Abstract

Traditional approaches to imaging require that an increase in depth of field is associated with a reduction in numerical aperture, and hence with a reduction in resolution and optical throughput. In their seminal work, Dowski and Cathey reported how the asymmetric point-spread function generated by a cubic-phase aberration encodes the detected image such that digital recovery can yield images with an extended depth of field without sacrificing resolution [Appl. Opt. 34, 1859 (1995) [CrossRef]  ]. Unfortunately recovered images are generally visibly degraded by artifacts arising from subtle variations in point-spread functions with defocus. We report a technique that involves determination of the spatially variant translation of image components that accompanies defocus to enable determination of spatially variant defocus. This in turn enables recovery of artifact-free, extended depth-of-field images together with a two-dimensional defocus and range map of the imaged scene. We demonstrate the technique for high-quality macroscopic and microscopic imaging of scenes presenting an extended defocus of up to two waves, and for generation of defocus maps with an uncertainty of 0.036 waves.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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  26. B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
    [Crossref]

2013 (3)

2012 (3)

2011 (1)

J. He, X. Zhuang, S. A. Jones, S.-H. Shim, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods 8, 499–505 (2011).
[Crossref]

2010 (4)

2009 (3)

M. Demenikov, E. Findlay, A. R. Harvey, “Miniaturization of zoom lenses with a single moving element,” Opt. Express 17, 6118–6127 (2009).
[Crossref]

G. Muyo, A. Singh, M. Andersson, D. Huckridge, A. Wood, A. R. Harvey, “Infrared imaging with a wavefront-coded singlet lens,” Opt. Express 17, 21118–21123 (2009).
[Crossref]

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[Crossref]

2008 (1)

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[Crossref]

2005 (2)

P. Favaro, S. Soatto, “A geometric approach to shape from defocus,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 406–417 (2005).
[Crossref]

G. Muyo, A. R. Harvey, “Decomposition of the optical transfer function: wavefront coding imaging systems,” Opt. Lett. 30, 2715–2717 (2005).
[Crossref]

2003 (3)

N. George, W. Chi, “Extended depth of field using a logarithmic asphere,” J. Opt. A 5, S157–S163 (2003).
[Crossref]

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1–12 (2003).

S. Mezouari, A. R. Harvey, “Phase pupil functions for reduction of defocus and spherical aberrations,” Opt. Lett. 28, 771–773 (2003).
[Crossref]

2002 (1)

F. Pereira, M. Gharib, “Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows,” Meas. Sci. Technol. 13, 683–694 (2002).
[Crossref]

2000 (1)

A. K. Prasad, “Stereoscopic particle image velocimetry,” Exp. Fluids 29, 103–116 (2000).
[Crossref]

1999 (1)

1997 (1)

1995 (1)

1972 (1)

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[Crossref]

Andersson, M.

Bates, M.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[Crossref]

Bhakta, V. R.

Blanchard, P. M.

Bosch, S.

G. Carles, G. Muyo, S. Bosch, A. Harvey, “Use of a spatial light modulator as an adaptable phase mask for wavefront coding,” J. Mod. Opt. 57, 893–900 (2010).
[Crossref]

Bradburn, S.

Bustin, N.

Carles, G.

G. Carles, “Analysis of the cubic-phase wavefront-coding function: physical insight and selection of optimal coding strength,” Opt. Lasers Eng. 50, 1377–1382 (2012).
[Crossref]

G. Carles, G. Muyo, S. Bosch, A. Harvey, “Use of a spatial light modulator as an adaptable phase mask for wavefront coding,” J. Mod. Opt. 57, 893–900 (2010).
[Crossref]

Cathey, W. T.

Chi, W.

N. George, W. Chi, “Extended depth of field using a logarithmic asphere,” J. Opt. A 5, S157–S163 (2003).
[Crossref]

Christensen, M. P.

Cogswell, C. J.

Cormack, R. H.

Dalgarno, P. A.

Das, B.

