Abstract

Digital holographic microcopy is a thriving imaging modality that attracts considerable research interest due to its ability not only to create excellent label-free contrast but also to supply valuable physical information regarding the density and dimensions of the sample with nanometer-scale axial sensitivity. Three basic holographic recording geometries currently exist, including on-axis, off-axis, and slightly off-axis holography, each of which enables a variety of architectures in terms of bandwidth use and compression capacity. Specifically, off-axis holography and slightly off-axis holography allow spatial hologram multiplexing, enabling one to compress more information into the same digital hologram. In this paper, we define an efficiency score to analyze the various possible architectures and compare the signal-to-noise ratio and the mean squared error obtained using each of them, thus determining the optimal holographic method.

© 2018 Optical Society of America

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References

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2018 (6)

2017 (5)

2016 (1)

2015 (5)

2014 (5)

2013 (3)

Y. Wu, Y. Yang, H. Zhai, Z. Ma, L. Deng, and Q. Ge, “Single-exposure approach for expanding the sampled area of a dynamic process by digital holography with combined multiplexing,” J. Opt. 15, 085402 (2013).
[Crossref]

P. Girshovitz and N. T. Shaked, “Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy,” Opt. Express 21, 5701–5714 (2013).
[Crossref]

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, O. Matoba, and T. Kubota, “Space-bandwidth capacity-enhanced digital holography,” Appl. Phys. Express 6, 022502 (2013).
[Crossref]

2012 (2)

2011 (1)

2010 (2)

2009 (2)

2007 (1)

2006 (2)

2005 (1)

2002 (1)

2000 (1)

1998 (1)

1994 (1)

1965 (1)

1873 (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosk. Anat. 9, 413–418 (1873).
[Crossref]

Abbe, E.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosk. Anat. 9, 413–418 (1873).
[Crossref]

Arai, Y.

T. Tahara, R. Mori, Y. Arai, and Y. Takaki, “Four-step phase-shifting digital holography simultaneously sensing dual-wavelength information using a monochromatic image sensor,” J. Opt. 17, 125707 (2015).
[Crossref]

Awatsuji, Y.

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, O. Matoba, and T. Kubota, “Space-bandwidth capacity-enhanced digital holography,” Appl. Phys. Express 6, 022502 (2013).
[Crossref]

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45, 2995–3002 (2006).
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Bai, H.

Z. Zhong, H. Bai, M. Shan, Y. Zhang, and L. Guo, “Fast phase retrieval in slightly off-axis holography,” Opt. Lasers Eng. 97, 9–18 (2017).
[Crossref]

Barnea, I.

Barty, A.

Burton, D. R.

Charrière, F.

Chowdhury, S.

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Cuche, E.

Dan, D.

Dardikman, G.

Deng, L.

Y. Wu, Y. Yang, H. Zhai, Z. Ma, L. Deng, and Q. Ge, “Single-exposure approach for expanding the sampled area of a dynamic process by digital holography with combined multiplexing,” J. Opt. 15, 085402 (2013).
[Crossref]

Depeursinge, C.

Duan, T.

Dürr, F.

Eldridge, W. J.

Ellenbogen, T.

Emery, Y.

Ferraro, P.

Finizio, A.

Fixler, D.

Frenklach, I.

P. Girshovitz, I. Frenklach, and N. T. Shaked, “Broadband quantitative phase microscopy with extended field of view using off-axis interferometric multiplexing,” J. Biomed. Opt. 20, 111217 (2015).
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I. Frenklach, P. Girshovitz, and N. T. Shaked, “Off-axis interferometric phase microscopy with tripled imaging area,” Opt. Lett. 39, 1525–1528 (2014).
[Crossref]

Fujii, A.

Gao, P.

Garcia, J.

Gdeisat, M. A.

Ge, Q.

Y. Wu, Y. Yang, H. Zhai, Z. Ma, L. Deng, and Q. Ge, “Single-exposure approach for expanding the sampled area of a dynamic process by digital holography with combined multiplexing,” J. Opt. 15, 085402 (2013).
[Crossref]

Ge, X. L.

Girshovitz, P.

Guo, C. S.

Guo, L.

Z. Zhong, H. Bai, M. Shan, Y. Zhang, and L. Guo, “Fast phase retrieval in slightly off-axis holography,” Opt. Lasers Eng. 97, 9–18 (2017).
[Crossref]

Guo, R.

Gur, A.

Herráez, M. A.

Izatt, J. A.

Jacob Eravuchira, P.

Javidi, B.

Jozwik, M.

Karepov, S.

