Abstract

We report on the fabrication and the experimental demonstration of Moiré diffractive spiral phase plates with adjustable helical charge. The proposed optical unit consists of two axially stacked diffractive elements of conjugate structure. The joint transmission function of the compound system corresponds to that of a spiral phase plate where the angle of mutual rotation about the central axis enables continuous adjustment of the helical charge. The diffractive elements are fabricated by gray-scale photolithography with a pixel size of 200 nm and 128 phase step levels in fused silica. We experimentally demonstrate the conversion of a TEM00 beam into approximated Laguerre-Gauss (LG) beams of variable helical charge, with a correspondingly variable radius of their ring-shaped intensity distribution.

© 2015 Optical Society of America

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References

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2014 (3)

2013 (3)

S. Bernet, W. Harm, and M. Ritsch-Marte, “Demonstration of focus-tunable diffractive Moiré-lenses,” Opt. Exp. 21, 6955–6966 (2013).
[Crossref]

R. Steiger, S. Bernet, and M. Ritsch-Marte, “Mapping of phase singularities with spiral phase contrast microscopy,” Opt. Exp. 21, 16282–16289 (2013).
[Crossref]

M. A. Lauterbach, M. Guillon, A. Soltani, and V. Emiliani, “STED microscope with spiral phase contrast,” Sci. Rep. 3, 2050 (2013)
[Crossref] [PubMed]

2012 (2)

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
[Crossref]

J. Yu, C. Zhou, W. Jia, A. Hu, W. Cao, J. Wu, and S. Wang, “Three-dimensional Dammann vortex array with tunable topological charge,” Appl. Opt. 51, 2485–2490 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (3)

N. Zhang, X. C. Yuan, and R. E. Burge, “Extending the detection range of optical vortices by Dammann vortex gratings,” Opt. Lett. 35, 3495–3497 (2010).
[Crossref] [PubMed]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12, 115707 (2010).
[Crossref]

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronograph: Laboratory results and first light at Palomar observatory,” Astrophys. J. 709, 53 (2010).
[Crossref]

2009 (1)

2008 (2)

S. Bernet and M. Ritsch-Marte, “Adjustable refractive power from diffractive Moire elements,” Appl. Opt. 47, 3722–3730 (2008).
[Crossref] [PubMed]

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134–142 (2008)
[Crossref] [PubMed]

2005 (2)

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[Crossref] [PubMed]

G. Foo, D. M. Palacios, and G. A. Swartzlander, “Optical vortex coronagraph,” Opt. Lett. 30, 3308–3310 (2005).
[Crossref]

2004 (2)

2003 (1)

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[Crossref] [PubMed]

2002 (1)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

1998 (1)

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” JOSA B 15, 2226–2234 (1998).
[Crossref]

1994 (1)

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 458185–8189 (1992).
[Crossref] [PubMed]

Ahmed, N.

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 458185–8189 (1992).
[Crossref] [PubMed]

Ament, C.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 458185–8189 (1992).
[Crossref] [PubMed]

Bernet, S.

R. Steiger, S. Bernet, and M. Ritsch-Marte, “Mapping of phase singularities with spiral phase contrast microscopy,” Opt. Exp. 21, 16282–16289 (2013).
[Crossref]

S. Bernet, W. Harm, and M. Ritsch-Marte, “Demonstration of focus-tunable diffractive Moiré-lenses,” Opt. Exp. 21, 6955–6966 (2013).
[Crossref]

S. Bernet and M. Ritsch-Marte, “Adjustable refractive power from diffractive Moire elements,” Appl. Opt. 47, 3722–3730 (2008).
[Crossref] [PubMed]

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134–142 (2008)
[Crossref] [PubMed]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[Crossref] [PubMed]

Birnbaum, K. M.

Burge, R. E.

Burruss, R.

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronograph: Laboratory results and first light at Palomar observatory,” Astrophys. J. 709, 53 (2010).
[Crossref]

Cao, W.

Cheong, W. C.

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[Crossref] [PubMed]

Dolinar, S. J.

Dreischuh, A.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
[Crossref]

Emiliani, V.

M. A. Lauterbach, M. Guillon, A. Soltani, and V. Emiliani, “STED microscope with spiral phase contrast,” Sci. Rep. 3, 2050 (2013)
[Crossref] [PubMed]

Erkmen, B. I.

Foo, G.

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134–142 (2008)
[Crossref] [PubMed]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[Crossref] [PubMed]

Grier, D. G.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[Crossref] [PubMed]

Guillon, M.

