Bernard Lyot in addition to his coronagraph machines Photons in addition to waves Image-plane coronagraphs Wide-b in addition to masks

Bernard Lyot in addition to his coronagraph machines Photons in addition to waves Image-plane coronagraphs Wide-b in addition to masks www.phwiki.com

Bernard Lyot in addition to his coronagraph machines Photons in addition to waves Image-plane coronagraphs Wide-b in addition to masks

Fisher, Anne, Managing Editor has reference to this Academic Journal, PHwiki organized this Journal Introduction to Coronagraph Optics Michelson Summer School on High-Contrast Imaging Caltech, Pasadena 20-23 July 2004 Wesley A. Traub Harvard-Smithsonian Center as long as Astrophysics Extrasolar planet science goals Bernard Lyot in addition to his coronagraph machines Photons in addition to waves Current coronagraphs Prototype coronographs: 1. Image plane 2. Pupil plane 3. Pupil mapping 4. Nulling coronagraph Perturbations: 1. Speckles 2. Polarization 3. Fraunhofer vs Fresnel 4. Refractive index of real materials 5. Internal scattering 6. Geometrical stability Outline of talk Solar system at 10 pc At visible wavelengths: Earth/sun = 10-10 = 25 mag Zodi per pixel is small

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Discovery space as long as coronagraphs Key coronagraph parameters Contrast C: The ratio dark/bright parts of image. Specifically, the average background brightness in the search area, divided by the central star brightness. Speckle/star. Example: C = 10-10 driven by Earth/Sun = 2×10-10. Inner working angle IWA: Smallest angle at which a planet can be detected. Inner boundary of high-contrast search area. Example: IWA = 3 /D driven by 1 AU/10pc = 0.100 arcsec. Outer working angle OWA: Largest angle at which a planet can be detected. Outer boundary of high-contrast search area. Example: OWA = 48 /D driven by N = 96 actuator DM. Planet albedo in addition to color

Bernard Lyot in addition to his coronagraph machines Early solar coronagraphs 1932 1963 radial angle intensity Bernard Lyot Lyot 2004 corona Stellar coronagraphs Ref: McCarthy & Zuckerman (2004); Macintosh et al (2003) 20 arcsec radius circle K~20 mag Bkgd objects 7 arcsec w in addition to J~21 mag Bkgd object

Extrasolar coronagraphs on the ground Jupiters: need 30-m telescope, with essentially perfect adaptive optics, in addition to will still have very large background. Earths: need 100-m telescope, with essentially perfect adaptive optics. Note: T ~ SNR2 (RMS wavefront)2 / D4 , so 30 m on ground is equivalent to ~ 2 m in space. Ref.: Stapelfeldt et al., SPIE 2002; Dekaney etal 2004. Photons in addition to waves Basic photon-wave-photon process We see individual photons. Here is the life history of each one: Each photon is emitted by a single atom somewhere on the star. After emission, the photon acts like a wave. This wave exp in addition to s as a sphere, over 4 steradians (Huygens). A portion of the wavefront enters our telescope pupil(s). The wave follows all possible paths through our telescope (Huygens again). Enroute, its polarization on each path may be changed. Enroute, its amplitude on each path may be changed,. Enroute, its phase on each path may be changed. At each possible detector, the wave “senses” that it has followed these multiple paths. At each detector, the electric fields from all possible paths are added, with their polarizations, amplitudes, in addition to phases. Each detector has probability = amplitude2 to detect the photon.

Photon wave photon 1x 1y 1z Ex Ey 1 count detected 1 photon emitted E(x,y,z) = 1xExsin(kz-wt-px) + 1yEysin(kz-wt-py) where the electric field amplitude in the x direction is sin(kz-wt-px) = Im{ ei(kz-wt-px) } in addition to likewise as long as the y-amplitude. At detector, add the waves from all possible paths. Fourier optics vs geometric optics Fourier optics (or physical optics) describes ideal diffraction- limited optical situations (coronagraphs, interferometers, gratings, lenses, prisms, radio telescopes, eyes, etc.): If the all photons start from the same atom, in addition to follow the same many-fold path to the detectors, with the same amplitudes & phase shifts & polarizations, then we will see a diffraction- controlled interference pattern at the detectors. In other words, waves are needed to describe what you see. Geometric optics describes the same situations but in the limit of zero wavelength, so no diffraction phenomena are seen. In other words, rays are all you need to describe what you see. Huygens wavelets Wavelets align here, in addition to make nearly flat wavefront, as expected from geometric optics. Wavelets add with various phases here, reducing the net amplitude, especially at large angles. Portion of large, spherical wavefront from distant atom. Blocking screen, with slit.

