Abstract

An external occulter is used as a means to suppress starlight and enable the observation of faint, Earth-like planets. A recent paper in this journal [J. Opt. Soc. Am. A 28, 1668 (2011) [CrossRef]  ] suggested there were unrecognized limits on starlight intensity suppression with an external occulter. It claimed that, at the level of intensity reduction needed, tips of petal-shaped occulters are too small to be manufactured. We present analysis of that publication’s apodization function and show that it is mathematically distinct from the external occulter apodization functions being discussed in the literature. Their broad conclusion that the tips cannot be built is therefore invalid. They suggest that transmitting screens might be superior but do not explain why. We show their transmission function is substantially similar to those in use for the last five years and therefore may not represent an advance in the field.

© 2012 Optical Society of America

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References

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  4. N. J. Kasdin, E. Cady, P. Dumont, P. D. Lisman, S. Shaklan, R. Soummer, D. Spergel, and R. J. Vanderbei, “Occulter design for THEIA,” Proc. SPIE 7440744005 (2009).
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  6. T. Glassman, A. S. Lo, J. Arenberg, W. Cash, and C. Noecker, “Starshade scaling relations,” Proc. SPIE 7440, 744013 (2009).
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  7. D. Savransky, D. N. Spergel, N. J. Kasdin, E. Cady, P. D. Lisman, S. Pravdo, S. Shaklan, and Y. Fujii, “Occulting ozone observatory science overview,” Proc. SPIE 7731, 77312H (2010).
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  15. D. Leviton, W. Cash, B. Gleeson, M. Kaiser, S. Levine, A. Lo, E. Schindhelm, and A. Shipley, “White-light demonstration of one hundred parts per billion irradiance suppression in air by new starshade occulters,” Proc. SPIE 6687-1B, 1–12 (2007).
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  25. M. Janson, “Celestial exoplanet survey occulter: a concept for direct imaging of extrasolar Earth-like planets from the ground,” Publ. Astron. Soc. Pac. 119, 214–227 (2007).
    [CrossRef]

2011

2010

D. Savransky, D. N. Spergel, N. J. Kasdin, E. Cady, P. D. Lisman, S. Pravdo, S. Shaklan, and Y. Fujii, “Occulting ozone observatory science overview,” Proc. SPIE 7731, 77312H (2010).
[CrossRef]

S. B. Shaklan, M. C. Noecker, T. Glassman, A. Lo, P. J. Dumont, N. J. Kasdin, E. J. Cady, R. Vanderbei, and P. R. Lawson, “Error budgeting and tolerancing of starshades for exoplanet detection,” Proc. SPIE 7731, 773112G (2010).

T. Glassman, A. Johnson, A. S. Lo, D. Dailey, H. Shelton, and J. Vogrin, “Error analysis on the NWO starshade,” Proc. SPIE 7731, 773150 (2010).

A. S. Lo, T. Glassman, D. Dailey, K. Sterk, J. Green, W. Cash, and R. Soummer, “New Worlds Probe,” Proc. SPIE 7731, 77312E (2010).

R. Samuele, R. Varshneya, T. Johnson, A. Johnson, and T. Glassman, “Progress at the starshade testbed at Northrop Grumman Aerospace Systems: comparisons with computer simulations,” Proc. SPIE 7731, 773151 (2010).

2009

N. J. Kasdin, E. Cady, P. Dumont, P. D. Lisman, S. Shaklan, R. Soummer, D. Spergel, and R. J. Vanderbei, “Occulter design for THEIA,” Proc. SPIE 7440744005 (2009).
[CrossRef]

W. Cash and 48 co-authors of the New Worlds Study Team, “The New Worlds Observer: the astrophysics strategic mission concept study,” Proc. SPIE 7436, 743606, DOI:10.1117/12.827486 (2009).
[CrossRef]

T. Glassman, A. S. Lo, J. Arenberg, W. Cash, and C. Noecker, “Starshade scaling relations,” Proc. SPIE 7440, 744013 (2009).
[CrossRef]

2007

R. J. Vanderbei, E. Cady, and N. J. Kasdin, “Optimal occulter design for finding extrasolar planets,” Astrophys. J. 665, 794–798 (2007).
[CrossRef]

D. Leviton, W. Cash, B. Gleeson, M. Kaiser, S. Levine, A. Lo, E. Schindhelm, and A. Shipley, “White-light demonstration of one hundred parts per billion irradiance suppression in air by new starshade occulters,” Proc. SPIE 6687-1B, 1–12 (2007).

E. Schindhelm, A. Shipley, P. Oakley, W. Leviton, D. Cash, and G. Card, “Laboratory studies of petal-shaped occulters,” Proc. SPIE 6693, 669305 (2007).

