Abstract

Simulated interferometric patterns of the wave fronts generated by a star–planet system and detected with a rotational shearing interferometer are derived analytically and presented graphically. They are identical to the patterns generated solely by a planet because of the insensitivity of the rotational shearing interferometer to the detection of a rotationally symmetric wave front. The variable shearing angle is shown to control the number of fringes and their orientation. For small shearing angles the phase difference in the argument of the cosine function reduces to the derivative of the wave front multiplied by the shearing angle. The analytical expression for the intensity detected with a rotational shearing interferometer demonstrates that the rotational shearing interferometer does not see the on-axis star.

© 1999 Optical Society of America

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  1. M. S. Scholl, Y. Wang, J. E. Randolph, J. A. Ayon, “Site certification imaging sensor for Mars exploration,” Opt. Eng. 30, 590–597 (1991).
    [CrossRef]
  2. M. S. Scholl, S. Eberlein, “Site characterization with robotic sample acquisition systems,” Opt. Eng. 32, 840–846 (1993).
    [CrossRef]
  3. M. S. Scholl, “Autonomous star field identification for solar system exploration,” in International Conference, from Galileo’s “Occhialino” to Optoelectronics, P. Mazzoldi, ed. (World Scientific, Teaneck, N.J., 1993), pp. 802–807.
  4. D. W. Davies, “Direct imaging of planetary systems around nearby stars,” Icarus 42, 145–152 (1980).
    [CrossRef]
  5. J. R. P. Angel, A. Y. S. Cheng, N. J. Woolf, “A space telescope for infrared spectroscopy of Earth-like planets,” Nature (London) 322, 341 (1986).
    [CrossRef]
  6. M. S. Scholl, “Infrared signal generated by an extra-solar-system planet detected by a rotating rotationally shearing interferometer,” J. Opt. Soc. Am. A 13, 1584–1592 (1996).
    [CrossRef]
  7. E. Skindrud, “Giant ears await alien broadcasts,” Science News 150, 152–153 (Sept.7, 1996).
    [CrossRef]
  8. D. J. Diner, E. F. Tubbs, S. L. Gaiser, R. P. Korechoff, “Infrared imaging of extrasolar planets,” J. Br. Interplanet. Soc. 44, 505–512 (1991).
  9. M. S. Scholl, G. Paez Padilla, “Using the y,y-bar diagram to control stray light noise in IR systems,” Infrared Phys. Technol. 38, 25–30 (1997).
    [CrossRef]
  10. M. S. Scholl, G. Paez Padilla, “Image-plane incidence for a baffled infrared telescope,” Infrared Phys. Technol. 38, 87–92 (1997).
    [CrossRef]
  11. M. S. Scholl, Y. Wang, “Diffraction effects due to an occulting aperture: comparison of theories,” in OSA Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989).
  12. M. S. Scholl, “Feasibility of extra solar planet detection with a modified Lyot coronagraph,” presented at the 16th Congress of the International Commission for Optics, Budapest, Hungary, August 3–5, 1993.
  13. R. N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature (London) 337, 32 (1978).
  14. M. S. Scholl, “An array of large deployable reflectors on the Moon,” in Space Optics for Astrophysics and Earth and Planetary Remote Sensing, Vol. 10 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. WB7-1–WB7-4 (postconference edition).
  15. M. S. Scholl, “Star-light suppression with a rotating rotationally-shearing interferometer for extra-solar planet detection,” in Signal Recovery and Synthesis, Vol. 11 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 54–57.
  16. J. D. Armitage, A. W. Lohmann, “Rotary shearing interferometry,” Opt. Acta 12, 185–192 (1965).
    [CrossRef]
  17. M. V. R. K. Murty, E. C. Hagerott, “Rotational shearing interferometry,” Appl. Opt. 5, 615–620 (1966).
    [CrossRef] [PubMed]
  18. F. Roddier, C. Roddier, J. DeMarcq, “A rotation shearing interferometer with phase-compensated roof prisms,” J. Opt. 9, 145–151 (1978).
    [CrossRef]
  19. C. Roddier, F. Roddier, J. DeMarcq, “Compact rotational shearing interferometer for astronomical applications,” Opt. Eng. 28, 66–70 (1989).
    [CrossRef]
  20. G. Páez, M. S. Scholl, “Versatility of the differential rotationally-shearing interferometer for testing the aspherical surfaces,” in Optical Fabrication and Testing, Vol. 12 of 1998 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1998), pp. 101–103.

