PHY 2049: Chapter 37 1Paul AveryUniversity of Floridahttp://www.phys.ufl.edu/~avery/[email protected] Interference and DiffractionPart 3: Telescopes and InterferometryPHY 2049Physics 2 with CalculusPHY 2049: Chapter 37 2Telescopes: Purpose is Light CollectionÎPupil of eye D ≈ 8mm (in very dim light)ÎLargest telescope (Keck) has D = 10mÎRatio of areas = (10/0.008)2= 1.5 × 106Can collect light for hours rather than 0.1 sec More sensitive light collectors (CCD arrays) Thus telescopes are several billiontimes more sensitiveÎCan see near the end of the known universePHY 2049: Chapter 37 3Telescope ConstructionÎAll 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 movingPHY 2049: Chapter 37 4Main Limitation on Earth: AtmosphereÎAir 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 mountainsΓAdaptive optics” just beginning to offset this distortionPHY 2049: Chapter 37 5Theoretical Performance Limit: DiffractionÎLight 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)PHY 2049: Chapter 37 6Example: Optical TelescopesÎKeck 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 atmosphereÎHubble 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 Two objects separated by Δθ < 1.22λ/D cannot be distinguished An approximate rule, shows roughly what is possiblePHY 2049: Chapter 37 7Single StarUnits in multiples of λ/DPHY 2049: Chapter 37 8Two Stars: Separation = 2.0Units in multiples of λ/DPHY 2049: Chapter 37 9Two Stars: Separation = 1.5Units in multiples of λ/DPHY 2049: Chapter 37 10Two Stars: Separation = 1.22Units in multiples of λ/DPHY 2049: Chapter 37 11Two Stars: Separation = 1.0Units in multiples of λ/DPHY 2049: Chapter 37 12Two Stars: Separation = 0.8Units in multiples of λ/DPHY 2049: Chapter 37 13Two Stars: Separation = 0.6Units in multiples of λ/DPHY 2049: Chapter 37 14Two Stars: Separation = 0.4Units in multiples of λ/DPHY 2049: Chapter 37 15Single StarUnits in multiples of λ/DPHY 2049: Chapter 37 16Gemini Telescope w/ Adaptive OpticsGemini = “twins”¾ D = 8.1 m¾ Hawaii, Chile¾ Both outfitted with adaptive opticsPHY 2049: Chapter 37 17Adaptive Optics in Infrared (936 nm)9× better!PHY 2049: Chapter 37 18Pluto and Its MoonPluto and its moon Charon (0.083″ resolution)PHY 2049: Chapter 37 19Gemini North Images (7x Improvement)Resolution = 0.6” Resolution = 0.09”PHY 2049: Chapter 37 20Interferometry: Multiple RadiotelescopesÎCombine 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 imageÎSingle telescope resolution Δθ = 1.22λ/D (D = diameter of dish or mirror)ÎTwo 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 – 500,000PHY 2049: Chapter 37 21Example of InterferometryÎTwo radiotelescopes D = 50m Separated by diameter of earth = 12,700 km 6 GHz radio waves, λ = 5 cmÎSingle telescope resolution Δθ = 1.22λ/D = 1.22 × 0.05 / 50 = 0.0012 rad = 200”ÎTwo telescope resolution Δθ ~ λ/D = 0.05 / 1.27 × 107= 4 × 10-9rad = 0.0004” Compare to 0.25” for best earthbound telescope, 0.06” for HubblePHY 2049: Chapter 37 22Radiotelescope (Mauna Kea)PHY 2049: Chapter 37 23Spaced Based Interferometry: JapanVSOP (VLBI Space Observatory Programme)http://www.vsop.isas.ac.jp/PHY 2049: Chapter 37 24VLBI Using Satellite (λ = 6cm)Quasar: VLBI ground only Quasar: VLBI ground plus spacePHY 2049: Chapter 37 25VLBI Using Satellite (λ = 17cm)Quasar: VLBI ground only Quasar: VLBI ground plus spaceSpace based ~ 30,000 km
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