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PHY 2049: Chapter 37 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
PHY 2049: Chapter 37 2
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
PHY 2049: Chapter 37 3
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
PHY 2049: Chapter 37 4
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
PHY 2049: Chapter 37 5
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)
PHY 2049: Chapter 37 6
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
PHY 2049: Chapter 37 7
Single Star
Units in multiples of λ/D
PHY 2049: Chapter 37 8
Two Stars: Separation = 2.0
Units in multiples of λ/D
PHY 2049: Chapter 37 9
Two Stars: Separation = 1.5
Units in multiples of λ/D
PHY 2049: Chapter 37 10
Two Stars: Separation = 1.22
Units in multiples of λ/D
PHY 2049: Chapter 37 11
Two Stars: Separation = 1.0
Units in multiples of λ/D
PHY 2049: Chapter 37 12
Two Stars: Separation = 0.8
Units in multiples of λ/D
PHY 2049: Chapter 37 13
Two Stars: Separation = 0.6
Units in multiples of λ/D
PHY 2049: Chapter 37 14
Two Stars: Separation = 0.4
Units in multiples of λ/D
PHY 2049: Chapter 37 15
Single Star
Units in multiples of λ/D
PHY 2049: Chapter 37 16
Gemini Telescope w/ Adaptive Optics
Gemini = “twins”D = 8.1 mHawaii, ChileBoth outfitted with
adaptive optics
PHY 2049: Chapter 37 17
Adaptive Optics in Infrared (936 nm)
9× better!
PHY 2049: Chapter 37 18
Pluto and Its Moon
Pluto and its moon Charon (0.083″ resolution)
PHY 2049: Chapter 37 19
Gemini North Images (7x Improvement)
Resolution = 0.6” Resolution = 0.09”
PHY 2049: Chapter 37 20
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
PHY 2049: Chapter 37 21
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
PHY 2049: Chapter 37 22
Radiotelescope (Mauna Kea)
PHY 2049: Chapter 37 23
Spaced Based Interferometry: Japan
VSOP (VLBI Space Observatory Programme)http://www.vsop.isas.ac.jp/
PHY 2049: Chapter 37 24
VLBI Using Satellite (λ = 6cm)
Quasar: VLBI ground only Quasar: VLBI ground plus space
PHY 2049: Chapter 37 25
VLBI Using Satellite (λ = 17cm)
Quasar: VLBI ground only Quasar: VLBI ground plus space
Space based ~ 30,000 km baseline