Abstract

For a coronagraph to detect faint exoplanets, it will require focal plane wavefront control techniques to continue reaching smaller angular separations and higher contrast levels. These correction algorithms are iterative and the control methods need an estimate of the electric field at the science camera, which requires nearly all of the images taken for the correction. The best way to make such algorithms the least disruptive to science exposures is to reduce the number required to estimate the field. We demonstrate a Kalman filter estimator that uses prior knowledge to create the estimate of the electric field, dramatically reducing the number of exposures required to estimate the image plane electric field while stabilizing the suppression against poor signal-to-noise. In addition to a significant reduction in exposures, we discuss the relative merit of this algorithm to estimation schemes that do not incorporate prior state estimate history, particularly in regard to estimate error and covariance. Ultimately the filter will lead to an adaptive algorithm which can estimate physical parameters in the laboratory for robustness to variance in the optical train.

© 2012 Optical Society of America

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References

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  1. S. B. Shaklan and J. J. Green, “Reflectivity and optical surface height requirements in a broadband coronagraph. 1. Contrast floor due to controllable spatial frequencies,” Appl. Opt. 45, 5143–5153 (2006).
    [CrossRef]
  2. S. Shaklan, L. Marchen, J. Krist, and M. Rud, “Stability error budget for an aggressive coronagraph on a 3.8 m telescope,” Proc. SPIE 8151, 815109 (2011).
    [CrossRef]
  3. R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
    [CrossRef]
  4. F. Malbet, J. Yu, and M. Shao, “High-dynamic-range imaging using a deformable mirror for space coronography,” Publ. Astron. Soc. Pac. 107, 386–398 (1995).
    [CrossRef]
  5. J. Trauger, C. Burrows, B. Gordon, J. Green, A. Lowman, D. Moody, A. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330–1336 (2004).
    [CrossRef]
  6. A. Give’on, B. Kern, S. Shaklan, D. Moody, and L. Pueyo, “Broadband wavefront correction algorithm for high-contrast imaging systems,” Proc. SPIE 6691, 66910A (2007).
    [CrossRef]
  7. A. Give’on, R. Belikov, S. Shaklan, and N. J. Kasdin, “Closed loop, dm diversity-based wavefront correction algorithm for high contrast imaging systems,” Opt. Express 15, 12338–12343 (2007).
    [CrossRef]
  8. L. Pueyo, J. Kay, N. Kasdin, T. Groff, M. McElwain, A. Give’on, and R. Belikov, “Optimal dark hole generation via two deformable mirrors with stroke minimization,” Appl. Opt. 48, 6296–6312 (2009).
    [CrossRef]
  9. O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov, “High-contrast imaging and wavefront control with a piaa coronagraph: laboratory system validation,” Publ. Astron. Soc. Pac. 122, 71–84 (2010).
    [CrossRef]
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  11. T. Groff and N. Kasdin, “Optimal wavefront estimation and control using adaptive techniques,” in 2012 IEEE Aerospace Conference (IEEE, 2012), pp. 1–9.
  12. P. Borde and W. Traub, “High-contrast imaging from space: speckle nulling in a low aberration regime,” Appl. Phys. 638, 488–498 (2006).
  13. A. Give’on, B. Kern, and S. Shaklan, “Pair-wise, deformable mirror, image plane-based diversity electric field estimation for high contrast coronagraphy,” Proc. SPIE 8151, 815110 (2011).
    [CrossRef]
  14. T. Groff, “Optimal electric field estimation and control for coronagraphy,” Ph.D. thesis (Princeton University, 2012).
  15. R. Stengel, Optimal Control and Estimation (Dover, 1994).
  16. A. Gelb, J. Kasper, R. Nash, C. Price, and A. Sutherland, Applied Optimal Estimation (MIT, 1974).
  17. S. Howell, Handbook of CCD Astronomy, Vol. 2 (Cambridge University, 2000).