M. Janson, “Celestial exoplanet survey occulter: a concept for direct imaging of extrasolar Earth-like planets from the ground,” Publ. Astron. Soc. Pac. 119, 214–227 (2007).
[CrossRef]

2006

W. Cash, “Detection of Earth-like planets around nearby stars using a petal-shaped occulter,” Nature 442, 51–53 (2006).
[CrossRef]

2002

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

2000

C. J. Copi and G. D. Starkman, “The Big Occulting Steerable Satellite (BOSS),” Astrophys. J. 532, 581–592 (2000).
[CrossRef]

1999

A. Dubra and J. Ferrari, “Diffracted field by an arbitrary aperture,” Am. J. Phys. 67, 87–92 (1999).
[CrossRef]

1998

G. D. Starkman and C. J. Copi, “The Improved Resolution and Image Separation (IRIS) satellite: astronomical observations with a large occulting satellite,” Proc. SPIE 3356, 608–621 (1998).
[CrossRef]

1985

C. Marchal, “Concept of a space telescope able to see the planets and even the satellites around the nearest stars,” Acta Astronaut. 12, 195–201 (1985).
[CrossRef]

1962

L. Spitzer, “The beginnings and future of space astronomy,” Am. Sci. 50, 473–484 (1962).

Arenberg, J.

T. Glassman, A. S. Lo, J. Arenberg, W. Cash, and C. Noecker, “Starshade scaling relations,” Proc. SPIE 7440, 744013 (2009).
[CrossRef]

Blandford, R

R Blandford, New Worlds, New Horizons in Astronomy and Astrophysics (National Academies, 2010).

Born, M.

M. Born and E. Wolf, Principles of Optics7th ed. (Cambridge University, 1999).

Bruhweiler, F.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

I. Jordan, A. Schultz, H. Hart, F. Bruhweiler, D. Fraquelli, F. Hamilton, and J. Hershey, “UMBRAS: design of a free-flying occulter for space telescopes,” presented at the AIAA Space 2000 Conference and Exposition, AIAA 2000-5230, Long Beach, California, USA, 19–21September2000.

Burns, R. D.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Cady, E.

D. Savransky, D. N. Spergel, N. J. Kasdin, E. Cady, P. D. Lisman, S. Pravdo, S. Shaklan, and Y. Fujii, “Occulting ozone observatory science overview,” Proc. SPIE 7731, 77312H (2010).
[CrossRef]

N. J. Kasdin, E. Cady, P. Dumont, P. D. Lisman, S. Shaklan, R. Soummer, D. Spergel, and R. J. Vanderbei, “Occulter design for THEIA,” Proc. SPIE 7440744005 (2009).
[CrossRef]

R. J. Vanderbei, E. Cady, and N. J. Kasdin, “Optimal occulter design for finding extrasolar planets,” Astrophys. J. 665, 794–798 (2007).
[CrossRef]

Cady, E. J.

S. B. Shaklan, M. C. Noecker, T. Glassman, A. Lo, P. J. Dumont, N. J. Kasdin, E. J. Cady, R. Vanderbei, and P. R. Lawson, “Error budgeting and tolerancing of starshades for exoplanet detection,” Proc. SPIE 7731, 773112G (2010).

Card, G.

E. Schindhelm, A. Shipley, P. Oakley, W. Leviton, D. Cash, and G. Card, “Laboratory studies of petal-shaped occulters,” Proc. SPIE 6693, 669305 (2007).

Carpenter, K. G.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Cash, D.

E. Schindhelm, A. Shipley, P. Oakley, W. Leviton, D. Cash, and G. Card, “Laboratory studies of petal-shaped occulters,” Proc. SPIE 6693, 669305 (2007).

Cash, W.

W. Cash, “Analytic modeling of starshades,” Astrophys. J. 738, 76–88 (2011).
[CrossRef]

A. S. Lo, T. Glassman, D. Dailey, K. Sterk, J. Green, W. Cash, and R. Soummer, “New Worlds Probe,” Proc. SPIE 7731, 77312E (2010).

W. Cash and 48 co-authors of the New Worlds Study Team, “The New Worlds Observer: the astrophysics strategic mission concept study,” Proc. SPIE 7436, 743606, DOI:10.1117/12.827486 (2009).
[CrossRef]

T. Glassman, A. S. Lo, J. Arenberg, W. Cash, and C. Noecker, “Starshade scaling relations,” Proc. SPIE 7440, 744013 (2009).
[CrossRef]

D. Leviton, W. Cash, B. Gleeson, M. Kaiser, S. Levine, A. Lo, E. Schindhelm, and A. Shipley, “White-light demonstration of one hundred parts per billion irradiance suppression in air by new starshade occulters,” Proc. SPIE 6687-1B, 1–12 (2007).

