Abstract

We introduce a new concept of nulling interferometer without any achromatic device, using polarization properties of light. This type of interferometer should enable a high rejection ratio in a theoretically unlimited spectral band. We analyze several consequences of the proposed design, notably, the possibility of fast internal modulation.

© 2006 Optical Society of America

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References

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  1. M. Mayor and D. Queloz, "A Jupiter-mass companion to a solar-type star," Nature 378, 355-359 (1995).
    [CrossRef]
  2. N. Woolf and J. R. Angel, "Astronomical searches for earth-like planets and signs of life," Astron. Astrophys. 36, 507-537 (1998).
    [CrossRef]
  3. G. W. Marcy and R. P. Butler, "Detection of extrasolar giant planets," Astron. Astrophys. 36, 57-97 (1998).
    [CrossRef]
  4. R. Bracewell, "Detecting nonsolar planets by spinning infrared interferometer," Nature 274, 780-781 (1978)
    [CrossRef]
  5. J. R. Angel, A. Y. S. Cheng and N. J. Woolf, "A space telescope for IR spectroscopy of Earthlike planets," Nature 232, 341-343 (1986)
    [CrossRef]
  6. N. Baba and N. Murakami, "A method to image extrasolar planets with polarized light," Publ. Astron. Soc. Pac. 115, 1363-1366 (2003)
    [CrossRef]
  7. J. Spronck, S. F. Pereira and J. J. M. Braat, "Chromatism compensation in wide-band nulling interferometry for exoplanet detection," Appl. Opt. 45 (4), 597-604 (2006).
    [CrossRef]
  8. R. M. A. Azzam and N. M. Bashara, "Ellipsometry and polarized light" (Elsevier, Amsterdam, 1987)
  9. P. Hariharan, "Achromatic and apochromatic halfwave and quarterwave retarders," Opt. Eng. 35 (11), 3335-3337 (1996).
    [CrossRef]
  10. <other>. D. Mawet, J. Baudrand, C. Lenaerts, V. Moreau, P. Riaud, D. Rouan and J. Surdej "Birefringent achromatic phase shifters for nulling interferometry and phase coronography," Proceedings of Towards Other Earths: DARWIN/ TPF and the Search for Extrasolar Terrestrial Planets, Heidelberg, Germany, 22-25 April 2003.</other>

2006

2003

N. Baba and N. Murakami, "A method to image extrasolar planets with polarized light," Publ. Astron. Soc. Pac. 115, 1363-1366 (2003)
[CrossRef]

1998

N. Woolf and J. R. Angel, "Astronomical searches for earth-like planets and signs of life," Astron. Astrophys. 36, 507-537 (1998).
[CrossRef]

G. W. Marcy and R. P. Butler, "Detection of extrasolar giant planets," Astron. Astrophys. 36, 57-97 (1998).
[CrossRef]

1996

P. Hariharan, "Achromatic and apochromatic halfwave and quarterwave retarders," Opt. Eng. 35 (11), 3335-3337 (1996).
[CrossRef]

1995

M. Mayor and D. Queloz, "A Jupiter-mass companion to a solar-type star," Nature 378, 355-359 (1995).
[CrossRef]

1986

J. R. Angel, A. Y. S. Cheng and N. J. Woolf, "A space telescope for IR spectroscopy of Earthlike planets," Nature 232, 341-343 (1986)
[CrossRef]

1978

R. Bracewell, "Detecting nonsolar planets by spinning infrared interferometer," Nature 274, 780-781 (1978)
[CrossRef]

Angel, J. R.

N. Woolf and J. R. Angel, "Astronomical searches for earth-like planets and signs of life," Astron. Astrophys. 36, 507-537 (1998).
[CrossRef]

J. R. Angel, A. Y. S. Cheng and N. J. Woolf, "A space telescope for IR spectroscopy of Earthlike planets," Nature 232, 341-343 (1986)
[CrossRef]

Baba, N.

