Abstract

Herein is discussed the performance of spaceborne nulling interferometers searching for extra-solar planets, in terms of their extinction maps projected on-sky. In particular, it is shown that the designs of Spatial Filtering (SF) and Achromatic Phase Shifter (APS) subsystems, both required to achieve planet detection and characterization, can sensibly affect the nulling maps produced by a simple Bracewell interferometer. Analytical relationships involving cross correlation products are provided and numerical simulations are performed, demonstrating marked differences in the aspect of extinction maps and the values of attained fringes contrasts. It is concluded that depending on their basic principles and designs, FS and APS will result in variable capacities for serendipitous discoveries of planets orbiting around their parent star. The mathematical relationships presented in this paper are assumed to be general, i.e. they should apply to other types of multi-apertures nulling interferometers.

© 2008 Optical Society of America

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References

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2006

O. Absil, R. den Hartog, P. Gondoin, P. Fabry, R. Wilhelm, P. Gitton and F. Puech, "Performance study of ground-based infrared Bracewell interferometers: Application to the detection of exozodiacal dust disks with GENIE," Astron. Astrophys. 448, 787-800 (2006).
[CrossRef]

B. F. Lane, M. W. Muterspaugh and M. Shao, "Calibrating an interferometric null," Astrophys. J. 648, 1276-1284 (2006).
[CrossRef]

F. Hénault, "Design of achromatic phase shifters for spaceborne nulling interferometry," Opt. Lett. 31, 3635-3637 (2006).
[CrossRef] [PubMed]

2005

O. P. Lay, "Imaging properties of rotating nulling interferometers," Appl. Opt. 44, 5859-5871 (2005).
[CrossRef] [PubMed]

M. Gillon, F. Courbin, P. Magain and B. Borguet, "On the potential of extrasolar transit planet survey," Astron. Astrophys. 442, 731-744 (2005).
[CrossRef]

2002

2001

1997

J. R. P. Angel and N. J. Woolf, "An imaging nulling interferometer to study extrasolar planets," Astrophys. J. 475, 373-379 (1997).
[CrossRef]

M. Ollivier and J. M. Mariotti "Improvement in the rejection rate of a nulling interferometer by spatial filtering," Appl. Opt. 36, 5340-5346 (1997).
[CrossRef] [PubMed]

1996

A. Léger, et al., "Could we search for primitive life on extrasolar planets in the near future? The Darwin project," Icarus 123, 249-255 (1996).
[CrossRef]

1995

M. Mayor and D. Queloz, "A Jupiter-Mass Companion to a Solar-Type Star," Nature 378, 355-359 (1995).
[CrossRef]

1988

1979

R. N. Bracewell and R. H. MacPhie "Searching for non solar planets," Icarus 38, 136-147 (1979).
[CrossRef]

Absil, O.

O. Absil, R. den Hartog, P. Gondoin, P. Fabry, R. Wilhelm, P. Gitton and F. Puech, "Performance study of ground-based infrared Bracewell interferometers: Application to the detection of exozodiacal dust disks with GENIE," Astron. Astrophys. 448, 787-800 (2006).
[CrossRef]

Angel, J. R. P.

J. R. P. Angel and N. J. Woolf, "An imaging nulling interferometer to study extrasolar planets," Astrophys. J. 475, 373-379 (1997).
[CrossRef]

Borguet, B.

M. Gillon, F. Courbin, P. Magain and B. Borguet, "On the potential of extrasolar transit planet survey," Astron. Astrophys. 442, 731-744 (2005).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell and R. H. MacPhie "Searching for non solar planets," Icarus 38, 136-147 (1979).
[CrossRef]

Cassaing, F.

Courbin, F.

M. Gillon, F. Courbin, P. Magain and B. Borguet, "On the potential of extrasolar transit planet survey," Astron. Astrophys. 442, 731-744 (2005).
[CrossRef]

den Hartog, R.

O. Absil, R. den Hartog, P. Gondoin, P. Fabry, R. Wilhelm, P. Gitton and F. Puech, "Performance study of ground-based infrared Bracewell interferometers: Application to the detection of exozodiacal dust disks with GENIE," Astron. Astrophys. 448, 787-800 (2006).
[CrossRef]

Fabry, P.

O. Absil, R. den Hartog, P. Gondoin, P. Fabry, R. Wilhelm, P. Gitton and F. Puech, "Performance study of ground-based infrared Bracewell interferometers: Application to the detection of exozodiacal dust disks with GENIE," Astron. Astrophys. 448, 787-800 (2006).
[CrossRef]

Gillon, M.

M. Gillon, F. Courbin, P. Magain and B. Borguet, "On the potential of extrasolar transit planet survey," Astron. Astrophys. 442, 731-744 (2005).
[CrossRef]

Gitton, P.