2011 (2)

S. Shaklan, L. Marchen, J. Krist, and M. Rud, “Stability error budget for an aggressive coronagraph on a 3.8 m telescope,” Proc. SPIE 8151, 815109 (2011).
[CrossRef]

A. Give’on, B. Kern, and S. Shaklan, “Pair-wise, deformable mirror, image plane-based diversity electric field estimation for high contrast coronagraphy,” Proc. SPIE 8151, 815110 (2011).
[CrossRef]

2010 (1)

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov, “High-contrast imaging and wavefront control with a piaa coronagraph: laboratory system validation,” Publ. Astron. Soc. Pac. 122, 71–84 (2010).
[CrossRef]

2009 (1)

2007 (3)

A. Give’on, R. Belikov, S. Shaklan, and N. J. Kasdin, “Closed loop, dm diversity-based wavefront correction algorithm for high contrast imaging systems,” Opt. Express 15, 12338–12343 (2007).
[CrossRef]

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

A. Give’on, B. Kern, S. Shaklan, D. Moody, and L. Pueyo, “Broadband wavefront correction algorithm for high-contrast imaging systems,” Proc. SPIE 6691, 66910A (2007).
[CrossRef]

2006 (2)

2004 (1)

J. Trauger, C. Burrows, B. Gordon, J. Green, A. Lowman, D. Moody, A. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

1995 (1)

F. Malbet, J. Yu, and M. Shao, “High-dynamic-range imaging using a deformable mirror for space coronography,” Publ. Astron. Soc. Pac. 107, 386–398 (1995).
[CrossRef]

Balasubramanian, K.

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

Belikov, R.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov, “High-contrast imaging and wavefront control with a piaa coronagraph: laboratory system validation,” Publ. Astron. Soc. Pac. 122, 71–84 (2010).
[CrossRef]

L. Pueyo, J. Kay, N. Kasdin, T. Groff, M. McElwain, A. Give’on, and R. Belikov, “Optimal dark hole generation via two deformable mirrors with stroke minimization,” Appl. Opt. 48, 6296–6312 (2009).
[CrossRef]

A. Give’on, R. Belikov, S. Shaklan, and N. J. Kasdin, “Closed loop, dm diversity-based wavefront correction algorithm for high contrast imaging systems,” Opt. Express 15, 12338–12343 (2007).
[CrossRef]

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

Blain, C.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov, “High-contrast imaging and wavefront control with a piaa coronagraph: laboratory system validation,” Publ. Astron. Soc. Pac. 122, 71–84 (2010).
[CrossRef]

C. Blain, R. Conan, C. Bradley, O. Guyon, and C. Vogel, “Characterisation of the influence function non-additivities for a 1024-actuator mems deformable mirror,” in Proceedings of the 1st AO for ELT Conference (EDP, 2010), paper 06009.

Borde, P.

P. Borde and W. Traub, “High-contrast imaging from space: speckle nulling in a low aberration regime,” Appl. Phys. 638, 488–498 (2006).

Bradley, C.

C. Blain, R. Conan, C. Bradley, O. Guyon, and C. Vogel, “Characterisation of the influence function non-additivities for a 1024-actuator mems deformable mirror,” in Proceedings of the 1st AO for ELT Conference (EDP, 2010), paper 06009.

Burrows, C.

J. Trauger, C. Burrows, B. Gordon, J. Green, A. Lowman, D. Moody, A. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

Cady, E.

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

Carr, M.

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

Conan, R.

C. Blain, R. Conan, C. Bradley, O. Guyon, and C. Vogel, “Characterisation of the influence function non-additivities for a 1024-actuator mems deformable mirror,” in Proceedings of the 1st AO for ELT Conference (EDP, 2010), paper 06009.

Dickie, M.

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

Echternach, P.

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

Gelb, A.

A. Gelb, J. Kasper, R. Nash, C. Price, and A. Sutherland, Applied Optimal Estimation (MIT, 1974).

Give’on, A.

A. Give’on, B. Kern, and S. Shaklan, “Pair-wise, deformable mirror, image plane-based diversity electric field estimation for high contrast coronagraphy,” Proc. SPIE 8151, 815110 (2011).
[CrossRef]

L. Pueyo, J. Kay, N. Kasdin, T. Groff, M. McElwain, A. Give’on, and R. Belikov, “Optimal dark hole generation via two deformable mirrors with stroke minimization,” Appl. Opt. 48, 6296–6312 (2009).
[CrossRef]

A. Give’on, R. Belikov, S. Shaklan, and N. J. Kasdin, “Closed loop, dm diversity-based wavefront correction algorithm for high contrast imaging systems,” Opt. Express 15, 12338–12343 (2007).
[CrossRef]

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

A. Give’on, B. Kern, S. Shaklan, D. Moody, and L. Pueyo, “Broadband wavefront correction algorithm for high-contrast imaging systems,” Proc. SPIE 6691, 66910A (2007).
[CrossRef]

Gordon, B.