Kostencka, J.

Kozacki, T.

Kubota, T.

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, O. Matoba, and T. Kubota, “Space-bandwidth capacity-enhanced digital holography,” Appl. Phys. Express 6, 022502 (2013).
[Crossref]

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45, 2995–3002 (2006).
[Crossref]

Kühn, J.

Lai, J.

Lalor, M. J.

Lei, M.

Li, X.

Li, Z.

Limberger, H. G.

Liu, X.

Lohmann, A. W.

Lu, Y. J.

Ma, B.

Ma, Z.

Y. Wu, Y. Yang, H. Zhai, Z. Ma, L. Deng, and Q. Ge, “Single-exposure approach for expanding the sampled area of a dynamic process by digital holography with combined multiplexing,” J. Opt. 15, 085402 (2013).
[Crossref]

Marquet, P.

Matoba, O.

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, O. Matoba, and T. Kubota, “Space-bandwidth capacity-enhanced digital holography,” Appl. Phys. Express 6, 022502 (2013).
[Crossref]

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45, 2995–3002 (2006).
[Crossref]

Memmolo, P.

Micó, V.

Min, J.

Mirsky, S. K.

Montfort, F.

Mori, R.

T. Tahara, R. Mori, Y. Arai, and Y. Takaki, “Four-step phase-shifting digital holography simultaneously sensing dual-wavelength information using a monochromatic image sensor,” J. Opt. 17, 125707 (2015).
[Crossref]

Mu, G.

Nativ, N.

Nishio, K.

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, O. Matoba, and T. Kubota, “Space-bandwidth capacity-enhanced digital holography,” Appl. Phys. Express 6, 022502 (2013).
[Crossref]

Nugent, K. A.

Nygate, Y.

Ohtsuka, Y.

Oka, K.

Paganin, D.

Paturzo, M.

Pelagotti, A.

Ramchandran, K.

Rinehart, M. T.

Roberts, A.

Rotman-Nativ, N.

Rubin, M.

Salathé, R.-P.

Saleh, B. A. E.

B. A. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

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Shaked, N.

Shaked, N. T.

G. Dardikman and N. T. Shaked, “Review on methods of solving the refractive index-thickness coupling problem in digital holographic microscopy of biological cells,” Opt. Commun. 422, 8–16 (2018).
[Crossref]

N. Rotman-Nativ, N. A. Turko, and N. T. Shaked, “Flipping interferometry with doubled imaging area,” Opt. Lett. 43, 5543–5546 (2018).
[Crossref]

L. Wolbromsky, N. A. Turko, and N. T. Shaked, “Single-exposure full-field multi-depth imaging using low-coherence holographic multiplexing,” Opt. Lett. 43, 2046–2049 (2018).
[Crossref]

Y. Nygate, G. Singh, N. A. Turko, and N. T. Shaked, “Simultaneous off-axis multiplexed holography and regular fluorescence microscopy of biological cells,” Opt. Lett. 43, 2587–2590 (2018).
[Crossref]

N. A. Turko, P. Jacob Eravuchira, I. Barnea, and N. T. Shaked, “Simultaneous three-wavelength unwrapping using external digital holographic multiplexing module,” Opt. Lett. 43, 1943–1946 (2018).
[Crossref]

G. Dardikman, G. Singh, and N. T. Shaked, “Four dimensional phase unwrapping of dynamic objects in digital holography,” Opt. Express 26, 3772–3778 (2018).
[Crossref]

M. Rubin, G. Dardikman, S. K. Mirsky, N. A. Turko, and N. T. Shaked, “Six-pack off-axis holography,” Opt. Lett. 42, 4611–4614 (2017).
[Crossref]

G. Dardikman, N. A. Turko, N. Nativ, S. K. Mirsky, and N. T. Shaked, “Optimal spatial bandwidth capacity in multiplexed off-axis holography for rapid quantitative phase reconstruction and visualization,” Opt. Express 25, 33400–33415 (2017).
[Crossref]

N. A. Turko and N. T. Shaked, “Simultaneous two-wavelength phase unwrapping using external module for multiplexing off-axis holography,” Opt. Lett. 42, 73–76 (2017).
[Crossref]

S. Karepov, N. T. Shaked, and T. Ellenbogen, “Off-axis interferometer with adjustable fringe contrast based on polarization encoding,” Opt. Lett. 40, 2273–2276 (2015).
[Crossref]

P. Girshovitz and N. T. Shaked, “Fast phase processing in off-axis holography using multiplexing with complex encoding and live-cell fluctuation map calculation in real-time,” Opt. Express 23, 8773–8787 (2015).
[Crossref]

