Abstract

An Airy beam can be used to implement a non-diffracting self-bending point-spread function (PSF), which can be utilized for computational 3D imaging. However, the parabolic depth-dependent spot trajectory limits the range and resolution in rangefinding. In this Letter, we propose a novel pupil-phase-modulation method to realize a non-diffracting linear-shift PSF. For the modulation, we use a focus-multiplexed computer-generated hologram, which is calculated by multiplexing multiple lens-function holograms with 2D sweeping of the foci. With this method, the depth-dependent trajectory of the non-diffracting spot is straightened, which improves the range and resolution in rangefinding. The proposed method was verified by numerical simulations and optical experiments. The method can be applied to laser-based microscopy, time-of-flight rangefinding, and so on.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (1)

2016 (1)

2015 (2)

2014 (1)

S. Jia, J. C. Vaughan, and X. Zhuang, Nat. Photonics 8, 302 (2014).
[Crossref]

2011 (2)

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, Opt. Lett. 36, 202 (2011).
[Crossref]

S. Kuthirummal, H. Nagahara, C. Zhou, and S. K. Nayar, IEEE Trans. Pattern Anal. Mach. Intell. 33, 58 (2011).
[Crossref]

2009 (1)

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 106, 2995 (2009).
[Crossref]

2007 (1)

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, ACM Trans. Graph. 26, 70 (2007).
[Crossref]

1995 (1)

1972 (2)

Badieirostami, M.

Barberis, A.

Biteen, J. S.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 106, 2995 (2009).
[Crossref]

Brady, D. J.

Carin, L.

Carles, G.

Cathey, W. T.

Chen, D.

Dahan, M.

Diaspro, A.

Dowski, E. R.

Duocastella, M.

Durand, F.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, ACM Trans. Graph. 26, 70 (2007).
[Crossref]

A. Levin and F. Durand, IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 1831–1838.

El Beheiry, M.

Fergus, R.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, ACM Trans. Graph. 26, 70 (2007).
[Crossref]

Freeman, W. T.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, ACM Trans. Graph. 26, 70 (2007).
[Crossref]

Hajj, B.

Harvey, A. R.

Häusler, G.

G. Häusler, Opt. Commun. 6, 38 (1972).
[Crossref]

Jia, S.

S. Jia, J. C. Vaughan, and X. Zhuang, Nat. Photonics 8, 302 (2014).
[Crossref]

Kuthirummal, S.

S. Kuthirummal, H. Nagahara, C. Zhou, and S. K. Nayar, IEEE Trans. Pattern Anal. Mach. Intell. 33, 58 (2011).
[Crossref]

Lanzanò, L.

Lee, S. F.

Levin, A.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, ACM Trans. Graph. 26, 70 (2007).
[Crossref]

A. Levin and F. Durand, IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 1831–1838.

Lew, M. D.

Li, H.

Liu, N.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 106, 2995 (2009).
[Crossref]

Llull, P.

Lord, S. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 106, 2995 (2009).
[Crossref]

Moerner, W. E.

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, Opt. Lett. 36, 202 (2011).
[Crossref]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 106, 2995 (2009).
[Crossref]

Nagahara, H.

S. Kuthirummal, H. Nagahara, C. Zhou, and S. K. Nayar, IEEE Trans. Pattern Anal. Mach. Intell. 33, 58 (2011).
[Crossref]

Nayar, S. K.

S. Kuthirummal, H. Nagahara, C. Zhou, and S. K. Nayar, IEEE Trans. Pattern Anal. Mach. Intell. 33, 58 (2011).
[Crossref]

Niu, H.

Pavani, S. R. P.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 106, 2995 (2009).
[Crossref]

Piestun, R.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 106, 2995 (2009).
[Crossref]

Ravasenga, T.

Richardson, W. H.

Sancataldo, G.

Scipioni, L.

Thompson, M. A.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 106, 2995 (2009).
[Crossref]

Twieg, R. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 106, 2995 (2009).
[Crossref]

Vaughan, J. C.

S. Jia, J. C. Vaughan, and X. Zhuang, Nat. Photonics 8, 302 (2014).
[Crossref]

Xu, G.

Yu, B.

Yuan, X.

Zammit, P.

Zhou, C.

S. Kuthirummal, H. Nagahara, C. Zhou, and S. K. Nayar, IEEE Trans. Pattern Anal. Mach. Intell. 33, 58 (2011).
[Crossref]

Zhou, Y.

Zhuang, X.

S. Jia, J. C. Vaughan, and X. Zhuang, Nat. Photonics 8, 302 (2014).
[Crossref]

ACM Trans. Graph. (1)

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, ACM Trans. Graph. 26, 70 (2007).
[Crossref]

Appl. Opt. (1)

Biomed. Opt. Express (1)

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. Kuthirummal, H. Nagahara, C. Zhou, and S. K. Nayar, IEEE Trans. Pattern Anal. Mach. Intell. 33, 58 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

Nat. Photonics (1)

S. Jia, J. C. Vaughan, and X. Zhuang, Nat. Photonics 8, 302 (2014).
[Crossref]

Opt. Commun. (1)

G. Häusler, Opt. Commun. 6, 38 (1972).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Optica (2)

Proc. Natl. Acad. Sci. USA (1)

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 106, 2995 (2009).
[Crossref]

Other (1)

A. Levin and F. Durand, IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 1831–1838.

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Figures (6)

Fig. 1.
Fig. 1. Concept of the proposed optical system generating the NDLS PSF using a focus-multiplexed CGH. The color represents the depth of the object.
Fig. 2.
Fig. 2. Calculated phase-only FMCGH. Phase maps (a) without and (b) with phase unwrapping.
Fig. 3.
Fig. 3. (a) 2D PSFs with defocus by non-PPM (lens PSF), CPM (SB PSF, also called Airy beam), and FMCGH (NDLS PSF). (b) 1D line profiles on the “slice” line of the PSFs. Scale bar indicates 300 μm.
Fig. 4.
Fig. 4. Simulation results of the z o -stack of 1D slices of the (a) lens, (b) SB, and (c) NDLS PSFs.
Fig. 5.
Fig. 5. Line profile of a captured image generated from multi-depth point sources and deconvolution result.
Fig. 6.
Fig. 6. (a) Setup for optical experiments and (b) the experimentally observed z o -stack of the 1D slices of the NDLS PSFs.

Equations (8)

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ϕ div ( x , y ) [ z , x ] = exp ( j k 2 ( x x ) 2 + y 2 z ) ,
ϕ lens ( x , y ; z o , x i ) = ϕ div ( x , y ) [ z o , 0 ] ϕ div ( x , y ) [ z i , x i ] .
ϕ eCGH ( x , y ; z o , x i ) = ϕ lens ( x , y ; z o , x i ) ϕ div ( x , y ) [ z fo , 0 ] ϕ div ( x , y ) [ z fi , 0 ] ,
x i = α z o ,
ϕ FMCGHc ( x , y ) = z o = z min z max ϕ eCGH ( x , y ; z o ) ,
g x = H ϕ FMCGH [ f z ] .
g x h ¯ * H z o x i [ f z ] ,
f ^ z = H z o x i 1 [ h ¯ 1 * g x ] ,