1997

M. S. Scholl, G. Paez Padilla, “Using the y,y-bar diagram to control stray light noise in IR systems,” Infrared Phys. Technol. 38, 25–30 (1997).
[CrossRef]

M. S. Scholl, G. Paez Padilla, “Image-plane incidence for a baffled infrared telescope,” Infrared Phys. Technol. 38, 87–92 (1997).
[CrossRef]

1996

1993

M. S. Scholl, S. Eberlein, “Site characterization with robotic sample acquisition systems,” Opt. Eng. 32, 840–846 (1993).
[CrossRef]

1991

M. S. Scholl, Y. Wang, J. E. Randolph, J. A. Ayon, “Site certification imaging sensor for Mars exploration,” Opt. Eng. 30, 590–597 (1991).
[CrossRef]

D. J. Diner, E. F. Tubbs, S. L. Gaiser, R. P. Korechoff, “Infrared imaging of extrasolar planets,” J. Br. Interplanet. Soc. 44, 505–512 (1991).

1989

C. Roddier, F. Roddier, J. DeMarcq, “Compact rotational shearing interferometer for astronomical applications,” Opt. Eng. 28, 66–70 (1989).
[CrossRef]

1986

J. R. P. Angel, A. Y. S. Cheng, N. J. Woolf, “A space telescope for infrared spectroscopy of Earth-like planets,” Nature (London) 322, 341 (1986).
[CrossRef]

1980

D. W. Davies, “Direct imaging of planetary systems around nearby stars,” Icarus 42, 145–152 (1980).
[CrossRef]

1978

R. N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature (London) 337, 32 (1978).

F. Roddier, C. Roddier, J. DeMarcq, “A rotation shearing interferometer with phase-compensated roof prisms,” J. Opt. 9, 145–151 (1978).
[CrossRef]

1966

1965

J. D. Armitage, A. W. Lohmann, “Rotary shearing interferometry,” Opt. Acta 12, 185–192 (1965).
[CrossRef]

Angel, J. R. P.

J. R. P. Angel, A. Y. S. Cheng, N. J. Woolf, “A space telescope for infrared spectroscopy of Earth-like planets,” Nature (London) 322, 341 (1986).
[CrossRef]

Armitage, J. D.

J. D. Armitage, A. W. Lohmann, “Rotary shearing interferometry,” Opt. Acta 12, 185–192 (1965).
[CrossRef]

Ayon, J. A.

M. S. Scholl, Y. Wang, J. E. Randolph, J. A. Ayon, “Site certification imaging sensor for Mars exploration,” Opt. Eng. 30, 590–597 (1991).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature (London) 337, 32 (1978).

Cheng, A. Y. S.

J. R. P. Angel, A. Y. S. Cheng, N. J. Woolf, “A space telescope for infrared spectroscopy of Earth-like planets,” Nature (London) 322, 341 (1986).
[CrossRef]

Davies, D. W.

D. W. Davies, “Direct imaging of planetary systems around nearby stars,” Icarus 42, 145–152 (1980).
[CrossRef]

DeMarcq, J.

C. Roddier, F. Roddier, J. DeMarcq, “Compact rotational shearing interferometer for astronomical applications,” Opt. Eng. 28, 66–70 (1989).
[CrossRef]

F. Roddier, C. Roddier, J. DeMarcq, “A rotation shearing interferometer with phase-compensated roof prisms,” J. Opt. 9, 145–151 (1978).
[CrossRef]

Diner, D. J.

D. J. Diner, E. F. Tubbs, S. L. Gaiser, R. P. Korechoff, “Infrared imaging of extrasolar planets,” J. Br. Interplanet. Soc. 44, 505–512 (1991).

Eberlein, S.

