Abstract

We introduce the Dammann phase-encoding method into original distorted gratings and propose a modified distorted grating, called a distorted Dammann grating (DDG), to realize multiplane imaging of several tens of layers within the object field onto a single image plane. This property implies that the DDG makes it possible to achieve simultaneously high axial resolving power and large axial imaging range without scanning. This DDG should be of high interest for its potential applications in real-time three-dimensional optical imaging and tracking. Multiplane imaging of 7×7 object layers onto a single camera plane is experimentally demonstrated using a 7×7 DDG for an objective of NA=0.127.

© 2013 Optical Society of America

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H. I. C. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, J. R. Soc. Interface 8, 942 (2011).
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X. Fengjie, J. Zongfu, X. Xiaojun, and G. Yifeng, J. Opt. Soc. Am. 24, 3444 (2007).
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H. Dammann and E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

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Bernet, S.

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Burge, R. E.

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H. I. C. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, J. R. Soc. Interface 8, 942 (2011).
[CrossRef]

Dalgarno, H. I. C.

H. I. C. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, J. R. Soc. Interface 8, 942 (2011).
[CrossRef]

P. A. Dalgarno, H. I. C. Dalgarno, A. Putoud, R. Lambert, L. Paterson, D. C. Logan, D. P. Towers, R. J. Warburton, and A. H. Greenaway, Opt. Express 18, 877 (2010).
[CrossRef]

Dalgarno, P. A.

H. I. C. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, J. R. Soc. Interface 8, 942 (2011).
[CrossRef]

P. A. Dalgarno, H. I. C. Dalgarno, A. Putoud, R. Lambert, L. Paterson, D. C. Logan, D. P. Towers, R. J. Warburton, and A. H. Greenaway, Opt. Express 18, 877 (2010).
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H. Dammann and E. Klotz, Opt. Acta 24, 505 (1977).
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Davis, I.

H. I. C. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, J. R. Soc. Interface 8, 942 (2011).
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Davis, J. A.

Fassl, S.

Fengjie, X.

X. Fengjie, J. Zongfu, X. Xiaojun, and G. Yifeng, J. Opt. Soc. Am. 24, 3444 (2007).
[CrossRef]

Gibson, G. J.

H. I. C. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, J. R. Soc. Interface 8, 942 (2011).
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Hu, A.

Jia, J.

Jia, W.

Khan, S.

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[CrossRef]

Lambert, R.

Lasser, T.

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Leutenegger, M.

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Ma, J.

Maurer, C.

Moreno, I.

Parton, R. M.

H. I. C. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, J. R. Soc. Interface 8, 942 (2011).
[CrossRef]

Paterson, L.

Putoud, A.

Rao, R.

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B. Richards and E. Wolf, Proc. R. Soc. Lond. 253, 358 (1959).
[CrossRef]

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Towers, C. E.

H. I. C. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, J. R. Soc. Interface 8, 942 (2011).
[CrossRef]

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[CrossRef]

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Warburton, R. J.

H. I. C. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, J. R. Soc. Interface 8, 942 (2011).
[CrossRef]

P. A. Dalgarno, H. I. C. Dalgarno, A. Putoud, R. Lambert, L. Paterson, D. C. Logan, D. P. Towers, R. J. Warburton, and A. H. Greenaway, Opt. Express 18, 877 (2010).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. Lond. 253, 358 (1959).
[CrossRef]

Wu, J.

Xiaojun, X.

X. Fengjie, J. Zongfu, X. Xiaojun, and G. Yifeng, J. Opt. Soc. Am. 24, 3444 (2007).
[CrossRef]

Yifeng, G.

X. Fengjie, J. Zongfu, X. Xiaojun, and G. Yifeng, J. Opt. Soc. Am. 24, 3444 (2007).
[CrossRef]

Yu, J.

Yuan, X. C.

Zhang, N.

Zhang, S.

Zhou, C.

Zongfu, J.

X. Fengjie, J. Zongfu, X. Xiaojun, and G. Yifeng, J. Opt. Soc. Am. 24, 3444 (2007).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

X. Fengjie, J. Zongfu, X. Xiaojun, and G. Yifeng, J. Opt. Soc. Am. 24, 3444 (2007).
[CrossRef]

J. R. Soc. Interface

H. I. C. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, J. R. Soc. Interface 8, 942 (2011).
[CrossRef]

Opt. Acta

H. Dammann and E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

Opt. Express

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B. Richards and E. Wolf, Proc. R. Soc. Lond. 253, 358 (1959).
[CrossRef]

Supplementary Material (1)

» Media 1: MOV (4893 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

Phase distributions of several DDGs with different parameters inside an objective aperture: 1×7 DDG for NA=0.1 with (a) W20=103λ, Nx0 (Λ0,x), (b) W20=0, Nx=20, and (c) W20=200λ, Nx=20; 1×7 DDG with (d) W20=20λ, Nx=20 for NA=0.45 and (e) W20=5λ, Nx=20 for NA=0.95; and (f) 7×7 DDG with W20,x=60λ, W20,y=420λ, and Nx=Ny=20 for NA=0.127. The origin (0,0) is always at the center of the objective aperture.

Fig. 2.
Fig. 2.

Illustration of simultaneous multiplane imaging using the combination of a DDG and an objective onto a single image plane.

Fig. 3.
Fig. 3.

Experimental demonstration of multiplane imaging 7×7 object layers onto a single camera plane by using a 7×7 DDG of W20,x=60λ, W20,y=420λ. (a) Schematic of experimental setup. The inset below the object mask is its microscopic image. (b)–(d) are the intensity distributions on the single camera plane when the object mask is located at z=0.5, 0, and 0.5 mm, and the scale bar is 500 μm. More detailed results can be found in Media 1.

Equations (3)

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TDDG(x,y)=m=Cmexp[i2mπ(x/Λ0+φw)],
Cm={12imπ[1+2n=1N1(1)nexp(i2πmxn)+(1)Nexp(i2πmxN)],m02n=1N1(1)nxn+(1)NxN,m=0,
Eo(x,y,z)=00{TDDG(kx,ky)Et(kx,ky)exp(ikzz)/cosθ}exp[i(kxx+kyy)]dkxdky=mCmδ(zmΔz)δ(xmΔx)EA(x,y,z),

Metrics