Abstract

Partially coherent light is often preferable to its completely coherent counterpart in applications such as imaging, sensing, and free-space optical communications. To fully exploit its advantages, techniques able to retrieve information carried by the beam are required. Here, we develop and experimentally demonstrate a phase-space optics technique for complete spatial analysis of widely used Schell-model beams. It allows for fast information recovery and can be applied for quantitative phase imaging of objects under partially coherent illumination.

© 2014 Optical Society of America

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References

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2013 (2)

2012 (1)

J. Clark, X. Huang, R. Harder, and I. Robinson, Nat. Commun. 3, 993 (2012).
[CrossRef]

2011 (1)

2009 (4)

2004 (1)

2002 (1)

1998 (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

1994 (1)

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef]

Abramochkin, E.

Alieva, T.

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

Barnett, S.

Beck, M.

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef]

Cai, Y.

Calvo, M. L.

Cámara, A.

Clark, J.

J. Clark, X. Huang, R. Harder, and I. Robinson, Nat. Commun. 3, 993 (2012).
[CrossRef]

Courtial, J.

Cristóbal, G.

Davidson, F. M.

Dholakia, K.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

Franke-Arnold, S.

Gibson, G.

Goodman, J. W.

J. W. Goodman, Statistical Optics, 1st ed. (Wiley-Interscience, 2000).

Harder, R.

J. Clark, X. Huang, R. Harder, and I. Robinson, Nat. Commun. 3, 993 (2012).
[CrossRef]

Henderson, C. A.

Huang, X.

J. Clark, X. Huang, R. Harder, and I. Robinson, Nat. Commun. 3, 993 (2012).
[CrossRef]

Korotkova, O.

Li, J.

J. Li and B. Lü, J. Opt. A 11, 045710 (2009).
[CrossRef]

Lü, B.

J. Li and B. Lü, J. Opt. A 11, 045710 (2009).
[CrossRef]

McAlister, D. F.

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef]

Nugent, K. A.

Padgett, M.

Padgett, M. J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

Pas’ko, V.

Peele, A. G.

Quiney, H. M.

Raymer, M. G.

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef]

Ricklin, J. C.

Robinson, I.

J. Clark, X. Huang, R. Harder, and I. Robinson, Nat. Commun. 3, 993 (2012).
[CrossRef]

Rodrigo, J. A.

Schell, A. C.

A. C. Schell, “The multiple plate antenna,” Ph.D. thesis (Massachusetts Institute of Technology, 1961).

Vasnetsov, M.

Wang, F.

Williams, G. J.

J. Mod. Opt. (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

J. Opt. A (1)

J. Li and B. Lü, J. Opt. A 11, 045710 (2009).
[CrossRef]

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

Nat. Commun. (1)

J. Clark, X. Huang, R. Harder, and I. Robinson, Nat. Commun. 3, 993 (2012).
[CrossRef]

Opt. Express (6)

Phys. Rev. Lett. (1)

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef]

Other (2)

A. C. Schell, “The multiple plate antenna,” Ph.D. thesis (Massachusetts Institute of Technology, 1961).

J. W. Goodman, Statistical Optics, 1st ed. (Wiley-Interscience, 2000).

Supplementary Material (1)

» Media 1: MOV (181 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

(a) Setup for generation of SMBs: light from an incoherent source is collimated by a lens (CL) to illuminate the object (hologram). The studied SMB is projected by the relay lenses (RL) into the FrFT setup sketched in (b).

Fig. 2.
Fig. 2.

Reconstruction of coherent and partially coherent vortices corresponding to LG4,1 mode. (Left panel) Constraint images measured for the (a), (b) coherent and (c), (d) partially coherent cases; see Media 1. The reconstructed beams, using M=4 and 12 constraint images, are displayed in the second panel. (e) Beam recovery is significantly degraded when the DoC is ignored.

Fig. 3.
Fig. 3.

(a) Vortex LG4,1 experimentally reconstructed using the DoC retrieved via RLD with aFrFT. (b) Amplitude profile of the retrieved DoC (red color) and the expected one (blue color). (c) Convergence of the iterative algorithm for coherent and partially coherent (PC) illumination: simulation (continuous line) and experimental (scatterplot) results.

Equations (5)

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Fαx,αy[f(ri)](ro)=f(ri)Kαx,αy(ri,ro)dri,
Ipcαx,αy(ro)=Γ(r1,r2)Kαx,αy(r1,ro)×Kαx,αy(r2,ro)dr1dr2,
Ipcα(ro)=(σsinα)2f(R+r2)f*(Rr2)×exp[i2πσcotα(XxYy)]dR×γ(r)exp[i2πσcscα(xox+yoy)]dr.
Ipcα(ro)=Icα(ro)γ˜α(ro)=Icα(ro)γ˜α(roro)dro,
Wm,n(ro)=Wm,n(ro)Ipcα(m)(ro)/Ipc,nα(m)(ro),

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