Telescopes Astronomy 320 Wednesday, February 14, 2018
Telescopes gather light and resolve detail A telescope is sometimes called a light bucket. Number of photons collected per second is proportional to the area of the lens/mirror: Area = p/4 x D 2 where D = diameter of the lens/mirror.
Two types of telescopes: refractor vs. reflector Galileo s telescope Newton s telescope
Refracting telescopes A convex lens (thicker in the middle) focuses light to a point: Light from a large area is funnelled into a small area.
Refracting telescopes Galilean telescope design
The world s largest refracting telescope Yerkes Observatory, Wisconsin 1 meter diameter Completed 1897
Today, the world s biggest telescopes are reflectors (mirrors), not refractors (lenses) The problem with lenses: 1) Lenses absorb light. 2) Lenses sag. 3) Lenses have chromatic aberration: colors do not focus at same point.
Reflecting telescopes Newtonian telescope, 1668
Reflecting telescopes A mirror shaped like a parabola focuses light to a point: Light from a large area is funnelled into a small area. Both lenses and mirrors (if shaped correctly) can produce an accurate image of an object.
Focal points and focal lengths Sign of convention for R (radii of curvature) in In case (a), R1 > 0, R2 > 0 and in case (b), R1 < 0, R2 < 0
Focal points and focal lengths Two kinds of mirrors: (a) a converging mirror, f > 0, (b) a diverging mirror, f < 0.
Cassegrain telescope design Concave (parabolic) primary, convex (hyperbolic) secondary Secondary Primary Focus
Gregorian telescope design Concave (parabolic) primary, concave (ellipsoidal) secondary Secondary Primary Focus
Focal points and focal lengths Focal Plane (out of the page) Focal Plane: a plane passing through the focal point and oriented perpendicular to the optical axis of the system.
Focal points and focal lengths Focal Plane (out of the page) Plate scale: relates the angular separation of the objects with linear separation of their images at the focal plane. As the focal plane is increased, the linear separation of the images of two point sources separated by an angle θ also increases.
Focal points and focal lengths Focal Plane (out of the page) For two point sources separated by a distance θ, simple geometry gives their distance on the focal plane as: y = f tan( θ ), or y fθ where the approximation is valid if the field of view of the telescope is small. The Plate Scale is:
Resolution Resolution: Our ability to see two objects separated by an angle θ. For two light rays traveling to the focal plane, if they are separated by one-half wavelength (λ/2) destructive interference occurs: In general, interference occurs from light passing through an aperture if the following is met: Where constructive interference occurs for integer m values and destructive interference for m+1/2 values Dark fringes occur when m=integers+1/2
Resolution Circular apertures act the same way, but involve more complicated math to compute locations of peaks. The intensity and locations of the minima and maxima are given by: Ring m I / I0 central max 0.00 1.00 1st minimum 1.22 2nd max 1.64 0.0175 2nd min 2.23 3rd max 2.68 0.004 3rd min 3.24 This gives a minimum resolution to resolve two point sources:
Resolution (a) sources are resolved (b) sources are barely resolved (c) sources are unresolved Rayleigh criterion is the minimum angular separation to resolve two point sources, given (for small angle approximation) at the location of the first minimum, where m = 1.22 for circular apertures: This is the Diffraction Limit where λ is the wavelength of light, and D is the diameter of the telescope mirror
Resolution 10 o 1 o 10 1
Where are the big telescopes?
Light pollution
Astronomical seeing Seeing refers to how the earth s atmosphere distorts incoming light Seeing is caused by turbulence in the atmosphere, which blurs light.
Astronomical seeing Good Unfortunately, sites in the world Earth s normally atmosphere achieve usually seeing sets ~1. the limit to how refined we can make the resolution. This is set by Turbulence in the atmosphere, which blurs light. We call this At the Seeing. best sites in the world, like Mauna Kea in Hawaii or the mountains in Northern Chile, the median seeing is ~0.5-0.6. Good sites in the world normally achieve seeing ~1. The Hubble Space Telescope, which is above most of the atmosphere, achieves the diffraction At the best limit. sites It in has the a world, D=2.4 like m primary Mauna Kea mirror. in Hawaii At a wavelength or the mountains of 1 micron in Northern (10-6 m) HST Chile, achieves the median a diffraction seeing is limit ~0.5-0.6. of: The Hubble Space Telescope, which is above most of the atmosphere, achieves the diffraction limit. It has a D=2.4 m primary mirror. At a wavelength of 1 micron (10-6 m) HST achieves a diffraction limit of: which is 5-10x better than what is achievable on Earth.
Adaptive optics AO can correct problems caused by seeing by compensating for the distortions caused by the atmosphere with deformable mirrors
Adaptive optics
Atmospheric transmission
Where are the big telescopes?
Near- to Mid-Infrared telescopes Gemini telescope Mauna Kea, Hawaii and Cerro Pachon, Chile IRTF telescope Mauna Kea, Hawaii
Submillimeter telescopes Need to be at high altitude (ALMA array, Chilean Atacama desert,16000 ft) Or else really cold (Viper telescope, South Pole)
Radio telescopes Wavelengths of a centimeter to about 10 meters. Increase resolution by using many radio telescopes spread over a large area
Space telescopes Space telescopes are above Earth s atmosphere: not limited by atmospheric transmission, seeing, weather, light pollution BUT: they re more expensive, and if they break are difficult to fix!