The Development of High-Resolution Imaging in Radio Astronomy

1. The Development of High-Resolution Imaging in Radio Astronomy Jim Moran Harvard-Smithsonian Center for Astrophysics 7th IRAM Interferometry School, Grenoble, October 4–7, 2010 It is an honor to give this lecture in the city where Joseph Fourier did the work that is so fundamental to our craft.

2. Outline of Talk I. Origins of Interferometry II. Fundamental Theorem of Interferometry (Van Cittert-Zernike Theorem) III. Limits to Resolution (uv plane coverage) IV. Quest for High Resolution in the 1950s V. Key Ideas in Image Calibration and Restoration VI. Back to Basics – Imaging Sgr A* in 2010 and beyond

3. Thomas Young (1773–1829) Albert Michelson (1852–1931) Martin Ryle (1918–1984) John Bolton (1922–1993) Martin Ryle (1918–1984) I. Origins of Interferometry A. Young’s Two-Slit Experiment B. Michelson’s Stellar Interferometer C. Basic Radio Implementation D. Ryle’s Correlator E. Sea Cliff Interferometer F. Earth Rotation Synthesis

4. quasi-monochromatic light source Source plane Aperture plane (screen with 2 small holes) Pupil or Image plane X I = (E1 + E2)2 = E12 + E22 + 2(E1E2) I Bright Fringes Dark X interference term bandwidth effect t  1 Imax– Imin Imax+ Imin V = Imax Imin Young’s Two-Slit Experiment (1805) 1. Move source  shift pattern (phase) 2. Change aperture hole spacing  change period of fringes 3. Enlarge source plane hole  reduce visibility

5. Michelson-Pease Stellar Interferometer (1890-1920) Two outrigger mirrors on the Mount Wilson 100 inch telescope Paths for on axis ray and slightly offset ray Image plane fringe pattern. Solid line: unresolved star Dotted line: resolved star

6.  s d R = I cos  = d s = cos 2  2d  2d  2d  dsin  d dt 2d sin    “fringes”  = 2 =  = e sin R d d = sin projected baseline  d sin  = Simple Radio Interferometer

7. Simple Adding Interferometer (Ryle, 1952) R = (a + b)2 = a2 +b2 +2ab Cassiopeia A Cygnus A

8. Phase Switching Interferometer (Ryle, 1952) R = (a + b)2 – (a–b)2 = 4ab

9. Sea Cliff Interferometer (Bolton and Stanley, 1948) Time in hours Response to Cygnus A at 100 MHz (Nature, 161, 313, 1948)

10. II. Fundamental Theorem A. Van Cittert-Zernike Theorem B. Projection Slice Theorem C. Some Fourier Transforms

11. 2  2  2  E1= ei r source distribution I(,) y′ 1  ( = y′/z) r1 E2= ei r Huygen’s principle Sky Plane 2 z r2 x′ 2 r1 r2  r2  r1 ( = x′/z) E1E2 = ei (r – r ) * 1 2 E1 E2  2 = I(,) r1r2  z2 Ground Plane Integrate over source y  =v  x  V(u,v) = I(,) ei2(u +v) d d =u • Assumptions • Incoherent source • Far field z>d2/ ; d =104 km,  =1 mm, z>3 pc ! • Small field of view • Narrow bandwidth  field = ( )  dmax   max Van Cittert–Zernike Theorem (1934)

12. “strip” integral F (u,v) = f(x,y) e–i2(ux + vy) dx dyF(u,0) = [f(x,y)dy ] e–i2ux dxF(u,0)  fs(x) Projection-Slice Theorem (Bracewell, 1956) Works for any arbitrary angle Strip integrals, also called back projections, are the common link between radio interferometry and medical tomography.

13. Visibility (Fringe) Amplitude Functions for Various Source Models Moran, PhD thesis, 1968

14. III. Limits to Resolution (uv plane coverage) A. Lunar Occultation B. uv Plane Coverage of a Single Aperture

15. Moon as a knife edge Im() = I()  H() Im(u) = I(u) H(u) where H(u) = 1/u H u  F.T. H Lunar Occultation Geometric optics  one-dimension integration of source intensity MacMahon (1909)

16. H H u   2R  F =   (wiggles) (R = earth-moon distance) 1  F = 5 mas @ 0.5 wavelength F = 2´ @ 10 m wavelength ´ Criticized by Eddington (1909) Same amplitude as response in geometric optics, but scrambled phase 2 H = e –iF usign(u)

