Abstract

Nulling interferometry in the thermal IR is the most promising technique for direct detection of Earth-like exoplanets. This technique requires a π phase shifter for the parent star of the planet to be completely extinguished by destructive interference. We investigate how thin films can be used to design π achromatic phase shifters. The design approach that we propose works on reflection and can be carried out by two steps, namely, the design of a mirror and an antireflection structure with no constraint on the phase properties of the thin film stacks. Phase-shift accuracy is derived analytically, and a numerical example illustrates this concept.

© 2003 Optical Society of America

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  1. A. Léger, J-M. Mariotti, B. Menneson, M. Ollivier, J-L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The Darwin project,” Icarus 123, 249–255 (1996).
    [CrossRef]
  2. R. N. Bracewell, “Detecting nonsolar planets by the spinning infrared interferometer,” Nature (London) 274, 780–781 (1978).
    [CrossRef]
  3. M. Fridlund, “The Darwin mission,” ESA SP-514 (European Space Agency, Munich, Germany, 2002), pp. 31–37.
  4. P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
    [CrossRef]
  5. J. Gay, Y. Rabbia, “Principe d’un coronographe interférentiel,” C. R. Acad. Sci., Ser. IIB: Mec. Phys. Chim. Astron. 322, 265–271 (1996).
  6. P. Baudoz, Y. Rabbia, J. Gay, “Achromatic Interfero Coronography I,” Astron. Astrophys. Suppl. Ser. 141, 319–329 (2000).
    [CrossRef]
  7. P. Baudoz, Y. Rabbia, J. Gay, R. Burg, L. Petro, B. Fleury, P. Y. Madec, F. Charbonnier, “Achromatic Interfero Coronography II,” Astron. Astrophys. Suppl. Ser. 145, 341–350 (2000).
    [CrossRef]
  8. D. Rouan, P. Riaud, A. Boccaletti, Y. Clenet, A. Labeyrie, “The four-quadrant phase-mask coronograph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
    [CrossRef]
  9. P. Riaud, A. Boccaletti, D. Rouan, F. Lemarquis, A. Labeyrie, “The four-quadrant phase-mask coronograph. II. Simulations,” Publ. Astron. Soc. Pac. 113, 1145–1154 (2001).
    [CrossRef]
  10. Y. Rabbia, J. Gay, E. Bascou, “Achromatic phase shifters for nulling interferometry,” in Proceedings of the International Conference on Space Optics, ICSO 2000 (Centre National d’Etudes Spatiales, Toulouse, France, 2000), pp. 389–400.
  11. E. Serabyn, M. M. Colavita, “Fully symmetric nulling beam combiners,” Appl. Opt. 40, 1668–1671 (2001).
    [CrossRef]
  12. A. V. Tikhonravov, P. W. Baumeister, K. V. Popov, “Phase properties of multilayers,” Appl. Opt. 36, 4382–4392 (1997).
    [CrossRef] [PubMed]
  13. F. Lemarquis, A. Fornier, E. Pelletier, “Compensation of phase shift induced by beam-splitter plate and compensating plate coatings in a Michelson-type interferometer,” Pure Appl. Opt. 4, 185–198 (1995).
    [CrossRef]
  14. G. J. Hawkins, “Spectral characterization of infrared optical materials and filters,” Ph.D. dissertation (University of Reading, Reading, UK, 1998), pp. 20, 30, 152, 158.
  15. P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
    [CrossRef]

2002

P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
[CrossRef]

2001

P. Riaud, A. Boccaletti, D. Rouan, F. Lemarquis, A. Labeyrie, “The four-quadrant phase-mask coronograph. II. Simulations,” Publ. Astron. Soc. Pac. 113, 1145–1154 (2001).
[CrossRef]

E. Serabyn, M. M. Colavita, “Fully symmetric nulling beam combiners,” Appl. Opt. 40, 1668–1671 (2001).
[CrossRef]

2000

P. Baudoz, Y. Rabbia, J. Gay, “Achromatic Interfero Coronography I,” Astron. Astrophys. Suppl. Ser. 141, 319–329 (2000).
[CrossRef]

