Abstract

We present a new design of a phase mask coronagraph implemented with subwavelength diffractive optical elements consisting of optimized surface-relief gratings. Phase mask coronagraphy is a recent technique that seeks to accommodate both high dynamic and high angular resolution imaging of faint sources around bright astrophysical objects such as exoplanets orbiting their host stars. The original design we propose is a new, integrated, and flexible solution to the π phase-shift chromaticity of the phase mask coronagraphs. It will allow broadband observations, i.e., shorter integration times and object characterizations, by means of spectroscopic analysis. The feasibility of the component manufacturing is also considered through a tolerance study.

© 2005 Optical Society of America

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References

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  1. B. Lyot, “A study of the solar corona and prominences without eclipses,” Mon. Not. R. Astron. Soc. 99, 580–594 (1939).
  2. B. A. Smith, R. Terrile, “A circumstellar disk around Beta Pictoris,” Science 226, 1421–1424 (1984).
    [Crossref] [PubMed]
  3. M. J. Kuchner, D. M. Spergel, “Notch-filter masks: practical image masks for planet-finding coronagraphs,” Astrophys. J. 594, 617–626 (2003).
    [Crossref]
  4. F. Roddier, Cl. Roddier, “Stellar coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
    [Crossref]
  5. D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
    [Crossref]
  6. P. Riaud, J. Baudrand, A. Boccaletti, D. Rouan, “The four-quadrant phase-mask coronagraph. III. Laboratory performance,” Publ. Astron. Soc. Pac. 115, 712–719 (2003).
    [Crossref]
  7. D. Gratadour, D. Rouan, A. Boccaletti, P. Riaud, Y. Clénet, “Four quadrant phase mask K-band coronagraphy of NGC 1068 with NAOS-CONICA at VLT,” Astron. Astrophys. 429, 433–437 (2005).
    [Crossref]
  8. D. Mouillet, T. Fusco, A.-M. Lagrange, J.-L. Beuzit, “Planet Finder on the VLT: context, goals, and critical specifications for adaptive optics,” EAS Publ. Ser. 8, 193–200 (2003).
    [Crossref]
  9. M. Born, E. Wolf, Principles of Optics (Cambridge University Press, 1999), Chap. 15, pp. 837–840.
  10. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).
  11. M. G. Moharam, T. K. Gaylord, “Rigourous coupled-wave analysis of planar grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [Crossref]
  12. H. Kikuta, Y. Ohira, K. Iwata, “Achromatic quarter-wave plates using the dispersion of form birefringence,” Appl. Opt. 36, 1566–1572 (1997).
    [Crossref] [PubMed]
  13. F. P. Bundy, “Melting point of graphite at high pressure: heat of fusion,” Science 137, 1055–1057 (1962).
    [Crossref] [PubMed]
  14. W. J. Tropf, “Temperature-dependent refractive index models, for BaF2, CaF2, MgF2, SrF2, LiF, NaF, KCl, ZnS, and ZnSe,” Opt. Eng. 34, 1369–1373 (1995).
    [Crossref]
  15. G. J. Hawkins, “Spectral Characterisation of Infrared Optical Materials and Filters,” Ph.D. dissertation (University of Reading, United Kingdom, 1998).
  16. F. Lemarquis, G. Marchand, C. Amra, “Design and manufacture of low-absorption ZnS–YF3 antireflection coatings in the 3.5–16 µm spectral range,” Appl. Opt. 37, 4239–4244 (1998).
    [Crossref]
  17. J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J Optim 9, 112–147 (1998).
    [Crossref]
  18. G. P. Nordin, P. C. Deguzman, “Broadband form birefringent quarter-wave plate for the mid-infrared wavelength region,” Opt. Express 5, 163–168 (1999).
    [Crossref] [PubMed]
  19. M. Karlsson, Fr. Nikolajeff, “Diamond micro-optics: micro-lenses and antireflection structured surfaces for the infrared spectral region,” Opt. Express 11, 502–507 (2003).
    [Crossref] [PubMed]
  20. M. Karlsson, K. Hjort, Fr. Nikolajeff, “Transfer of continuous-relief diffractive structures into diamond by use of inductively coupled plasma dry etching,” Opt. Lett. 26, 1752–1754 (2001).
    [Crossref]
  21. P. Riaud, A. Boccaletti, D Rouan, F. Lemarquis, A. Labeyrie, “The four-quadrant phase-mask coronagraph. II. Simulations,” Publ. Astron. Soc. Pac. 113, 1145–1154 (2001).
    [Crossref]