N. Baba and N. Murakami, "A method to image extrasolar planets with polarized light," Publ. Astron. Soc. Pac. 115, 1363-1366 (2003)
[CrossRef]

Braat, J. J. M.

Bracewell, R.

R. Bracewell, "Detecting nonsolar planets by spinning infrared interferometer," Nature 274, 780-781 (1978)
[CrossRef]

Butler, R. P.

G. W. Marcy and R. P. Butler, "Detection of extrasolar giant planets," Astron. Astrophys. 36, 57-97 (1998).
[CrossRef]

Cheng, A. Y. S.

J. R. Angel, A. Y. S. Cheng and N. J. Woolf, "A space telescope for IR spectroscopy of Earthlike planets," Nature 232, 341-343 (1986)
[CrossRef]

Hariharan, P.

P. Hariharan, "Achromatic and apochromatic halfwave and quarterwave retarders," Opt. Eng. 35 (11), 3335-3337 (1996).
[CrossRef]

Marcy, G. W.

G. W. Marcy and R. P. Butler, "Detection of extrasolar giant planets," Astron. Astrophys. 36, 57-97 (1998).
[CrossRef]

Mayor, M.

M. Mayor and D. Queloz, "A Jupiter-mass companion to a solar-type star," Nature 378, 355-359 (1995).
[CrossRef]

Murakami, N.

N. Baba and N. Murakami, "A method to image extrasolar planets with polarized light," Publ. Astron. Soc. Pac. 115, 1363-1366 (2003)
[CrossRef]

Pereira, S. F.

Queloz, D.

M. Mayor and D. Queloz, "A Jupiter-mass companion to a solar-type star," Nature 378, 355-359 (1995).
[CrossRef]

Spronck, J.

Woolf, N.

N. Woolf and J. R. Angel, "Astronomical searches for earth-like planets and signs of life," Astron. Astrophys. 36, 507-537 (1998).
[CrossRef]

Woolf, N. J.

J. R. Angel, A. Y. S. Cheng and N. J. Woolf, "A space telescope for IR spectroscopy of Earthlike planets," Nature 232, 341-343 (1986)
[CrossRef]

Appl. Opt.

Astron. Astrophys.

N. Woolf and J. R. Angel, "Astronomical searches for earth-like planets and signs of life," Astron. Astrophys. 36, 507-537 (1998).
[CrossRef]

G. W. Marcy and R. P. Butler, "Detection of extrasolar giant planets," Astron. Astrophys. 36, 57-97 (1998).
[CrossRef]

Nature

R. Bracewell, "Detecting nonsolar planets by spinning infrared interferometer," Nature 274, 780-781 (1978)
[CrossRef]

J. R. Angel, A. Y. S. Cheng and N. J. Woolf, "A space telescope for IR spectroscopy of Earthlike planets," Nature 232, 341-343 (1986)
[CrossRef]

M. Mayor and D. Queloz, "A Jupiter-mass companion to a solar-type star," Nature 378, 355-359 (1995).
[CrossRef]

Opt. Eng.

P. Hariharan, "Achromatic and apochromatic halfwave and quarterwave retarders," Opt. Eng. 35 (11), 3335-3337 (1996).
[CrossRef]

Publ. Astron. Soc. Pac.

N. Baba and N. Murakami, "A method to image extrasolar planets with polarized light," Publ. Astron. Soc. Pac. 115, 1363-1366 (2003)
[CrossRef]

Other

<other>. D. Mawet, J. Baudrand, C. Lenaerts, V. Moreau, P. Riaud, D. Rouan and J. Surdej "Birefringent achromatic phase shifters for nulling interferometry and phase coronography," Proceedings of Towards Other Earths: DARWIN/ TPF and the Search for Extrasolar Terrestrial Planets, Heidelberg, Germany, 22-25 April 2003.</other>

R. M. A. Azzam and N. M. Bashara, "Ellipsometry and polarized light" (Elsevier, Amsterdam, 1987)

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Figures (9)

Fig. 1.
Fig. 1.