M. S. Scholl, S. Eberlein, “Site characterization with robotic sample acquisition systems,” Opt. Eng. 32, 840–846 (1993).
[CrossRef]

Gaiser, S. L.

D. J. Diner, E. F. Tubbs, S. L. Gaiser, R. P. Korechoff, “Infrared imaging of extrasolar planets,” J. Br. Interplanet. Soc. 44, 505–512 (1991).

Hagerott, E. C.

Korechoff, R. P.

D. J. Diner, E. F. Tubbs, S. L. Gaiser, R. P. Korechoff, “Infrared imaging of extrasolar planets,” J. Br. Interplanet. Soc. 44, 505–512 (1991).

Lohmann, A. W.

J. D. Armitage, A. W. Lohmann, “Rotary shearing interferometry,” Opt. Acta 12, 185–192 (1965).
[CrossRef]

Murty, M. V. R. K.

Páez, G.

G. Páez, M. S. Scholl, “Versatility of the differential rotationally-shearing interferometer for testing the aspherical surfaces,” in Optical Fabrication and Testing, Vol. 12 of 1998 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1998), pp. 101–103.

Paez Padilla, G.

M. S. Scholl, G. Paez Padilla, “Using the y,y-bar diagram to control stray light noise in IR systems,” Infrared Phys. Technol. 38, 25–30 (1997).
[CrossRef]

M. S. Scholl, G. Paez Padilla, “Image-plane incidence for a baffled infrared telescope,” Infrared Phys. Technol. 38, 87–92 (1997).
[CrossRef]

Randolph, J. E.

M. S. Scholl, Y. Wang, J. E. Randolph, J. A. Ayon, “Site certification imaging sensor for Mars exploration,” Opt. Eng. 30, 590–597 (1991).
[CrossRef]

Roddier, C.

C. Roddier, F. Roddier, J. DeMarcq, “Compact rotational shearing interferometer for astronomical applications,” Opt. Eng. 28, 66–70 (1989).
[CrossRef]

F. Roddier, C. Roddier, J. DeMarcq, “A rotation shearing interferometer with phase-compensated roof prisms,” J. Opt. 9, 145–151 (1978).
[CrossRef]

Roddier, F.

C. Roddier, F. Roddier, J. DeMarcq, “Compact rotational shearing interferometer for astronomical applications,” Opt. Eng. 28, 66–70 (1989).
[CrossRef]

F. Roddier, C. Roddier, J. DeMarcq, “A rotation shearing interferometer with phase-compensated roof prisms,” J. Opt. 9, 145–151 (1978).
[CrossRef]

Scholl, M. S.

M. S. Scholl, G. Paez Padilla, “Image-plane incidence for a baffled infrared telescope,” Infrared Phys. Technol. 38, 87–92 (1997).
[CrossRef]

M. S. Scholl, G. Paez Padilla, “Using the y,y-bar diagram to control stray light noise in IR systems,” Infrared Phys. Technol. 38, 25–30 (1997).
[CrossRef]

M. S. Scholl, “Infrared signal generated by an extra-solar-system planet detected by a rotating rotationally shearing interferometer,” J. Opt. Soc. Am. A 13, 1584–1592 (1996).
[CrossRef]

M. S. Scholl, S. Eberlein, “Site characterization with robotic sample acquisition systems,” Opt. Eng. 32, 840–846 (1993).
[CrossRef]

M. S. Scholl, Y. Wang, J. E. Randolph, J. A. Ayon, “Site certification imaging sensor for Mars exploration,” Opt. Eng. 30, 590–597 (1991).
[CrossRef]

M. S. Scholl, “Autonomous star field identification for solar system exploration,” in International Conference, from Galileo’s “Occhialino” to Optoelectronics, P. Mazzoldi, ed. (World Scientific, Teaneck, N.J., 1993), pp. 802–807.

M. S. Scholl, Y. Wang, “Diffraction effects due to an occulting aperture: comparison of theories,” in OSA Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989).

M. S. Scholl, “An array of large deployable reflectors on the Moon,” in Space Optics for Astrophysics and Earth and Planetary Remote Sensing, Vol. 10 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. WB7-1–WB7-4 (postconference edition).

