interferometer optical design -...
TRANSCRIPT
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Interferometer Optical DesignWesley A. Traub
Harvard-Smithsonian Center for Astrophysics
Michelson Summer SchoolCaltech, Pasadena 8 July 2003
Goals of this talk:
1. Learn to think in terms of wavelets.2. Learn how to calculate the interference of wavefronts
for any optical system.3. Learn how to separate astrophysical from instrumental effects.
Note: Direct combination of wavefronts (homodyne detection) is discussed here, i.e. λ < 10 µm; see radio for heterodyne detection.
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Summation of wavelets
Aout u,v( )= 1λf
Ain∫ x,y( )e− ik(xu+yv ) / f dxdy
where
A(x,y) 2 = energy /area = Intensity
Born and Wolf (7th edition, p. 428) define the wavelet summationintegral as the Fourier-transform relation between amplitude in the pupil Ain(x,y) and amplitude in the focal plane Aout(u,v).
Image amplitude = Sum of wavelet amplitudes
Simplify: (1) 2D→1D; (2) coef.= 1; (3) u/f = θ = angle in focal plane.
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Derive single-
telescope response to point source
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Single telescope again
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Derive interferometer (2-tel.) response
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Derive binary-star
response
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Binary star interferograms
Model interferogram for a binary star, with well-separated fringe packets.
Observed interferogram of avery wide-spaced binary.CCD detector, no filter, IOTA interferometer, 1996 data.
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Derive uniform disk response
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Uniform disk: interferograms
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Van Cittert-Zernike theorem
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Michelson’s stellar
interferometer
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Image-plane interferometer
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Pupil-plane interferometer
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Colors in interferogram
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Nulling
Nulling interferometer (Bracewell)
Stellar interferometer (Michelson)
Star at x=0,I=0
Planet at x=0,I=Iplanet
Star at x=0, I=Istar
Planet at x=0,I=Iplanet
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Theta2 nulling
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Theta4 nulling
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Multiplexing in the image plane
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Multiplexing in the pupil plane
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Golden rule
Output pupil must be a scaled version of input pupil in orderto obtain a wide field of view.
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Pupil densification
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Instrumental effects: 1
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Instrumental effects: 2
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Filter and interferogram shapes
K-band filtertransmission
K-band interferogram
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Measuring visibility
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Strehl: 1
Strehl ratio is approximately S = e-ϕ2
where ϕ is the rms phase error across a wavefront.
Observed visibility is the product of 3 terms:
Vobserved = SatmosSinstrumVobject
Instrumental Strehl ratio is the product of many terms:
Sinstrum = SservoSflatSalignSdiffractionSfluxSoverlapSvibrationSwindowSpolarization
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Strehl: 2
Atmospheric variance, with tip-tilt removed by a servo system with bandwidth v/πD, is
ϕ2 = (0.134 + 0.096)(D/r0)5/3(λ0/λ)2
Wavefront flatness variance from mirror surfaces is ϕ2 = ϕ1
2 + … + ϕn2
Mirrors are often specified in terms of surface peak-to-valleywhere an empirical relation is
PV = 5.5 RMS
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Polarization and visibility
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Visibility reduction factor
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Single-mode fiber optics
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Injecting starlight
into a fiber
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Electric vector control
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Integrated optics: 1
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Integrated optics: 2