J. Trauger, C. Burrows, B. Gordon, J. Green, A. Lowman, D. Moody, A. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

Green, J.

J. Trauger, C. Burrows, B. Gordon, J. Green, A. Lowman, D. Moody, A. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

Green, J. J.

Groff, T.

L. Pueyo, J. Kay, N. Kasdin, T. Groff, M. McElwain, A. Give’on, and R. Belikov, “Optimal dark hole generation via two deformable mirrors with stroke minimization,” Appl. Opt. 48, 6296–6312 (2009).
[CrossRef]

T. Groff, “Optimal electric field estimation and control for coronagraphy,” Ph.D. thesis (Princeton University, 2012).

T. Groff and N. Kasdin, “Optimal wavefront estimation and control using adaptive techniques,” in 2012 IEEE Aerospace Conference (IEEE, 2012), pp. 1–9.

Guyon, O.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov, “High-contrast imaging and wavefront control with a piaa coronagraph: laboratory system validation,” Publ. Astron. Soc. Pac. 122, 71–84 (2010).
[CrossRef]

C. Blain, R. Conan, C. Bradley, O. Guyon, and C. Vogel, “Characterisation of the influence function non-additivities for a 1024-actuator mems deformable mirror,” in Proceedings of the 1st AO for ELT Conference (EDP, 2010), paper 06009.

Howell, S.

S. Howell, Handbook of CCD Astronomy, Vol. 2 (Cambridge University, 2000).

Kasdin, N.

L. Pueyo, J. Kay, N. Kasdin, T. Groff, M. McElwain, A. Give’on, and R. Belikov, “Optimal dark hole generation via two deformable mirrors with stroke minimization,” Appl. Opt. 48, 6296–6312 (2009).
[CrossRef]

T. Groff and N. Kasdin, “Optimal wavefront estimation and control using adaptive techniques,” in 2012 IEEE Aerospace Conference (IEEE, 2012), pp. 1–9.

Kasdin, N. J.

A. Give’on, R. Belikov, S. Shaklan, and N. J. Kasdin, “Closed loop, dm diversity-based wavefront correction algorithm for high contrast imaging systems,” Opt. Express 15, 12338–12343 (2007).
[CrossRef]

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

Kasper, J.

A. Gelb, J. Kasper, R. Nash, C. Price, and A. Sutherland, Applied Optimal Estimation (MIT, 1974).

Kay, J.

Kern, B.

A. Give’on, B. Kern, and S. Shaklan, “Pair-wise, deformable mirror, image plane-based diversity electric field estimation for high contrast coronagraphy,” Proc. SPIE 8151, 815110 (2011).
[CrossRef]

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

A. Give’on, B. Kern, S. Shaklan, D. Moody, and L. Pueyo, “Broadband wavefront correction algorithm for high-contrast imaging systems,” Proc. SPIE 6691, 66910A (2007).
[CrossRef]

Krist, J.

S. Shaklan, L. Marchen, J. Krist, and M. Rud, “Stability error budget for an aggressive coronagraph on a 3.8 m telescope,” Proc. SPIE 8151, 815109 (2011).
[CrossRef]

Kuhnert, A.

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

Lowman, A.

J. Trauger, C. Burrows, B. Gordon, J. Green, A. Lowman, D. Moody, A. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

Malbet, F.

F. Malbet, J. Yu, and M. Shao, “High-dynamic-range imaging using a deformable mirror for space coronography,” Publ. Astron. Soc. Pac. 107, 386–398 (1995).
[CrossRef]

Marchen, L.

S. Shaklan, L. Marchen, J. Krist, and M. Rud, “Stability error budget for an aggressive coronagraph on a 3.8 m telescope,” Proc. SPIE 8151, 815109 (2011).
[CrossRef]

Martinache, F.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov, “High-contrast imaging and wavefront control with a piaa coronagraph: laboratory system validation,” Publ. Astron. Soc. Pac. 122, 71–84 (2010).
[CrossRef]

Matsuo, T.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov, “High-contrast imaging and wavefront control with a piaa coronagraph: laboratory system validation,” Publ. Astron. Soc. Pac. 122, 71–84 (2010).
[CrossRef]

McElwain, M.

Moody, D.

A. Give’on, B. Kern, S. Shaklan, D. Moody, and L. Pueyo, “Broadband wavefront correction algorithm for high-contrast imaging systems,” Proc. SPIE 6691, 66910A (2007).
[CrossRef]

J. Trauger, C. Burrows, B. Gordon, J. Green, A. Lowman, D. Moody, A. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

Nash, R.