W. Cash, “Detection of Earth-like planets around nearby stars using a petal-shaped occulter,” Nature 442, 51–53 (2006).
[CrossRef]

Cheng, K.-P.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Copi, C. J.

C. J. Copi and G. D. Starkman, “The Big Occulting Steerable Satellite (BOSS),” Astrophys. J. 532, 581–592 (2000).
[CrossRef]

G. D. Starkman and C. J. Copi, “The Improved Resolution and Image Separation (IRIS) satellite: astronomical observations with a large occulting satellite,” Proc. SPIE 3356, 608–621 (1998).
[CrossRef]

Dailey, D.

T. Glassman, A. Johnson, A. S. Lo, D. Dailey, H. Shelton, and J. Vogrin, “Error analysis on the NWO starshade,” Proc. SPIE 7731, 773150 (2010).

A. S. Lo, T. Glassman, D. Dailey, K. Sterk, J. Green, W. Cash, and R. Soummer, “New Worlds Probe,” Proc. SPIE 7731, 77312E (2010).

DiSanti, M.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Dubra, A.

A. Dubra and J. Ferrari, “Diffracted field by an arbitrary aperture,” Am. J. Phys. 67, 87–92 (1999).
[CrossRef]

Dumont, P.

N. J. Kasdin, E. Cady, P. Dumont, P. D. Lisman, S. Shaklan, R. Soummer, D. Spergel, and R. J. Vanderbei, “Occulter design for THEIA,” Proc. SPIE 7440744005 (2009).
[CrossRef]

Dumont, P. J.

S. B. Shaklan, M. C. Noecker, T. Glassman, A. Lo, P. J. Dumont, N. J. Kasdin, E. J. Cady, R. Vanderbei, and P. R. Lawson, “Error budgeting and tolerancing of starshades for exoplanet detection,” Proc. SPIE 7731, 773112G (2010).

Fadali, M. S.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Ferrari, J.

A. Dubra and J. Ferrari, “Diffracted field by an arbitrary aperture,” Am. J. Phys. 67, 87–92 (1999).
[CrossRef]

Fraquelli, D.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

I. Jordan, A. Schultz, H. Hart, F. Bruhweiler, D. Fraquelli, F. Hamilton, and J. Hershey, “UMBRAS: design of a free-flying occulter for space telescopes,” presented at the AIAA Space 2000 Conference and Exposition, AIAA 2000-5230, Long Beach, California, USA, 19–21September2000.

Fujii, Y.

D. Savransky, D. N. Spergel, N. J. Kasdin, E. Cady, P. D. Lisman, S. Pravdo, S. Shaklan, and Y. Fujii, “Occulting ozone observatory science overview,” Proc. SPIE 7731, 77312H (2010).
[CrossRef]

Glassman, T.

T. Glassman, A. Johnson, A. S. Lo, D. Dailey, H. Shelton, and J. Vogrin, “Error analysis on the NWO starshade,” Proc. SPIE 7731, 773150 (2010).

A. S. Lo, T. Glassman, D. Dailey, K. Sterk, J. Green, W. Cash, and R. Soummer, “New Worlds Probe,” Proc. SPIE 7731, 77312E (2010).

R. Samuele, R. Varshneya, T. Johnson, A. Johnson, and T. Glassman, “Progress at the starshade testbed at Northrop Grumman Aerospace Systems: comparisons with computer simulations,” Proc. SPIE 7731, 773151 (2010).

S. B. Shaklan, M. C. Noecker, T. Glassman, A. Lo, P. J. Dumont, N. J. Kasdin, E. J. Cady, R. Vanderbei, and P. R. Lawson, “Error budgeting and tolerancing of starshades for exoplanet detection,” Proc. SPIE 7731, 773112G (2010).

T. Glassman, A. S. Lo, J. Arenberg, W. Cash, and C. Noecker, “Starshade scaling relations,” Proc. SPIE 7440, 744013 (2009).
[CrossRef]

Gleeson, B.

D. Leviton, W. Cash, B. Gleeson, M. Kaiser, S. Levine, A. Lo, E. Schindhelm, and A. Shipley, “White-light demonstration of one hundred parts per billion irradiance suppression in air by new starshade occulters,” Proc. SPIE 6687-1B, 1–12 (2007).

Green, J.

A. S. Lo, T. Glassman, D. Dailey, K. Sterk, J. Green, W. Cash, and R. Soummer, “New Worlds Probe,” Proc. SPIE 7731, 77312E (2010).