P. Girshovitz, I. Frenklach, and N. T. Shaked, “Broadband quantitative phase microscopy with extended field of view using off-axis interferometric multiplexing,” J. Biomed. Opt. 20, 111217 (2015).
[Crossref]

P. Girshovitz and N. T. Shaked, “Doubling the field of view in off-axis low-coherence interferometric imaging,” Light Sci. Appl. 3, e151 (2014).
[Crossref]

P. Girshovitz and N. T. Shaked, “Real-time quantitative phase reconstruction in off-axis digital holography using multiplexing,” Opt. Lett. 39, 2262–2265 (2014).
[Crossref]

I. Frenklach, P. Girshovitz, and N. T. Shaked, “Off-axis interferometric phase microscopy with tripled imaging area,” Opt. Lett. 39, 1525–1528 (2014).
[Crossref]

P. Girshovitz and N. T. Shaked, “Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy,” Opt. Express 21, 5701–5714 (2013).
[Crossref]

N. T. Shaked, “Quantitative phase microscopy of biological samples using a portable interferometer,” Opt. Lett. 37, 2016–2018 (2012).
[Crossref]

Shan, M.

Z. Zhong, H. Bai, M. Shan, Y. Zhang, and L. Guo, “Fast phase retrieval in slightly off-axis holography,” Opt. Lasers Eng. 97, 9–18 (2017).
[Crossref]

Singh, G.

Tahara, T.

T. Tahara, R. Mori, Y. Arai, and Y. Takaki, “Four-step phase-shifting digital holography simultaneously sensing dual-wavelength information using a monochromatic image sensor,” J. Opt. 17, 125707 (2015).
[Crossref]

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, O. Matoba, and T. Kubota, “Space-bandwidth capacity-enhanced digital holography,” Appl. Phys. Express 6, 022502 (2013).
[Crossref]

Takaki, Y.

T. Tahara, R. Mori, Y. Arai, and Y. Takaki, “Four-step phase-shifting digital holography simultaneously sensing dual-wavelength information using a monochromatic image sensor,” J. Opt. 17, 125707 (2015).
[Crossref]

Teich, M. C.

B. A. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Tian, L.

Tulino, A.

Turko, N. A.

Ura, S.

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, O. Matoba, and T. Kubota, “Space-bandwidth capacity-enhanced digital holography,” Appl. Phys. Express 6, 022502 (2013).
[Crossref]

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, 1979).

Waller, L.

Wang, S.

Wang, X.

Wax, A.

Wolbromsky, L.

Wu, Y.

Y. Wu, Y. Yang, H. Zhai, Z. Ma, L. Deng, and Q. Ge, “Single-exposure approach for expanding the sampled area of a dynamic process by digital holography with combined multiplexing,” J. Opt. 15, 085402 (2013).
[Crossref]

Xie, Y. Y.

Xue, L.

Yan, S.

Yang, Y.

Y. Wu, Y. Yang, H. Zhai, Z. Ma, L. Deng, and Q. Ge, “Single-exposure approach for expanding the sampled area of a dynamic process by digital holography with combined multiplexing,” J. Opt. 15, 085402 (2013).
[Crossref]

J. Min, B. Yao, P. Gao, R. Guo, B. Ma, J. Zheng, M. Lei, S. Yan, D. Dan, T. Duan, Y. Yang, and T. Ye, “Dual-wavelength slightly off-axis digital holographic microscopy,” Appl. Opt. 51, 191–196 (2012).
[Crossref]

Yao, B.

Ye, T.

Yue, Q. Y.

Zalevsky, Z.

Zhai, H.

Y. Wu, Y. Yang, H. Zhai, Z. Ma, L. Deng, and Q. Ge, “Single-exposure approach for expanding the sampled area of a dynamic process by digital holography with combined multiplexing,” J. Opt. 15, 085402 (2013).
[Crossref]

X. Wang, H. Zhai, and G. Mu, “Pulsed digital holography system recording ultrafast process of the femtosecond order,” Opt. Lett. 31, 1636–1638 (2006).
[Crossref]

Zhang, Y.

Z. Zhong, H. Bai, M. Shan, Y. Zhang, and L. Guo, “Fast phase retrieval in slightly off-axis holography,” Opt. Lasers Eng. 97, 9–18 (2017).
[Crossref]

Zheng, J.

Zhong, Z.

Z. Zhong, H. Bai, M. Shan, Y. Zhang, and L. Guo, “Fast phase retrieval in slightly off-axis holography,” Opt. Lasers Eng. 97, 9–18 (2017).
[Crossref]

Zhu, Y.

