Abstract

We obtain an expression for the probability density function of partially developed speckles formed by light with an arbitrary degree of polarization. From the probability density we calculate the detection threshold corresponding to the 5σ confidence level of a normal distribution. We show that unpolarized light has an advantage in high contrast imaging for low ratios of the deterministic part of the point spread function to the halo, typical in coronagraphy.

© 2009 Optical Society of America

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References

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  1. C. Aime and R. Soummer, Astrophys. J. Lett. 612, L85 (2004).
    [CrossRef]
  2. S. Gladysz and J. Christou, Astrophys. J. 684, 1486 (2008).
    [CrossRef]
  3. C. Marois, D. Lafreniere, B. Macintosh, and R. Doyon, Astrophys. J. 673, 647 (2008).
    [CrossRef]
  4. J. Goodman, in Laser Speckle and Related Phenomana, 2nd ed., J.C.Dainty, ed. (Springer-Verlag, 1984).
  5. J. Goodman, Statistical Optics (Wiley Interscience, 1985).
  6. J. Kemp, G. Henson, C. Steiner, and E. Powell, Nature 326, 270 (1987).
    [CrossRef]
  7. J. Breckinridge and B. Oppenheimer, Astrophys. J. 600, 1091 (2004).
    [CrossRef]
  8. N. Yaitskova, J. Opt. Soc. Am. A 26, 59 (2009).
    [CrossRef]
  9. P. Steeger, T. Asakura, K. Zocha, and A. Fercher, J. Opt. Soc. Am. A 1, 677 (1984).
    [CrossRef]
  10. J. Ohtsubo and T. Asakura, Opt. Lett. 1, 98 (1977).
    [CrossRef] [PubMed]
  11. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

2009 (1)

2008 (2)

S. Gladysz and J. Christou, Astrophys. J. 684, 1486 (2008).
[CrossRef]

C. Marois, D. Lafreniere, B. Macintosh, and R. Doyon, Astrophys. J. 673, 647 (2008).
[CrossRef]

2004 (2)

J. Breckinridge and B. Oppenheimer, Astrophys. J. 600, 1091 (2004).
[CrossRef]

C. Aime and R. Soummer, Astrophys. J. Lett. 612, L85 (2004).
[CrossRef]

1987 (1)

J. Kemp, G. Henson, C. Steiner, and E. Powell, Nature 326, 270 (1987).
[CrossRef]

1984 (1)

1977 (1)

Abramowitz, M.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

Aime, C.

C. Aime and R. Soummer, Astrophys. J. Lett. 612, L85 (2004).
[CrossRef]

Asakura, T.

Breckinridge, J.

J. Breckinridge and B. Oppenheimer, Astrophys. J. 600, 1091 (2004).
[CrossRef]

Christou, J.

S. Gladysz and J. Christou, Astrophys. J. 684, 1486 (2008).
[CrossRef]

Doyon, R.

C. Marois, D. Lafreniere, B. Macintosh, and R. Doyon, Astrophys. J. 673, 647 (2008).
[CrossRef]

Fercher, A.

Gladysz, S.

S. Gladysz and J. Christou, Astrophys. J. 684, 1486 (2008).
[CrossRef]

Goodman, J.

J. Goodman, in Laser Speckle and Related Phenomana, 2nd ed., J.C.Dainty, ed. (Springer-Verlag, 1984).

J. Goodman, Statistical Optics (Wiley Interscience, 1985).

Henson, G.

J. Kemp, G. Henson, C. Steiner, and E. Powell, Nature 326, 270 (1987).
[CrossRef]

Kemp, J.

J. Kemp, G. Henson, C. Steiner, and E. Powell, Nature 326, 270 (1987).
[CrossRef]

Lafreniere, D.

C. Marois, D. Lafreniere, B. Macintosh, and R. Doyon, Astrophys. J. 673, 647 (2008).
[CrossRef]

Macintosh, B.

C. Marois, D. Lafreniere, B. Macintosh, and R. Doyon, Astrophys. J. 673, 647 (2008).
[CrossRef]

Marois, C.

C. Marois, D. Lafreniere, B. Macintosh, and R. Doyon, Astrophys. J. 673, 647 (2008).
[CrossRef]

Ohtsubo, J.