2005 (1)

D. Gratadour, D. Rouan, A. Boccaletti, P. Riaud, Y. Clénet, “Four quadrant phase mask K-band coronagraphy of NGC 1068 with NAOS-CONICA at VLT,” Astron. Astrophys. 429, 433–437 (2005).
[Crossref]

2003 (4)

D. Mouillet, T. Fusco, A.-M. Lagrange, J.-L. Beuzit, “Planet Finder on the VLT: context, goals, and critical specifications for adaptive optics,” EAS Publ. Ser. 8, 193–200 (2003).
[Crossref]

P. Riaud, J. Baudrand, A. Boccaletti, D. Rouan, “The four-quadrant phase-mask coronagraph. III. Laboratory performance,” Publ. Astron. Soc. Pac. 115, 712–719 (2003).
[Crossref]

M. J. Kuchner, D. M. Spergel, “Notch-filter masks: practical image masks for planet-finding coronagraphs,” Astrophys. J. 594, 617–626 (2003).
[Crossref]

M. Karlsson, Fr. Nikolajeff, “Diamond micro-optics: micro-lenses and antireflection structured surfaces for the infrared spectral region,” Opt. Express 11, 502–507 (2003).
[Crossref] [PubMed]

2001 (2)

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

M. Karlsson, K. Hjort, Fr. Nikolajeff, “Transfer of continuous-relief diffractive structures into diamond by use of inductively coupled plasma dry etching,” Opt. Lett. 26, 1752–1754 (2001).
[Crossref]

2000 (1)

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

1999 (1)

1998 (2)

J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J Optim 9, 112–147 (1998).
[Crossref]

F. Lemarquis, G. Marchand, C. Amra, “Design and manufacture of low-absorption ZnS–YF3 antireflection coatings in the 3.5–16 µm spectral range,” Appl. Opt. 37, 4239–4244 (1998).
[Crossref]

1997 (2)

1995 (1)

W. J. Tropf, “Temperature-dependent refractive index models, for BaF2, CaF2, MgF2, SrF2, LiF, NaF, KCl, ZnS, and ZnSe,” Opt. Eng. 34, 1369–1373 (1995).
[Crossref]

1984 (1)

B. A. Smith, R. Terrile, “A circumstellar disk around Beta Pictoris,” Science 226, 1421–1424 (1984).
[Crossref] [PubMed]

1981 (1)

1962 (1)

F. P. Bundy, “Melting point of graphite at high pressure: heat of fusion,” Science 137, 1055–1057 (1962).
[Crossref] [PubMed]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

1939 (1)

B. Lyot, “A study of the solar corona and prominences without eclipses,” Mon. Not. R. Astron. Soc. 99, 580–594 (1939).

Amra, C.

Baudrand, J.

P. Riaud, J. Baudrand, A. Boccaletti, D. Rouan, “The four-quadrant phase-mask coronagraph. III. Laboratory performance,” Publ. Astron. Soc. Pac. 115, 712–719 (2003).
[Crossref]

Beuzit, J.-L.

D. Mouillet, T. Fusco, A.-M. Lagrange, J.-L. Beuzit, “Planet Finder on the VLT: context, goals, and critical specifications for adaptive optics,” EAS Publ. Ser. 8, 193–200 (2003).
[Crossref]

Boccaletti, A.