M. A. Lauterbach, M. Guillon, A. Soltani, and V. Emiliani, “STED microscope with spiral phase contrast,” Sci. Rep. 3, 2050 (2013)
[Crossref] [PubMed]

Hansinger, P.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
[Crossref]

Hao, X.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12, 115707 (2010).
[Crossref]

Harm, W.

S. Bernet, W. Harm, and M. Ritsch-Marte, “Demonstration of focus-tunable diffractive Moiré-lenses,” Opt. Exp. 21, 6955–6966 (2013).
[Crossref]

Heckenberg, N. R.

Hell, S. W.

Hickey, J.

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronograph: Laboratory results and first light at Palomar observatory,” Astrophys. J. 709, 53 (2010).
[Crossref]

Hu, A.

Huang, H.

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134–142 (2008)
[Crossref] [PubMed]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[Crossref] [PubMed]

Jia, W.

Johnson, L.

Kern, C.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
[Crossref]

Kuang, C.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12, 115707 (2010).
[Crossref]

Lauterbach, M. A.

M. A. Lauterbach, M. Guillon, A. Soltani, and V. Emiliani, “STED microscope with spiral phase contrast,” Sci. Rep. 3, 2050 (2013)
[Crossref] [PubMed]

Lavery, M. P. J.

Leach, J.

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

Lee, W. M.

Liewer, K.

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronograph: Laboratory results and first light at Palomar observatory,” Astrophys. J. 709, 53 (2010).
[Crossref]

Liu, X.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12, 115707 (2010).
[Crossref]

Lucero, A.

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 2007).
[Crossref]

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134–142 (2008)
[Crossref] [PubMed]

Mawet, D.

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronograph: Laboratory results and first light at Palomar observatory,” Astrophys. J. 709, 53 (2010).
[Crossref]

McDuff, R.

Milster, T.

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

Osten, W.

Padgett, M. J.

Palacios, D. M.

Pedrini, G.

Polynkin, P.

Ren, Y.

Ritsch-Marte, M.

R. Steiger, S. Bernet, and M. Ritsch-Marte, “Mapping of phase singularities with spiral phase contrast microscopy,” Opt. Exp. 21, 16282–16289 (2013).
[Crossref]

S. Bernet, W. Harm, and M. Ritsch-Marte, “Demonstration of focus-tunable diffractive Moiré-lenses,” Opt. Exp. 21, 6955–6966 (2013).
[Crossref]

S. Bernet and M. Ritsch-Marte, “Adjustable refractive power from diffractive Moire elements,” Appl. Opt. 47, 3722–3730 (2008).
[Crossref] [PubMed]

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134–142 (2008)
[Crossref] [PubMed]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[Crossref] [PubMed]

Rogawski, D.

Rozas, D.

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” JOSA B 15, 2226–2234 (1998).
[Crossref]

Sacks, Z. S.

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” JOSA B 15, 2226–2234 (1998).
[Crossref]

Schmitt-Sody, A.

Serabyn, E.

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronograph: Laboratory results and first light at Palomar observatory,” Astrophys. J. 709, 53 (2010).
[Crossref]

Shemo, D.

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronograph: Laboratory results and first light at Palomar observatory,” Astrophys. J. 709, 53 (2010).
[Crossref]

Shen, B.

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

Shi, Y.

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

Situ, G.

Smith, C. P.

Soltani, A.

M. A. Lauterbach, M. Guillon, A. Soltani, and V. Emiliani, “STED microscope with spiral phase contrast,” Sci. Rep. 3, 2050 (2013)
[Crossref] [PubMed]

Spielmann, Ch.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
[Crossref]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 458185–8189 (1992).
[Crossref] [PubMed]

Steiger, R.

R. Steiger, S. Bernet, and M. Ritsch-Marte, “Mapping of phase singularities with spiral phase contrast microscopy,” Opt. Exp. 21, 16282–16289 (2013).
[Crossref]

Swartzlander, G. A.

G. Foo, D. M. Palacios, and G. A. Swartzlander, “Optical vortex coronagraph,” Opt. Lett. 30, 3308–3310 (2005).
[Crossref]

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” JOSA B 15, 2226–2234 (1998).
[Crossref]

Tur, M.

Wang, S.

Wang, T.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12, 115707 (2010).
[Crossref]

Wang, W.

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

White, A. G.

Wichmann, J.

Willner, A. E.

Willner, M. J.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 458185–8189 (1992).
[Crossref] [PubMed]

Wu, J.

Xie, G.

Xu, Z.

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

Yan, Y.