A. Gelb, J. Kasper, R. Nash, C. Price, and A. Sutherland, Applied Optimal Estimation (MIT, 1974).

Niessner, A.

J. Trauger, C. Burrows, B. Gordon, J. Green, A. Lowman, D. Moody, A. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

Pluzhnik, E.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov, “High-contrast imaging and wavefront control with a piaa coronagraph: laboratory system validation,” Publ. Astron. Soc. Pac. 122, 71–84 (2010).
[CrossRef]

Price, C.

A. Gelb, J. Kasper, R. Nash, C. Price, and A. Sutherland, Applied Optimal Estimation (MIT, 1974).

Pueyo, L.

L. Pueyo, J. Kay, N. Kasdin, T. Groff, M. McElwain, A. Give’on, and R. Belikov, “Optimal dark hole generation via two deformable mirrors with stroke minimization,” Appl. Opt. 48, 6296–6312 (2009).
[CrossRef]

A. Give’on, B. Kern, S. Shaklan, D. Moody, and L. Pueyo, “Broadband wavefront correction algorithm for high-contrast imaging systems,” Proc. SPIE 6691, 66910A (2007).
[CrossRef]

Rud, M.

S. Shaklan, L. Marchen, J. Krist, and M. Rud, “Stability error budget for an aggressive coronagraph on a 3.8 m telescope,” Proc. SPIE 8151, 815109 (2011).
[CrossRef]

Shaklan, S.

S. Shaklan, L. Marchen, J. Krist, and M. Rud, “Stability error budget for an aggressive coronagraph on a 3.8 m telescope,” Proc. SPIE 8151, 815109 (2011).
[CrossRef]

A. Give’on, B. Kern, and S. Shaklan, “Pair-wise, deformable mirror, image plane-based diversity electric field estimation for high contrast coronagraphy,” Proc. SPIE 8151, 815110 (2011).
[CrossRef]

A. Give’on, R. Belikov, S. Shaklan, and N. J. Kasdin, “Closed loop, dm diversity-based wavefront correction algorithm for high contrast imaging systems,” Opt. Express 15, 12338–12343 (2007).
[CrossRef]

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

A. Give’on, B. Kern, S. Shaklan, D. Moody, and L. Pueyo, “Broadband wavefront correction algorithm for high-contrast imaging systems,” Proc. SPIE 6691, 66910A (2007).
[CrossRef]

Shaklan, S. B.

Shao, M.

F. Malbet, J. Yu, and M. Shao, “High-dynamic-range imaging using a deformable mirror for space coronography,” Publ. Astron. Soc. Pac. 107, 386–398 (1995).
[CrossRef]

Shi, F.

J. Trauger, C. Burrows, B. Gordon, J. Green, A. Lowman, D. Moody, A. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

Stengel, R.

R. Stengel, Optimal Control and Estimation (Dover, 1994).

Sutherland, A.

A. Gelb, J. Kasper, R. Nash, C. Price, and A. Sutherland, Applied Optimal Estimation (MIT, 1974).

Tanaka, S.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov, “High-contrast imaging and wavefront control with a piaa coronagraph: laboratory system validation,” Publ. Astron. Soc. Pac. 122, 71–84 (2010).
[CrossRef]

Totems, J.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov, “High-contrast imaging and wavefront control with a piaa coronagraph: laboratory system validation,” Publ. Astron. Soc. Pac. 122, 71–84 (2010).
[CrossRef]

Traub, W.

P. Borde and W. Traub, “High-contrast imaging from space: speckle nulling in a low aberration regime,” Appl. Phys. 638, 488–498 (2006).

Trauger, J.

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

J. Trauger, C. Burrows, B. Gordon, J. Green, A. Lowman, D. Moody, A. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

Vogel, C.

C. Blain, R. Conan, C. Bradley, O. Guyon, and C. Vogel, “Characterisation of the influence function non-additivities for a 1024-actuator mems deformable mirror,” in Proceedings of the 1st AO for ELT Conference (EDP, 2010), paper 06009.

White, V.

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

Wilson, D.

J. Trauger, C. Burrows, B. Gordon, J. Green, A. Lowman, D. Moody, A. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

Yu, J.

F. Malbet, J. Yu, and M. Shao, “High-dynamic-range imaging using a deformable mirror for space coronography,” Publ. Astron. Soc. Pac. 107, 386–398 (1995).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. (1)

P. Borde and W. Traub, “High-contrast imaging from space: speckle nulling in a low aberration regime,” Appl. Phys. 638, 488–498 (2006).

