# CCD and CID Applications

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```					Optical Interferometry
Elliott Horch, University of Massachusetts Dartmouth, USA

19 July 2005       Yale Astrometry Workshop / Horch 2      1
Interferometry Tutorial
    Three “spaces.”

Aperture                       Image                     Spatial Frequency

A(w,z)                            I(x,y)                        Î(u,v)
z                         y                              v

w                           x                             u

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

19 July 2005                Yale Astrometry Workshop / Horch 2                          2
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

19 July 2005       Yale Astrometry Workshop / Horch 2   3
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

w                                      u
B

19 July 2005                Yale Astrometry Workshop / Horch 2               4
Example #1 - Point Source,
Two-aperture Interferometer

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

19 July 2005      Yale Astrometry Workshop / Horch 2           5
Aperture Synthesis
    Multiple-baseline
interferometer.

    “Sparcely fill” (u,v)-
plane.                                                 (w,z)

    Reconstruct high-
resolution images
through Fourier
inversion.                                             (u,v)

19 July 2005       Yale Astrometry Workshop / Horch 2           6
What does interferometry
offer astronomers?

    High spatial
resolution.

    High precision in
position
determinations.

    But, these are
generally obtained at
the cost of sensitivity.

19 July 2005       Yale Astrometry Workshop / Horch 2   7
Fundamental Astronomy
    Direct measures of stellar radii.
    Improved distances to stars through parallax
measures (direct measure) stellar luminosities,
    Resolution of close binaries/spectroscopic binaries
stellar masses.
    Indirect imaging of extrasolar planets.
    Surface features on normal and YSOs, surface
eruptions?
    More….

19 July 2005      Yale Astrometry Workshop / Horch 2   8

• Single Stars                                  • Star Clusters
Limb Darkening                                    Proper Motions
Linear Diameters                                  Duplicity Surveys
Star Formation Phenomena & Dynamics
Pre-Main Sequence Objects                    • Extragalactic
Absolute Rotation                                 Binaries in Magellanic Clouds
Flare Star Phenomena                              AGN Structure
Cepheid P-L Calibration
Mira Pulsations
• Solar System
Planetary Satellites
P-Mode Oscillations
Minor Planets & Comets
Hot Star Phenomena (shells, winds, etc.)
Solar Surface
Cool Star Shells
• Binary & Multiple Stars                       • Extrasolar Planets
Duplicity Surveys                                 Astrometric Detection
Close Binary Phenomena                            Not Vulnerable to sin i

Courtesy of H. McAlister

19 July 2005           Yale Astrometry Workshop / Horch 2                       9
Interferometry

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

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

19 July 2005   Yale Astrometry Workshop / Horch 2   10
Overcoming Technological
Challenges
    Nanometer-level control and stabilization
of optics.
    Sub-nanometer sensing of optical element
positions.
    Space: instrument complexity and
deployment.

19 July 2005   Yale Astrometry Workshop / Horch 2   11
Beam Combining Essentials
“Simple” Long-Baseline Interferometer

Starlight                                   Starlight
to Star
s                           
“Delay”
B sin 

                                            Tel. #2
Tel. #1
“Baseline” B

Fringe Position
Delay Compensator

d1                                    d2

Courtesy of H. McAlister

Anaheim - 23 Jan 99                Interferometry on Mt. Wilson                                   4
19 July 2005                 Yale Astrometry Workshop / Horch 2                            12
Basic math…
Fields at two apertures from a monochromatic point source:
1 ~ eikx e it  e iksˆx e it
1                  1

2 ~ eikx e it  e iksˆx e it  e iksˆx e iksˆB e it
2                     2               1

Up to normalization factors:

1 ~ e it
2 ~ e iksˆB e it
Add in distances to get beams together:
1 ~ eikd e it
1

2 ~ eikd e iksˆB e it
2

19 July 2005              Yale Astrometry Workshop / Horch 2                  13
Continued…

net  1  2 ~ e         it
e   ikd1
e   ikd2
e    iksB
ˆ

I  netnet  2 AF 1  cos k (s  B  d1  d 2 ) 

ˆ
This is easy, Right?       No way!
Finite Coherence: Fringes die away as
the argument of cos grows.
- finite aperture size
- non-monochromatic signal
- etc.
19 July 2005              Yale Astrometry Workshop / Horch 2                        14
Optical Path Length Equalization

19 July 2005   Yale Astrometry Workshop / Horch 2   15
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
edited by Peter Lawson), available at olbin.jpl.nasa.gov/intro/

Courtesy of H. McAlister

19 July 2005           Yale Astrometry Workshop / Horch 2               16
Effect of Increasing Angular Diameter a
a= 0.50 mas
a a== 2.5mas
1.0
0.75 mas
0.55 mas
5.0
1.5
1
1

0.8
Visibility Squared

0.6

V2( B)

Visibility 2                                         0.4

0.2

 10
11
12
1.77110
2.496
1.549
4.859
7.099
6.321
1.928              0
0        50      100      150      200   250     300
0.01                        B                  299.97
Baseline

Baseline (meters)
Courtesy of H. McAlister

19 July 2005                                                    Yale Astrometry Workshop / Horch 2                      17
Effect of Increasing Binary Star Separation 

a1 = a2 = 1.0 mas; Dm = 0               = 0.1mas
0.3 mas
0.2 mas
0.75
0.5
2.0
1.5
1.0
3.0
10
5.0
1

0.8
Visibility Squared

0.6

Visibility 2
0.4

0.2

0
0   20       40         60       80      100    120
Baseline

Baseline (meters)
Courtesy of H. McAlister

19 July 2005                                  Yale Astrometry Workshop / Horch 2                      18
Effect of Increasing Binary Star Relative Brightness

mas;  System
a1 = a2 = 1.0 Binary = 2.5 maswith   D m = 10
3.0
2.5
2.0
1.5
5.0
0.75
0.5
0.25
0
4.0
7.5
1.0
1
1