P. Baudoz, Y. Rabbia, J. Gay, R. Burg, L. Petro, B. Fleury, P. Y. Madec, F. Charbonnier, “Achromatic Interfero Coronography II,” Astron. Astrophys. Suppl. Ser. 145, 341–350 (2000).
[CrossRef]

D. Rouan, P. Riaud, A. Boccaletti, Y. Clenet, A. Labeyrie, “The four-quadrant phase-mask coronograph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

1997

1996

J. Gay, Y. Rabbia, “Principe d’un coronographe interférentiel,” C. R. Acad. Sci., Ser. IIB: Mec. Phys. Chim. Astron. 322, 265–271 (1996).

A. Léger, J-M. Mariotti, B. Menneson, M. Ollivier, J-L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The Darwin project,” Icarus 123, 249–255 (1996).
[CrossRef]

1995

F. Lemarquis, A. Fornier, E. Pelletier, “Compensation of phase shift induced by beam-splitter plate and compensating plate coatings in a Michelson-type interferometer,” Pure Appl. Opt. 4, 185–198 (1995).
[CrossRef]

1978

R. N. Bracewell, “Detecting nonsolar planets by the spinning infrared interferometer,” Nature (London) 274, 780–781 (1978).
[CrossRef]

1972

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Arnold, L.

P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
[CrossRef]

Bascou, E.

Y. Rabbia, J. Gay, E. Bascou, “Achromatic phase shifters for nulling interferometry,” in Proceedings of the International Conference on Space Optics, ICSO 2000 (Centre National d’Etudes Spatiales, Toulouse, France, 2000), pp. 389–400.

Baudoz, P.

P. Baudoz, Y. Rabbia, J. Gay, “Achromatic Interfero Coronography I,” Astron. Astrophys. Suppl. Ser. 141, 319–329 (2000).
[CrossRef]

P. Baudoz, Y. Rabbia, J. Gay, R. Burg, L. Petro, B. Fleury, P. Y. Madec, F. Charbonnier, “Achromatic Interfero Coronography II,” Astron. Astrophys. Suppl. Ser. 145, 341–350 (2000).
[CrossRef]

Baudrand, J.

P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
[CrossRef]

Baumeister, P. W.

Boccaletti, A.

P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
[CrossRef]

P. Riaud, A. Boccaletti, D. Rouan, F. Lemarquis, A. Labeyrie, “The four-quadrant phase-mask coronograph. II. Simulations,” Publ. Astron. Soc. Pac. 113, 1145–1154 (2001).
[CrossRef]

D. Rouan, P. Riaud, A. Boccaletti, Y. Clenet, A. Labeyrie, “The four-quadrant phase-mask coronograph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

Borkowski, V.

P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
[CrossRef]

Bousquet, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, “Detecting nonsolar planets by the spinning infrared interferometer,” Nature (London) 274, 780–781 (1978).
[CrossRef]

Burg, R.

P. Baudoz, Y. Rabbia, J. Gay, R. Burg, L. Petro, B. Fleury, P. Y. Madec, F. Charbonnier, “Achromatic Interfero Coronography II,” Astron. Astrophys. Suppl. Ser. 145, 341–350 (2000).
[CrossRef]

Charbonnier, F.

P. Baudoz, Y. Rabbia, J. Gay, R. Burg, L. Petro, B. Fleury, P. Y. Madec, F. Charbonnier, “Achromatic Interfero Coronography II,” Astron. Astrophys. Suppl. Ser. 145, 341–350 (2000).
[CrossRef]

Clenet, Y.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clenet, A. Labeyrie, “The four-quadrant phase-mask coronograph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

Colavita, M. M.

Dejonghe, J.

P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
[CrossRef]

Fleury, B.

P. Baudoz, Y. Rabbia, J. Gay, R. Burg, L. Petro, B. Fleury, P. Y. Madec, F. Charbonnier, “Achromatic Interfero Coronography II,” Astron. Astrophys. Suppl. Ser. 145, 341–350 (2000).
[CrossRef]

Fornier, A.