Image-plane coronagraphs Huygens’ wavelets -> Fraunhofer -> Fourier trans as long as m The phase of each wavelet on a surface Tilted by theta = x/f in addition to focussed by the Lens at position x in the focal plane is The sum of the wavelets across the potential wavefront at angle theta is All waves add in phase here The net amplitude is zero here The net amplitude mostly cancels, but not exactly, here Fourier relations: pupil in addition to image We see that an ideal lens (or focussing mirror) acts on the amplitude in the pupil plane, with a Fourier-trans as long as m operation, to generate the amplitude in the image plane. A second lens, after the image plane, would convert the image-plane amplitude, with a second Fourier-trans as long as m, to the plane where the initial pupil is re-imaged. A third lens after the re-imaged pupil would create a re-imaged image plane, via a third FT. At each stage we can modify the amplitude with masks, stops, polarization shifts, in addition to phase changes. These all go into the net transmitted amplitude, be as long as e the next FT operation.

Classical Coronagraph Ref.: Sivaramakrishnan et al., ApJ, 552, p.397, 2001; Kuchner 2004. L(u)·[M(u)A(u)]~0 L(x)[M(x)·A(x)]~0 u u u u x x x x A(u) A(x) M(x) MA MA L(u) L[MA] L[MA] aperture image mask Lyot stop detector Final pupil = L(u)·[M(u)(A(u)·E(u))] E(u) = 1 is input field across pupil A(u) = pupil transmission fn. M(u)(A(u)E(u)) = pupil field L(u) = Lyot pupil transmission A(x) = FT(A(u)E(u)) = image (x) M(x) = mask transmission fn For on-axis point-like star to be zero across exit pupil, we need L(u)·[M(u)A(u)] = 0 How to satisfy L·(MA)(u) = 0 L(u) = 0 here L(u) = 0 here M(u)=0 here M(u)=0 here M(u)du=0 here Lyot stop Nominal pupil diameter 1/2 1/2-e/2 e/2 M(u)=anything = 0 (b in addition to -limited) 0 (notch) M(u)=anything = 0 (b in addition to -limited) 0 (notch) u 0

Wide-b in addition to masks = gaussian gives M(u) = delta – gaussian which has M(u) ~ 0 inside ± e/2 in addition to M(u) ~ 0 outside ± e/2, but not exactly. = rectangle gives M(u) = delta – sinc (hard disk mask) which has M(u) ~ 0 inside ± e/2 in addition to M(u) ~ 0 outside ± e/2, but not exactly. = 1 if x > 0 (phase mask) -1 if x < 0 gives M(u) = sinc which has M(u) ~ 0 inside ± e/2 in addition to M(u) ~ 0 outside ± e/2, but not exactly. Wide-b in addition to (gaussian) mask Amplitude of on-axis star = 1 ei0 FT( gauss(x) ) = delta(u) - gauss(u) Convolution Lyot stop blocks bright edges Leakage transmission of on-axis star Wide-b in addition to (quadrant-phase) mask Star image is centered on mask which transmits half of image shifted by 1/2 wavelength, in addition to 1/2 unshifted, so symmetric parts cancel. Ref.: Riaud et al., PASP 113 1145 2001. Fisher, Anne CompactPCI and AdvancedTCA Systems Managing Editor www.phwiki.com

4-Quadrant phase mask Sub-wavelength phase mask, from silicon, as long as K-b in addition to region. X-Y phase knife experiment theory X-Y phase knife: double star in lab Binary star without coronagraph Binary with X Phase knife Binary with X + Y phase knives; Bright star nulled

B in addition to -limited masks = sin2(kx) (sin4(kx) transmission mask) gives M(u) = 2 delta(0) – delta(u-k) + delta(u+k) which has M(u) = 0 inside ±e/2 in addition to M(u) = 0 outside ±e/2, exactly. = 1 – sin(kx)/kx ([1-sinc(kx)]2 transmission mask) gives M(u) = delta(0) – (/k)·( u/k) which has M(u) = 0 inside ±e/2 in addition to M(u) = 0 outside ±e/2, exactly. Kuchner in addition to Traub, ApJ 570, 900-908, 2002 B in addition to -Limited Image Mask Example: this 1-D image mask transmits the b in addition to -limited function (1-sin x/x)2 . Ref.: Kuchner & Traub ApJ 570, 900, 2002 On-axis star is totally blocked In re-imaged pupil. Off-axis planet is ~fully transmitted In re-imaged pupil. Image-plane coronagraph simulation Ref.: Pascal Borde 2004 1st pupil 1st image with Airy rings mask, centered on star image 2nd pupil Lyot stop, blocks bright edges 2nd image, no star, bright planet

“Top 10” Contrast Contributions For TPF-C, this table shows that de as long as mations of the optical system are second only to mask leakage in addition to telescope pointing as sources of speckles in the focal plane. Ref.: Shaklan in addition to Marchen (2004). Summary Extrasolar planets can be detected in addition to characterized in visible light with a coronagraph. One of the key challenges to overcome is to eliminate even the smallest optical imperfections in the system, because each imperfection can be decomposed into constituent ripples, in addition to each ripple generates a pair of speckles, in addition to each speckle looks just like a planet. Infrared interferometers can also detect in addition to characterize extrasolar planets, in addition to they will be subject to all of the same caveats about optical imperfections, though sometimes arising from different mechanisms.

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