Abstract

Chromatic aberrations are a primary limiting factor in thin, high-quality imaging systems. Recent advances in nanoscale manufacturing, however, have enabled the creation of metasurfaces: ultra-thin optical components with sub-wavelength features that can locally manipulate the wavefront phase. Meanwhile, there has been renewed interest in GRadient-INdex (GRIN) lenses due to the extended degrees of design freedom they offer. When combined, these two technologies can provide unparalleled imaging system performance while realizing drastic reductions in size, weight, and power. Through paraxial theory and full ray tracing we produce a lens singlet that can achieve three-color (apochromatic) correction by employing a metasurface-augmented GRIN. This apochromatic singlet has the potential for application in high-quality optical systems.

© 2018 Optical Society of America

Full Article  |  PDF Article
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References

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2017 (2)

M. Khorasaninejad, Z. Shi, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, Nano Lett. 17, 1819 (2017).
[Crossref]

D. T. Nguyen, C. Meyers, T. D. Yee, N. A. Dudukovic, J. F. Destino, C. Zhu, E. B. Duoss, E. F. Baumann, T. Suratwala, and J. E. Smay, Adv. Mater. 29, 1701181 (2017).
[Crossref]

2016 (5)

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, Proc. Natl. Acad. Sci. USA 113, 10473 (2016).
[Crossref]

Y. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, Sci. Rep. 6, 19885 (2016).
[Crossref]

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, Nat. Commun. 7, 13682 (2016).
[Crossref]

J. Xing, J. Kim, and H. Yoo, Opt. Express 24, 1037 (2016).
[Crossref]

S. D. Campbell, D. Brocker, J. Nagar, and D. H. Werner, Appl. Opt. 55, 3594 (2016).
[Crossref]

2013 (1)

2012 (1)

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, IEEE Trans. Antennas Propag. Mag. 54(2), 10 (2012).
[Crossref]

2011 (1)

N. Yu, P. Geneveet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[Crossref]

2003 (1)

N. Hansen, S. D. Müller, and P. Koumoutsakos, Evol. Comput. 11, 1 (2003).
[Crossref]

2001 (1)

M. R. Gordova, A. A. Lipovskii, V. V. Zhurihina, D. K. Tagantsev, B. V. Tatarintsev, and J. Turunen, Opt. Eng. 40, 1507 (2001).
[Crossref]

1992 (1)

Aieta, F.

N. Yu, P. Geneveet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[Crossref]

Arbabi, A.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, Nat. Commun. 7, 13682 (2016).
[Crossref]

Arbabi, E.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, Nat. Commun. 7, 13682 (2016).
[Crossref]

Baumann, E. F.

D. T. Nguyen, C. Meyers, T. D. Yee, N. A. Dudukovic, J. F. Destino, C. Zhu, E. B. Duoss, E. F. Baumann, T. Suratwala, and J. E. Smay, Adv. Mater. 29, 1701181 (2017).
[Crossref]

Beadie, G.

Booth, J.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, IEEE Trans. Antennas Propag. Mag. 54(2), 10 (2012).
[Crossref]

Brocker, D.

S. D. Campbell, D. Brocker, J. Nagar, and D. H. Werner, Appl. Opt. 55, 3594 (2016).
[Crossref]

J. P. Turpin, D. Brocker, and D. H. Werner, “Optimization of quasi-conformal transformation optics lenses with an arbitrary GRIN-capable ray tracer,” in IEEE AP-S Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, Orlando, Florida (IEEE, 2013), pp. 1898–1899.

Brocker, D. E.

S. D. Campbell, D. E. Brocker, D. H. Werner, C. Dupuy, S. K. Park, and P. Harmon, IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2015), 605.

Campbell, S. D.

S. D. Campbell, D. Brocker, J. Nagar, and D. H. Werner, Appl. Opt. 55, 3594 (2016).
[Crossref]

S. D. Campbell, D. E. Brocker, D. H. Werner, C. Dupuy, S. K. Park, and P. Harmon, IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2015), 605.

