Abstract

A means to extract spatial information from an extremely unresolved source of light using a single element detector is demonstrated by use of an optical vortex coronagraph. Applications may range from astronomy to microscopy. For example, the centroid and angular extent of an unresolved collection of incoherent point sources is revealed.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
    [CrossRef]
  2. G. Foo, D. M. Palacios, and G. A. Swartzlander, Opt. Lett. 30, 3308 (2005).
    [CrossRef]
  3. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
    [CrossRef]
  4. S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Express 13, 689 (2005).
    [CrossRef]
  5. G. A. Swartzlander, Opt. Lett. 26, 497 (2001).
    [CrossRef]
  6. E. Serabyn, D. Mawet, and R. Burruss, Nature 464, 1018 (2010).
    [CrossRef]
  7. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, 1972).

2010 (1)

E. Serabyn, D. Mawet, and R. Burruss, Nature 464, 1018 (2010).
[CrossRef]

2005 (3)

2001 (1)

1992 (1)

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, 1972).

Absil, O.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

Bernet, S.

Burruss, R.

E. Serabyn, D. Mawet, and R. Burruss, Nature 464, 1018 (2010).
[CrossRef]

Foo, G.

Furhapter, S.

Jesacher, A.

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Mawet, D.

E. Serabyn, D. Mawet, and R. Burruss, Nature 464, 1018 (2010).
[CrossRef]

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

Palacios, D. M.

Riaud, P.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

Ritsch-Marte, M.

Serabyn, E.

E. Serabyn, D. Mawet, and R. Burruss, Nature 464, 1018 (2010).
[CrossRef]

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, 1972).

Surdej, J.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

Swartzlander, G. A.

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Astrophys. J. (1)

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

J. Mod. Opt. (1)

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Nature (1)

E. Serabyn, D. Mawet, and R. Burruss, Nature 464, 1018 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (1)

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, 1972).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Optical vortex coronagraph with objective lens of radius R(L1), vortex lens (VL), collimating lens (L2), Lyot stop of radius RLyot (LS), condenser lens (L3), and photo detector (PD). Ray trace for incident plane wave (dashed lines).

Fig. 2.
Fig. 2.

Light from an object of extent a is transmitted to the circular aperture of an objective lens of radius R.

Fig. 3.
Fig. 3.

Distribution of point sources with centroid at the origin of the dashed axes. Coronagraph optical axis at origin of solid axes. Circle depicts the radial deviation of the distribution.

Fig. 4.
Fig. 4.

Computer-generated signals with additive noise for an OVC (m=2) and a conventional imaging system (m=0) having respective widths 0.318λ/D and 1.22λ/D (λ wavelength, D objective aperture diameter). The offset OVC minimum indicates that the radiating object has a nonzero angular extent.

Equations (16)

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

f(r0,θ0)=l=Bl(r0)exp(ilθ0),
El(r,θ)=(2π/λz)(i)lexp(ilθ)HTl{Bl(r0)},
γ=2πRa/λz1.
Jl(krr0)=σ(l)(krr02)Ln=0((krr02)2)n/(n!(n+L)!),
E(r,θ)=l=n=0Cl,n(r/R)pexp(ilθ),
Cl,n=(1)n(i)l2πn!(n+L)!(πR/λz)pλz0aBl(r0)r0p+1dr0.
gl,n(m)(r,θ)=2π(i)lCl,nei(m+l)θ0R(rR)p+1Jl(krr)dr,
Al,n(m)(θ)=4π2(i)2l+mCl,nei(l+m)θ,
Il,n(m)(r)=00R((r/R)pJl(krr)rdr)Jl+m(krr)rdr,
G0,0(m)(r,θ)=G0eiΦj{1,m=00,m=±2,±4,
G1,0(2)(r,θ)=i(G0/2)(r/R)γjei(θj+Φj+θ),
G0,1(2)(r,θ)=(G0/8)(r/R)2γj2ei(Φj+2θ).
P(2)=02π0RLyot|G1,0(2)+G0,1(2)+|2rdrdθ.
P(0)=02π0RLyot|G0|2rdrdθ,
η(2)=P(2)/P(0)=(1/8)γj2+O(γj4).
η(2)(x0,y0)=(1/8)j=1Nγj2εj,

Metrics