Opt. Express (1)

Proc. SPIE (5)

J. Trauger, C. Burrows, B. Gordon, J. Green, A. Lowman, D. Moody, A. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

A. Give’on, B. Kern, S. Shaklan, D. Moody, and L. Pueyo, “Broadband wavefront correction algorithm for high-contrast imaging systems,” Proc. SPIE 6691, 66910A (2007).
[CrossRef]

A. Give’on, B. Kern, and S. Shaklan, “Pair-wise, deformable mirror, image plane-based diversity electric field estimation for high contrast coronagraphy,” Proc. SPIE 8151, 815110 (2011).
[CrossRef]

S. Shaklan, L. Marchen, J. Krist, and M. Rud, “Stability error budget for an aggressive coronagraph on a 3.8 m telescope,” Proc. SPIE 8151, 815109 (2011).
[CrossRef]

R. Belikov, A. Give’on, B. Kern, E. Cady, M. Carr, S. Shaklan, K. Balasubramanian, V. White, P. Echternach, M. Dickie, J. Trauger, A. Kuhnert, and N. J. Kasdin, “Demonstration of high contrast in 10% broadband light with the shaped pupil coronagraph,” Proc. SPIE 6693, 66930Y (2007).
[CrossRef]

Publ. Astron. Soc. Pac. (2)

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Figures (9)

Fig. 1.
Fig. 1.

Optical layout of the Princeton HCIL. Collimated light is incident on two DMs in series, which propagates through a Shaped pupil, the core of the PSF is removed with an image plane mask, and the 90° search areas are reimaged on the final camera.

Fig. 2.
Fig. 2.

(a) Shaped pupil. (b) Ideal PSF from a system using a shaped-pupil coronagraph. (c) Shaped pupil with aberrations generated by Fresnel propagating the measured nominal shapes of the DMs to the pupil plane. Other sources of aberrations are not included because they have not been measured. (d) PSF of the shaped pupil with the simulated aberrations. The figures are in a log scale, and the log of contrast is shown in the colorbars.

Fig. 3.
Fig. 3.

Experimental results of sequential DM correction using the DM diversity estimation algorithm. The dark hole is a square opening from 710×22λ/D on both sides of the image plane. (a) Aberrated image. (b) Contrast plot. (c) Corrected image. Image units are log(contrast).

Fig. 4.
Fig. 4.

Block diagram of a standard FPWC control loop. At time step k, only the intensity measurements, zk, provide any feedback to estimate the current state, xk. The dashed lines show additional feedback included in this paper from the prior electric field (or state) estimate, x^k, and the control signal, uk.

Fig. 5.
Fig. 5.

Experimental results of sequential DM correction using the discrete time extended Kalman filter with 4 image pairs to build the image plane measurement, zk. The dark hole is a square opening from 710×22λ/D on both sides of the image plane. (a) Aberrated image. (b) Contrast plot. (c) Corrected image. Image units are log(contrast).

Fig. 6.
Fig. 6.

Experimental results of sequential DM correction using the discrete time extended Kalman filter with 3 image pairs to build the image plane measurement, zk. The dark hole is a square opening from 710×22λ/D on both sides of the image plane. (a) Aberrated image. (b) Contrast plot. (c) Corrected image. Image units are log(contrast).

Fig. 7.
Fig. 7.

Experimental results of sequential DM correction using the discrete time extended Kalman filter with 2 image pairs to build the image plane measurement, zk. The dark hole is a square opening from (710)×(22)λ/D on both sides of the image plane. (a) Aberrated image. (b) Contrast plot. (c) Corrected image. Image units are log(contrast).

Fig. 8.
Fig. 8.

Experimental results of sequential DM correction using the discrete time extended Kalman filter with one image pair to build the image plane measurement, zk. The dark hole is a square opening from (710)×(22)λ/D on both sides of the image plane. (a) Aberrated image. (b) Contrast plot. (c) Corrected image. Image units are log(contrast).

Fig. 9.
Fig. 9.

Experimental results of sequential DM correction using the discrete time extended Kalman filter with the control effect and it’s conjugate shape used as the only probe pair for the measurement update, zk. The dark hole is a square opening from (710)×(22)λ/D on both sides of the image plane. (a) Aberrated image. (b) Contrast plot. (c) Corrected image. Image units are log(contrast).