D. Gratadour, D. Rouan, A. Boccaletti, P. Riaud, Y. Clénet, “Four quadrant phase mask K-band coronagraphy of NGC 1068 with NAOS-CONICA at VLT,” Astron. Astrophys. 429, 433–437 (2005).
[Crossref]

P. Riaud, J. Baudrand, A. Boccaletti, D. Rouan, “The four-quadrant phase-mask coronagraph. III. Laboratory performance,” Publ. Astron. Soc. Pac. 115, 712–719 (2003).
[Crossref]

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

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

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge University Press, 1999), Chap. 15, pp. 837–840.

Bundy, F. P.

F. P. Bundy, “Melting point of graphite at high pressure: heat of fusion,” Science 137, 1055–1057 (1962).
[Crossref] [PubMed]

Clénet, Y.

D. Gratadour, D. Rouan, A. Boccaletti, P. Riaud, Y. Clénet, “Four quadrant phase mask K-band coronagraphy of NGC 1068 with NAOS-CONICA at VLT,” Astron. Astrophys. 429, 433–437 (2005).
[Crossref]

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

Deguzman, P. C.

Fusco, T.

D. Mouillet, T. Fusco, A.-M. Lagrange, J.-L. Beuzit, “Planet Finder on the VLT: context, goals, and critical specifications for adaptive optics,” EAS Publ. Ser. 8, 193–200 (2003).
[Crossref]

Gaylord, T. K.

Gratadour, D.

D. Gratadour, D. Rouan, A. Boccaletti, P. Riaud, Y. Clénet, “Four quadrant phase mask K-band coronagraphy of NGC 1068 with NAOS-CONICA at VLT,” Astron. Astrophys. 429, 433–437 (2005).
[Crossref]

Hawkins, G. J.

G. J. Hawkins, “Spectral Characterisation of Infrared Optical Materials and Filters,” Ph.D. dissertation (University of Reading, United Kingdom, 1998).

Hjort, K.

Iwata, K.

Karlsson, M.

Kikuta, H.

Kuchner, M. J.

M. J. Kuchner, D. M. Spergel, “Notch-filter masks: practical image masks for planet-finding coronagraphs,” Astrophys. J. 594, 617–626 (2003).
[Crossref]

Labeyrie, A.

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

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

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J Optim 9, 112–147 (1998).
[Crossref]

Lagrange, A.-M.

D. Mouillet, T. Fusco, A.-M. Lagrange, J.-L. Beuzit, “Planet Finder on the VLT: context, goals, and critical specifications for adaptive optics,” EAS Publ. Ser. 8, 193–200 (2003).
[Crossref]

Lemarquis, F.

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

F. Lemarquis, G. Marchand, C. Amra, “Design and manufacture of low-absorption ZnS–YF3 antireflection coatings in the 3.5–16 µm spectral range,” Appl. Opt. 37, 4239–4244 (1998).
[Crossref]

Lyot, B.

B. Lyot, “A study of the solar corona and prominences without eclipses,” Mon. Not. R. Astron. Soc. 99, 580–594 (1939).

Marchand, G.

Moharam, M. G.

Mouillet, D.

D. Mouillet, T. Fusco, A.-M. Lagrange, J.-L. Beuzit, “Planet Finder on the VLT: context, goals, and critical specifications for adaptive optics,” EAS Publ. Ser. 8, 193–200 (2003).
[Crossref]

Nikolajeff, Fr.

Nordin, G. P.

Ohira, Y.

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J Optim 9, 112–147 (1998).
[Crossref]

Riaud, P.

