PSF and Field of View characteristics of imaging and nulling interferometers
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1 PSF ad FoV characteristics of imagig ad ullig iterferometers PSF ad Field of View characteristics of imagig ad ullig iterferometers Fraçois Héault UMR CNRS 6525 H. Fizeau UNS, CNRS, CA Aveue Nicolas Coperic Grasse - Frace Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th
2 PSF ad FoV characteristics of imagig ad ullig iterferometers peig questios I the frame of Darwi/TPF-I exoplaet fidig space missios - Do ullig maps deped o the type of combiig optics (axial vs. multi-axial combiatio schemes)? - Has it some cosequece o their ullig imagig capacity? Previous publicatios Simple Fourier optics formalism for high agular resolutio systems ad ullig iterferometry, JSA A 27, p (2010) Fibered ullig telescope for extra-solar coroagraphy, ptics Letters 34, 7, p (2009) Computig extictio maps of star ullig iterferometers, ptics Express 16, (2008) Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th
3 PSF ad FoV characteristics of imagig ad ullig iterferometers V -sky agular coordiates Sky object u v U s s Y P 1 Etrace pupil plae (P) X D Y Exit pupil plae (P ) P 2 P 3 B D P 4 P 1 P 2 B P 3 P 4 s s X F Y Detectio plae X Coordiates systems M Z M Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th
4 PSF ad FoV characteristics of imagig ad ullig iterferometers Image of a sky object (s) projected back o sky I( s) = s T Ω = 1 ( s ) PSF ( s - s ) N a exp [ iφ ] exp[ ik ( s P s' P' / m) ] 2 dω with PSF T (s) : PSF of oe idividual collectig telescope, beig projected back o-sky a : amplitude trasmissio factor of the th telescope ϕ : phase-shift alog the th iterferometer arm for cophasig or ullig purpose k = 2π/λ : waveumber of moochromatic electro-magetic field m : optical compressio factor betwee telescopes ad their relay optics Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th
5 PSF ad FoV characteristics of imagig ad ullig iterferometers Geeral layout of a multi-aperture iterferometer B P 1 P 2 (P) Telescope 1 F C Telescope 2 Relay optics 1 APS 1 APS 2 Metrology Metrology beam 1 B beam 2 Relay optics 2 Covergig optics Divergig optics Fold mirror Beamsplitter Acromatic Phase Shifter Combiig optics (P ) F Focal plae All telescopes assumed to be idetical All exit pupils optically cojugated with etrace pupils Coferece 7734 ptical ad Ifrared Iterferometry II Z Sa Diego, Jue 30 th
6 PSF ad FoV characteristics of imagig ad ullig iterferometers PSF ad Field of View characteristics Geeralized Poit Spread Fuctio (PSF) PSF [ ] [ ] [ ( )] 2 iφ exp ik s'p' / m exp ik s P ' P' N G ( s, s ) PSFT ( s) a exp / = 1 = m Chagig over the whole istrumet Field of View bject-image relatioship is ot a covolutio product Maximal achievable Field of View (FoV) Neglectig ay kid of apertures or stops, Neglectig geometrical aberratios ad diffractio effects N = 1 [ ] [ ( )] 2 iφ exp ik s P ' P' FoV( s) = a m exp / Suitable for fast polychromatic FoV computatios: FoV δλ ( s) = δλ FoV ( s) λ B δλ (λ) dλ δλ B δλ (λ) dλ Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th
7 PSF ad FoV characteristics of imagig ad ullig iterferometers Golde rule of Fizeau iterferometers ly occurs whe: P = m P Geeralized PSF becomes: Pupil I Pupil ut PSF N G ( s, xs ) PSFT ( s) a exp / = 1 [ ] [ ] 2 iφ exp ik s' P' = m Costat over the whole FoV Classical bject-image relatioship I(s) = (s) * PSF(s) holds Maximal achievable Field of View: Becomes ifiite whatever the wavelegth Costat trasmissio equal to: x FoV( s) = a exp i N = 1 [ ] 2 φ Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th
8 PSF ad FoV characteristics of imagig ad ullig iterferometers Numerical simulatios: a 8-telescope Fizeau iterferometer i imagig ad ullig modes Iput pupils Y D X PSF (FoV ceter) PSF (half FoV) Maximal achievable FoV B 5 arcsec Y 0 π 0 D π π X 0 π 0 B Golde rule exteds destructive frige over the whole FoV, killig the cetral star ad all its surroudig plaets (this is ot what we wat ) Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th arcsec 8
