Optical Interferometry

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Optical Interferometry

• Elliott Horch, University of Massachusetts
  Dartmouth, USA

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Interferometry Tutorial

• Three spaces.

Aperture
Image
Spatial Frequency
A(w,z)
I(x,y)
Î(u,v)
z
y
w
x
(w,z)
(x,y)
(u,v)
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Fraunhofer Diffraction

• Image of a point source formed by a general
  aperture is the modulus square of the Fourier
  transform of the aperture.
• Connects (w,z)-plane to (x,y)-plane.
• I(x,y) FT(A(w,z))2

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Baselines Van Cittert-Zernike Theorem

• Define a baseline (B). That baseline contributes
  to 1 and only 1 Fourier component (b) of the
  image.
• Connects (w,z)-plane to (u,v)-plane.

z
v
A(w,z)
b
u
w
B
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Example 1 - Point Source, Two-aperture
Interferometer

(w,z)
(x,y)
(u,v)
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Aperture Synthesis

• Multiple-baseline interferometer.
• Sparcely fill (u,v)-plane.
• Reconstruct high-resolution images through
  Fourier inversion.

(w,z)
(u,v)
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What does interferometry offer astronomers?

• High spatial resolution.
• High precision in position determinations.
• But, these are generally obtained at the cost of
  sensitivity.

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Fundamental Astronomy

• Direct measures of stellar radii.
• Improved distances to stars through parallax
  measures (direct measure) stellar
  luminosities, fundamental distance ladder.
• Resolution of close binaries/spectroscopic
  binaries stellar masses.
• Indirect imaging of extrasolar planets.
• Surface features on normal and YSOs, surface
  eruptions?
• More.

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Additional Interferometry Science

• Single Stars
• Limb Darkening
• Linear Diameters
• Star Formation Phenomena Dynamics
• Pre-Main Sequence Objects
• Absolute Rotation
• Flare Star Phenomena
• Cepheid P-L Calibration
• Mira Pulsations
• P-Mode Oscillations
• Hot Star Phenomena (shells, winds, etc.)
• Cool Star Shells
• Binary Multiple Stars
• Duplicity Surveys
• Close Binary Phenomena

• Star Clusters
• Proper Motions
• Duplicity Surveys
• Extragalactic
• Binaries in Magellanic Clouds
• AGN Structure
• Solar System
• Planetary Satellites
• Minor Planets Comets
• Solar Surface
• Extrasolar Planets
• Astrometric Detection
• Not Vulnerable to sin i

Courtesy of H. McAlister
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Optical Interferometry versus Radio Interferometry

• Why is optical interferometry a young field while
  radio interferometry has been around a long time?

Radio l 1m T 3 x 10-9 s
Visible l 600nm T 2 x 10-15 s
Atmosphere disturbs The wavefronts.
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Overcoming Technological Challenges

• Nanometer-level control and stabilization of
  optics.
• Sub-nanometer sensing of optical element
  positions.
• Space instrument complexity and deployment.

