Telescopes
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Telescopes
ÎMain
purposes
‹ Resolution
of closely spaced objects
‹ Light collection (measure spectra, see distant and dim objects)
ÎResolution
through magnification
‹ mθ = − f objective / feyepiece
(discussed in textbook)
ÎLight
collection: compare to eye
of eye D ≈ 8mm (in very dim light)
‹ Largest telescope (Keck) has D = 10m
‹ Ratio of areas = (10/0.008)2 = 1.5 × 106
‹ Can collect light for hours rather than 0.1 sec
‹ More sensitive light collectors (CCD arrays)
‹ Pupil
ÎLarge
‹ Can
telescopes favored by several billion over eye!
see near the end of the known universe
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Stellar Spectra (telescope + diffraction grating)
Spectrum of star
Helium
Mercury
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Main Limitation on Earth: Atmosphere
ÎAir
cells in atmosphere
‹ Air
cells above telescope mirror cause distortion of light
‹ Best performance is ≈ 0.25 – 0.5″ resolution on the ground
‹ This is why telescopes are sited on high mountains
ΓAdaptive
ÎTwo
optics” just beginning to offset this distortion
main components in adaptive optics
‹ Mechanism
to measure wave distortion above mirror
‹ Actuators under mirror move surface to offset distortions
‹ Easier for infrared wavelengths than for optical wavelengths
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Adaptive Optics: Gemini Telescope
Gemini = “twins”
¾ D = 8.1 m
¾ Hawaii, Chile
¾ Both outfitted with
adaptive optics
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Adaptive Optics in Infrared (936 nm)
9× better!
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Gemini North Images (7x Improvement)
Resolution = 0.6”
Resolution = 0.09”
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Theoretical Performance Limit: Diffraction
ÎLight
rays hitting mirror spread due to diffraction
‹ These
rays interfere, just like for single slit
‹ Calculation a little different because of circular shape
‹ Angle of spread Δθ = 1.22λ/D (D = diameter)
Intensity vs angle
1.22 λ/D
1.22 λ/D
θ in units of λ/D
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Example: Optical Telescopes
ÎKeck
telescope: D = 10m, λ = 550nm
‹ Δθ
= 1.22 × 550 × 10-9 / 10 = 6.7 × 10-8 rad = 0.014”
‹ Compare this to 0.25” – 0.5” from atmosphere
ÎHubble
space telescope: D = 2.4m, λ = 550nm
‹ Δθ
= 1.22 × 550 × 10-9 / 2.4 = 2.8 × 10-7 rad = 0.058”
‹ But actually can achieve this resolution!
ÎRayleigh
criterion
objects separated by Δθ < 1.22λ/D cannot be distinguished
‹ An approximate rule, shows roughly what is possible
‹ Two
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Pluto and Its Moon Charon
Gemini North w/ adaptive optics (0.083″ resolution)
1999 image
Hubble image
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Pluto Seen by Keck w/ Adaptive Optics
Resolution = 0.035”
λ = 1.6μm (2007)
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New Pluto Moons Seen with Adaptive Optics
Charon
Nix and Hydra
Resolution = 0.035”
λ = 1.6μm (2007)
Star trails
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Single Star
Units in multiples of λ/D
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Two Stars: Separation = 2.0 λ/D
Units in multiples of λ/D
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Two Stars: Separation = 1.5 λ/D
Units in multiples of λ/D
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Two Stars: Separation = 1.22 λ/D
Units in multiples of λ/D
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Two Stars: Separation = 1.0 λ/D
Units in multiples of λ/D
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Two Stars: Separation = 0.8 λ/D
Units in multiples of λ/D
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Two Stars: Separation = 0.6 λ/D
Units in multiples of λ/D
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Two Stars: Separation = 0.4 λ/D
Units in multiples of λ/D
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Single Star
Units in multiples of λ/D
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Interferometry: Multiple Radiotelescopes
ÎCombine
information from multiple radiotelescopes
‹ Atomic
clocks to keep time information (time = phase)
‹ Each telescope records signals on tape with time stamp
‹ Tapes brought to “correlator” to build synthetic image
ÎSingle
‹ Δθ
ÎTwo
telescope resolution
= 1.22λ/D (D = diameter of dish or mirror)
telescope resolution
‹ Δθ
~ λ/D (D = distance between telescopes)
ÎSpectacular
improvement in resolution
‹ Diameter
of dish ~ 20 – 50m
‹ Distance between two dishes ~ 12,000 km (diameter of earth)
‹ Improvement is factor of ~ 200,000 – 500,000
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Radiotelescope at Mauna Kea (Hawaii)
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Interferometry using widely spaced radiotelescopes
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Example of Interferometry
ÎTwo
radiotelescopes
‹D
= 50m
‹ Separated by diameter of earth = 12,700 km
‹ 6 GHz radio waves, λ = 5 cm
ÎSingle
‹ Δθ
ÎTwo
telescope resolution
= 1.22λ/D = 1.22 × 0.05 / 50 = 0.0012 rad = 200”
telescope resolution
‹ Δθ
~ λ/D = 0.05 / 1.27 × 107 = 4 × 10-9 rad = 0.0004”
‹ Compare to 0.25” for best earthbound telescope, 0.06” for Hubble
VLBI: “Very Long Baseline Interferometry”
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Worldwide VLBI Radiotelescope Network
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Spaced Based Interferometry: VSOP
VSOP (VLBI Space Observatory Programme)
http://www.vsop.isas.ac.jp/
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VLBI Using Satellite (λ = 6cm)
Quasar: VLBI ground only
Quasar: VLBI ground plus space
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VLBI Using Satellite (λ = 17cm)
Quasar: VLBI ground only
Quasar: VLBI ground plus space
Space based ~ 30,000 km baseline
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