D. Gratadour, D. Rouan, A. Boccaletti, P. Riaud, Y. Clénet, “Four quadrant phase mask K-band coronagraphy of NGC 1068 with NAOS-CONICA at VLT,” Astron. Astrophys. 429, 433–437 (2005).
[Crossref]

P. Riaud, J. Baudrand, A. Boccaletti, D. Rouan, “The four-quadrant phase-mask coronagraph. III. Laboratory performance,” Publ. Astron. Soc. Pac. 115, 712–719 (2003).
[Crossref]

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

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

Roddier, Cl.

F. Roddier, Cl. Roddier, “Stellar coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
[Crossref]

Roddier, F.

F. Roddier, Cl. Roddier, “Stellar coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
[Crossref]

Rouan, D

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

Rouan, D.

D. Gratadour, D. Rouan, A. Boccaletti, P. Riaud, Y. Clénet, “Four quadrant phase mask K-band coronagraphy of NGC 1068 with NAOS-CONICA at VLT,” Astron. Astrophys. 429, 433–437 (2005).
[Crossref]

P. Riaud, J. Baudrand, A. Boccaletti, D. Rouan, “The four-quadrant phase-mask coronagraph. III. Laboratory performance,” Publ. Astron. Soc. Pac. 115, 712–719 (2003).
[Crossref]

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

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Smith, B. A.

B. A. Smith, R. Terrile, “A circumstellar disk around Beta Pictoris,” Science 226, 1421–1424 (1984).
[Crossref] [PubMed]

Spergel, D. M.

M. J. Kuchner, D. M. Spergel, “Notch-filter masks: practical image masks for planet-finding coronagraphs,” Astrophys. J. 594, 617–626 (2003).
[Crossref]

Terrile, R.

B. A. Smith, R. Terrile, “A circumstellar disk around Beta Pictoris,” Science 226, 1421–1424 (1984).
[Crossref] [PubMed]

Tropf, W. J.

W. J. Tropf, “Temperature-dependent refractive index models, for BaF2, CaF2, MgF2, SrF2, LiF, NaF, KCl, ZnS, and ZnSe,” Opt. Eng. 34, 1369–1373 (1995).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Cambridge University Press, 1999), Chap. 15, pp. 837–840.

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J Optim 9, 112–147 (1998).
[Crossref]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J Optim 9, 112–147 (1998).
[Crossref]

Appl. Opt. (2)

Astron. Astrophys. (1)

D. Gratadour, D. Rouan, A. Boccaletti, P. Riaud, Y. Clénet, “Four quadrant phase mask K-band coronagraphy of NGC 1068 with NAOS-CONICA at VLT,” Astron. Astrophys. 429, 433–437 (2005).
[Crossref]

Astrophys. J. (1)

M. J. Kuchner, D. M. Spergel, “Notch-filter masks: practical image masks for planet-finding coronagraphs,” Astrophys. J. 594, 617–626 (2003).
[Crossref]

EAS Publ. Ser. (1)

D. Mouillet, T. Fusco, A.-M. Lagrange, J.-L. Beuzit, “Planet Finder on the VLT: context, goals, and critical specifications for adaptive optics,” EAS Publ. Ser. 8, 193–200 (2003).
[Crossref]

J. Opt. Soc. Am. (1)

Mon. Not. R. Astron. Soc. (1)

B. Lyot, “A study of the solar corona and prominences without eclipses,” Mon. Not. R. Astron. Soc. 99, 580–594 (1939).

Opt. Eng. (1)

W. J. Tropf, “Temperature-dependent refractive index models, for BaF2, CaF2, MgF2, SrF2, LiF, NaF, KCl, ZnS, and ZnSe,” Opt. Eng. 34, 1369–1373 (1995).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Publ. Astron. Soc. Pac. (4)

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

F. Roddier, Cl. Roddier, “Stellar coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
[Crossref]

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

P. Riaud, J. Baudrand, A. Boccaletti, D. Rouan, “The four-quadrant phase-mask coronagraph. III. Laboratory performance,” Publ. Astron. Soc. Pac. 115, 712–719 (2003).
[Crossref]

Science (2)

B. A. Smith, R. Terrile, “A circumstellar disk around Beta Pictoris,” Science 226, 1421–1424 (1984).
[Crossref] [PubMed]

F. P. Bundy, “Melting point of graphite at high pressure: heat of fusion,” Science 137, 1055–1057 (1962).
[Crossref] [PubMed]

SIAM J Optim (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J Optim 9, 112–147 (1998).
[Crossref]

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Other (2)

G. J. Hawkins, “Spectral Characterisation of Infrared Optical Materials and Filters,” Ph.D. dissertation (University of Reading, United Kingdom, 1998).