Appl. Opt. (7)

Appl. Phys. Express (1)

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, O. Matoba, and T. Kubota, “Space-bandwidth capacity-enhanced digital holography,” Appl. Phys. Express 6, 022502 (2013).
[Crossref]

Arch. Mikrosk. Anat. (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosk. Anat. 9, 413–418 (1873).
[Crossref]

Biomed. Opt. Express (2)

Chin. Opt. Lett. (1)

J. Biomed. Opt. (1)

P. Girshovitz, I. Frenklach, and N. T. Shaked, “Broadband quantitative phase microscopy with extended field of view using off-axis interferometric multiplexing,” J. Biomed. Opt. 20, 111217 (2015).
[Crossref]

J. Opt. (2)

Y. Wu, Y. Yang, H. Zhai, Z. Ma, L. Deng, and Q. Ge, “Single-exposure approach for expanding the sampled area of a dynamic process by digital holography with combined multiplexing,” J. Opt. 15, 085402 (2013).
[Crossref]

T. Tahara, R. Mori, Y. Arai, and Y. Takaki, “Four-step phase-shifting digital holography simultaneously sensing dual-wavelength information using a monochromatic image sensor,” J. Opt. 17, 125707 (2015).
[Crossref]

Light Sci. Appl. (1)

P. Girshovitz and N. T. Shaked, “Doubling the field of view in off-axis low-coherence interferometric imaging,” Light Sci. Appl. 3, e151 (2014).
[Crossref]

Opt. Commun. (1)

G. Dardikman and N. T. Shaked, “Review on methods of solving the refractive index-thickness coupling problem in digital holographic microscopy of biological cells,” Opt. Commun. 422, 8–16 (2018).
[Crossref]

Opt. Express (10)

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Figures (7)

Fig. 1.
Fig. 1. Schematic illustrations of the SFD for the three typical holographic recording geometries. (a) On-axis holography. (b) Off-axis holography. (c) Slightly off-axis holography. DC denotes the autocorrelation terms, illustrated by an orange circle. Red circles illustrate the CC terms, where the coinciding complex conjugate CC terms are denoted by a number and an asterisk.
Fig. 2.
Fig. 2. Schematic illustrations of the SFD power spectra for various spatial-bandwidth-efficient holographic imaging architectures, including bandwidth calculations, assuming the same number of camera pixels. (a) Optimal on-axis holography. (b) SPACE. (c) Diagonal off-axis multiplexing. (d) 6PH. (e) 8PH with the DC terms removed. (f) Diagonal slightly off-axis multiplexing with the DC terms removed. DC denotes the autocorrelation terms, and the numbered circles around it denote the CC terms, where coinciding complex conjugate CC terms are denoted by the same number with and without an asterisk.
Fig. 3.
Fig. 3. Numerical simulation inputs. (a) 3D RI distribution of simulated biological cell. Yellow indicates an RI value of 1.35, and red indicates an RI value of 1.37. (b) Original phase image. (c) Original amplitude image. (d) Filtered phase image. (e) Filtered amplitude image.
Fig. 4.
Fig. 4. Numerical simulation of the SFD power spectra for various spatial bandwidth-efficient holographic imaging architectures. (a) Optimal on-axis holography. (b) SPACE. (c) Diagonal off-axis multiplexing. (d) 6PH. (e) 8PH. (f) Diagonal slightly off-axis multiplexing. For (e) and (f), the final SFD, obtained after subtracting the two phase-shifted holograms, is presented.
Fig. 5.
Fig. 5. Simulated holograms for the various architectures. (a) Optimal on-axis holography. (b) SPACE. (c) Diagonal off-axis holographic multiplexing. (d) 6PH. (e) 8PH. (f) Diagonal slightly off-axis holographic multiplexing. For (a), (e), and (f), several phase-shifted holograms were generated as needed for reconstruction, but only one is shown. Red rectangle shows a close-up image of the interference fringes. Note that different magnifications were required for the different spatial bandwidth-efficient architectures, for optimal usage of the spatial bandwidth.
Fig. 6.
Fig. 6. Amplitude reconstruction results for an 8-bit ideal detector. (a) Various off-axis holographic architectures using ωc=4ωs; top left: ground truth; top right: reconstruction from nonmultiplexed off-axis holography; bottom left: reconstruction from 6PH; bottom right: reconstruction from 8PH. (b) Optimal on-axis holography; left: ground truth; right: reconstruction. (c) SPACE; left: ground truth; right: reconstruction. (d) Diagonal off-axis holographic multiplexing; left: ground truth; right: reconstruction. (e) Diagonal slightly off-axis holographic multiplexing; left: ground truth; right: reconstruction. For architectures where several wavefronts are multiplexed, only the first reconstruction is displayed.
Fig. 7.
Fig. 7. Phase reconstruction results. (a) Optimal on-axis holography. (b) SPACE. (c) Diagonal off-axis holographic multiplexing. (d) Nonmultiplexed off-axis holography. (e) 6PH. (f) 8PH. (g) Diagonal slightly off-axis holographic multiplexing. First column to the left: ground truth without amplitude modulation. Second column: reconstruction without amplitude modulation for an 8-bit ideal detector. Third column: reconstruction without amplitude modulation for a 16-bit ideal detector. Fourth column: ground truth with amplitude modulation. Fifth column: reconstruction with amplitude modulation for an 8-bit ideal detector. Sixth column: reconstruction with amplitude modulation for a 16-bit ideal detector. For architectures where several wavefronts are multiplexed, only the first reconstruction is displayed. The phase maps we chose to present here have MSE values close to the average, as seen in Tables 2 and 3.