Hamilton, F.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

I. Jordan, A. Schultz, H. Hart, F. Bruhweiler, D. Fraquelli, F. Hamilton, and J. Hershey, “UMBRAS: design of a free-flying occulter for space telescopes,” presented at the AIAA Space 2000 Conference and Exposition, AIAA 2000-5230, Long Beach, California, USA, 19–21September2000.

Hart, H.

I. Jordan, A. Schultz, H. Hart, F. Bruhweiler, D. Fraquelli, F. Hamilton, and J. Hershey, “UMBRAS: design of a free-flying occulter for space telescopes,” presented at the AIAA Space 2000 Conference and Exposition, AIAA 2000-5230, Long Beach, California, USA, 19–21September2000.

Hart, H. M.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Hershey, J.

I. Jordan, A. Schultz, H. Hart, F. Bruhweiler, D. Fraquelli, F. Hamilton, and J. Hershey, “UMBRAS: design of a free-flying occulter for space telescopes,” presented at the AIAA Space 2000 Conference and Exposition, AIAA 2000-5230, Long Beach, California, USA, 19–21September2000.

Hollis, J. M.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Janson, M.

M. Janson, “Celestial exoplanet survey occulter: a concept for direct imaging of extrasolar Earth-like planets from the ground,” Publ. Astron. Soc. Pac. 119, 214–227 (2007).
[CrossRef]

Johnson, A.

T. Glassman, A. Johnson, A. S. Lo, D. Dailey, H. Shelton, and J. Vogrin, “Error analysis on the NWO starshade,” Proc. SPIE 7731, 773150 (2010).

R. Samuele, R. Varshneya, T. Johnson, A. Johnson, and T. Glassman, “Progress at the starshade testbed at Northrop Grumman Aerospace Systems: comparisons with computer simulations,” Proc. SPIE 7731, 773151 (2010).

Johnson, T.

R. Samuele, R. Varshneya, T. Johnson, A. Johnson, and T. Glassman, “Progress at the starshade testbed at Northrop Grumman Aerospace Systems: comparisons with computer simulations,” Proc. SPIE 7731, 773151 (2010).

Jordan, I.

I. Jordan, A. Schultz, H. Hart, F. Bruhweiler, D. Fraquelli, F. Hamilton, and J. Hershey, “UMBRAS: design of a free-flying occulter for space telescopes,” presented at the AIAA Space 2000 Conference and Exposition, AIAA 2000-5230, Long Beach, California, USA, 19–21September2000.

Jordan, I. J. E.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Kaiser, M.

D. Leviton, W. Cash, B. Gleeson, M. Kaiser, S. Levine, A. Lo, E. Schindhelm, and A. Shipley, “White-light demonstration of one hundred parts per billion irradiance suppression in air by new starshade occulters,” Proc. SPIE 6687-1B, 1–12 (2007).

Kasdin, N. J.

S. B. Shaklan, M. C. Noecker, T. Glassman, A. Lo, P. J. Dumont, N. J. Kasdin, E. J. Cady, R. Vanderbei, and P. R. Lawson, “Error budgeting and tolerancing of starshades for exoplanet detection,” Proc. SPIE 7731, 773112G (2010).

D. Savransky, D. N. Spergel, N. J. Kasdin, E. Cady, P. D. Lisman, S. Pravdo, S. Shaklan, and Y. Fujii, “Occulting ozone observatory science overview,” Proc. SPIE 7731, 77312H (2010).
[CrossRef]

N. J. Kasdin, E. Cady, P. Dumont, P. D. Lisman, S. Shaklan, R. Soummer, D. Spergel, and R. J. Vanderbei, “Occulter design for THEIA,” Proc. SPIE 7440744005 (2009).
[CrossRef]

R. J. Vanderbei, E. Cady, and N. J. Kasdin, “Optimal occulter design for finding extrasolar planets,” Astrophys. J. 665, 794–798 (2007).
[CrossRef]

Kochte, M.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Lawson, P. R.

S. B. Shaklan, M. C. Noecker, T. Glassman, A. Lo, P. J. Dumont, N. J. Kasdin, E. J. Cady, R. Vanderbei, and P. R. Lawson, “Error budgeting and tolerancing of starshades for exoplanet detection,” Proc. SPIE 7731, 773112G (2010).

Leitner, J.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Levine, S.

D. Leviton, W. Cash, B. Gleeson, M. Kaiser, S. Levine, A. Lo, E. Schindhelm, and A. Shipley, “White-light demonstration of one hundred parts per billion irradiance suppression in air by new starshade occulters,” Proc. SPIE 6687-1B, 1–12 (2007).