F. Lemarquis, A. Fornier, E. Pelletier, “Compensation of phase shift induced by beam-splitter plate and compensating plate coatings in a Michelson-type interferometer,” Pure Appl. Opt. 4, 185–198 (1995).
[CrossRef]

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Fridlund, M.

M. Fridlund, “The Darwin mission,” ESA SP-514 (European Space Agency, Munich, Germany, 2002), pp. 31–37.

Gay, J.

P. Baudoz, Y. Rabbia, J. Gay, “Achromatic Interfero Coronography I,” Astron. Astrophys. Suppl. Ser. 141, 319–329 (2000).
[CrossRef]

P. Baudoz, Y. Rabbia, J. Gay, R. Burg, L. Petro, B. Fleury, P. Y. Madec, F. Charbonnier, “Achromatic Interfero Coronography II,” Astron. Astrophys. Suppl. Ser. 145, 341–350 (2000).
[CrossRef]

J. Gay, Y. Rabbia, “Principe d’un coronographe interférentiel,” C. R. Acad. Sci., Ser. IIB: Mec. Phys. Chim. Astron. 322, 265–271 (1996).

Y. Rabbia, J. Gay, E. Bascou, “Achromatic phase shifters for nulling interferometry,” in Proceedings of the International Conference on Space Optics, ICSO 2000 (Centre National d’Etudes Spatiales, Toulouse, France, 2000), pp. 389–400.

Gillet, S.

P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
[CrossRef]

Hawkins, G. J.

G. J. Hawkins, “Spectral characterization of infrared optical materials and filters,” Ph.D. dissertation (University of Reading, Reading, UK, 1998), pp. 20, 30, 152, 158.

Kowalczyk, R.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Labeyrie, A.

P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
[CrossRef]

P. Riaud, A. Boccaletti, D. Rouan, F. Lemarquis, A. Labeyrie, “The four-quadrant phase-mask coronograph. II. Simulations,” Publ. Astron. Soc. Pac. 113, 1145–1154 (2001).
[CrossRef]

D. Rouan, P. Riaud, A. Boccaletti, Y. Clenet, A. Labeyrie, “The four-quadrant phase-mask coronograph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

Lardilière, O.

P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
[CrossRef]

Léger, A.

A. Léger, J-M. Mariotti, B. Menneson, M. Ollivier, J-L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The Darwin project,” Icarus 123, 249–255 (1996).
[CrossRef]

Lemarquis, F.

P. Riaud, A. Boccaletti, D. Rouan, F. Lemarquis, A. Labeyrie, “The four-quadrant phase-mask coronograph. II. Simulations,” Publ. Astron. Soc. Pac. 113, 1145–1154 (2001).
[CrossRef]

F. Lemarquis, A. Fornier, E. Pelletier, “Compensation of phase shift induced by beam-splitter plate and compensating plate coatings in a Michelson-type interferometer,” Pure Appl. Opt. 4, 185–198 (1995).
[CrossRef]

Madec, P. Y.

P. Baudoz, Y. Rabbia, J. Gay, R. Burg, L. Petro, B. Fleury, P. Y. Madec, F. Charbonnier, “Achromatic Interfero Coronography II,” Astron. Astrophys. Suppl. Ser. 145, 341–350 (2000).
[CrossRef]

Mariotti, J-M.

A. Léger, J-M. Mariotti, B. Menneson, M. Ollivier, J-L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The Darwin project,” Icarus 123, 249–255 (1996).
[CrossRef]

Menneson, B.

A. Léger, J-M. Mariotti, B. Menneson, M. Ollivier, J-L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The Darwin project,” Icarus 123, 249–255 (1996).
[CrossRef]

Ollivier, M.

A. Léger, J-M. Mariotti, B. Menneson, M. Ollivier, J-L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The Darwin project,” Icarus 123, 249–255 (1996).
[CrossRef]

Pelletier, E.