O. Absil, R. den Hartog, P. Gondoin, P. Fabry, R. Wilhelm, P. Gitton and F. Puech, "Performance study of ground-based infrared Bracewell interferometers: Application to the detection of exozodiacal dust disks with GENIE," Astron. Astrophys. 448, 787-800 (2006).
[CrossRef]

Gondoin, P.

O. Absil, R. den Hartog, P. Gondoin, P. Fabry, R. Wilhelm, P. Gitton and F. Puech, "Performance study of ground-based infrared Bracewell interferometers: Application to the detection of exozodiacal dust disks with GENIE," Astron. Astrophys. 448, 787-800 (2006).
[CrossRef]

Hénault, F.

Lane, B. F.

B. F. Lane, M. W. Muterspaugh and M. Shao, "Calibrating an interferometric null," Astrophys. J. 648, 1276-1284 (2006).
[CrossRef]

Lay, O.P.

Léger, A.

A. Léger, et al., "Could we search for primitive life on extrasolar planets in the near future? The Darwin project," Icarus 123, 249-255 (1996).
[CrossRef]

MacPhie, R. H.

R. N. Bracewell and R. H. MacPhie "Searching for non solar planets," Icarus 38, 136-147 (1979).
[CrossRef]

Magain, P.

M. Gillon, F. Courbin, P. Magain and B. Borguet, "On the potential of extrasolar transit planet survey," Astron. Astrophys. 442, 731-744 (2005).
[CrossRef]

Mariotti, J. M.

Mayor, M.

M. Mayor and D. Queloz, "A Jupiter-Mass Companion to a Solar-Type Star," Nature 378, 355-359 (1995).
[CrossRef]

Mennesson, B.

Muterspaugh, M. W.

B. F. Lane, M. W. Muterspaugh and M. Shao, "Calibrating an interferometric null," Astrophys. J. 648, 1276-1284 (2006).
[CrossRef]

Ollivier, M.

Puech, F.

O. Absil, R. den Hartog, P. Gondoin, P. Fabry, R. Wilhelm, P. Gitton and F. Puech, "Performance study of ground-based infrared Bracewell interferometers: Application to the detection of exozodiacal dust disks with GENIE," Astron. Astrophys. 448, 787-800 (2006).
[CrossRef]

Queloz, D.

M. Mayor and D. Queloz, "A Jupiter-Mass Companion to a Solar-Type Star," Nature 378, 355-359 (1995).
[CrossRef]

Roddier, F.

Ruilier, C.

Shaklan, S.

Shao, M.

B. F. Lane, M. W. Muterspaugh and M. Shao, "Calibrating an interferometric null," Astrophys. J. 648, 1276-1284 (2006).
[CrossRef]

Wilhelm, R.

O. Absil, R. den Hartog, P. Gondoin, P. Fabry, R. Wilhelm, P. Gitton and F. Puech, "Performance study of ground-based infrared Bracewell interferometers: Application to the detection of exozodiacal dust disks with GENIE," Astron. Astrophys. 448, 787-800 (2006).
[CrossRef]

Woolf, N. J.

J. R. P. Angel and N. J. Woolf, "An imaging nulling interferometer to study extrasolar planets," Astrophys. J. 475, 373-379 (1997).
[CrossRef]

Appl. Opt.

Astron. Astrophys.

M. Gillon, F. Courbin, P. Magain and B. Borguet, "On the potential of extrasolar transit planet survey," Astron. Astrophys. 442, 731-744 (2005).
[CrossRef]

O. Absil, R. den Hartog, P. Gondoin, P. Fabry, R. Wilhelm, P. Gitton and F. Puech, "Performance study of ground-based infrared Bracewell interferometers: Application to the detection of exozodiacal dust disks with GENIE," Astron. Astrophys. 448, 787-800 (2006).
[CrossRef]

Astrophys. J.

J. R. P. Angel and N. J. Woolf, "An imaging nulling interferometer to study extrasolar planets," Astrophys. J. 475, 373-379 (1997).
[CrossRef]

B. F. Lane, M. W. Muterspaugh and M. Shao, "Calibrating an interferometric null," Astrophys. J. 648, 1276-1284 (2006).
[CrossRef]

Icarus

R. N. Bracewell and R. H. MacPhie "Searching for non solar planets," Icarus 38, 136-147 (1979).
[CrossRef]

A. Léger, et al., "Could we search for primitive life on extrasolar planets in the near future? The Darwin project," Icarus 123, 249-255 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Nature

M. Mayor and D. Queloz, "A Jupiter-Mass Companion to a Solar-Type Star," Nature 378, 355-359 (1995).
[CrossRef]

Opt. Lett.

Other

Y. Rabbia, J. Gay, J.P. Rivet and J.L. Schneider, "Review of Concepts and Constraints for Achromatic Phase Shifters," in Proceedings of GENIE-DARWIN Workshop - Hunting for Planets, H. Lacoste ed., ESA SP-522 (European Space Agency, 2003), 7.1.

