1. Telescope Optics: A Primer for Amateur Astronomers Part 1: Fundamental Geometric Optics Marc Baril West Hawaii Astronomy Club, August 11, 2009

2. Overview Reflection / Refraction Image formation The visual telescope Telescope performance: focal ratio, resolution, magnification, exit pupil. Telescope types, broad comparisons What won’t be covered here (Part 2): Aberrations and specific performance comparisons between telescope systems.

3. Angle of reflected ray vector with respect to the normal vector is equal to the angle of the incident ray vector. The normal, incident and reflected vectors lie in the same plane. Reflection

4. Refraction When light enters a transparent dielectric (non conductive) material its phase speed is reduced compared to its phase speed in the vacuum. The resultant bending of the wavefront at non-normal incidences is called refraction.

5. “Real” Image formation of an object at infinity with a concave mirror Spherical mirror Focal length ≈ Radius of curvature / 2 Parabolic mirror

6. “Real” and “virtual” Image formation of an object at infinity with lenses “Lensmaker’s” equation:

7. General properties of image formation Thin lens equation Linear image magnification:

8. A telescope consists of two parts: An image forming optic (lens, mirror or combination of both) and an eyepiece to “collimate” the light at the image plane. The visual telescope

9. Telescope Performance Metrics Light gathering “power” – F number or f-ratio: At fixed objective focal length and magnification, a “faster” telescope (smaller F number) will provide a view that is brighter by the ratio of the square of the two apertures. Example: A 12” diameter f/5 telescope will provide an image that is 4 times as bright as a 6” f/10 telescope; note that both have the same focal length. Diffraction limited resolution: The size of the diffraction spot on an ideal telescope is inversely proportional to the aperture; Diameter in arc-seconds ≈ 6 / (aperture diameter in inches). Since seeing is rarely below 1 arc-second at most sites, the limiting aperture for visual use is usually ~6”. Useful field of view: Off-axis aberrations limit the useable field of view of different designs (to be discussed in the next installment…). Exit pupil: Much thought must be given to this when selecting a telescope for a given visual application! Magnification is NOT a useful metric: Can be arbitrarily changed by selecting different eyepieces. For a reasonably good telescope, the seeing almost always limits the maximum useful magnification (usually below 300 times).

10. The angular diameter of the Airy disk: Where D is the diameter of the telescope and λ is the wavelength Simulation of the ideal telescope point spread function

11. The influence of exit pupil on visual telescope selection for wide field use Focal length1600 Aperture12131415161718192021 mm304.8330.2355.6381.0406.4431.8457.2482.6508.0533.4 f ratio5.24.84.54.23.93.73.53.33.13.0 EyepieceExit pupil 203.84.14.44.85.15.45.76.06.46.7 275.15.66.06.46.97.37.78.18.69.0 356.77.27.88.38.99.410.010.611.111.7 417.88.59.19.810.411.111.712.413.013.7 5510.511.412.213.114.014.815.716.617.518.3 EyepieceBrightness factor 201.01.21.31.51.82.02.22.5 271.82.12.5 352.5 412.5 552.5 Field of view in 27 mm, 68 degree apparent f.o.v. eyepiece = 1 degree

12. Focal length 2000. 0 Aperture12.013.014.015.016.017.018.019.020.021.022.023.024.0 mm304.8330.2355.6381.0406.4431.8457.2482.6508.0533.4558.8584.2609.6 f ratio6.66.15.65.24.94.64.44.13.93.73.63.43.3 EyepieceExit pupil 203.03.33.63.84.14.34.64.85.15.35.65.86.1 274.14.54.85.15.55.86.26.56.97.27.57.98.2 355.35.86.26.77.17.68.08.48.99.39.810.210.7 416.26.87.37.88.38.99.49.910.410.911.512.012.5 558.49.19.810.511.211.912.613.314.014.715.416.116.8 EyepieceBrightness factor 201.01.11.31.51.71.92.12.42.62.93.23.53.8 271.72.02.42.73.13.53.94.0 352.93.44.0 414.0 554.0 Field of view in 27 mm, 68 degree apparent f.o.v. eyepiece = 0.8 degree

14. Examples of most commonly used telescopes Schmidt Cassegrain (catadioptric) Newtonian reflector (Dobson mount) Air spaced doublet refractor

15. Comparison of designs by application Planetary and other bright object visual observations Refractor: Excellent, but use limited by cost and weight when going to sufficiently large apertures (i.e. greater than 10 cm). Much of the anecdotal advantages over reflectors/SCTs are due to poor thermal management in the latter – there is no physically meaningful advantage in many cases. SCT: Can be excellent depending on design. The difficultly of baffling an SCT and the large central obstruction in most fast (i.e. f/10 or faster) designs reduces image contrast. Reflector: Excellent depending on implementation; small secondary and good thermal management are essential.

16. Visual observation of small, faint objects: Planetary nebulae, galaxies, tight globular clusters Refractor: Poor. SCT: Fair to good, depending on the object. However, large SCTs (above 12”) are comparably ungainly compared to a similarly sized Newtonian. Reflector: This is where a fast Newtonian really shines. It is important however to maintain a magnification sufficiently high that the exit pupil remains below 6 mm. If you really like galaxies, go for the largest aperture possible.

17. Visual observation of extended, faint objects: Large emission nebulae / supernova remnants, star clouds, star clusters, dark nebulae Refractor: A rich field refractor (e.g. binoculars) is excellent at very low powers on some very wide objects. SCT: Fair to good, depending on the object. The slow F ratios (typically f/10 or more) do not lend themselves well here. Reflector: Excellent in a fast Newtonian, however the exit pupil must be carefully watched. To maintain close to a 1 degree field of view (which is a sweet spot for many of these objects), the sweet spot will be in the 14” to 18” aperture range, with a focal ratio above f/4. If you really prefer observing wide objects, go for the smaller aperture and a higher f-ratio near f/5 (e.g. 14” f/5).

18. Photography: Refractor: Excellent for wide field photography where the setup can be very compact and free of alignment drift in the optics. Fast, focal reduced systems are available at moderate to high cost. SCT: Good for small objects but may require a field flattener for extended objects. Excellent for planetary photography, especially at the larger apertures. Newtonian reflector: Generally poorly suited to faint object photography outside an observatory as windshake presents a big problem. Furthermore, the more stable Alt/azimuth mounted configuration requires field de-rotation. Planetary photography is certainly do-able but not as easy as on an SCT. Other: A number of fast photographic telescope options exist that are excellent in principle but depend strongly on the implementation, e.g.: Meade and AstroSysteme’s Schmidt Newtonians, AstroTech’s fast Ritchey-Cretien cassegrains. The Wright Newtonian is an excellent, relatively simple option that has not been pursued commercially.

19. Other things to consider… You know your telescope is too big when it has a license plate! Storage: Monolithic tube Newtonians can take up a lot of room in storage. Portability: Can your scope be set up by a single person or does it take an infantry division to assemble it? Can you take it on a plane? Weather worthiness: Open designs are susceptible to dew and rain on the optics. Susceptibility to wind: Read, large Dobsonians… Mechanical ineptitude of operator: Refractors are relatively low fuss telescopes, almost all others require regular collimation. For most people, the amount a telescope gets used is inversely proportional to the square of its weight.