F. Lemarquis, A. Fornier, E. Pelletier, “Compensation of phase shift induced by beam-splitter plate and compensating plate coatings in a Michelson-type interferometer,” Pure Appl. Opt. 4, 185–198 (1995).
[CrossRef]

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Petro, L.

P. Baudoz, Y. Rabbia, J. Gay, R. Burg, L. Petro, B. Fleury, P. Y. Madec, F. Charbonnier, “Achromatic Interfero Coronography II,” Astron. Astrophys. Suppl. Ser. 145, 341–350 (2000).
[CrossRef]

Popov, K. V.

Puget, J-L.

A. Léger, J-M. Mariotti, B. Menneson, M. Ollivier, J-L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The Darwin project,” Icarus 123, 249–255 (1996).
[CrossRef]

Rabbia, Y.

P. Baudoz, Y. Rabbia, J. Gay, “Achromatic Interfero Coronography I,” Astron. Astrophys. Suppl. Ser. 141, 319–329 (2000).
[CrossRef]

P. Baudoz, Y. Rabbia, J. Gay, R. Burg, L. Petro, B. Fleury, P. Y. Madec, F. Charbonnier, “Achromatic Interfero Coronography II,” Astron. Astrophys. Suppl. Ser. 145, 341–350 (2000).
[CrossRef]

J. Gay, Y. Rabbia, “Principe d’un coronographe interférentiel,” C. R. Acad. Sci., Ser. IIB: Mec. Phys. Chim. Astron. 322, 265–271 (1996).

Y. Rabbia, J. Gay, E. Bascou, “Achromatic phase shifters for nulling interferometry,” in Proceedings of the International Conference on Space Optics, ICSO 2000 (Centre National d’Etudes Spatiales, Toulouse, France, 2000), pp. 389–400.

Riaud, P.

P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
[CrossRef]

P. Riaud, A. Boccaletti, D. Rouan, F. Lemarquis, A. Labeyrie, “The four-quadrant phase-mask coronograph. II. Simulations,” Publ. Astron. Soc. Pac. 113, 1145–1154 (2001).
[CrossRef]

D. Rouan, P. Riaud, A. Boccaletti, Y. Clenet, A. Labeyrie, “The four-quadrant phase-mask coronograph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

Roche, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Rouan, D.

P. Riaud, A. Boccaletti, D. Rouan, F. Lemarquis, A. Labeyrie, “The four-quadrant phase-mask coronograph. II. Simulations,” Publ. Astron. Soc. Pac. 113, 1145–1154 (2001).
[CrossRef]

D. Rouan, P. Riaud, A. Boccaletti, Y. Clenet, A. Labeyrie, “The four-quadrant phase-mask coronograph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

A. Léger, J-M. Mariotti, B. Menneson, M. Ollivier, J-L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The Darwin project,” Icarus 123, 249–255 (1996).
[CrossRef]

Schneider, J.

P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
[CrossRef]

A. Léger, J-M. Mariotti, B. Menneson, M. Ollivier, J-L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The Darwin project,” Icarus 123, 249–255 (1996).
[CrossRef]

Serabyn, E.

Tikhonravov, A. V.

Appl. Opt.

Astron. Astrophys.

P. Riaud, A. Boccaletti, S. Gillet, J. Schneider, A. Labeyrie, L. Arnold, J. Baudrand, O. Lardilière, J. Dejonghe, V. Borkowski, “Coronographic search for exoplanets with a hypertelescope: I in the thermal IR,” Astron. Astrophys. 396, 345–352 (2002).
[CrossRef]

Astron. Astrophys. Suppl. Ser.

P. Baudoz, Y. Rabbia, J. Gay, “Achromatic Interfero Coronography I,” Astron. Astrophys. Suppl. Ser. 141, 319–329 (2000).
[CrossRef]

P. Baudoz, Y. Rabbia, J. Gay, R. Burg, L. Petro, B. Fleury, P. Y. Madec, F. Charbonnier, “Achromatic Interfero Coronography II,” Astron. Astrophys. Suppl. Ser. 145, 341–350 (2000).
[CrossRef]

C. R. Acad. Sci., Ser. IIB: Mec. Phys. Chim. Astron.

J. Gay, Y. Rabbia, “Principe d’un coronographe interférentiel,” C. R. Acad. Sci., Ser. IIB: Mec. Phys. Chim. Astron. 322, 265–271 (1996).