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[Crossref]

Demenikov, M.

Dowski, E. R.

Dowski, R.

Edward, J.

Favaro, P.

P. Favaro, S. Soatto, “A geometric approach to shape from defocus,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 406–417 (2005).
[Crossref]

Feng, Y.

Findlay, E.

George, N.

N. George, W. Chi, “Extended depth of field using a logarithmic asphere,” J. Opt. A 5, S157–S163 (2003).
[Crossref]

Gharib, M.

F. Pereira, M. Gharib, “Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows,” Meas. Sci. Technol. 13, 683–694 (2002).
[Crossref]

Greenaway, A. H.

Harvey, A.

G. Carles, G. Muyo, S. Bosch, A. Harvey, “Use of a spatial light modulator as an adaptable phase mask for wavefront coding,” J. Mod. Opt. 57, 893–900 (2010).
[Crossref]

Harvey, A. R.

Hausler, G.

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[Crossref]

He, J.

J. He, X. Zhuang, S. A. Jones, S.-H. Shim, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods 8, 499–505 (2011).
[Crossref]

Huang, B.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[Crossref]

Huckridge, D.

Jones, S. A.

J. He, X. Zhuang, S. A. Jones, S.-H. Shim, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods 8, 499–505 (2011).
[Crossref]

Joseph, J.

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[Crossref]

Lee, D.

Mezouari, S.

Mo, X.

X. Mo, J. Wang, “Phase transfer function based method to alleviate image artifacts in wavefront coding imaging system,” Proc. SPIE 8907, 89074H (2013).

Muyo, G.

Pauca, V. P.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1–12 (2003).

Pereira, F.

F. Pereira, M. Gharib, “Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows,” Meas. Sci. Technol. 13, 683–694 (2002).
[Crossref]

Piestun, R.

Plemmons, R. J.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1–12 (2003).

Prasad, A. K.

A. K. Prasad, “Stereoscopic particle image velocimetry,” Exp. Fluids 29, 103–116 (2000).
[Crossref]

Prasad, S.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1–12 (2003).

Quirin, S.

Senthilkumaran, P.

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[Crossref]

Shim, S.-H.

J. He, X. Zhuang, S. A. Jones, S.-H. Shim, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods 8, 499–505 (2011).
[Crossref]

Singh, A.

Singh, K.

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[Crossref]

Soatto, S.

P. Favaro, S. Soatto, “A geometric approach to shape from defocus,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 406–417 (2005).
[Crossref]

Somayaji, M.

Thomson, R. R.

Torgersen, T. C.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1–12 (2003).

van der Gracht, J.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1–12 (2003).

Vettenburg, T.

Vyas, S.

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[Crossref]

Wang, J.

X. Mo, J. Wang, “Phase transfer function based method to alleviate image artifacts in wavefront coding imaging system,” Proc. SPIE 8907, 89074H (2013).

Wang, W.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[Crossref]

Wood, A.

Yang, Y.

Zahreddine, R. N.

Zhuang, X.

J. He, X. Zhuang, S. A. Jones, S.-H. Shim, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods 8, 499–505 (2011).
[Crossref]

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[Crossref]

Appl. Opt. (5)

Exp. Fluids (1)

A. K. Prasad, “Stereoscopic particle image velocimetry,” Exp. Fluids 29, 103–116 (2000).
[Crossref]

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

P. Favaro, S. Soatto, “A geometric approach to shape from defocus,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 406–417 (2005).
[Crossref]

J. Mod. Opt. (1)

G. Carles, G. Muyo, S. Bosch, A. Harvey, “Use of a spatial light modulator as an adaptable phase mask for wavefront coding,” J. Mod. Opt. 57, 893–900 (2010).
[Crossref]

J. Opt. A (1)

N. George, W. Chi, “Extended depth of field using a logarithmic asphere,” J. Opt. A 5, S157–S163 (2003).
[Crossref]

Meas. Sci. Technol. (1)