Leviton, D.

D. Leviton, W. Cash, B. Gleeson, M. Kaiser, S. Levine, A. Lo, E. Schindhelm, and A. Shipley, “White-light demonstration of one hundred parts per billion irradiance suppression in air by new starshade occulters,” Proc. SPIE 6687-1B, 1–12 (2007).

Leviton, W.

E. Schindhelm, A. Shipley, P. Oakley, W. Leviton, D. Cash, and G. Card, “Laboratory studies of petal-shaped occulters,” Proc. SPIE 6693, 669305 (2007).

Lisman, P. D.

D. Savransky, D. N. Spergel, N. J. Kasdin, E. Cady, P. D. Lisman, S. Pravdo, S. Shaklan, and Y. Fujii, “Occulting ozone observatory science overview,” Proc. SPIE 7731, 77312H (2010).
[CrossRef]

N. J. Kasdin, E. Cady, P. Dumont, P. D. Lisman, S. Shaklan, R. Soummer, D. Spergel, and R. J. Vanderbei, “Occulter design for THEIA,” Proc. SPIE 7440744005 (2009).
[CrossRef]

Lo, A.

S. B. Shaklan, M. C. Noecker, T. Glassman, A. Lo, P. J. Dumont, N. J. Kasdin, E. J. Cady, R. Vanderbei, and P. R. Lawson, “Error budgeting and tolerancing of starshades for exoplanet detection,” Proc. SPIE 7731, 773112G (2010).

D. Leviton, W. Cash, B. Gleeson, M. Kaiser, S. Levine, A. Lo, E. Schindhelm, and A. Shipley, “White-light demonstration of one hundred parts per billion irradiance suppression in air by new starshade occulters,” Proc. SPIE 6687-1B, 1–12 (2007).

Lo, A. S.

T. Glassman, A. Johnson, A. S. Lo, D. Dailey, H. Shelton, and J. Vogrin, “Error analysis on the NWO starshade,” Proc. SPIE 7731, 773150 (2010).

A. S. Lo, T. Glassman, D. Dailey, K. Sterk, J. Green, W. Cash, and R. Soummer, “New Worlds Probe,” Proc. SPIE 7731, 77312E (2010).

T. Glassman, A. S. Lo, J. Arenberg, W. Cash, and C. Noecker, “Starshade scaling relations,” Proc. SPIE 7440, 744013 (2009).
[CrossRef]

Lyon, R. G.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Marchal, C.

C. Marchal, “Concept of a space telescope able to see the planets and even the satellites around the nearest stars,” Acta Astronaut. 12, 195–201 (1985).
[CrossRef]

Miskey, C.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Noecker, C.

T. Glassman, A. S. Lo, J. Arenberg, W. Cash, and C. Noecker, “Starshade scaling relations,” Proc. SPIE 7440, 744013 (2009).
[CrossRef]

Noecker, M. C.

S. B. Shaklan, M. C. Noecker, T. Glassman, A. Lo, P. J. Dumont, N. J. Kasdin, E. J. Cady, R. Vanderbei, and P. R. Lawson, “Error budgeting and tolerancing of starshades for exoplanet detection,” Proc. SPIE 7731, 773112G (2010).

Oakley, P.

E. Schindhelm, A. Shipley, P. Oakley, W. Leviton, D. Cash, and G. Card, “Laboratory studies of petal-shaped occulters,” Proc. SPIE 6693, 669305 (2007).

Pravdo, S.

D. Savransky, D. N. Spergel, N. J. Kasdin, E. Cady, P. D. Lisman, S. Pravdo, S. Shaklan, and Y. Fujii, “Occulting ozone observatory science overview,” Proc. SPIE 7731, 77312H (2010).
[CrossRef]

Rodrigue, M.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Samuele, R.

R. Samuele, R. Varshneya, T. Johnson, A. Johnson, and T. Glassman, “Progress at the starshade testbed at Northrop Grumman Aerospace Systems: comparisons with computer simulations,” Proc. SPIE 7731, 773151 (2010).

Savransky, D.

D. Savransky, D. N. Spergel, N. J. Kasdin, E. Cady, P. D. Lisman, S. Pravdo, S. Shaklan, and Y. Fujii, “Occulting ozone observatory science overview,” Proc. SPIE 7731, 77312H (2010).
[CrossRef]

Schindhelm, E.

E. Schindhelm, A. Shipley, P. Oakley, W. Leviton, D. Cash, and G. Card, “Laboratory studies of petal-shaped occulters,” Proc. SPIE 6693, 669305 (2007).