17. Occultation of Beta Capricorni with Mt. Wilson 100 Inch Telescope and Fast Photoelectric Detector Whitford, Ap.J., 89, 472, 1939

18. Radio Occultation Curves (Hazard et al., 1963) 3C273

19. D F.T. D  D  v u Single Aperture Single Pixel Airy Pattern Restore high spatial frequencies up to u = D/  no super resolution = 1.2 /D Chinese Hat Function

20. IV. Quest for High Resolution in the 1950s A. Hanbury Brown’s Three Ideas B. The Cygnus A Story

21. Hanbury Brown’s Three Ideasfor High Angular Resolution 1. Let the Earth Move (250 km/s, but beware the radiometer formula!) 2. Reflection off Moon (resolution too high) 3. Intensity Interferometer (inspired the field of quantum optics) In about 1950, when sources were called “radio stars,” Hanbury Brown had several ideas of how to dramatically increase angular resolution to resolve them.

22. v1 v2 Normal Interferometer  = v1v2  V Intensity Interferometer  = v12v22 Intensity Interferometry Fourth-order moment theorem for Gaussian processes v1v2v3v4 = v1v2 v3v4 + v1v3 v2v4 + v1v4 v2v3  = v12v22 = v12v22 + v1v2 2  = P1P2 + V2 constant square of visibility

23. Observations of Cygnus A with Jodrell Bank Intensity Interferometer Square of Visibility at 125 MHz Jennison and Das Gupta, 1952, see Sullivan 2010

24. Cygnus A with Cambridge 1-mile Telescope at 1.4 GHz 3 telescopes 20 arcsec resolution Ryle, Elsmore, and Neville, Nature, 205, 1259, 1965

25. Cygnus A with Cambridge 5 km Interferometer at 5 GHz 16 element E-W Array, 3 arcsec resolution Hargrave and Ryle, MNRAS, 166, 305, 1974

26. V. Key Ideas in Image Calibration and Restoration A. CLEAN B. Phase and Amplitude Closure C. Self Calibration D. Mosaicking E. The Cygnus A Story Continued Jan Högbom (1930–) Roger Jennison (1922–2006) Alan Rogers (1942–) several Ron Eker (~1944–) Arnold Rots (1946–)

27. First Illustration of Clean Algorithm on 3C224.1 at 2.7 GHz with Green Bank Interferometer Zero, 1, 2 and 6 iterations J. Högbom, Astron. Astrophys. Suppl., 15, 417, 1974

28. to source 3 2 3 1 2 d12 0 d12 + d23 + d31 = 0 2   12 = d12 s + 1– 2  2   C = 12 + 23 + 31 = [d12 + d23 + d31] s  noise 1 2 m= v+ (i – j) + ij N(N– 1) 2 ij ij C = m + m + m = v + v + v + noise 12 23 31 12 23 31 2 N N stations  baselines, (N – 1)(N – 2) closure conditions fraction of phases N = 27, f 0.9 f = 1 – “cloud” with phase shift 1 = 2 t Observe a Point Source Closure Phase “Necessity is the Mother of Invention” Arbitrary Source Distribution R. Jennison, 1952 (thesis): MNRAS, 118, 276, 1956; A. Rogers et al., Ap.J., 193, 293, 1974

29. Unknown voltage gain factors for each antenna gi (i = 1–4) Closure Amplitude N ≥ 4

30. A Half Century of Improvements in Imaging of Cygnus A Kellermann and Moran, Ann. Rev. Astron., 39, 457, 2001

31. VI. Back to Basics Imaging Sgr A* in 2010 and beyond

32. 908 km 4030 km 4630 km 230 GHz Observations of SgrA* VLBI program led by large consortium led by Shep Doeleman, MIT/Haystack

33. Visibility Amplitude on SgrA* at 230 GHz, March 2010 Days 96 and 97 (2010) Model fits: (solid) Gaussian, 37 uas FWHM; (dotted) Annular ring, 105/48 as diameter – both with 25 as of interstellar scattering Doeleman et al., private communication

34. New (sub)mm VLBI Sites Phase 1: 7 Telescopes (+ IRAM, PdB, LMT, Chile) Phase 2: 10 Telescopes (+ Spole, SEST, Haystack) Phase 3: 13 Telescopes (+ NZ, Africa)

35. GR Model 7 Stations 13 Stations Progression to an Image Doeleman et al., “The Event Horizon Telescope,” Astro2010: The Astronomy and Astrophysics Decadal Survey, Science White Papers, no. 68