M. Born, E. Wolf, Principles of Optics (Cambridge University Press, 1999), Chap. 15, pp. 837–840.

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Figures (13)

Fig. 1
Fig. 1

Basic FQPM coronagraphic optical bench scheme: L1, L2, and L3 are three lenses in the optical system. L1 provides a large (to minimize spatial defects) F/D ratio on the FQPM; L2 images the pupil in the second plane. The Lyot stop (L-S) suppresses the diffracted starlight, and, finally, L3 forms the coronagraphic image on detector D.

Fig. 2
Fig. 2

ZOG schematic presenting the main parameters of the grating: the grating vector | K | = 2π/Λ perpendicular to the grating lines with Λ being the period, the grating depth h, and the filling factor F = a/Λ. (a) Two AR-layer design, where the AR-layer thickness is h1 = h3. and h2 + h3 = h. (b) One AR-layer design, where the AR-layer thickness is h1 and h2 = h. The grating (medium II) is surrounded by the media I (superstrate) and III (substrate). The incident light, making an angle θ with the grating normal, can be decomposed in its TE (transverse electric) and TM (transverse magnetic) states of polarization.

Fig. 3
Fig. 3

4QZOG implementation: s and p are the vectorial complex amplitude components of the incoming light of wave vector k. In each of the four quadrants, the s and p global polarization states are decomposed in the corresponding TEi and TMi vectorial complex amplitudes according to the local grating line orientations (i is the quadrant number). Two effective indices nTEi and nTM can be assigned to the corresponding perpendicular polarization states. The four gratings engraved on a unique substrate are strictly identical and implemented in the following way: two of them in two quadrants along one diagonal are rotated by 90° around their normals with respect to the two others. This antisymmetrical configuration achieves the FQPM particular focal plane π-phase distribution (see text for explanations).

Fig. 4
Fig. 4

Design level of performance according to the substrate refractive index n. The ghost intensity level increases significantly with n. We also note that the rough null depth performance is inversely proportional to n. The best compromise is therefore for the low-index values.

Fig. 5
Fig. 5

H-band 4QZOG null depth (logarithmic scale) vs wavelength. The continuous curve is for the diamond YF3 AR-coated 4QZOG, the dashed curve for the ZnSe YF3 AR-coated one. μ ≈ 3.5 × 10−5 is the mean null depth over the whole H band.

Fig. 6
Fig. 6

K-band 4QZOG null depth (logarithmic scale) vs wavelength. The continuous curve is for the diamond YF3 AR-coated 4QZOG, the dashed curve for the ZnSe YF3 AR-coated one. μ ≈ 1.7 × 10−5 is the mean null depth over the whole K band.

Fig. 7
Fig. 7

K-band 4QZOG phase shift between the TE and TM polarization states vs wavelength: the phase-shift quality is quantified by the phase-shift standard deviation σΔϕ (the less, the better), which is at the very good level of 7 × 10−3 rad rms.

Fig. 8
Fig. 8

K-band 4QZOG transmittances (zero-order diffraction efficiencies in transmission for the TE and TM components) vs wavelength, including the mean optical throughput of the component, which is ≈93.6%, taking absorption into account. The amplitude peak-to-valley variations for the two polarizations TE and TM over the whole band range from 1.5% to 3%.