0.8
0.8
Visibility Squared
Visibility Squared

0.6
0.6

Visibility 2
0.4
0.4

0.2
0.2

0
00
0      20
20       40
40        60
60       80
80       100
100    120
120
Baseline
Baseline

Baseline (meters)
Courtesy of H. McAlister

19 July 2005                                 Yale Astrometry Workshop / Horch 2                      19
Detected Signals

I                       I
1                       2

<IA> = GA<I1R +               <IB> = GB<I1T +
I2T>                          I2R>
IA(x) = 1 + {[2V(I1I2)0.5|r||t|] / [I1|r|2 + I2|t|2]} sinc(pDx) cos(2pox + 

IB(x) = 1 – {[2V(I1I2)0.5|r||t|] / [I1|t|2 + I2|r|2]} sinc(pDx) cos(2pox + 

Based on Benson et al. APPLIED OPTICS, 34, 51 1995.
Courtesy of H. McAlister

19 July 2005           Yale Astrometry Workshop / Horch 2                    20
Signal Processing I. Slice & Pack Scans

1000
1000
Signal
Level
800
IA j k
ScIA j+200

ScIB j j k 200

IB 600

400 400
0    200       400        600       800       1000      1200
0                          k                            1023
Milliseconds from Scan Start

Courtesy of H. McAlister

19 July 2005                      Yale Astrometry Workshop / Horch 2                         21
Signal Processing II. Smooth with Low-Pass Filter

400
400

lpIA j j k
300
Signal
ScDIA j j k
Level
200
150
0   200        400       600        800       1000
0               Milliseconds from Scan Start
k                          1030

1.5
1.3

Normaliz
ed
ScDNIA j j k      1
Signal

0.7 0.5
0       200       400        600        800       1000
0                                          Start
Milliseconds from Scan Courtesy of H. McAlister
k                       1030
19 July 2005                     Yale Astrometry Workshop / Horch 2                 22
Signal Processing III. Subtract B from A for Analysis

0.35

VisScanj j k   0
Signal

 0.35
0   200          400           600           800        1000
0                Milliseconds from Scan Start
k                                1023

Courtesy of H. McAlister

19 July 2005             Yale Astrometry Workshop / Horch 2                         23
Signal Processing IV. Locate Fringe Center in PS

0.25
0.2
Relativ
Unfilt k

filt k
e
Power 0.1
( 0.25Filt) j j k

0
 0.02
0   100           200          300          400         500
0                 Frequency
k                                 512

Courtesy of H. McAlister

19 July 2005                   Yale Astrometry Workshop / Horch 2                        24
Signal Processing V. Apply High-Pass Filter

0.7

0.6

0.4

ore k 0.5
ef
0.2
er k                                                                     M  0.2

0

0.2

 0.2   0.4
0        200          400            600              800         1000
0                                k                                  1030

Courtesy of H. McAlister

19 July 2005             Yale Astrometry Workshop / Horch 2                          25
Signal Processing VI. Fit Fringe to Determine Amplitude

Original Fringe Fit
0.1

0.05
Intensity

0

0.05

0.1
0.05                    0                          0.05
Time

Courtesy of H. McAlister

19 July 2005                 Yale Astrometry Workshop / Horch 2                      26
Nearby Stars Currently Accessible to
CHARA
From RECONS sample provided by T. Henry, H. McAlister
66
63 stars including:                                                                        GJ 880
13 spectroscopic binaries
44         2 astrometric binaries
2 exoplanetary systems

22                                                                                  e Eri

Vega               Altair
00
Procyon

Sirius

-22    30            25             20         15          10        5         0            5         10        15
A0            A5            F0         F5          G0       G5        K0            K5       M0         M5
Spectral Type

19 July 2005                           Yale Astrometry Workshop / Horch 2                                27
Diameter Results for GJ 880
(d = 6.88 pc, Sp = M1.5V, V = +8.7, K = +5.1)

1

0.8

0.6

0.4

a = 0.89+/-0.04 mas (UD)

0.2                                                 D = 0.66+/-0.03 Dsun

0
50      100         150          200             250          300
Baseline (m)
Courtesy of H. McAlister
19 July 2005         Yale Astrometry Workshop / Horch 2                            28
M Dwarf Interferometric Diameters
0.8

GJ 887                          PTI: Lane et al. ApJ, 551, L81, 2001
GJ 880                 VLTI: Segransan et al. A&A, 397, L7, 2003
CHARA: New
0.6

GJ 887

0.4                 GJ 411            GJ 15A

GJ 191

0.2                                                             GJ 699
GJ 551

0
M0        M1               M2            M3        M4        M5         M6
Spectral Type   Courtesy of H. McAlister

19 July 2005                   Yale Astrometry Workshop / Horch 2                                       29
Check Star Visibilities & Diameter
Fit
1

0.9                              HD 88547
  1.307           mean res  0.00018
0.8
  0.091               res  0.058

0.7

0.6
Visibility

0.5

0.4

0.3

0.2

0.1

0
0    50   100     150      200              250        300       350              400       450
Baseline (meters)

Courtesy of H. McAlister

19 July 2005          Yale Astrometry Workshop / Horch 2                                           30
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

19 July 2005                 Yale Astrometry Workshop / Horch 2                       31
CHARA Layout on Mt.
Wilson

South
Arm

Shop                                                     West Arm
Beam Synthesis Facility

East
19 July 2005       Arm
Yale Astrometry Workshop / Horch 2                  32
Courtesy of H. McAlister

```
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