Capasso, F.

M. Khorasaninejad, Z. Shi, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, Nano Lett. 17, 1819 (2017).
[Crossref]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, Proc. Natl. Acad. Sci. USA 113, 10473 (2016).
[Crossref]

N. Yu, P. Geneveet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[Crossref]

Chen, W. T.

M. Khorasaninejad, Z. Shi, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, Nano Lett. 17, 1819 (2017).
[Crossref]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, Proc. Natl. Acad. Sci. USA 113, 10473 (2016).
[Crossref]

Deng, Z. L.

Z. L. Deng, X. Li, and G. P. Wang, “A multifunctional metasurface: from extraordinary optical transmission to extraordinary optical diffraction in a single structure,” arXiv:1705.10171 (2017).

Destino, J. F.

D. T. Nguyen, C. Meyers, T. D. Yee, N. A. Dudukovic, J. F. Destino, C. Zhu, E. B. Duoss, E. F. Baumann, T. Suratwala, and J. E. Smay, Adv. Mater. 29, 1701181 (2017).
[Crossref]

Devlin, R. C.

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, Proc. Natl. Acad. Sci. USA 113, 10473 (2016).
[Crossref]

Dudukovic, N. A.

D. T. Nguyen, C. Meyers, T. D. Yee, N. A. Dudukovic, J. F. Destino, C. Zhu, E. B. Duoss, E. F. Baumann, T. Suratwala, and J. E. Smay, Adv. Mater. 29, 1701181 (2017).
[Crossref]

Duoss, E. B.

D. T. Nguyen, C. Meyers, T. D. Yee, N. A. Dudukovic, J. F. Destino, C. Zhu, E. B. Duoss, E. F. Baumann, T. Suratwala, and J. E. Smay, Adv. Mater. 29, 1701181 (2017).
[Crossref]

Dupuy, C.

S. D. Campbell, D. E. Brocker, D. H. Werner, C. Dupuy, S. K. Park, and P. Harmon, IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2015), 605.

Faraon, A.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, Nat. Commun. 7, 13682 (2016).
[Crossref]

Fleet, E. F.

Flynn, R. A.

Gaburro, Z.

N. Yu, P. Geneveet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[Crossref]

Geneveet, P.

N. Yu, P. Geneveet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[Crossref]

Gordon, J. A.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, IEEE Trans. Antennas Propag. Mag. 54(2), 10 (2012).
[Crossref]

Gordova, M. R.

M. R. Gordova, A. A. Lipovskii, V. V. Zhurihina, D. K. Tagantsev, B. V. Tatarintsev, and J. Turunen, Opt. Eng. 40, 1507 (2001).
[Crossref]

Han, S.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, Nat. Commun. 7, 13682 (2016).
[Crossref]

Hansen, N.

N. Hansen, S. D. Müller, and P. Koumoutsakos, Evol. Comput. 11, 1 (2003).
[Crossref]

Harmon, P.

S. D. Campbell, D. E. Brocker, D. H. Werner, C. Dupuy, S. K. Park, and P. Harmon, IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2015), 605.

Holloway, C. L.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, IEEE Trans. Antennas Propag. Mag. 54(2), 10 (2012).
[Crossref]

Horie, Y.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, Nat. Commun. 7, 13682 (2016).
[Crossref]

Kamali, S. M.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, Nat. Commun. 7, 13682 (2016).
[Crossref]

Kats, M. A.

N. Yu, P. Geneveet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[Crossref]

Khorasaninejad, M.

M. Khorasaninejad, Z. Shi, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, Nano Lett. 17, 1819 (2017).
[Crossref]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, Proc. Natl. Acad. Sci. USA 113, 10473 (2016).
[Crossref]

Kim, J.

Koumoutsakos, P.