V. Coudé Du Foresto, G. Perrin, C. Ruilier, B.P. Mennesson, W.A. Traub and M.G. Lacasse, "FLUOR fibered instrument at the IOTA interferometer," Proc. SPIE 3350, 856-863 (1998).

J. M. Le Duigou, M. Ollivier, A. Léger, F. Cassaing, B. Sorrente, B. Fleury, G. Rousset, O. Absil, D. Mourard, Y. Rabbia, L. Escarrat, F. Malbet, D. Rouan, R. Clédassou, M. Delpech, P. Duchon, B. Meyssignac, P. Y. Guidotti and N. Gorius, "Pegase: a space-based nulling interferometer," Proc. SPIE 6265, 62651M (2006).

M. Fridlund, "Darwin and TPF: technology and prospects," Proc. SPIE 5491, 227-235 (2004).

TPF-I Science Working Group Report, JPL Publication 07-1, P.R. Lawson, O.P. Lay, K.J. Johnston and C.A. Beichman eds., Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California (2007).

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Figures (5)

Fig. 1.
Fig. 1.

Computing sky maps of a Bracewell interferometer

Fig. 2.
Fig. 2.

Extinction map generated by pinhole filtering with no FoV reversal (left, 3D view; right, gray scale levels)

Fig. 3.
Fig. 3.

Extinction map generated by pinhole filtering with FoV-reversal APS (left, 3D view; right, gray scale levels)

Fig. 4.
Fig. 4.

Extinction map generated by SMF filtering (left, 3D view; right, gray scale levels)

Fig. 5.
Fig. 5.

Slices along U-axis of extinction maps for different SF and APS devices (dashed line: pinhole filtering with no FoV reversal; dotted line: pinhole filtering with FoV reversal; solid line: SMF filtering)

Tables (1)

Tables Icon

Table 1. Variation of extinction ratio between dark and white fringes

Equations (14)

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E ( u , v ) = A 0 2 sin 2 ( ϕ ) = A 0 2 sin 2 ( π Bu λ )
A ( u , v , x , y ) = A 0 [ exp ( i ϕ ) exp ( i ϕ ) ] B ̂ D ( x Fu , y Fv ) 2
B ̂ D ( x , y ) = 2 J 1 ( π D ρ λ F ) ( π D ρ λ F )
E ( u , v ) = A 0 2 sin 2 ( ϕ ) x , y B ̂ D ( x Fu , y Fv ) 2 B P ( x , y ) dx dy A 0 2 x , y B P ( x , y ) dx dy
E ( u , v ) = sin 2 ( π Bu λ ) [ B ̂ D 2 B P ] ( Fu , Fv ) S P
A ( u , v , x , y ) = A 0 [ exp ( i ϕ ) B ̂ D ( x - Fu , y - Fv ) exp ( i ϕ ) B ̂ D ( x + Fu , y + Fv ) ] 2
E ( u , v ) = { [ B ̂ D 2 B P ] ( Fu , Fv ) + [ B ̂ D 2 B P ] ( Fu , Fv ) 2 cos ( 2 ϕ ) x , y B ̂ D ( x Fu , y Fv ) B ̂ D ( x + Fu , y + Fv ) B P ( x , y ) dx dy } 4 S p
A 1 ( u , v , x , y ) = A 0 2 exp [ i ϕ ] x , y B ̂ D ( x Fu , y Fv ) exp ( x 2 + y 2 ) R F 2 dx dy 2 A 0 2 C
C = [ x , y B ̂ D ( x Fu , y Fv ) 2 dx dy ] 1 2 [ x , y exp [ 2 ( x 2 + y 2 ) R F 2 ] dx dy ] 1 2 = 2 1 2 λ FR F D
A 1 ( u , v , x , y ) = exp ( i ϕ ) { B ̂ D exp ( x 2 + y 2 ) R F 2 } ( Fu , Fv ) 2 C
E ( u , v ) = sin 2 ( π Bu λ ) B ̂ D exp [ ( x 2 + y 2 ) R F 2 ] 2 ( Fu , Fv ) C 2
A 1 ( u , v , x , y ) = exp [ i ϕ ] x , y T ̂ ( x Fu , y Fv ) exp ( x 2 + y 2 ) R F 2 dx dy 2 C T
A 2 ( u , v , x , y ) = exp [ i ϕ ] x , y T ̂ ( x + Fu , y + Fv ) exp ( x 2 + y 2 ) R F 2 dx dy 2 C T
E ( u , v ) = { T ̂ exp [ ( x 2 + y 2 ) R F 2 ] 2 ( Fu , Fv ) + T ̂ exp [ ( x 2 + y 2 ) R F 2 ] 2 ( Fu , Fv ) 2 cos ( 2 ϕ ) × T ̂ exp ( x 2 + y 2 ) R F 2 ( Fu , fv ) × T ̂ exp ( x 2 + y 2 ) R F 2 ( Fu , Fv ) } 4 C T 2

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