Wave Interference and Diffraction Part 3: Telescopes and Interferometry
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1 Wave Interference and Diffraction Part 3: Telescopes and Interferometry Paul Avery University of Florida PHY 2049 Physics 2 with Calculus PHY 2049: Chapter 36 1
2 Telescopes: Purpose is Light Collection Pupil of eye D 8mm (in very dim light) Largest telescope (Keck) has D = 10m Ratio of areas = (10/0.008) 2 = Can collect light for hours rather than 0.1 sec More 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 36 2
3 Telescope Construction All 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 36 3
4 Main Limitation on Earth: Atmosphere Air cells in atmosphere Air cells above telescope mirror cause distortion of light Best performance is resolution on the ground This is why telescopes are sited on high mountains Adaptive optics just beginning to offset this distortion PHY 2049: Chapter 36 4
5 Diffraction Through Circular Opening Intensity of light after passing through a circular opening. Spreading caused by diffraction. PHY 2049: Chapter 36 5
6 Theoretical Performance Limit: Diffraction Light 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 36 6
7 Example: Optical Telescopes Keck telescope: D = 10m, λ = 550nm Δθ = / 10 = rad = Compare this to from atmosphere Hubble space telescope: D = 2.4m, λ = 550nm Δθ = / 2.4 = rad = But actually can achieve this resolution! Rayleigh criterion Two objects separated by Δθ < 1.22λ/D cannot be distinguished An approximate rule, shows roughly what is possible PHY 2049: Chapter 36 7
8 Single Star Units in multiples of λ/d PHY 2049: Chapter 36 8
9 Two Stars: Separation = 2.0 Units in multiples of λ/d PHY 2049: Chapter 36 9
10 Two Stars: Separation = 1.5 Units in multiples of λ/d PHY 2049: Chapter 36 10
11 Two Stars: Separation = 1.22 Units in multiples of λ/d PHY 2049: Chapter 36 11
12 Two Stars: Separation = 1.0 Units in multiples of λ/d PHY 2049: Chapter 36 12
13 Two Stars: Separation = 0.8 Units in multiples of λ/d PHY 2049: Chapter 36 13
14 Two Stars: Separation = 0.6 Units in multiples of λ/d PHY 2049: Chapter 36 14
15 Two Stars: Separation = 0.4 Units in multiples of λ/d PHY 2049: Chapter 36 15
16 Single Star Units in multiples of λ/d PHY 2049: Chapter 36 16
17 Gemini Telescope w/ Adaptive Optics Gemini = twins D = 8.1 m Hawaii, Chile Both outfitted with adaptive optics PHY 2049: Chapter 36 17
18 Adaptive Optics in Infrared (936 nm) 9 better! PHY 2049: Chapter 36 18
19 Pluto and Its Moon Pluto and its moon Charon (0.083 resolution) PHY 2049: Chapter 36 19
20 Gemini North Images (7x Improvement) Resolution = 0.6 Resolution = 0.09 PHY 2049: Chapter 36 20
21 Interferometry: Multiple Radiotelescopes Combine 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 Single telescope resolution Δθ = 1.22λ/D (D = diameter of dish or mirror) Two telescope resolution Δθ ~ λ/d (D = distance between telescopes) Spectacular improvement in resolution Diameter of dish ~ 20 50m Distance between two dishes ~ 12,000 km (diameter of earth) Improvement is factor of ~ 200, ,000 PHY 2049: Chapter 36 21
22 Example of Interferometry Two radiotelescopes D = 50m Separated by diameter of earth = 12,700 km 6 GHz radio waves, λ = 5 cm Single telescope resolution Δθ = 1.22λ/D = / 50 = rad = 200 Two telescope resolution Δθ ~ λ/d = 0.05 / = rad = Compare to 0.25 for best earthbound telescope, 0.06 for Hubble PHY 2049: Chapter 36 22
23 Radiotelescope (Mauna Kea) PHY 2049: Chapter 36 23
24 Spaced Based Interferometry: Japan VSOP (VLBI Space Observatory Programme) PHY 2049: Chapter 36 24
25 VLBI Using Satellite (λ = 6cm) Quasar: VLBI ground only Quasar: VLBI ground plus space PHY 2049: Chapter 36 25
26 VLBI Using Satellite (λ = 17cm) Quasar: VLBI ground only Quasar: VLBI ground plus space Space based ~ 30,000 km baseline PHY 2049: Chapter 36 26
Telescopes. PHY2054: Chapter 25 26
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