N. Hansen, S. D. Müller, and P. Koumoutsakos, Evol. Comput. 11, 1 (2003).
[Crossref]

Kuester, E. F.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, IEEE Trans. Antennas Propag. Mag. 54(2), 10 (2012).
[Crossref]

Li, X.

Z. L. Deng, X. Li, and G. P. Wang, “A multifunctional metasurface: from extraordinary optical transmission to extraordinary optical diffraction in a single structure,” arXiv:1705.10171 (2017).

Li, Y.

Y. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, Sci. Rep. 6, 19885 (2016).
[Crossref]

Lipovskii, A. A.

M. R. Gordova, A. A. Lipovskii, V. V. Zhurihina, D. K. Tagantsev, B. V. Tatarintsev, and J. Turunen, Opt. Eng. 40, 1507 (2001).
[Crossref]

Luo, X.

Y. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, Sci. Rep. 6, 19885 (2016).
[Crossref]

Ma, X.

Y. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, Sci. Rep. 6, 19885 (2016).
[Crossref]

Marchand, E. W.

E. W. Marchand, Gradient Index Optics (Academic, 1978).

McCarthy, P.

P. McCarthy and D. T. Moore, Optical Fabrication and Testing (2012), OTu4D-2.

Meyers, C.

D. T. Nguyen, C. Meyers, T. D. Yee, N. A. Dudukovic, J. F. Destino, C. Zhu, E. B. Duoss, E. F. Baumann, T. Suratwala, and J. E. Smay, Adv. Mater. 29, 1701181 (2017).
[Crossref]

Moore, D. T.

P. McCarthy and D. T. Moore, Optical Fabrication and Testing (2012), OTu4D-2.

Müller, S. D.

N. Hansen, S. D. Müller, and P. Koumoutsakos, Evol. Comput. 11, 1 (2003).
[Crossref]

Nagar, J.

Nguyen, D. T.

D. T. Nguyen, C. Meyers, T. D. Yee, N. A. Dudukovic, J. F. Destino, C. Zhu, E. B. Duoss, E. F. Baumann, T. Suratwala, and J. E. Smay, Adv. Mater. 29, 1701181 (2017).
[Crossref]

O’Hara, J.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, IEEE Trans. Antennas Propag. Mag. 54(2), 10 (2012).
[Crossref]

Oh, J.

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, Proc. Natl. Acad. Sci. USA 113, 10473 (2016).
[Crossref]

Park, S. K.

S. D. Campbell, D. E. Brocker, D. H. Werner, C. Dupuy, S. K. Park, and P. Harmon, IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2015), 605.

Pu, M.

Y. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, Sci. Rep. 6, 19885 (2016).
[Crossref]

Sanjeev, V.

M. Khorasaninejad, Z. Shi, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, Nano Lett. 17, 1819 (2017).
[Crossref]

Shi, Z.

M. Khorasaninejad, Z. Shi, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, Nano Lett. 17, 1819 (2017).
[Crossref]

Shirk, J. S.

Smay, J. E.

D. T. Nguyen, C. Meyers, T. D. Yee, N. A. Dudukovic, J. F. Destino, C. Zhu, E. B. Duoss, E. F. Baumann, T. Suratwala, and J. E. Smay, Adv. Mater. 29, 1701181 (2017).
[Crossref]

Smith, D. R.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, IEEE Trans. Antennas Propag. Mag. 54(2), 10 (2012).
[Crossref]

Smith, W. J.

W. J. Smith, Modern Optical Engineering (Tata McGraw-Hill Education, 2000).

Suratwala, T.

D. T. Nguyen, C. Meyers, T. D. Yee, N. A. Dudukovic, J. F. Destino, C. Zhu, E. B. Duoss, E. F. Baumann, T. Suratwala, and J. E. Smay, Adv. Mater. 29, 1701181 (2017).
[Crossref]

Tagantsev, D. K.

