wave interference and diffraction part 3: telescopes and … · 2006. 12. 1. · wave interference...

$: Wave Interference and Diffraction Part 3: Telescopes and … · 2006. 12. 1. · Wave Interference and Diffraction Part 3: Telescopes and Interferometry PHY 2049 Physics 2 with Calculus$
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


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


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


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


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)


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


Single Star

Units in multiples of λ/D


Two Stars: Separation = 2.0



Single Star



Gemini Telescope w/ Adaptive Optics

Gemini = “twins”D = 8.1 mHawaii, ChileBoth outfitted with

adaptive optics


Adaptive Optics in Infrared (936 nm)

9× better!


Pluto and Its Moon

Pluto and its moon Charon (0.083″ resolution)


Gemini North Images (7x Improvement)

Resolution = 0.6” Resolution = 0.09”


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


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


Radiotelescope (Mauna Kea)


Spaced Based Interferometry: Japan

VSOP (VLBI Space Observatory Programme)http://www.vsop.isas.ac.jp/


VLBI Using Satellite (λ = 6cm)

Quasar: VLBI ground only Quasar: VLBI ground plus space


VLBI Using Satellite (λ = 17cm)

Quasar: VLBI ground only Quasar: VLBI ground plus space

Space based ~ 30,000 km baseline

wave interference and diffraction part 3: telescopes and … · 2006. 12. 1. · wave interference...

Documents