9 PSF ad FoV characteristics of imagig ad ullig iterferometers Sheared-Pupil Telescopes (SPT) Secodary Mirror Moolithic telescope Relay optics Primary Mirror (P) APS 1 APS 2 ad PD compesatio Metrology beam 1 Beam desifier May be replaced with a modified Mach-Zehder combier Beam combier (exit pupil plae) P 1 P 2 [or Michelso B equipped with cube-corers] Metrology beam 2 F (P ) Metrology beams F Z (P ) Focal plae Coferece 7734 ptical ad Ifrared Iterferometry II Z Focal plae Sa Diego, Jue 30 th
10 PSF ad FoV characteristics of imagig ad ullig iterferometers Two differet types of Sheared-Pupil Telescope Iput pupil plae Y utput pupil plae Y Umasked output sub-pupils X D X D Y Moolithic pupil telescope B Y Lyot stop o Exit pupil Masked output sub-pupils D X D X B B Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th
11 PSF ad FoV characteristics of imagig ad ullig iterferometers Iterest ad limitatios of ullig SPTs Usable for exploratory sciece missios: exo-zodi characterizatio, Jupiter-like plaets If rotatig, allow to validate most of the Darwi/TPF-I algorithms evisaged for plaets fidig ad characterizatio Whe umasked, they cocetrate eergy i very small core, overcomig Rayleigh s diffractio limit But o real super-resolvig power, sice PSF are sharpeed after sub-aperture filterig: Specific bject- Image relatioship: N [ iφ ] exp[ iks'p' / m] [ PSF ( s) *( s) ] Ι( s) = a exp T = 1 2 Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th
12 PSF ad FoV characteristics of imagig ad ullig iterferometers PSF ad Field of View simulatios of SPTs Masked SPT B = 1 m D = 3 m 5 arcsec Masked SPT B = 0.5 m D = 4 m Sheared-Pupil Telescope D = 5 m Umasked SPT: high throughput, residual star leakage Masked SPT: o leakage, elarged ulled area of low throughput Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th
13 PSF ad FoV characteristics of imagig ad ullig iterferometers Axially Combied Iterferometer (ACI) Telescope 1 Relay optics 1 P 1 Metrology beam 1 Axial beam combier Coferece 7734 ptical ad Ifrared Iterferometry II F B Z Telescope 2 APS 1 APS 2 Frige tracker (P ) Focal plae Metrology beam 2 Ι( s) = P 2 Relay optics 2 PSF T (P) ( s) * Co-axial recombiatio by meas of a balaced set of beamsplitters Equivalet to the previous moolithic, masked SPT Nulls all diffracted light origiatig from cetral star Specific bject-image relatioship: N = 1 a exp Sa Diego, Jue 30 th 2010 [ iφ ] exp[ iksp ] 2 ( s) 13
14 PSF ad FoV characteristics of imagig ad ullig iterferometers Nullig imagig capacities of SPT Masked SPT B = 1 m D = 3 m Masked SPT B = 0.5 m D = 4 m Fictitious sky object 2 arcsec No gai i agular resolutio, but diffracted starlight cleaed before fial image blurrig Progressive leakage from cetral objects (to be traded agaist throughput) Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th
15 PSF ad FoV characteristics of imagig ad ullig iterferometers Nullig imagig capacities of ACI ACI B = 20 m D = 5 m ACI B = 10 m D = 5 m Fictitious sky object 2 arcsec For loger baselies, ullig ACI behaves as a sigle-dish telescope Nullig capacity seems to be lost Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th
16 PSF ad FoV characteristics of imagig ad ullig iterferometers Coclusios Nullig maps ad ulled images produced by differet types of multi-aperture optical systems ca be rapidly evaluated by meas of a simple Fourier optics formalism From the results of theory ad first umerical computatios: Golde rule for iterferometric imagig exteds the destructive frige patter of ullig iterferometers over their whole Field of View A ullig moolithic, sheared-pupil telescope is a attractive solutio Requires further tradeoff o throughput/leakage Theoretical bject-image relatioship of the Bracewell iterferometer allows full extictio of diffracted starlight, but o super-resolutio is possible [ I the Please case retai: of fibered this is ullig all very iterferometers, prelimiary, evetually best aecdotal throughput are ] achieved ad usig somewhat axial heuristic. recombiatio Further schemes work is required (ullig ad ACIs) cooperatios are welcome Coferece 7734 ptical ad Ifrared Iterferometry II Sa Diego, Jue 30 th
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