Fig. 9
Fig. 9

Null depth (logarithmic scale) versus the grating filling factor (F). An optimal solution has been calculated at each F value. We note that best null depths occur for the largest F values with some local minima. We have overplotted in gray the one AR-layer case in which we notice a tiny average degradation of the null depth (negligible in our application) but a nonnegligible shift in optimal filling factors for the manufacturing.

Fig. 10
Fig. 10

Double plot of the grating depth and period vs the filling factor (F). The calculations show the optimal recomputed grating period (left) and depth (right) for the best null depth at each F. We note that the depth increases with F. The period shows a parabolic behavior.

Fig. 11
Fig. 11

4QZOG null depth sensitivity (logarithmic scale) to the grating depth h and filling factor F parameter variations. Each point in this figure represents the average null depth over the whole K band for a given set of h and F but retaining the best solution among several AR-layer thicknesses (with a 2% tolerance) to accommodate this a posteriori possibility of correction.

Fig. 12
Fig. 12

K-band 4QZOG coronagraphic profile (logarithmic scale) vs the angular separation in λmed/D unity, D being the telescope diameter. The gray curve corresponds to the polychromatic Airy disk. The dashed curve represents the wide band 4QZOG azimuth-ally averaged profile where the peak-to-peak null depth is about 6 × 10−6. The continuous curve corresponds to the previous case with a tiny circular Lyot opaque mask (0.55 λmed/D of diameter) to get rid of the chromatic residuals and ghost image. The peak-to-peak null depth is approximately 10−6.

Fig. 13
Fig. 13

N-band 4QZOG null depth (logarithmic scale) versus wavelength. The continuous curve is for the diamond YF3 AR-coated 4QZOG, the dashed curve for the ZnSe YF3 AR-coated one. μ ≈ 4 × 10−5 is the mean null depth over the whole K band.

Tables (2)

Tables Icon

Table 1 Coefficients for Material Refractive-Index Representations

Tables Icon

Table 2 K-Band Diamond and ZnSe 4QZOG Parameters (Two AR-Layer Design)

Equations (13)

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Δ ϕ = 2 π λ ( n 1 ) h .
Λ λ = m n I sin θ + n I , III sin θ m ,
Λ λ 1 n I sin θ + max ( n I , n III ) .
Δ ϕ TE TM = 2 π λ h Δ n TE TM .
n eff , 0 TE = [ F n a 2 + ( 1 F ) n b 2 ] 1 / 2 ,
n eff , 0 TM = [ n a 2 n b 2 F n b 2 + ( 1 F ) n a 2 ] 1 / 2 ,
n eff , 2 TE = [ ( n eff , 0 TE ) 2 + 1 3 ( Λ λ ) 2 π 2 F 2 ( 1 F ) 2 × ( n a 2 n b 2 ) 2 ] 1 / 2 ,
n eff , 2 TM = [ ( n eff , 0 TM ) 2 + 1 3 ( Λ λ ) 2 π 2 F 2 ( 1 F ) 2 × ( 1 n a 2 1 n b 2 ) 2 ( n eff , 0 TM ) 6 ( n eff , 0 TE ) 2 ] 1 / 2 .
Δ ϕ TE i TM i = 2 π λ h Δ n TE i TM i = 2 π λ h Δ n TE TM π ,
Δ ϕ TE i TM j = 2 π λ h ( n TE i n TM j ) = 2 π λ h ( n TE i n TM i ) = Δ ϕ TE i TM i π .
N ( λ ) = [ 1 q ( λ ) ] 2 + ɛ ( λ ) 2 q ( λ ) [ 1 + q ( λ ) ] 2 .
n diamond , ZnSe , CdTe , Ge ( λ ) = ( A + B λ 2 λ 2 C + D λ 2 λ 2 E + F λ 2 λ 2 G ) 1 / 2 ,
n Si ( λ ) = A + B λ + C λ 2 + D λ 3 + E λ 4 .

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