Fine art of computing nulling interferometer maps

Transcription

1 Fine art of computing nulling François Hénault UMR 6525 CNRS H. FIZEAU UNS, OCA Avenue Nicolas Copernic GRASSE - FRANCE 1

2 In the frame of arwin/tpf-i space missions: o nulling maps depend on the types of Spatial Filtering and Achromatic Phase Shifting (APS) devices? Previous publications esign of achromatic phase shifters for spaceborne nulling interferometry, Opt. Lett. 31, (2006) Computing extinction maps of star nulling interferometers, Opt. Exp. 16, (2008) 2

3 Redefining the nulling ratio T(u,v) Fringes T Max Envelope T Max Transmission curve T Max T Min Achieved Null 0 U N = T Min /T Max instead of T Min /T Max N may change with the employed spatial filtering device 3

4 Z S V u On-sky angular coordinates U v T 1 T 2 B Y Y O S B X T 4 X Entrance pupil plane Y O Recombination plane X Y etector plane X T 3 F O Coordinates systems y x Z 4

5 Case of pinhole filtering, APS with no Pupil-flip Nulling map is the product of the fringe pattern F(u,v) with an envelope E(u,v) E(u,v) is the cross correlation of PSF and pinhole functions: T(u, v) = F(u, v) { } 2 Bˆ BP (Fu,Fv) SP 2 B (u) B P (u) P E(u) = PSF Pinhole Actual FoV U 5

6 Case of Single Mode Fiber (SMF) filtering, any type of APS E(u,v) is the square modulus of cross correlation between diffracted amplitude and SMF functions: T(u, v) = Â(u, v) 2 F(u, v) Bˆ G W 2 (Fu,Fv) B (u) G W (u) E(u) iffacted amplitude 2 = SMF W Actual FoV U 6

7 Example of three well-known configurations Bracewell Y Angel Cross Y ϕ 2 = π ϕ 1 = 0 X array with phase chopping ϕ 2 = ±π/2 Y ϕ 1 = 0 ϕ 2 = π ϕ 1 = 0 O S B X X B Y O S X B Y O S X ϕ 3 = 0 B X ϕ 4 = π ϕ 3 = π/2 ± B X ϕ 4 = π Type of N (number of B X (baseline B Y (baseline Analytical expressions of fringe patterns interferometer apertures) along X) along Y) Bracewell 2 50 m F(u,v) = sin 2 (πb X u/λ) Angel Cross 4 50 m 50 m F(u,v) = sin 2 (πb X u/λ) sin 2 (πb Y v/λ) Stretched X-array, m 25 m F (u,v) = [1+sin(2πB X u/λ)] sin 2 (πb Y v/λ) / 2 no phase chopping Stretched X-array with phase chopping m 25 m F(u,v) = sin(2πb X u/λ) sin 2 (πb Y v/λ) 7

8 First results on a Bracewell interferometer Pinhole filtering, APS with no Pupil-flip Pinhole filtering, Pupil-flip APS SMF filtering 25 mas λ = 1 µm, = 20 m, B = 100 m Widest FoV achieved with pinhole filtering, APS with no Pupil-flip Worst results with pinhole filtering associated to Pupil-flip APS Technical solution to be ruled out SMF filtering not sensitive to APS type if all functions are centro-symmetric 8

9 Spectral dependency λ = 1 µm, λ = 0.5 µm Extinction ratios for different SF devices Pinhole, no FoV-reversal SMF Pinhole filtering Extinction ratio U (mas) SMF filtering Major conclusions unchanged 9

10 Nulling maps with pinholes or SMF spatial filtering λ = 10 µm, = 5 m, B = m, λ/ λ = 40 Angel Cross X array, 4x-stretched, no phase chopping X array, 4x-stretched, with phase chopping SMF filtering 200 mas Pinhole filtering 1 arcsec 10

11 Pinhole filtering SMF filtering Bracewell Theta-Lambda diagrams Angel Cross X array, 4x-stretched, with phase chopping 0 π 2π 0 π 2π 0 π 2π 5 µm 10 µm 15 µm 5 µm 10 µm 15 µm Pinhole filtering looks better but Only one pinhole/smf was used on the whole spectral band Numerical model to be improved 11

12 Conclusions Pinhole filtering is back in the race! Provides wider FoVs suitable for blind planet detection Future works on numerical model Introduction of different pinholes/smfs on the whole spectral band Introduction of real SMF modes (Bessel functions) Improvement of cross correlation algorithm (speed) It is likely that a future arwin/tpf-i optical payload shall provide both types of spatial filtering (pinholes and SMFs) 12