Fine art of computing nulling interferometer maps
Fine art of computing nulling interferometer maps
François Hénault UMR 6525 CNRS H. FIZEAU – UNS, OCA Avenue Nicolas Copernic 06130 GRASSE - FRANCE
Conference 7013: Optical and Infrared Interferometry
Marseille, June 26th 2008
1
Fine art of computing nulling interferometer maps
In the frame of Darwin/TPF-I space missions: Do nulling maps depend on the types of Spatial Filtering and Achromatic Phase Shifting (APS) devices ?
Previous publications • “Design of achromatic phase shifters for spaceborne nulling interferometry,” Opt. Lett. 31, 3635-3637 (2006) • “Computing extinction maps of star nulling interferometers,” Opt. Exp. 16, 4537-4546 (2008)
Conference 7013: Optical and Infrared Interferometry
Marseille, June 26th 2008
2
Fine art of computing nulling interferometer maps
Redefining the nulling ratio T(u,v) Fringes TMax T’Max
Envelope
Transmission curve T’’Max
TMin
U Achieved Null
0
• N = TMin/T’Max instead of TMin/TMax • N may change with the employed spatial filtering device Conference 7013: Optical and Infrared Interferometry
Marseille, June 26th 2008
3
Fine art of computing nulling interferometer maps
V
On-sky angular coordinates
U
Entrance pupil plane D
ZS
T1
Y
v
X
u
T2 BY
Recombination plane
Y
OS
X
T4 BX
T3
Y’
O
Detector plane
X’
D F
O’ y’
Coordinates systems
Z
x’ Conference 7013: Optical and Infrared Interferometry
Marseille, June 26th 2008
4
Fine art of computing nulling interferometer maps
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:
{
}
ˆ 2 ⊗ B (Fu, Fv) S T(u, v) = F(u, v) × B D P P 2
E(u)
BP(u)
BD(u)
P
⊗ PSF
Pinhole
Conference 7013: Optical and Infrared Interferometry
= Actual FoV Marseille, June 26th 2008
U 5
Fine art of computing nulling interferometer maps
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: 2
2
ˆ (u, v) ∝ F(u, v) × B ˆ ⊗ G (Fu, Fv) T(u, v) = A D W GW(u)
BD(u)
|…|2 =
⊗ Diffacted amplitude
E(u)
W
SMF
Conference 7013: Optical and Infrared Interferometry
Actual FoV
Marseille, June 26th 2008
U 6
Fine art of computing nulling interferometer maps
Example of three well-known configurations Bracewell
Angel Cross
Y
Y
X array with phase chopping Y
ϕ1= 0
ϕ2= π ϕ2= π
ϕ1= 0 OS
D D
X
BX
OS
D
X
BY
OS
N (number of apertures) 2 4 4
BX (baseline along X) 50 m 50 m 100 m
4
100 m
Conference 7013: Optical and Infrared Interferometry
BX
ϕ4= π
±
ϕ3= 0
X
BY
BX
Type of interferometer Bracewell Angel Cross Stretched X-array, no phase chopping Stretched X-array with phase chopping
ϕ1= 0
ϕ2= ±π/2
ϕ3= π/2
ϕ4= π
BY (baseline Analytical expressions of fringe patterns along Y) – F(u,v) = sin2(πBXu/λ) 50 m F(u,v) = sin2(πBXu/λ) sin2(πBYv/λ) 25 m F–(u,v) = [1+sin(2πBXu/λ)] sin2(πBYv/λ) / 2 25 m
F(u,v) = sin(2πBXu/λ) sin2(πBYv/λ) Marseille, June 26th 2008
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Fine art of computing nulling interferometer maps
First results on a Bracewell interferometer Pinhole filtering, APS with no Pupil-flip
25 mas
• • •
Pinhole filtering, Pupil-flip APS
SMF filtering
λ = 1 µm, D = 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
Conference 7013: Optical and Infrared Interferometry
Marseille, June 26th 2008
8
Fine art of computing nulling interferometer maps
Spectral dependency λ = 1 µm, ∆λ = 0.5 µm Extinction ratios for different SF devices 1 0.9
Pinhole, no FoV-reversal
0.8
SMF
Pinhole filtering
Extinction ratio
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -12
-9
-6
-3
0
3
6
9
12
U (mas)
SMF filtering
• Major conclusions unchanged Conference 7013: Optical and Infrared Interferometry
Marseille, June 26th 2008
9
Fine art of computing nulling interferometer maps
Nulling maps with pinholes or SMF spatial filtering λ = 10 µm, D = 5 m, B = 25-100 m, λ/∆ ∆λ = 40
X array, 4x-stretched, no phase chopping
X array, 4x-stretched, with phase chopping
Conference 7013: Optical and Infrared Interferometry
200 mas
SMF filtering
1 arcsec
Pinhole filtering
Angel Cross
Marseille, June 26th 2008
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Fine art of computing nulling interferometer maps
“Theta-Lambda” diagrams X array, 4x-stretched, with phase chopping
Angel Cross
Bracewell Pinhole filtering
5 µm 10 µm 15 µm
SMF filtering
5 µm 10 µm 15 µm 0
π
2π
0
π
2π
0
π
2π
• Pinhole filtering looks better but… – Only one pinhole/SMF was used on the whole spectral band – Numerical model to be improved Conference 7013: Optical and Infrared Interferometry
Marseille, June 26th 2008
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Fine art of computing nulling interferometer maps
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 Darwin/TPF-I optical payload shall provide both types of spatial filtering (pinholes and SMFs)
Conference 7013: Optical and Infrared Interferometry
Marseille, June 26th 2008
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