Tables (3)

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Table 1. Comparison of Various Digital Holography Architecturesa

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Table 2. Phase Reconstruction Quality Estimation for an 8-bit Ideal Detectora,b

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Table 3. Phase Reconstruction Quality Estimation for a 16-bit Ideal Detectora,b

Equations (17)

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φ(x,y)=2πλOPD(x,y),
Ion-axis(x,y)=|Es(x,y)+Er|2=|Es(x,y)|2+|Er|2+|Es(x,y)||Er|exp[j·φs(x,y)]+|Es(x,y)||Er|exp[j·φs(x,y)],
CC1=I1+I2·exp(2πj3)+I3·exp(2πj3),
Ioff-axis(x,y)=|Es(x,y)+Er·exp[j·φo(x,y)]|2=|Es(x,y)|2+|Er|2+|Es(x,y)||Er|exp{j·[φs(x,y)φo(x,y)]}+|Es(x,y)||Er|exp{j·[φs(x,y)φo(x,y)]},
φo(x,y)=2πλ[xsin(θx)+ysin(θy)],
FT{Ioff-axis(x,y)}=FT{|Es(x,y)|2}+|Er|2·δ(u,v)+|Er|·FT{|Es(x,y)|exp[j·φs(x,y)]}*δ[u+2πλ·sin(θx),v+2πλ·sin(θy)]+|Er|·FT{|Es(x,y)|exp[j·φs(x,y)]}*δ[u2πλ·sin(θx),v2πλ·sin(θy)],
u0=2πλ·sin(θx)θx=sin1(λ2π·u0),v0=2πλ·sin(θy)θy=sin1(λ2π·v0),
Imultiplexed(x,y)=k=1N|Es,k(x,y)+Er,k·exp[j·φo,k(x,y)]|2.
FT{Imultiplexed(x,y)}=k=1N[FT{|Es,k(x,y)|2}+|Er,k|2·δ(u,v)]+k=1N|Er,k|·FT{|Es,k(x,y)|exp[j·φs,k(x,y)]}*δ[u+2πλ·sin(θx,k),v+2πλ·sin(θy,k)]+k=1N|Er,k|·FT{|Es,k(x,y)|exp[j·φs,k(x,y)]}*δ[u2πλ·sin(θx,k),v2πλ·sin(θy,k)],
Imultiplexed(x,y)=k=1Nexp[j(x·us,k+y·vs,k)]·|Es,k(x,y)+Er,k·exp[j·φo(x,y)]|2,
FT{Imultiplexed(x,y)}=k=1Nδ[uus,k,vvs,k]*{FT{|Es,k(x,y)|2}+|Er,k|2·δ(u,v)+|Er,k|·FT{|Es,k(x,y)|exp[j·φs,k(x,y)]}*δ[u+2πλ·sin(θx),v+2πλ·sin(θy)]+|Er,k|·FT{|Es,k(x,y)|exp[j·φs,k(x,y)]}*δ[u2πλ·sin(θx),v2πλ·sin(θy)]}.
Imultiplexed(x,y)=I1(x,y)+j·I2(x,y).
ωc,u=2π2Δx=πΔx,ωc,v=2π2Δy=πΔy.
ωs=2πM·d,
d=λNA.
Ef=ωsωc·NwNa,
φ(i,j)=2πλΔkk=1Nn(i,j,k),

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