M. S. Scholl, “Star-light suppression with a rotating rotationally-shearing interferometer for extra-solar planet detection,” in Signal Recovery and Synthesis, Vol. 11 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 54–57.

M. S. Scholl, “Feasibility of extra solar planet detection with a modified Lyot coronagraph,” presented at the 16th Congress of the International Commission for Optics, Budapest, Hungary, August 3–5, 1993.

G. Páez, M. S. Scholl, “Versatility of the differential rotationally-shearing interferometer for testing the aspherical surfaces,” in Optical Fabrication and Testing, Vol. 12 of 1998 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1998), pp. 101–103.

Skindrud, E.

E. Skindrud, “Giant ears await alien broadcasts,” Science News 150, 152–153 (Sept.7, 1996).
[CrossRef]

Tubbs, E. F.

D. J. Diner, E. F. Tubbs, S. L. Gaiser, R. P. Korechoff, “Infrared imaging of extrasolar planets,” J. Br. Interplanet. Soc. 44, 505–512 (1991).

Wang, Y.

M. S. Scholl, Y. Wang, J. E. Randolph, J. A. Ayon, “Site certification imaging sensor for Mars exploration,” Opt. Eng. 30, 590–597 (1991).
[CrossRef]

M. S. Scholl, Y. Wang, “Diffraction effects due to an occulting aperture: comparison of theories,” in OSA Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989).

Woolf, N. J.

J. R. P. Angel, A. Y. S. Cheng, N. J. Woolf, “A space telescope for infrared spectroscopy of Earth-like planets,” Nature (London) 322, 341 (1986).
[CrossRef]

Appl. Opt.

Icarus

D. W. Davies, “Direct imaging of planetary systems around nearby stars,” Icarus 42, 145–152 (1980).
[CrossRef]

Infrared Phys. Technol.

M. S. Scholl, G. Paez Padilla, “Using the y,y-bar diagram to control stray light noise in IR systems,” Infrared Phys. Technol. 38, 25–30 (1997).
[CrossRef]

M. S. Scholl, G. Paez Padilla, “Image-plane incidence for a baffled infrared telescope,” Infrared Phys. Technol. 38, 87–92 (1997).
[CrossRef]

J. Br. Interplanet. Soc.

D. J. Diner, E. F. Tubbs, S. L. Gaiser, R. P. Korechoff, “Infrared imaging of extrasolar planets,” J. Br. Interplanet. Soc. 44, 505–512 (1991).

J. Opt.

F. Roddier, C. Roddier, J. DeMarcq, “A rotation shearing interferometer with phase-compensated roof prisms,” J. Opt. 9, 145–151 (1978).
[CrossRef]

J. Opt. Soc. Am. A

Nature (London)

R. N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature (London) 337, 32 (1978).

J. R. P. Angel, A. Y. S. Cheng, N. J. Woolf, “A space telescope for infrared spectroscopy of Earth-like planets,” Nature (London) 322, 341 (1986).
[CrossRef]

Opt. Acta

J. D. Armitage, A. W. Lohmann, “Rotary shearing interferometry,” Opt. Acta 12, 185–192 (1965).
[CrossRef]

Opt. Eng.

M. S. Scholl, Y. Wang, J. E. Randolph, J. A. Ayon, “Site certification imaging sensor for Mars exploration,” Opt. Eng. 30, 590–597 (1991).
[CrossRef]

M. S. Scholl, S. Eberlein, “Site characterization with robotic sample acquisition systems,” Opt. Eng. 32, 840–846 (1993).
[CrossRef]

C. Roddier, F. Roddier, J. DeMarcq, “Compact rotational shearing interferometer for astronomical applications,” Opt. Eng. 28, 66–70 (1989).
[CrossRef]

Science News

E. Skindrud, “Giant ears await alien broadcasts,” Science News 150, 152–153 (Sept.7, 1996).
[CrossRef]

Other

M. S. Scholl, “An array of large deployable reflectors on the Moon,” in Space Optics for Astrophysics and Earth and Planetary Remote Sensing, Vol. 10 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. WB7-1–WB7-4 (postconference edition).