Oppenheimer, B.

J. Breckinridge and B. Oppenheimer, Astrophys. J. 600, 1091 (2004).
[CrossRef]

Powell, E.

J. Kemp, G. Henson, C. Steiner, and E. Powell, Nature 326, 270 (1987).
[CrossRef]

Soummer, R.

C. Aime and R. Soummer, Astrophys. J. Lett. 612, L85 (2004).
[CrossRef]

Steeger, P.

Stegun, I.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

Steiner, C.

J. Kemp, G. Henson, C. Steiner, and E. Powell, Nature 326, 270 (1987).
[CrossRef]

Yaitskova, N.

Zocha, K.

Astrophys. J. (3)

S. Gladysz and J. Christou, Astrophys. J. 684, 1486 (2008).
[CrossRef]

C. Marois, D. Lafreniere, B. Macintosh, and R. Doyon, Astrophys. J. 673, 647 (2008).
[CrossRef]

J. Breckinridge and B. Oppenheimer, Astrophys. J. 600, 1091 (2004).
[CrossRef]

Astrophys. J. Lett. (1)

C. Aime and R. Soummer, Astrophys. J. Lett. 612, L85 (2004).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature (1)

J. Kemp, G. Henson, C. Steiner, and E. Powell, Nature 326, 270 (1987).
[CrossRef]

Opt. Lett. (1)

Other (3)

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

J. Goodman, in Laser Speckle and Related Phenomana, 2nd ed., J.C.Dainty, ed. (Springer-Verlag, 1984).

J. Goodman, Statistical Optics (Wiley Interscience, 1985).

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Figures (3)

Fig. 1
Fig. 1

PDFs for different values of the degree of polarization when the DL PSF is equal to the halo.

Fig. 2
Fig. 2

Detection threshold as a function of the ratio between the DL PSF and the halo. Curves are shown for three different values of the degrees of polarization.

Fig. 3
Fig. 3

Detection threshold as a function of the degree of polarization in absence of the DL PSF.

Equations (10)

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I = I 1 + I 2 .
p ( I 1 ) = 1 H 1 exp ( I 1 + D 1 H 1 ) I 0 ( 2 I 1 D 1 H 1 ) ,
D 1 ( 2 ) = 1 2 ( 1 ± P ) | C ( w ) | 2 ,     H 1 ( 2 ) = 1 2 ( 1 ± P ) | S ( w ) | 2 ,
p 1 ( 2 ) ( x 1 ( 2 ) ) = 2 1 + r 1 ± P exp [ 2 x 1 ( 2 ) ( 1 + r ) 1 ± P r ] I 0 [ 2 2 x 1 ( 2 ) ( 1 + r ) r 1 ± P ] ,
Ξ 1 ( 2 ) ( z ) = exp [ r 1 i z 1 ± P 2 ( 1 + r ) r ] 1 1 i z 1 ± P 2 ( 1 + r ) ,
1 2 π ( α i z ) ( l + 1 ) ( β i z ) ( k + 1 ) exp ( i z x ) d z = exp ( α x ) x k + l + 1 Γ ( k + l + 2 ) M [ k + 1 , k + l + 2 , ( α β ) x ] ,
p ( x ) = 4 x ( 1 + r ) 2 1 P 2 exp { 2 1 P [ x ( 1 + r ) + r ( 1 P ) ] } l , k = 0 1 Γ ( k + l + 2 ) k ! l ! [ 2 r ( 1 + r ) x 1 P ] l [ 2 r ( 1 + r ) x 1 + P ] k M [ k + 1 , k + l + 2 , 4 x P ( 1 + r ) 1 P 2 ] .
p ( x , P = 0 ) = 4 ( 1 + r ) 2 2 x   exp [ 2 ( 1 + r ) x 2 r ] I 1 [ 4 r ( 1 + r ) x ] 4 r ( 1 + r ) x ,
σ x ( P , r ) = 1 + P 2 2 1 + 2 r 1 + r .
n ( r , P ) [ n ( 0 , P ) 5 ] 1 + 2.4 ( 2 r ) 1 + 2.4 r + 5.

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