19 July 2005Yale Astrometry Workshop / Horch 21 Optical Interferometry Elliott Horch, University of Massachusetts Dartmouth, USA

19 July 2005Yale Astrometry Workshop / Horch 22 Interferometry Tutorial n Three “spaces.” (w,z)(x,y)(u,v) ApertureImageSpatial Frequency A(w,z) I(x,y) w z x y u v Î(u,v)

19 July 2005Yale Astrometry Workshop / Horch 23 Fraunhofer Diffraction n Image of a point source formed by a general aperture is the modulus square of the Fourier transform of the aperture. n Connects ( w,z )-plane to ( x,y )-plane. I( x,y ) = |FT(A( w,z ))| 2

19 July 2005Yale Astrometry Workshop / Horch 24 Baselines: Van Cittert-Zernike Theorem Define a baseline (B). That baseline contributes to 1 and only 1 Fourier component (  ) of the image. n Connects ( w,z )-plane to ( u,v )-plane. A(w,z) u v B w z 

19 July 2005Yale Astrometry Workshop / Horch 25 Example #1 - Point Source, Two-aperture Interferometer (w,z)(x,y)(u,v)

19 July 2005Yale Astrometry Workshop / Horch 26 Aperture Synthesis n Multiple-baseline interferometer. n “Sparcely fill” (u,v)- plane. n Reconstruct high- resolution images through Fourier inversion. (w,z) (u,v)

19 July 2005Yale Astrometry Workshop / Horch 27 What does interferometry offer astronomers? n High spatial resolution. n High precision in position determinations. n But, these are generally obtained at the cost of sensitivity.

19 July 2005Yale Astrometry Workshop / Horch 28 Fundamental Astronomy n Direct measures of stellar radii. n Improved distances to stars through parallax measures (direct measure) stellar luminosities, fundamental distance ladder. n Resolution of close binaries/spectroscopic binaries stellar masses. n Indirect imaging of extrasolar planets. n Surface features on normal and YSOs, surface eruptions? n More….

19 July 2005Yale Astrometry Workshop / Horch 29 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 Additional Interferometry Science Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 210 Optical Interferometry versus Radio Interferometry n Why is optical interferometry a young field while radio interferometry has been around a long time? Radio: ~ 1m T ~ 3 x s Visible: ~ 600nm T ~ 2 x s Atmosphere disturbs The wavefronts.

19 July 2005Yale Astrometry Workshop / Horch 211 Overcoming Technological Challenges n Nanometer-level control and stabilization of optics. n Sub-nanometer sensing of optical element positions. n Space: instrument complexity and deployment.

19 July 2005Yale Astrometry Workshop / Horch 212 “Simple” Long-Baseline Interferometer Courtesy of H. McAlister d1d1 d2d2

19 July 2005Yale Astrometry Workshop / Horch 213 Basic math… Fields at two apertures from a monochromatic point source: Up to normalization factors: Add in distances to get beams together:

19 July 2005Yale Astrometry Workshop / Horch 214 Continued… Add fields at detector: 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 2005Yale Astrometry Workshop / Horch 215 Optical Path Length Equalization

19 July 2005Yale Astrometry Workshop / Horch 216 Michelson defined the quantity “Visibility” as: I max – I min V =. I max + I min 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/ Fringe Visibility Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 217  = 0.50 mas Baseline (meters)  = 0.55 mas  = 0.75 mas Visibility 2  = 1.0 mas  = 1.5 mas  = 2.5 mas  = 5.0 mas Effect of Increasing Angular Diameter  Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 218  1 =  2 = 1.0 mas;  m = 0 Visibility 2 Baseline (meters) Effect of Increasing Binary Star Separation  Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 219 Baseline (meters) Visibility 2  1 =  2 = 1.0 mas;  = 2.5 mas Effect of Increasing Binary Star Relative Brightness Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 220 I A ( x ) = 1 + {[2V(I 1 I 2 ) 0.5 | r || t |] / [I 1 | r | 2 + I 2 | t | 2 ]} sinc(  x ) cos(2  o x +  ) I B ( x ) = 1 – {[2V(I 1 I 2 ) 0.5 | r || t |] / [I 1 | t | 2 + I 2 | r | 2 ]} sinc(  x ) cos(2  o x +  ) Based on Benson et al. APPLIED OPTICS, 34, = G A = G B I1I1 I2I2 Detected Signals Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 221 Milliseconds from Scan Start Signal Level IBIB I A +200 Signal Processing I. Slice & Pack Scans Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 222 Milliseconds from Scan Start Signal Level Normaliz ed Signal Signal Processing II. Smooth with Low-Pass Filter Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 223 Milliseconds from Scan Start Signal Signal Processing III. Subtract B from A for Analysis Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 224 Frequency Relativ e Power Signal Processing IV. Locate Fringe Center in PS Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 225 Signal Processing V. Apply High-Pass Filter Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 226 Signal Processing VI. Fit Fringe to Determine Amplitude Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 227 A0 A5 F0 F5 G0 G5 K0 K5 M0 M5 Spectral Type Apparent K Magnitude Nearby Stars Currently Accessible to CHARA Procyon Sirius AltairVega  Eri GJ 880 From RECONS sample provided by T. Henry, H. McAlister 63 stars including: 13 spectroscopic binaries 2 astrometric binaries 2 exoplanetary systems

19 July 2005Yale Astrometry Workshop / Horch 228 Diameter Results for GJ 880 (d = 6.88 pc, Sp = M1.5V, V = +8.7, K = +5.1) Diameter Results for GJ 880 (d = 6.88 pc, Sp = M1.5V, V = +8.7, K = +5.1) Baseline (m) Visibility  = / mas (UD) D = / D sun Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 229 M Dwarf Interferometric Diameters M0 M1 M2 M3 M4 M5 M6 Spectral Type D / D sun PTI: Lane et al. ApJ, 551, L81, 2001 VLTI: Segransan et al. A&A, 397, L7, 2003 CHARA: New GJ 880 GJ 15A GJ 699 GJ 411 GJ 887 GJ 191 GJ 551 Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 230 Check Star Visibilities & Diameter Fit HD Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 231 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 nm (0.2 mas limiting resolution) microns (1 mas limiting resolution) Science Emphasis on Fundamental Stellar Parameters Diameters, T eff, Masses, Luminosities Limb darkening, shapes, pulsations, etc. Courtesy of H. McAlister

19 July 2005Yale Astrometry Workshop / Horch 232 West Arm Shop Beam Synthesis Facility South Arm East Arm CHARA Layout on Mt. Wilson Courtesy of H. McAlister