F. Pereira, M. Gharib, “Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows,” Meas. Sci. Technol. 13, 683–694 (2002).
[Crossref]

Nat. Methods (1)

J. He, X. Zhuang, S. A. Jones, S.-H. Shim, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods 8, 499–505 (2011).
[Crossref]

Opt. Commun. (1)

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[Crossref]

Opt. Express (7)

Opt. Lasers Eng. (2)

G. Carles, “Analysis of the cubic-phase wavefront-coding function: physical insight and selection of optimal coding strength,” Opt. Lasers Eng. 50, 1377–1382 (2012).
[Crossref]

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[Crossref]

Opt. Lett. (2)

Proc. SPIE (2)

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1–12 (2003).

X. Mo, J. Wang, “Phase transfer function based method to alleviate image artifacts in wavefront coding imaging system,” Proc. SPIE 8907, 89074H (2013).

Science (1)

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[Crossref]

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Figures (10)

Fig. 1.
Fig. 1.

Disparity maps. (a) r+W˜20=0,W20 with negative disparity (arrows pointing from upper-right to lower-left corner). (b) rW˜20=0,W20 with positive disparity (arrows pointing from lower-left to upper-right corner). (c) Resultant disparity, 2ρ(ξ,η) (i.e., difference in the previous two) superimposed on the conventional image.

Fig. 2.
Fig. 2.

Uniform four waves of defocus. (a) Diffraction-limited reference. (b) Conventional optics imaging. (c) WC with α=5. (d) CKM with α=5. (e) Calculated metric for defocus detection.

Fig. 3.
Fig. 3.

Images with varying amounts of defocus up to three waves; spoke target shows angular step change in defocus and boat image shows continuous vertical defocus change. (a) Diffraction-limited reference. (b) Conventional optics imaging. (c) WC with α=4. (d) CKM with α=4.

Fig. 4.
Fig. 4.

Possible layouts for a single-snapshot acquisition. (a) Dual-detector system. (b), (c) Single detector systems. O, object; CL, collimating lens; BS, beam splitter; PM, phase mask; L, lens; IP, image plane; M, Mirror; G, Grating.

Fig. 5.
Fig. 5.

Experimental setup. L, imaging lens; LS, light source; TS, tilted slide; SLM, spatial light modulator; I, detector.

Fig. 6.
Fig. 6.

Calibration process. Measured translation, ρ, against W20 for ψ (negative curve) and for ψ* (positive curve). Fitted quadratic curves shown as blue solid lines and data as black dots.

Fig. 7.
Fig. 7.

Tilted petiole section captured with (a) conventional imaging system, (b) WC system, and (c) CKM system.

Fig. 8.
Fig. 8.

Step-defocus pine-leaf section and seeds. (a) Conventional imaging system, (b) WC system, (c) CKM system, and (d) focus stack. (e) Line profile taken along the lines with the corresponding color in (b)–(d). Red is for the WC system, blue is for the CKM system, and green is for the focus stack.

Fig. 9.
Fig. 9.

Tilted distortion target captured with (a) conventional imaging system, (b) WC system, and (c) CKM system.

Fig. 10.
Fig. 10.

Tilted distortion target. (a) 3D reconstruction. (b) Slope estimate by CKM (blue curve), slope estimate by focus stacking (black curve), and ground truth slope (red broken line).

Equations (4)

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

P±=exp[2πi(W20(x2+y2)±ϕ)],
r+W˜20,W20(ξρ(ξ,η)2,ηρ(ξ,η)2)=rW˜20,W20(ξ+ρ(ξ,η)2,η+ρ(ξ,η)2),
W˜20σ(ξ,η)=argminW˜20{Gσ[(r+W˜20,W20(ξ,η)rW˜20,W20(ξ,η))2]},
r(ξ,η)=F(i=1nr+W˜20σi(ξ,η),W20(ξ,η)+rW˜20σi(ξ,η),W20(ξ,η)2n,νc),

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