Icarus

A. Léger, J-M. Mariotti, B. Menneson, M. Ollivier, J-L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The Darwin project,” Icarus 123, 249–255 (1996).
[CrossRef]

Nature (London)

R. N. Bracewell, “Detecting nonsolar planets by the spinning infrared interferometer,” Nature (London) 274, 780–781 (1978).
[CrossRef]

Publ. Astron. Soc. Pac.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clenet, A. Labeyrie, “The four-quadrant phase-mask coronograph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

P. Riaud, A. Boccaletti, D. Rouan, F. Lemarquis, A. Labeyrie, “The four-quadrant phase-mask coronograph. II. Simulations,” Publ. Astron. Soc. Pac. 113, 1145–1154 (2001).
[CrossRef]

Pure Appl. Opt.

F. Lemarquis, A. Fornier, E. Pelletier, “Compensation of phase shift induced by beam-splitter plate and compensating plate coatings in a Michelson-type interferometer,” Pure Appl. Opt. 4, 185–198 (1995).
[CrossRef]

Thin Solid Films

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Other

G. J. Hawkins, “Spectral characterization of infrared optical materials and filters,” Ph.D. dissertation (University of Reading, Reading, UK, 1998), pp. 20, 30, 152, 158.

Y. Rabbia, J. Gay, E. Bascou, “Achromatic phase shifters for nulling interferometry,” in Proceedings of the International Conference on Space Optics, ICSO 2000 (Centre National d’Etudes Spatiales, Toulouse, France, 2000), pp. 389–400.

M. Fridlund, “The Darwin mission,” ESA SP-514 (European Space Agency, Munich, Germany, 2002), pp. 31–37.

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Figures (9)

Fig. 1
Fig. 1

Top, schematic representation of the initial coating; bottom, reciprocal coating. Refractive indices are linked by ñ i = α/n i , while optical thicknesses are identical for both coatings: ñ i i = n i d i . Reflectance is identical for both coatings while the phase shifts upon reflection differ from π.

Fig. 2
Fig. 2

General design for a thin-film achromatic phase shifter. Each mirror is formed with a central stack (initial or reciprocal) embedded between two antireflection structures that match external medium and substrate refractive indices n 0 and n S with the index value n m = (n H n L )1/2. The π phase shift is obtained on both sides.

Fig. 3
Fig. 3

Schematic representation of the APS mirrors used in the numerical example. The APS is illuminated from the substrate side and, assuming high-reflectance central mirrors, the air-side antireflection stack can be suppressed. The substrate is prismatic to avoid parasitic light in the main reflected beam.

Fig. 4
Fig. 4

Reflectance of the central mirror, considering an external medium of refractive index n m on both sides. The angle of incidence is equal to 20° in the air. Layer thicknesses are given in Table 1.

Fig. 5
Fig. 5

Reflectance of the antireflection structure used between the substrate and the central mirror. This antireflection stack is optimized between indices n S and n m . The angle of incidence is equal to 20° in the air. The layer thicknesses are in Table 1.

Fig. 6
Fig. 6

Phase-shift deviation from π for the APS formed with the central mirror and antireflection structure of Figs. 4 and 5. The angle of incidence is equal to 20° in the air.

Fig. 7
Fig. 7

Phase-shift deviation from π for the APS in Fig. 6 after optimization. The angle of incidence is equal to 20° in the air. The layer thicknesses of the two APS coatings are in Table 1.

Fig. 8
Fig. 8

Reflectance ratio for the optimized APS in Fig. 7. The angle of incidence is equal to 20° in the air.