Yao, A. M.

Yao, E.

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

Yu, J.

Yuan, X. C.

Yuan, X.-C.

Yue, Y.

Zhang, L.

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

Zhang, N.

Zhang, X.

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

Zhou, C.

Zürch, M.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Opt. (3)

Astrophys. J. (1)

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronograph: Laboratory results and first light at Palomar observatory,” Astrophys. J. 709, 53 (2010).
[Crossref]

J. Microsc. (1)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134–142 (2008)
[Crossref] [PubMed]

J. Opt. (1)

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12, 115707 (2010).
[Crossref]

J. Opt. Soc. Am. A (1)

JOSA B (1)

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” JOSA B 15, 2226–2234 (1998).
[Crossref]

Nat. Phys. (1)

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
[Crossref]

New J. Phys. (1)

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

Opt. Exp. (2)

S. Bernet, W. Harm, and M. Ritsch-Marte, “Demonstration of focus-tunable diffractive Moiré-lenses,” Opt. Exp. 21, 6955–6966 (2013).
[Crossref]

R. Steiger, S. Bernet, and M. Ritsch-Marte, “Mapping of phase singularities with spiral phase contrast microscopy,” Opt. Exp. 21, 16282–16289 (2013).
[Crossref]

Opt. Lett. (6)

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 458185–8189 (1992).
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Phys. Rev. Lett. (4)

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M. A. Lauterbach, M. Guillon, A. Soltani, and V. Emiliani, “STED microscope with spiral phase contrast,” Sci. Rep. 3, 2050 (2013)
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Figures (5)

Fig. 1
Fig. 1 Phase functions for a design parameter a = 90 of (a) Φ1(ϕ), (b) Φ2(ϕ) and (c) of the compound unit for an exemplary angle of mutual rotation ϕ = 8° resulting in a helicity of = 4. The grey levels in the figure correspond to phase shifts in an interval between −π and π.
Fig. 2
Fig. 2 (a): Photograph of one of the fabricated MDOEs. (b): Height measurement of its phase profile in the central region by white light interferometry. (c): Phase profile along the vertical line indicated in B.
Fig. 3
Fig. 3 Experimentally measured phase distribution of a plane wave (λ = 532 nm) after passing the vortex MDOE at different angles of mutual rotation θ. Upper row: Sketch of the interferometric setup, and 3 exemplary interferograms measured at different phase shifts α (indicated in the figure). Below: Phase behind the vortex plate, reconstructed from the corresponding interferograms, as a function of the rotation angle θ. The corresponding helicity of the combined vortex plate corresponds to the number of radially appearing 2π-phase jumps. Note that only positive helicities are shown, but the opposite sign can be obtained by reversing the mutual rotation direction of the two DOEs in the combined MDOE.
Fig. 4
Fig. 4 Normalized intensity distribution of a TEM00 beam at λ = 532 nm, passing an MDOE spiral phase plate set at different angles of mutual rotation, focused on a digital sensor (mvBlueFOX-224G). (a) Unmodified TEM00 beam (θ = 0°). (b)–(g) TEM00 beam converted to LG-like beams of various helical charges .
Fig. 5
Fig. 5 (a) Line profiles, as indicated in the insets, comparison of an unmodified TEM00 beam with θ = 0° (green curve) and a LG-like beam with helical charge = 1 (blue curve). The transformation efficiency is 94%. (b) Experimental results (blue circles) for the linear scaling of the radius of the ring-shaped intensity distribution with .

Equations (7)

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Φ 1 ( ϕ ) = + a ϕ 2 / 2 π Φ 2 ( ϕ ) = a ϕ 2 / 2 π ,
Φ 2 ( ϕ ) = { a ( ϕ θ ) 2 / 2 π for θ ϕ < 2 π a ( ϕ θ + 2 π ) 2 / 2 π for 0 ϕ < θ .
T joint ( ϕ ) = { exp { i [ 2 θ ϕ θ 2 ] a / 2 π } for θ ϕ < 2 π exp { i [ ( 2 θ 4 π ) ϕ θ 2 4 π 2 + 4 π θ ] a / 2 π } for 0 ϕ < θ .
= { a π θ for θ ϕ < 2 π a π θ 2 a for 0 ϕ < θ ,
Φ 1 ( ϕ ) = mod 2 π { a ϕ 2 / 2 π } Φ 2 ( ϕ ) = mod 2 π { a ϕ 2 / 2 π } ,
a < R min π 2 p ,
R = b λ f π Σ ( 1 + 0 ) ,

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