D. Leviton, W. Cash, B. Gleeson, M. Kaiser, S. Levine, A. Lo, E. Schindhelm, and A. Shipley, “White-light demonstration of one hundred parts per billion irradiance suppression in air by new starshade occulters,” Proc. SPIE 6687-1B, 1–12 (2007).

Schultz, A.

I. Jordan, A. Schultz, H. Hart, F. Bruhweiler, D. Fraquelli, F. Hamilton, and J. Hershey, “UMBRAS: design of a free-flying occulter for space telescopes,” presented at the AIAA Space 2000 Conference and Exposition, AIAA 2000-5230, Long Beach, California, USA, 19–21September2000.

Schultz, A. B.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Shaklan, S.

D. Savransky, D. N. Spergel, N. J. Kasdin, E. Cady, P. D. Lisman, S. Pravdo, S. Shaklan, and Y. Fujii, “Occulting ozone observatory science overview,” Proc. SPIE 7731, 77312H (2010).
[CrossRef]

N. J. Kasdin, E. Cady, P. Dumont, P. D. Lisman, S. Shaklan, R. Soummer, D. Spergel, and R. J. Vanderbei, “Occulter design for THEIA,” Proc. SPIE 7440744005 (2009).
[CrossRef]

Shaklan, S. B.

S. B. Shaklan, M. C. Noecker, T. Glassman, A. Lo, P. J. Dumont, N. J. Kasdin, E. J. Cady, R. Vanderbei, and P. R. Lawson, “Error budgeting and tolerancing of starshades for exoplanet detection,” Proc. SPIE 7731, 773112G (2010).

Shelton, H.

T. Glassman, A. Johnson, A. S. Lo, D. Dailey, H. Shelton, and J. Vogrin, “Error analysis on the NWO starshade,” Proc. SPIE 7731, 773150 (2010).

Shipley, A.

D. Leviton, W. Cash, B. Gleeson, M. Kaiser, S. Levine, A. Lo, E. Schindhelm, and A. Shipley, “White-light demonstration of one hundred parts per billion irradiance suppression in air by new starshade occulters,” Proc. SPIE 6687-1B, 1–12 (2007).

E. Schindhelm, A. Shipley, P. Oakley, W. Leviton, D. Cash, and G. Card, “Laboratory studies of petal-shaped occulters,” Proc. SPIE 6693, 669305 (2007).

Shiri, S.

Skelton, D.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Soummer, R.

A. S. Lo, T. Glassman, D. Dailey, K. Sterk, J. Green, W. Cash, and R. Soummer, “New Worlds Probe,” Proc. SPIE 7731, 77312E (2010).

N. J. Kasdin, E. Cady, P. Dumont, P. D. Lisman, S. Shaklan, R. Soummer, D. Spergel, and R. J. Vanderbei, “Occulter design for THEIA,” Proc. SPIE 7440744005 (2009).
[CrossRef]

Spergel, D.

N. J. Kasdin, E. Cady, P. Dumont, P. D. Lisman, S. Shaklan, R. Soummer, D. Spergel, and R. J. Vanderbei, “Occulter design for THEIA,” Proc. SPIE 7440744005 (2009).
[CrossRef]

Spergel, D. N.

D. Savransky, D. N. Spergel, N. J. Kasdin, E. Cady, P. D. Lisman, S. Pravdo, S. Shaklan, and Y. Fujii, “Occulting ozone observatory science overview,” Proc. SPIE 7731, 77312H (2010).
[CrossRef]

Spitzer, L.

L. Spitzer, “The beginnings and future of space astronomy,” Am. Sci. 50, 473–484 (1962).

Starin, S. R.

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

Starkman, G. D.

C. J. Copi and G. D. Starkman, “The Big Occulting Steerable Satellite (BOSS),” Astrophys. J. 532, 581–592 (2000).
[CrossRef]

G. D. Starkman and C. J. Copi, “The Improved Resolution and Image Separation (IRIS) satellite: astronomical observations with a large occulting satellite,” Proc. SPIE 3356, 608–621 (1998).
[CrossRef]

Sterk, K.

A. S. Lo, T. Glassman, D. Dailey, K. Sterk, J. Green, W. Cash, and R. Soummer, “New Worlds Probe,” Proc. SPIE 7731, 77312E (2010).

Vanderbei, R.

S. B. Shaklan, M. C. Noecker, T. Glassman, A. Lo, P. J. Dumont, N. J. Kasdin, E. J. Cady, R. Vanderbei, and P. R. Lawson, “Error budgeting and tolerancing of starshades for exoplanet detection,” Proc. SPIE 7731, 773112G (2010).

Vanderbei, R. J.

