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Wave Interference and Diffraction Part 3: Telescopes and Interferometry Paul Avery University of Florida http://www.phys.ufl.edu/~avery/ [email protected] PHY 2049 Physics 2 with Calculus PHY 2049: Chapter 37 1 Telescopes: Purpose is Light Collection ÎPupil of eye D ≈ 8mm (in very dim light) ÎLargest ÎRatio telescope (Keck) has D = 10m 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) Thus telescopes are several billion times more sensitive ÎCan see near the end of the known universe PHY 2049: Chapter 37 2 Telescope Construction ÎAll 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 3 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 optics” just beginning to offset this distortion PHY 2049: Chapter 37 4 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) PHY 2049: Chapter 37 5 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 PHY 2049: Chapter 37 6 Single Star Units in multiples of λ/D PHY 2049: Chapter 37 7 Two Stars: Separation = 2.0 Units in multiples of λ/D PHY 2049: Chapter 37 8 Two Stars: Separation = 1.5 Units in multiples of λ/D PHY 2049: Chapter 37 9 Two Stars: Separation = 1.22 Units in multiples of λ/D PHY 2049: Chapter 37 10 Two Stars: Separation = 1.0 Units in multiples of λ/D PHY 2049: Chapter 37 11 Two Stars: Separation = 0.8 Units in multiples of λ/D PHY 2049: Chapter 37 12 Two Stars: Separation = 0.6 Units in multiples of λ/D PHY 2049: Chapter 37 13 Two Stars: Separation = 0.4 Units in multiples of λ/D PHY 2049: Chapter 37 14 Single Star Units in multiples of λ/D PHY 2049: Chapter 37 15 Gemini Telescope w/ Adaptive Optics Gemini = “twins” ¾ D = 8.1 m ¾ Hawaii, Chile ¾ Both outfitted with adaptive optics PHY 2049: Chapter 37 16 Adaptive Optics in Infrared (936 nm) 9× better! PHY 2049: Chapter 37 17 Pluto and Its Moon Pluto and its moon Charon (0.083″ resolution) PHY 2049: Chapter 37 18 Gemini North Images (7x Improvement) Resolution = 0.6” Resolution = 0.09” PHY 2049: Chapter 37 19 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 PHY 2049: Chapter 37 20 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 PHY 2049: Chapter 37 21 Radiotelescope (Mauna Kea) PHY 2049: Chapter 37 22 Spaced Based Interferometry: Japan VSOP (VLBI Space Observatory Programme) http://www.vsop.isas.ac.jp/ PHY 2049: Chapter 37 23 VLBI Using Satellite (λ = 6cm) Quasar: VLBI ground only Quasar: VLBI ground plus space PHY 2049: Chapter 37 24 VLBI Using Satellite (λ = 17cm) Quasar: VLBI ground only Quasar: VLBI ground plus space Space based ~ 30,000 km baseline PHY 2049: Chapter 37 25