more sharp, less blurry, regardless of how large it is.

Basic Principle

• An objective or primary optical element forms an image (i.e. an accurate representation of original scene) at a usable focus, where it can be studied by eye, recorded by film or other detectors (as in a camera), or fed into yet other instruments

Objectives: Two Types

1. Lens: transparent glass shaped to refract (or bend) light rays to a focus. The image at the left below shows how a flat glass surface bends light rays (in this case, two flat surfaces at an angle combine to make a prism). The shorter the wavelength, the stronger the bending. The image at the right shows how a glass surface can be continuously curved to bring all the light rays passing through it from a distant object to a common focal point. Each element of the lens acts like a small prism.

   Refraction of Light By a Prism (click for descriptive animation)	Shaped Convex Lens

   
   

   • Note that light rays travel in straight lines through empty space or through any medium (air, glass, water, etc) that has uniform properties. It will only be at the boundaries between two uniform media that light rays can be deflected or "bent." The optical elements of a telescope therefore only change the directions of light rays at their surfaces (which represent glass/air boundaries).

2. Mirror: shaped glass which reflects light rays off its front surface to a common focus. A mirror shaped like a parabola will focus all rays that are parallel to its optical axis to a single point. See picture below.

Reflection of Light by a Figured Mirror

Applet. Here is a Java applet illustrating the differences between refraction, reflection, and diffraction.

• Note: Because the primary optical element is the most important element of a telescope, the "size" of a telescope is characterized by the diameter of its primary.
  Thus, the "26-in" McCormick refracting telescope has a primary lens that is 26 inches in diameter. The 200-in Palomar telescope has a primary mirror that is 200 inches in diameter.

Focal point

• For distant objects (including all astronomical objects), the incoming rays from each point on the source are parallel to each other. In this case, the image is formed at a position which is one focal length from the objective.
  • For nearer objects, the image is formed at a larger distance from the objective. Click on the button below for a Java applet illustrating image formation.

Applet

• Note that the image is inverted with respect to the original, as in the drawing below:
  

"Visual" Use

• In order to look through a telescope, a small lens called an eyepiece is used to magnify the image at the focal point and make the rays parallel again. This allows the eye to form a sharp image of it.

• Although the lens of your eye is partially adjustable and can adjust to focus on nearby or distant objects, the light beam from the objective of a telescope is converging or diverging too strongly to correct in the absence of an eyepiece.

Aberrations

No simple lens or mirror can precisely focus rays coming from different directions within the field of view to a single flat focal surface. Parabolic mirrors, for instance, produce a blur that increases with off-axis angular distance called coma. This kind of "aberration" effect can be reduced using multi-mirror, multi-lens, or lens+mirror designs.
Light ray-traces of some important aberrations in mirrors can be found here.

D. MEADE TELESCOPES USED IN ASTR 130

E. TELESCOPE PERFORMANCE CHARACTERISTICS

• Resolution is quantitatively defined to be the smallest measurable detail in an image (in seconds of arc). Depends both on telescope optics and Earth's atmosphere.

• Basic limit is set by the physics of light: since it is a wave phenomenon, light spreads out or diffracts.
  Diffraction
  The picture above shows how light diffracts when passing through a narrow aperture, such as the objective lens of a telescope.
  Because of the interference of light waves from different parts of the aperture, the larger the aperture, the more concentrated the emerging beam, implying better resolution.

• The resolution is proportional to (Wavelength/Objective Diameter). The larger the telescope, the better the resolution.
  This picture illustrates the effects of telescope size on the image of a binary star.
  Note that all stars are so distant that they appear as point sources in smaller telescopes. You cannot actually detect any detail on star surfaces except in the largest telescopes.

• A 10-in diameter telescope with perfect optics will produce a 1 arc-sec diameter image of a star (assuming a perfectly stable atmosphere).

The Earth's atmosphere also refracts light, and because it is constantly moving, there is always a blurring and jittering of images in a scope. Astronomers call this "seeing."
Quantitatively, seeing is defined to be the diameter of a star image (in seconds of arc) caused by atmospheric turbulence.
Expect typical seeing of 2-4 seconds of arc at the Student Observatory. Seeing can be measured by observing a double star of known separation (see writeup for Lab 3).
Seeing actually dominates diffraction in most cases, so having a better telescope often does not improve performance. Instead, you may need a better observing site.
Below is an enlarged image of the bright star Betelgeuse taken with a large telescope. It is a large blob, broken up into smaller near point-like units by seeing effects in the Earth's atmosphere. (The small "speckles" represent the image you could see in the absence of atmospheric effects.) Click on the image for a video of the seeing effects. Click here for an illustration of seeing effects on an extended object (the Moon).
"Seeing" Produced by Earth's Atmosphere

F. TELESCOPE TYPES

• Refracting: objective is a lens; bends rays. Galileo's of this type. McCormick 26-in of this type. Largest: 40-in diameter (built 1896).

• Reflecting: objective is a mirror; reflects rays. Invented by Gregory; improved by Newton. All large telescopes are reflectors. Largest 400" (10-m) diameter (built 1993).

• Catadioptric: combines lenses and mirrors, e.g. to produce a larger well defined field of view. Most famous: Schmidt wide field survey telescopes. These use a spherical primary mirror surface, which by itself would produce serious blurring but add a specially-shaped correcting lens at the front of the telescope that eliminates the blur.

