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Transcript
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 36
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 36
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 36
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 36
4
Diffraction Through Circular Opening
Intensity of light after passing
through a circular opening.
Spreading caused by diffraction.
PHY 2049: Chapter 36
5
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 36
6
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 36
7
Single Star
Units in multiples of λ/D
PHY 2049: Chapter 36
8
Two Stars: Separation = 2.0
Units in multiples of λ/D
PHY 2049: Chapter 36
9
Two Stars: Separation = 1.5
Units in multiples of λ/D
PHY 2049: Chapter 36
10
Two Stars: Separation = 1.22
Units in multiples of λ/D
PHY 2049: Chapter 36
11
Two Stars: Separation = 1.0
Units in multiples of λ/D
PHY 2049: Chapter 36
12
Two Stars: Separation = 0.8
Units in multiples of λ/D
PHY 2049: Chapter 36
13
Two Stars: Separation = 0.6
Units in multiples of λ/D
PHY 2049: Chapter 36
14
Two Stars: Separation = 0.4
Units in multiples of λ/D
PHY 2049: Chapter 36
15
Single Star
Units in multiples of λ/D
PHY 2049: Chapter 36
16
Gemini Telescope w/ Adaptive Optics
Gemini = “twins”
¾ D = 8.1 m
¾ Hawaii, Chile
¾ Both outfitted with
adaptive optics
PHY 2049: Chapter 36
17
Adaptive Optics in Infrared (936 nm)
9× better!
PHY 2049: Chapter 36
18
Pluto and Its Moon
Pluto and its moon Charon (0.083″ resolution)
PHY 2049: Chapter 36
19
Gemini North Images (7x Improvement)
Resolution = 0.6”
Resolution = 0.09”
PHY 2049: Chapter 36
20
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 36
21
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 36
22
Radiotelescope (Mauna Kea)
PHY 2049: Chapter 36
23
Spaced Based Interferometry: Japan
VSOP (VLBI Space Observatory Programme)
http://www.vsop.isas.ac.jp/
PHY 2049: Chapter 36
24
VLBI Using Satellite (λ = 6cm)
Quasar: VLBI ground only
Quasar: VLBI ground plus space
PHY 2049: Chapter 36
25
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