N. J. Kasdin, E. Cady, P. Dumont, P. D. Lisman, S. Shaklan, R. Soummer, D. Spergel, and R. J. Vanderbei, “Occulter design for THEIA,” Proc. SPIE 7440744005 (2009).
[CrossRef]

R. J. Vanderbei, E. Cady, and N. J. Kasdin, “Optimal occulter design for finding extrasolar planets,” Astrophys. J. 665, 794–798 (2007).
[CrossRef]

Varshneya, R.

R. Samuele, R. Varshneya, T. Johnson, A. Johnson, and T. Glassman, “Progress at the starshade testbed at Northrop Grumman Aerospace Systems: comparisons with computer simulations,” Proc. SPIE 7731, 773151 (2010).

Vogrin, J.

T. Glassman, A. Johnson, A. S. Lo, D. Dailey, H. Shelton, and J. Vogrin, “Error analysis on the NWO starshade,” Proc. SPIE 7731, 773150 (2010).

Wasylkiwskyj, W.

Wolf, E.

M. Born and E. Wolf, Principles of Optics7th ed. (Cambridge University, 1999).

Woodcock, G. R.

G. R. Woodcock, “Concept analysis and discussion: observation of extrasolar planets with an LST,” in Boeing contract study for NASA, Future Space Transportation Systems Analysis, NAS9-14323, D180-18501-2 (1974), Appendix D.

Acta Astronaut.

C. Marchal, “Concept of a space telescope able to see the planets and even the satellites around the nearest stars,” Acta Astronaut. 12, 195–201 (1985).
[CrossRef]

Am. J. Phys.

A. Dubra and J. Ferrari, “Diffracted field by an arbitrary aperture,” Am. J. Phys. 67, 87–92 (1999).
[CrossRef]

Am. Sci.

L. Spitzer, “The beginnings and future of space astronomy,” Am. Sci. 50, 473–484 (1962).

Astrophys. J.

W. Cash, “Analytic modeling of starshades,” Astrophys. J. 738, 76–88 (2011).
[CrossRef]

C. J. Copi and G. D. Starkman, “The Big Occulting Steerable Satellite (BOSS),” Astrophys. J. 532, 581–592 (2000).
[CrossRef]

R. J. Vanderbei, E. Cady, and N. J. Kasdin, “Optimal occulter design for finding extrasolar planets,” Astrophys. J. 665, 794–798 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Nature

W. Cash, “Detection of Earth-like planets around nearby stars using a petal-shaped occulter,” Nature 442, 51–53 (2006).
[CrossRef]

Proc. SPIE

G. D. Starkman and C. J. Copi, “The Improved Resolution and Image Separation (IRIS) satellite: astronomical observations with a large occulting satellite,” Proc. SPIE 3356, 608–621 (1998).
[CrossRef]

N. J. Kasdin, E. Cady, P. Dumont, P. D. Lisman, S. Shaklan, R. Soummer, D. Spergel, and R. J. Vanderbei, “Occulter design for THEIA,” Proc. SPIE 7440744005 (2009).
[CrossRef]

W. Cash and 48 co-authors of the New Worlds Study Team, “The New Worlds Observer: the astrophysics strategic mission concept study,” Proc. SPIE 7436, 743606, DOI:10.1117/12.827486 (2009).
[CrossRef]

T. Glassman, A. S. Lo, J. Arenberg, W. Cash, and C. Noecker, “Starshade scaling relations,” Proc. SPIE 7440, 744013 (2009).
[CrossRef]

D. Savransky, D. N. Spergel, N. J. Kasdin, E. Cady, P. D. Lisman, S. Pravdo, S. Shaklan, and Y. Fujii, “Occulting ozone observatory science overview,” Proc. SPIE 7731, 77312H (2010).
[CrossRef]

S. B. Shaklan, M. C. Noecker, T. Glassman, A. Lo, P. J. Dumont, N. J. Kasdin, E. J. Cady, R. Vanderbei, and P. R. Lawson, “Error budgeting and tolerancing of starshades for exoplanet detection,” Proc. SPIE 7731, 773112G (2010).

T. Glassman, A. Johnson, A. S. Lo, D. Dailey, H. Shelton, and J. Vogrin, “Error analysis on the NWO starshade,” Proc. SPIE 7731, 773150 (2010).

A. B. Schultz, I. J. E. Jordan, M. Kochte, D. Fraquelli, F. Bruhweiler, J. M. Hollis, K. G. Carpenter, R. G. Lyon, M. DiSanti, C. Miskey, J. Leitner, R. D. Burns, S. R. Starin, M. Rodrigue, M. S. Fadali, D. Skelton, H. M. Hart, F. Hamilton, and K.-P. Cheng, “UMBRAS: a matched occulter and telescope for imaging extrasolar planets,” Proc. SPIE 486054–61(2002).
[CrossRef]

A. S. Lo, T. Glassman, D. Dailey, K. Sterk, J. Green, W. Cash, and R. Soummer, “New Worlds Probe,” Proc. SPIE 7731, 77312E (2010).