Normalized detected intensity (simulation) as a function of the optical path differences (OPD) between the three beams.

Fig. 2.
Fig. 2.

The polarization of each beam (initially linear in the x direction (horizontal)) is changed after a waveplate whose principal axis makes an angle α with the horizontal.

Fig. 3.
Fig. 3.

Design of a new type of nulling interferometer, each beam encounters a horizontal linear polarizer, a waveplate and a vertical linear polarizer.

Fig. 4.
Fig. 4.

Array of telescopes (dots) situated in the plane z = 0 and looking in the z direction. The angles θ and φ define the direction of the incoming light. The position of the jth telescope is given in polar coordinates by (Lj , δj ).

Fig. 5.
Fig. 5.

Simulated three-telescope transmission maps corresponding to different waveplate orientations. All these maps have been calculated with the following parameters: A 1 = A 2 = A 3, L 1 = L 2 = L 3 = 25m and δ 1 = 0, δ 2 = 2π/3, δ 3 = 4π/3, and for a spectral band going from 500 to 650nm. (a) 2α 1 = 0, 2α 2 = 2π/3, 2α 3 = 4π/3, (b) 2α 1 = π/6, 2α 2 = π/6+2π/3, 2α 3 = π/6+4π/3, (c) 2α 1 = 2π/6, 2α 2 = 2π/6+2π/3, 2α 3 = 2π/6+4π/3, (d) 2α 1 = 3π/6, 2α 2 = 3π/6+2π/3, 2α 3 = 3π/6+4π/3, (e) 2α 1 = 4π/6, 2α 2 = 4π/6+2π/3, 2α 3 = 4π/6+4π/3, (f) 2α 1 = 5π/6, 2α 2 = 5π/6+2π/3, 2α 3 = 5π/6+4π/3

Fig. 6.
Fig. 6.

Spectral response of the interferometer in the visible domain in the case of quartz waveplates (dash-dot lines) and in the case of constant-birefringence approximation (solid lines). We also compare zeroth-order (blue lines), first-order (green lines) and second-order (red lines) waveplates. The magenta solid line represents the spectral response in the case of an achromatic waveplate made of a combination of quartz and magnesium fluoride.

Fig. 7.
Fig. 7.

Rejection ratio as a function of an amplitude-mismatching δA 1

Fig. 8.
Fig. 8.

Rejection ratio with randomly-chosen ε 1,j and ε 2,j .

Fig. 9.
Fig. 9.

(a) Rejection ratio when one of the waveplates is rotated with respect to its normal position for 2α 1 = 7π/6 (solid line) and 2α 3 = π/2 (dash-dot line) and (b) rejection ratio with a differential birefringence δB.

Equations (43)