Fig. 9
Fig. 9

Maximum and average phase-shift deviation versus thickness errors for one mirror of the APS in Fig. 7. Thickness errors are proportional to layer thicknesses with a standard thickness deviation equal to 10-4. From 7 to 8 μm the maximum and average phase deviations are approximately 1.4 × 10-3 and 4 × 10-4 rad.

Tables (1)

Tables Icon

Table 1 Layer Optical Thicknesses for the Initial Mirror, the Antireflection Stack, and the Optimized APS Coatings Discussed in Section 5

Equations (41)

Equations on this page are rendered with MathJax. Learn more.

ñ0=nLnH/n0, ñS=nLnH/nS,
nM=nLnH1/2.
AR1=t1t1-r1r1t1r1t1-r1t11t1
M=tmtm-rmrmtmrmtm-rmtm1tm
AR2=t2t2-r2r2t2r2t2-r2t21t2
APS1=AR1×M×AR2.
rAPS1=r1+t1t1tmtm-rmrmr2+rm1-rmr2-r1tmtm-rmrmr2+rm.
rAPS2=r1+t1t1tmtm-rmrmr1-rm1+rmr2-r1tmtm-rmrmr2-rm.
rAPS1=t1t1rm, rAPS2=-t1t1rm.
rAPS1=rm exp2jφt1; rAPS2=-rm exp2jφt1.
rAPS1=r1+t1t1rm1-rmr1; rAPS2=r1-t1t1rm1+rmr1.
rAPS1=expjφ1+r1 exp-jφ1+r1 exp-jφ*; rAPS2=-expjφ1-r1 exp-jφ1-r1 exp-jφ*,
Δφ=φrAPS1-φrAPS2=argrAPS1rAPS2 =π+2 arg1+r1 exp-jφ×1-r1 exp-jφ*, Δφ=π+2 arg1-R1+2j Imr1 exp-jφ.
|Δφ-π|2 arctan2R11-R1,
|Δφ-π|4R1.
Ni=ni cos θi for the S state of polarization,Ni=ni/cos θi for the P state of polarization,
NM=nH cos θHnL cos θL1/2 for the S state of polarization,NM=nHnLcos θH cos θL1/2 for the P state of polarization.
NM=nM cos θM for the S state of polarization,NM=nM/cos θM for the P state of polarization.
nGe=9.23928+6.79386λ2λ2-0.437274+0.21598λ2λ2-3880.7241/2, nZnS=2.298824-1.82313×10-2λ+2.23347×10-3λ2-1.63609×10-4λ3+2.59×10-6λ4.
nM=nGe · nZnS1/2,
E0-E0+=M11M12M21M22ES-ES+.
M=B0L1B1L2B2,, LpBp.
Bi=ni+ni+12nini-ni+12nini-ni+12nini+ni+12ni, Li=exp-jδi00expjδi,
δi=2πnidiλ.
det M=nSn0.
r=E0-E0+=M12M22, t=ES+E0+=1M22.
r=ES+ES-=-M21M22, t=E0-ES-=nSn01M22=nSn0 t.
R=|r|2, R=|r|2, T=T=nSn0 |t|2=n0nS |t|2.
φr=argr, φr=argr, φt=φt=argt.
M=tt-rrtrt-rt1t.
M11=M22*, M12=M21*,
tt-rr=exp2jφt, R=R, R+T=1.
δi=2πnidi cos θiλ,
niñi=α/ni.
B˜i=ni+1+ni2ni+1ni+1-ni2ni+1ni+1-ni2ni+1ni+1+ni2ni+1.
B˜i=nini+1100-1Bi100-1.
M˜=B˜0L1B˜1L2B˜2LpB˜p.
100-1Li100-1=Li,
M˜=n0nS100-1B0L1B1L2B2LpBp100-1=n0nS100-1M100-1, M˜=n0nSM11-M12-M21M22,
r˜=-r, r˜=-r, t˜=nSn0 t, t˜=t.
R˜=R˜=R=R, T˜=T,φt˜=φt,φr˜=φr+π,φr˜=φr+π.

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