Tables (2)

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Table 1. Definition of All Propagation Matricesa

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Table 2. Definition of All Noise Matricesa

Equations (56)

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E0(u,v)=A(u,v)(1+g(u,v))eiϕ˜(u,v).
E0(u,v)A(u,v)eiϕ0(1+g(u,v)+iϕ(u,v)).
Eim(x,y)=C{E0(u,v)},
=C{A(u,v)eiϕ0}+C{A(u,v)eiϕ0g(u,v)}+iC{A(u,v)eiϕ0ϕ(u,v)}.
Iim(x,y)=|C{A(u,v)eiϕ0}+C{A(u,v)eiϕ0g(u,v)}+iC{A(u,v)eiϕ0ϕ(u,v)}|2.
Iim=C{Aϕ},C{Aϕ}+2R{C{A(1+g)},iC{Aϕ}}+C{A(1+g)},C{A(1+g)}.
ϕ(u,v)=2πλ0H(x,y).
ϕ(u,v)=2πλ0q=1Nacthq(u,v).
ϕ(u,v)=2πλ0q=1Nactaqfq(u,v),
G=C{Af}[Npix×Nact].
C{Aϕ},C{Aϕ}=uTG*Gu,
IDH=4π2λ2uTMu+4πλuTI{b}+d,
M=C{Af},C{Af}=G*G,
b=C{A(1+g)},C{Af}=G*C{A(1+g)},
d=C{A(1+g)},C{A(1+g)}=C{A(1+g)}*C{A(1+g)}.
minimizek=1Nak2=uTu,subject toIDH10C.
J=uT(I+μ4π2λ2M)u+μ4πλuTI{b}+μ(d10C).
uopt=μ(λ2πI+μ2πλM)1I{b}.
I+I=4R{C{A(1+g)},iC{Aϕ}}.
zk=[I1,k+I1,kIj,k+Ij,k].
Hk=4[R{C{Aϕ1,k}}I{C{Aϕ1,k}}R{C{Aϕj,k}}I{C{Aϕj,k}}].
xk=[R{C{Agk}}I{C{Agk}}].
zk=Hkxk+nk.
J=12[Hkx^kzk]TRk1[Hkx^kzk],
Rk=E[nknkT].
x^k=(HkTRk1Hk)1HkTRk1zk.
Rk=σk2I,
x^k=(HkTHk)1HkTzk.
Pk=E[(xkx^k)(xkx^k)T],
=(HkTRk1Hk)1.
ϕ(u,v)=sinc(wxu)sinc(wyv)cos(au+θu)cos(bv+θv),
J=12[x^kx^k()]TPk()1[x^kx^k()]+12[Hkx^kzk]TRk1[Hkx^kzk].
J=12[x^kx^k()Hkx^kzk]T[Pk()00Rk]1[x^kx^k()Hkx^kzk],
=12(H˜kx^kz˜k)TR˜k1(H˜kx^kz˜k),
H˜k=[IHk],
z˜k=[x^k()zk],
R˜k=[Pk()00Rk].
x^k(+)=x^k()+Pk()HkT[HkPk()HkT+Rk]1[zkHkx^k()].
Kk=Pk()HkT[HkPk()HkT+Rk]1.
Pk(+)=E[(x^k(+)xk)(x^k(+)xk)T],
Pk(+)=[Pk()1+HkTRk1Hk]1.
x^k()=Φk1x^k1(+)+Γk1uk1+Λk1wk1.
x^k()=Φk1x^k1(+)+Γk1uk1.
Pk()=Φk1Pk1(+)Φk1T+Qk1.
x^k()=Φk1x^k1(+)+Γk1uk1,
Pk()=Φk1Pk1(+)Φk1T+Qk1,
Kk=Pk()HkT[HkPk()HkT+Rk]1,
x^k(+)=x^k()+Kk[zkHkx^k()],
Pk(+)=[Pk()1+HkTRk1Hk]1.
x^p,k()=x^p1,k(+),
Pp,k()=Φp1,kPp1,k(+)Φp1,kT+Qp1,k,
Kp,k=Pp,k()Hp,kT[Hp,kPp,k()Hp,kT+Rp,k]1,
x^p,k(+)=x^p,k()+Kp,k[zp,kHp,kx^p,k()],
Pp,k(+)=[Pp,k()1+Hp,kTRp,k1Hp,k]1.
Q=σu2ΓIΓT.
R=σCCD2I00INpairs×Npairs,

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