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j = 1 N A j exp ( i ϕ j ) = 0 .
j = 1 N A j exp ( i ϕ j ) = j = 1 N A x , j A y , j exp ( i ϕ j ) = 0 ,
A 1 exp ( i ϕ 1 ) = A 2 exp ( i ϕ 2 ) .
A 1 exp ( i ϕ 1 ) + A 2 exp ( i ϕ 2 ) + A 3 exp ( i ϕ 3 ) = 0 .
A 1 + A 2 + A 3 = 0 .
A 1 = A 0 1 0 ,
A 2 = A 0 cos ( 2 π 3 ) sin ( 2 π 3 ) sin ( 2 π 3 ) cos ( 2 π 3 ) 1 0 = A 0 cos ( 2 π 3 ) sin ( 2 π 3 ) ,
A 3 = A 0 cos ( 4 π 3 ) sin ( 4 π 3 ) sin ( 4 π 3 ) cos ( 4 π 3 ) 1 0 = A 0 cos ( 4 π 3 ) sin ( 4 π 3 ) .
A tot = A 1 + A 2 exp ( i 2 πOP D 21 λ ) + A 3 exp ( i 2 πOP D 31 λ ) .
M w ( 0 ) = T r 0 0 T α .
M w ( α ) = R ( α ) M w ( 0 ) R ( α ) = T r cos 2 α + T α sin 2 α 1 2 sin 2 α ( T r T α ) 1 2 sin 2 α ( T r T α ) T r sin 2 α + T α cos 2 α ,
A = A T r cos 2 α + T α sin 2 α 1 2 sin 2 α ( T r T α ) 1 2 sin 2 α ( T r T α ) T r sin 2 α + T α cos 2 α 1 0 = A T r cos 2 α + T α sin 2 α 1 2 sin 2 α ( T r T α ) .
j = 1 N A j T r cos 2 α j + T α sin 2 α j 1 2 sin 2 α j ( T r T α ) = T r j = 1 N A j cos 2 α j + T α j = 1 N A j sin 2 α j 1 2 ( T r T α ) j = 1 N A j sin 2 α j = 0
A j = 0 1 2 A j ( T r T α ) sin 2 α j ,
j = 1 N A j sin 2 α j = 0 .
f φ ( θ ) = j = 1 N A j exp ( ik L j θ cos ( δ j φ ) )
= j = 1 N 0 1 2 A j ( T r T α ) sin 2 α j exp ( ik L j θ cos ( δ j φ ) ) .
T φ ( θ ) = f φ ( θ ) 2 max [ f φ ( θ ) 2 ] .
j = 1 N A j sin 2 α j L j cos ( δ j φ ) = 0 .
j = 1 N A j sin 2 α j L j cos δ j = 0 ,
j = 1 N A j sin 2 α j L j sin δ j = 0 .
I T r T α 2 ,
I 1 exp ( i Δ ϕ ) 2 = 4 sin 2 Δ ϕ 2 ,
Δ ϕ = 2 π λ ( n e ( λ ) n o ( λ ) ) d = 2 π λ B ( λ ) ,
( 4 n + 1 ) π 2 Δ ϕ = 2 π λ B ( λ ) ( 4 n + 3 ) π 2 ,
B = ( 2 n + 1 ) λ 0 2 .
λ min = 4 n + 2 4 n + 3 λ 0 and λ max = 4 n + 2 4 n + 1 λ 0 .
M = λ max λ min = 4 n + 3 4 n + 1 .
A j = A j ε 2 , j 0 0 1 T r , j cos 2 α j + T α , j sin 2 α j 1 2 sin 2 α j ( T r , j T α , j ) 1 2 sin 2 α j ( T r , j T αj ) T r , j sin 2 α j + T α , j cos 2 α j 1 ε 1 , j .
I λ = j = 1 N A j ε 2 , j [ T r , j cos 2 α j + T α , j sin 2 α j + 1 2 ε 1 , j sin 2 α j ( T r , j T α , j ) ] 2
+ j = 1 N A j [ 1 2 sin 2 α j ( T r , j T α , j ) + ε 1 , j ( T r , j sin 2 α j + T α , j cos 2 α j ) ] 2 .
A 1 = A 2 = A 2 = 1 ,
2 α 1 = 7 π 6 , 2 α 2 = 11 π 6 , 2 α 3 = π 2 ,
ε 1,1 = ε 1,2 = ε 1,3 = 0 ,
ε 2,1 = ε 2,2 = ε 2,3 = 0 ,
T r , 1 = T r , 2 = T r , 3 = T r = 1 ,
T α , 1 = T α , 2 = T α , 3 = T α = exp ( i 5 π λ 0 λ ) ,
λ min = 500 nm , λ max = 650 nm , λ 0 = 562 nm .
I λ = δ A l sin 2 θ l 2 ( T r T α ) 2 4 δ A l 2 .
I λ = δ ϕ l sin 2 θ l 2 ( T r T α ) 2 4 δ ϕ l 2 .
I ( εδ ) 2 ,
I λ = T r T α 2 A l ( δ α l cos 2 α l δ α l 2 sin 2 α l ) 2 .
I λ = A l sin 2 α l πδB λ 2 .

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