Optical Interferometry

1. Optical Interferometry Elliott Horch, University of Massachusetts Dartmouth, USA Yale Astrometry Workshop / Horch 2

2. v u Interferometry Tutorial • Three “spaces.” Aperture Image Spatial Frequency A(w,z) I(x,y) Î(u,v) z y x w (w,z) (x,y) (u,v) Yale Astrometry Workshop / Horch 2

3. 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 Yale Astrometry Workshop / Horch 2

4. 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 Yale Astrometry Workshop / Horch 2

5. Example #1 - Point Source, Two-aperture Interferometer (w,z) (x,y) (u,v) Yale Astrometry Workshop / Horch 2

6. Multiple-baseline interferometer. “Sparcely fill” (u,v)-plane. Reconstruct high-resolution images through Fourier inversion. Aperture Synthesis (w,z) (u,v) Yale Astrometry Workshop / Horch 2

7. High spatial resolution. High precision in position determinations. But, these are generally obtained at the cost of sensitivity. What does interferometry offer astronomers? Yale Astrometry Workshop / Horch 2

8. 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…. Yale Astrometry Workshop / Horch 2

9. 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 Yale Astrometry Workshop / Horch 2

10. 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. Yale Astrometry Workshop / Horch 2

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

12. “Simple” Long-Baseline Interferometer d1 d2 Courtesy of H. McAlister Yale Astrometry Workshop / Horch 2

13. Basic math… Fields at two apertures from a monochromatic point source: Up to normalization factors: Add in distances to get beams together: Yale Astrometry Workshop / Horch 2

14. 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. Yale Astrometry Workshop / Horch 2

15. Optical Path Length Equalization Yale Astrometry Workshop / Horch 2

16. 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 atolbin.jpl.nasa.gov/intro/ Courtesy of H. McAlister Yale Astrometry Workshop / Horch 2

17. 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 Yale Astrometry Workshop / Horch 2

18. Effect of Increasing Binary Star Separation r a1 = a2 = 1.0 mas; Dm = 0 Visibility 2 Baseline (meters) Courtesy of H. McAlister Yale Astrometry Workshop / Horch 2

19. Effect of Increasing Binary Star Relative Brightness a1 = a2 = 1.0 mas; r = 2.5 mas Visibility 2 Baseline (meters) Courtesy of H. McAlister Yale Astrometry Workshop / Horch 2

20. Detected Signals I1 I2 <IA> = GA<I1R + I2T> <IB> = GB<I1T + I2R> IA(x) = 1 + {[2V(I1I2)0.5|r||t|] / [I1|r|2 + I2|t|2]} sinc(pDsx) cos(2psox + f) IB(x) = 1 – {[2V(I1I2)0.5|r||t|] / [I1|t|2 + I2|r|2]} sinc(pDsx) cos(2psox + f) Based on Benson et al. APPLIED OPTICS, 34, 51 1995. Courtesy of H. McAlister Yale Astrometry Workshop / Horch 2

21. Signal Processing I. Slice & Pack Scans Signal Level IA+200 IB Milliseconds from Scan Start Courtesy of H. McAlister Yale Astrometry Workshop / Horch 2

22. Signal Processing II. Smooth with Low-Pass Filter Signal Level Milliseconds from Scan Start Normalized Signal Milliseconds from Scan Start Courtesy of H. McAlister Yale Astrometry Workshop / Horch 2

23. Signal Processing III. Subtract B from A for Analysis Signal Milliseconds from Scan Start Courtesy of H. McAlister Yale Astrometry Workshop / Horch 2

24. Signal Processing IV. Locate Fringe Center in PS Relative Power Frequency Courtesy of H. McAlister Yale Astrometry Workshop / Horch 2

25. Signal Processing V. Apply High-Pass Filter Courtesy of H. McAlister Yale Astrometry Workshop / Horch 2

26. Signal Processing VI. Fit Fringe to Determine Amplitude Courtesy of H. McAlister Yale Astrometry Workshop / Horch 2

27. 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 Vega Altair Procyon Sirius A0 A5 F0 F5 G0 G5 K0 K5 M0 M5 Spectral Type Yale Astrometry Workshop / Horch 2

28. 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 Yale Astrometry Workshop / Horch 2

29. M Dwarf Interferometric Diameters PTI: Lane et al. ApJ, 551, L81, 2001 VLTI: Segransan et al. A&A, 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 Yale Astrometry Workshop / Horch 2

30. Check Star Visibilities & Diameter Fit HD 88547 Courtesy of H. McAlister Yale Astrometry Workshop / Horch 2

31. 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 Yale Astrometry Workshop / Horch 2

32. CHARA Layout on Mt. Wilson South Arm West Arm Shop Beam Synthesis Facility East Arm Yale Astrometry Workshop / Horch 2 Courtesy of H. McAlister