PHY 2049: Chapter 36 1
Paul AveryUniversity of Florida
http://www.phys.ufl.edu/~avery/[email protected]
Wave Interference and Diffraction
Part 3: Telescopes and Interferometry
PHY 2049Physics 2 with Calculus
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Telescopes: Purpose is Light CollectionPupil 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 secMore sensitive light collectors (CCD arrays)Thus telescopes are several billion times more sensitive
Can see near the end of the known universe
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Telescope ConstructionAll large telescopes are reflectors: Why?
Mirror only needs single high quality surface(lens needs perfect volume since light passes through it)No chromatic aberration (no lens for refracting)Full support for mirror, no distortion from moving
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Main Limitation on Earth: AtmosphereAir cells in atmosphere
Air cells above telescope mirror cause distortion of lightBest performance is ≈ 0.25 – 0.5″ resolution on the groundThis is why telescopes are sited on high mountains
“Adaptive optics” just beginning to offset this distortion
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Diffraction Through Circular Opening
Intensity of light after passingthrough a circular opening.Spreading caused by diffraction.
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Theoretical Performance Limit: DiffractionLight rays hitting mirror spread due to diffraction
These rays interfere, just like for single slitCalculation a little different because of circular shapeAngle of spread Δθ = 1.22λ/D (D = diameter)
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Example: Optical TelescopesKeck 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
Hubble space telescope: D = 2.4m, λ = 550nmΔθ = 1.22 × 550 × 10-9 / 2.4 = 2.8 × 10-7 rad = 0.058”But actually can achieve this resolution!
Rayleigh criterionTwo objects separated by Δθ < 1.22λ/D cannot be distinguishedAn approximate rule, shows roughly what is possible
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Single Star
Units in multiples of λ/D
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Two Stars: Separation = 2.0
Units in multiples of λ/D
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Two Stars: Separation = 1.5
Units in multiples of λ/D
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Two Stars: Separation = 1.22
Units in multiples of λ/D
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Two Stars: Separation = 1.0
Units in multiples of λ/D
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Two Stars: Separation = 0.8
Units in multiples of λ/D
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Two Stars: Separation = 0.6
Units in multiples of λ/D
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Two Stars: Separation = 0.4
Units in multiples of λ/D
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Single Star
Units in multiples of λ/D
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Gemini Telescope w/ Adaptive Optics
Gemini = “twins”D = 8.1 mHawaii, ChileBoth outfitted with
adaptive optics
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Adaptive Optics in Infrared (936 nm)
9× better!
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Pluto and Its Moon
Pluto and its moon Charon (0.083″ resolution)
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Gemini North Images (7x Improvement)
Resolution = 0.6” Resolution = 0.09”
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Interferometry: Multiple RadiotelescopesCombine information from multiple radiotelescopes
Atomic clocks to keep time information (time = phase)Each telescope records signals on tape with time stampTapes brought to “correlator” to build synthetic image
Single telescope resolutionΔθ = 1.22λ/D (D = diameter of dish or mirror)
Two telescope resolutionΔθ ~ λ/D (D = distance between telescopes)
Spectacular improvement in resolutionDiameter of dish ~ 20 – 50mDistance between two dishes ~ 12,000 km (diameter of earth)Improvement is factor of ~ 200,000 – 500,000
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Example of InterferometryTwo radiotelescopes
D = 50mSeparated by diameter of earth = 12,700 km6 GHz radio waves, λ = 5 cm
Single telescope resolutionΔθ = 1.22λ/D = 1.22 × 0.05 / 50 = 0.0012 rad = 200”
Two telescope resolutionΔθ ~ 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
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Radiotelescope (Mauna Kea)
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Spaced Based Interferometry: Japan
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