M. S. Scholl, “Star-light suppression with a rotating rotationally-shearing interferometer for extra-solar planet detection,” in Signal Recovery and Synthesis, Vol. 11 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 54–57.

G. Páez, M. S. Scholl, “Versatility of the differential rotationally-shearing interferometer for testing the aspherical surfaces,” in Optical Fabrication and Testing, Vol. 12 of 1998 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1998), pp. 101–103.

M. S. Scholl, “Autonomous star field identification for solar system exploration,” in International Conference, from Galileo’s “Occhialino” to Optoelectronics, P. Mazzoldi, ed. (World Scientific, Teaneck, N.J., 1993), pp. 802–807.

M. S. Scholl, Y. Wang, “Diffraction effects due to an occulting aperture: comparison of theories,” in OSA Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989).

M. S. Scholl, “Feasibility of extra solar planet detection with a modified Lyot coronagraph,” presented at the 16th Congress of the International Commission for Optics, Budapest, Hungary, August 3–5, 1993.

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Figures (6)

Fig. 1
Fig. 1

Diagram of a cold planet orbiting a nearby star.

Fig. 2
Fig. 2

Two plane waves incident on the interferometer aperture from a distant solar system.

Fig. 3
Fig. 3

Rotational shearing interferometer detecting asymmetrical wave fronts.

Fig. 4
Fig. 4

Interferometric pattern of a wave front with ten waves of tilt as might be observed in a Mach–Zehnder interferometer.

Fig. 5
Fig. 5

Wave front of Fig. 4, as predicted to be detected in a rotational shearing interferometer, calculated with Eq. (11). The shearing angle Θ increases from 0 to 8.0° in increments of 1.6°.

Fig. 6
Fig. 6

As in Fig. 4, but the shearing angle Θ increases from 0 to 180° in increments of 36°.

Equations (16)

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

Ψsps(ρ, θ, 0)=As+ap exp[ikp(ρ cos θ cos φ sin α+ρ sin θ sin φ sin α)].
ϕp(ρ, θ, 0)=kp[ρ cos θ cos φ sin α+ρ sin θ sin φ sin α]=ϕsps(x, y, 0).
I(ρ, θ, 0; Θ)=[Ψ+(ρ, θ+Θ/2, 0)]2+[Ψ-(ρ, θ-Θ/2, 0)]2-[Ψ-(ρ, θ-Θ/2, 0)×Ψ+(ρ, θ+Θ/2, 0)*+Ψ+(ρ, θ+Θ/2, 0)×Ψ-(ρ, θ-Θ/2, 0)*].
Ψ+(ρ, θ+Θ/2, 0)
=As/2+ap/2 exp{ikp[a10ρ cos(θ+Θ/2)
+a01ρ sin(θ+Θ/2)]}
Ψ-(ρ, θ-Θ/2, 0)
=As/2+ap/2 exp{ikp[a10ρ cos(θ-Θ/2) 
+a01ρ sin(θ-Θ/2)]}.
I(ρ, θ, 0; Θ)=ap/2{1-cos[ϕ-(ρ, θ-Θ/2, 0)]×cos[ϕ+(ρ, θ+Θ/2, 0)]-sin[ϕ-(ρ, θ-Θ/2, 0)]×sin[ϕ+(ρ, θ+Θ/2, 0)]}.
I(ρ, θ, 0; Θ)=ap/2{1-cos[a10ρ cos(θ-Θ/2)]
×cos[a10ρ cos(θ+Θ/2)]-sin[a10ρ cos(θ-Θ/2)]×sin[a10ρ cos(θ+Θ/2)]}.
I(ρ, θ, 0; Θ)=ap/2(1+cos{[2 sin(Θ/2)]a10ρ sin θ}).
I(ρ, θ, 0)=I0(ρ, θ, 0){1+cos[(a10)MZρ sin θ]}.
(a10)RS=(a10)MZ/[2 sin(Θ/2)].
I(ρ, θ, 0)=I0(ρ, θ, 0){1+cos[ϕ+(ρ, θ+Θ/2, 0)-ϕ-(ρ, θ-Θ/2, 0)]}.

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