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Simple Long-Baseline Interferometer
d1
d2
Courtesy of H. McAlister
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Basic math
Fields at two apertures from a monochromatic
point source
Up to normalization factors
Add in distances to get beams together
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Continued
Add fields at detector
No way!
This is easy, Right?
Finite Coherence Fringes die away as the
argument of cos grows. - finite aperture size -
non-monochromatic signal - etc.
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Optical Path Length Equalization
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Fringe Visibility
Michelson defined the quantity Visibility as
Imax
Imin V
.
Imax Imin This is the basic observable
for an interferometer.
For an excellent and detailed tutorial on
interferometry, see Principles of Long-Baseline
Stellar Interferometry, Proceedings of the 1999
Michelson Summer School (published by JPL and
edited by Peter Lawson), available at
olbin.jpl.nasa.gov/intro/
Courtesy of H. McAlister
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Effect of Increasing Angular Diameter a
a 0.50 mas
a 0.55 mas
a 0.75 mas
a 1.0 mas
a 1.5 mas
a 2.5 mas
a 5.0 mas
Visibility 2
Baseline (meters)
Courtesy of H. McAlister
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Effect of Increasing Binary Star Separation r
a1 a2 1.0 mas Dm 0
Visibility 2
Baseline (meters)
Courtesy of H. McAlister
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Effect of Increasing Binary Star Relative
Brightness
a1 a2 1.0 mas r 2.5 mas
Visibility 2
Baseline (meters)
Courtesy of H. McAlister
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Detected Signals
I1
I2
ltIAgt GAltI1R I2Tgt
ltIBgt GBltI1T I2Rgt
IA(x) 1 2V(I1I2)0.5rt / I1r2
I2t2 sinc(pDsx) cos(2psox f) IB(x) 1
2V(I1I2)0.5rt / I1t2 I2r2
sinc(pDsx) cos(2psox f)
Based on Benson et al. APPLIED OPTICS, 34, 51
1995.
Courtesy of H. McAlister
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Signal Processing I. Slice Pack Scans
Signal Level
IA200
IB

Milliseconds from Scan Start

Courtesy of H. McAlister
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Signal Processing II. Smooth with Low-Pass Filter
Signal Level

Milliseconds from Scan Start

Normalized Signal

Milliseconds from Scan Start

Courtesy of H. McAlister
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Signal Processing III. Subtract B from A for
Analysis
Signal

Milliseconds from Scan Start

Courtesy of H. McAlister
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Signal Processing IV. Locate Fringe Center in PS
Relative Power

Frequency

Courtesy of H. McAlister
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Signal Processing V. Apply High-Pass Filter
Courtesy of H. McAlister
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Signal Processing VI. Fit Fringe to Determine
Amplitude
Courtesy of H. McAlister
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Nearby Stars Currently Accessible to CHARA
From RECONS sample provided by T. Henry, H.
McAlister
6 4 2 0 -2
63 stars including 13 spectroscopic binaries 2
astrometric binaries 2 exoplanetary systems
GJ 880
Apparent K Magnitude
e Eri
Altair
Vega
Procyon
Sirius
A0 A5 F0 F5
G0 G5 K0 K5
M0 M5 Spectral Type
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Diameter Results for GJ 880 (d 6.88 pc, Sp
M1.5V, V 8.7, K 5.1)
Visibility
a 0.89/-0.04 mas (UD) D 0.66/-0.03 Dsun
Baseline (m)
Courtesy of H. McAlister
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M Dwarf Interferometric Diameters
PTI Lane et al. ApJ, 551, L81, 2001 VLTI
Segransan et al. AA, 397, L7, 2003 CHARA New
GJ 887
GJ 880
GJ 887
D / Dsun
GJ 411
GJ 15A
GJ 191
GJ 699
GJ 551
M0 M1 M2
M3 M4 M5
M6 Spectral Type
Courtesy of H. McAlister
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Check Star Visibilities Diameter Fit
HD 88547
Courtesy of H. McAlister
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CHARA Overview

• Located on Mt. Wilson, California
• Excellent Seeing Logistics
• Night Sky Brightness Irrelevant
• Y-shaped Array Configuration
• 331-meter Maximum Baseline
• Six 1.0-meter Collecting Telescopes
• Can Accommodate 2 More Telescopes
• Dual Operating Wavelength Regimes
• 470 - 800 nm (0.2 mas limiting resolution)
• 2.0 - 2.5 microns (1 mas limiting resolution)
• Science Emphasis on Fundamental Stellar
  Parameters
• Diameters, Teff, Masses, Luminosities
• Limb darkening, shapes, pulsations, etc.

Courtesy of H. McAlister
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CHARA Layout on Mt. Wilson
South Arm
West Arm
Shop
Beam Synthesis Facility
East Arm
Courtesy of H. McAlister