D. Leviton, W. Cash, B. Gleeson, M. Kaiser, S. Levine, A. Lo, E. Schindhelm, and A. Shipley, “White-light demonstration of one hundred parts per billion irradiance suppression in air by new starshade occulters,” Proc. SPIE 6687-1B, 1–12 (2007).

E. Schindhelm, A. Shipley, P. Oakley, W. Leviton, D. Cash, and G. Card, “Laboratory studies of petal-shaped occulters,” Proc. SPIE 6693, 669305 (2007).

R. Samuele, R. Varshneya, T. Johnson, A. Johnson, and T. Glassman, “Progress at the starshade testbed at Northrop Grumman Aerospace Systems: comparisons with computer simulations,” Proc. SPIE 7731, 773151 (2010).

Publ. Astron. Soc. Pac.

M. Janson, “Celestial exoplanet survey occulter: a concept for direct imaging of extrasolar Earth-like planets from the ground,” Publ. Astron. Soc. Pac. 119, 214–227 (2007).
[CrossRef]

Other

I. Jordan, A. Schultz, H. Hart, F. Bruhweiler, D. Fraquelli, F. Hamilton, and J. Hershey, “UMBRAS: design of a free-flying occulter for space telescopes,” presented at the AIAA Space 2000 Conference and Exposition, AIAA 2000-5230, Long Beach, California, USA, 19–21September2000.

G. R. Woodcock, “Concept analysis and discussion: observation of extrasolar planets with an LST,” in Boeing contract study for NASA, Future Space Transportation Systems Analysis, NAS9-14323, D180-18501-2 (1974), Appendix D.

M. Born and E. Wolf, Principles of Optics7th ed. (Cambridge University, 1999).

R Blandford, New Worlds, New Horizons in Astronomy and Astrophysics (National Academies, 2010).

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Figures (4)

Fig. 1.
Fig. 1.

A petal is formed from an apodization function by making the half-width of the petal in angle vary as the apodization function.

Fig. 2.
Fig. 2.

Comparison between WS2011 and the Cash2006 apodization. Solid lines represent the Cash2006 apodization, and the dashed lines represent the WS2011 apodization function. (a) Plot of representative values of p. (b) Difference between the Cash2006 edges and the WS2011 edges, which show significant (0.16m) variation.

Fig. 3.
Fig. 3.

The WS2011 function truncates at the maximum value of ρ. Three values of p (dashed lines) are compared to the Cash apodization function (solid lines). This truncation is at least partially responsible for the low suppression values obtained by WS2011.

Fig. 4.
Fig. 4.

Comparison between WS2011 and a Vanderbei apodization. Subtle variations in the petal tips, shown in the inset, are not reproduced. These variations are key to high intensity suppression.

Equations (18)

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

I(0,rf)=1(2π)2|02πexp(iπ[ρ(φ)/R]2/rf)dφ|2,
θ=φ,k=k0,F=z,
I(0,rf)=1(2π)2|02πexp(ikρ22F)dθ|2.
E=12π02πexp(ikρ22F)dθ,
E=kiFeikF0A(ρ)exp(ikρ22F)ρdρ,
θ=πPNA(ρ)
ρ(θ)=A1(PNθπ).
ρ(φ)R=r0+1r0fmaxf(φ),
f(φ)=|ln(1+p)(πN)2(φπN)2+p(πN)2|1/m.
ρ(φ)R=r0+1r0fmax[ln(1+p)(πN)2(φπN)2+p(πN)2]1/m,
φ=πN±πN(1+p)exp{[(ρRr0)fmax1r0]m}p.
fmax=f(πN)=(ln1+pp)1/m,
φ=πN±πN(1+p)exp[(ρRr0RRr0)mln(1+pp)]p.
=0ρ<Rr0A(ρ)=1±(1+p)exp[(ρRr0RRr0)mln(1+pp)]pRr0ρR=1ρ<R.
E0=Rr0Reikρ22F1+pexp[(ρRr0RRr0)mln(1+pp)]1p1+pexp[(ρRr0RRr0)mln(1+pp)]ρdρ.
E01+pexp[12(RRr0RRr0)mln(1+pp)]=p.
φ=2πPN±1+p2πPNexp[2(ρab)m]p1+p.
φ=2πPN±122πPNexp[(ρab)m].

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