Note that in three of the designs shown, a "secondary" mirror at the top of the telescope tube is used to redirect the light beam. Although the secondary does block part of the primary, this has only a small effect on the net image quality. In particular, it does not produce a "hole" in the center of the image. In the Cassegrain design, a hole is actually made in the primary itself.
The Meade 8-in telescopes are catadioptric systems. They combine a spherical mirror and Schmidt corrector plate with a Cassegrain through-the-primary light beam design. See diagram below:

• To produce a good image, telescope optics must be figured to a minimum tolerance of about 1/4 of the wavelength. For optical telescopes, this is 10^-5 cm. Small!

• Good polishing/test techniques were not developed until the 19th century. To overcome limitations in figuring technology, early astronomers favored telescopes with very long focal lengths (click here for an example).

• Altitude-Azimuth (Alt/Az) mount: one vertical axis and one horizontal axis. Lowest cost but require computer control for large scopes since must move in two axes simultaneously to track stars.

• Equatorial mount: two axes, but polar axis is tilted to parallel the Earth's rotation axis. See this illustration. Motion around this one axis then tracks the stars. Harder to engineer, easier to operate. Most telescopes use equatorial mounts but largest ones are Alt-Az. Your 8" telescopes are fork-mounted equatorials.

• Lenses produce chromatic aberration: light of different wavelengths comes to focus at different points. This was evident in the drawing of a prism above and is further illustrated below:
  

  
  

• Mirrors need be figured only on one side

• Mirrors easy to support accurately from behind; lenses require support at edges, tend to sag.

• Harder to support heavy lens mechanically at top end of tube than mirror at bottom end.

• Folding action of primary and secondary mirrors (see below) means that telescope tube is much shorter than in "straight through" refracting design.

• More discussion

Glass mirror blank for one of the two 8.4-m diameter
mirrors of the Large Binocular Telescope.

G. TELESCOPE MILESTONES (More details in Lecture 7)

• Largest refractor: Yerkes 40-in (1896)

• Largest monolithic reflector: Large Binocular Telescope (one mirror pictured above); 8.4-m (330 in)

• Largest reflector (segmented): Keck 10-m (395 in)

H. BINOCULARS

• Additional optics (prisms---see at right) are used so that the view is "right side up."

• The view for nearby objects is 3-dimensional; special optics may be used to increase the separation of the objective lenses for better 3-D resolution.

• Astronomical objects are so distant that there can be no 3-D effect. However, views with binoculars can be especially vivid because simultaneous use of both eyes produces less eye strain, and the optics of binoculars usually allow for easy centering of the eyes on the emergent beam. It is much easier to find your target with binoculars than with a telescope (assuming it's bright enough).

• Binocular optics are usually classified in the form "7 x 35". Here, the first number is the net magnification of the binoculars, and the second is the diameter of the primary lenses in millimeters. Good types for general astronomical observations are 7x35 or 8x50. Binoculars higher than 10 power require tripods for stability. The field of view is also often marked on the binoculars, typically given as the diameter in feet for objects at a distance of 1000 yards.

• Binoculars produce some of the best views of the Moon, rich star fields, comets, and the Milky Way.

I. JUDGING SKY CONDITIONS

• Transparency: means an absence of clouds, haze, or fog. Although low-altitude clouds are the most obvious, high-altitude "cirrus" clouds are more commonly a problem. Transparency predictions for 48 hour blocks for Charlottesville (based on infrared satellite data) can be found at cleardarksky.com.
  A quantitative measure of transparency is given by the magnitude of the faintest star you can see with the naked eye. The bowl of the "Little Dipper" provides a convenient set of standard stars, with approximate magnitudes of 2,3,4,5. See this image.

• Seeing: see discussion above. "Twinkling" of stars is a sign of an unstable atmosphere, which will probably produce bad seeing. But you can only actually measure the seeing through a telescope.

• Moonlight: If the Moon is more than "half-full" (which astronomers call first quarter), Moonlight scattered by the atmosphere can easily obscure fainter telescopic targets (like nebulae and galaxies). Judge effects by the faintest stars you can see.

• Light Pollution: a growing problem here in Charlottesville. Terrible when the Stadium lights are on. Impact will vary with the amount of low-level dust or mist in the atmosphere. Again, judge effects by the faintest stars you can see.

J. LAB REPORTS & OBSERVING FORMS

• Appendices D and E in the ASTR 130 Lab Manual describe how you are expected to use the standard observing forms to record observations with binoculars or telescopes and how to write up your lab reports. Read these sections carefully.

• You are expected to have filled out the "prep" part of each form before going to the Observatory.

• To keep forms neater, fill out all sections in pencil.

• Blank observing forms and a sample, filled-out form can be found here.

Sunset over the William Herschel
Telescope (La Palma, Spain)

Homework:

• Download, print, and read the notes for Lecture 2.
  Review questions for Lecture 2

• Read Appendix C in the Manual on "Telescope Basics"

• Complete Lab I (Constellations) at the next observing opportunity

• Begin Lab 2 ASAP. TA's ready to support you after Lab I observations are complete.
  Prepare for Laboratory 2 by reading the writeup in the Manual.
  Read Appendices D and E on preparing lab reports and filling out observing forms.

Web links

Overview of electromagnetism, from Encyclopedia Britannica
Early history of telescopes, with references.
More detailed notes on telescopes (Nick Strobel).
Tutorial on telescope and eyepiece design (Frosty Drew Observatory)
The Amateur Telescope Maker Page (Now is subscription-based)
Atmospheric Effects--Seeing & Extinction (M. Richmond)

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Last modified September 2006 by rwo

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Text copyright © 1998-2006 Robert W. O'Connell. All rights reserved. Some images copyright © by Prentice-Hall and by the University of Tennessee at Knoxville. WHT image copyright © by N. Szymanek. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 130 at the University of Virginia.