M. R. Gordova, A. A. Lipovskii, V. V. Zhurihina, D. K. Tagantsev, B. V. Tatarintsev, and J. Turunen, Opt. Eng. 40, 1507 (2001).
[Crossref]

Tatarintsev, B. V.

M. R. Gordova, A. A. Lipovskii, V. V. Zhurihina, D. K. Tagantsev, B. V. Tatarintsev, and J. Turunen, Opt. Eng. 40, 1507 (2001).
[Crossref]

Tetienne, J. P.

N. Yu, P. Geneveet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[Crossref]

Turpin, J. P.

J. P. Turpin, D. Brocker, and D. H. Werner, “Optimization of quasi-conformal transformation optics lenses with an arbitrary GRIN-capable ray tracer,” in IEEE AP-S Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, Orlando, Florida (IEEE, 2013), pp. 1898–1899.

Turunen, J.

M. R. Gordova, A. A. Lipovskii, V. V. Zhurihina, D. K. Tagantsev, B. V. Tatarintsev, and J. Turunen, Opt. Eng. 40, 1507 (2001).
[Crossref]

Wang, G. P.

Z. L. Deng, X. Li, and G. P. Wang, “A multifunctional metasurface: from extraordinary optical transmission to extraordinary optical diffraction in a single structure,” arXiv:1705.10171 (2017).

Wang, Y.

Y. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, Sci. Rep. 6, 19885 (2016).
[Crossref]

Werner, D. H.

S. D. Campbell, D. Brocker, J. Nagar, and D. H. Werner, Appl. Opt. 55, 3594 (2016).
[Crossref]

J. P. Turpin, D. Brocker, and D. H. Werner, “Optimization of quasi-conformal transformation optics lenses with an arbitrary GRIN-capable ray tracer,” in IEEE AP-S Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, Orlando, Florida (IEEE, 2013), pp. 1898–1899.

S. D. Campbell, D. E. Brocker, D. H. Werner, C. Dupuy, S. K. Park, and P. Harmon, IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2015), 605.

Wood, A. P.

Xing, J.

Yee, T. D.

D. T. Nguyen, C. Meyers, T. D. Yee, N. A. Dudukovic, J. F. Destino, C. Zhu, E. B. Duoss, E. F. Baumann, T. Suratwala, and J. E. Smay, Adv. Mater. 29, 1701181 (2017).
[Crossref]

Yoo, H.

Yu, N.

N. Yu, P. Geneveet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[Crossref]

Zaidi, A.

M. Khorasaninejad, Z. Shi, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, Nano Lett. 17, 1819 (2017).
[Crossref]

Zhao, Z.

Y. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, Sci. Rep. 6, 19885 (2016).
[Crossref]

Zhu, C.

D. T. Nguyen, C. Meyers, T. D. Yee, N. A. Dudukovic, J. F. Destino, C. Zhu, E. B. Duoss, E. F. Baumann, T. Suratwala, and J. E. Smay, Adv. Mater. 29, 1701181 (2017).
[Crossref]

Zhurihina, V. V.

M. R. Gordova, A. A. Lipovskii, V. V. Zhurihina, D. K. Tagantsev, B. V. Tatarintsev, and J. Turunen, Opt. Eng. 40, 1507 (2001).
[Crossref]

Adv. Mater. (1)

D. T. Nguyen, C. Meyers, T. D. Yee, N. A. Dudukovic, J. F. Destino, C. Zhu, E. B. Duoss, E. F. Baumann, T. Suratwala, and J. E. Smay, Adv. Mater. 29, 1701181 (2017).
[Crossref]

Appl. Opt. (2)

Evol. Comput. (1)

N. Hansen, S. D. Müller, and P. Koumoutsakos, Evol. Comput. 11, 1 (2003).
[Crossref]

IEEE Trans. Antennas Propag. Mag. (1)

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, IEEE Trans. Antennas Propag. Mag. 54(2), 10 (2012).
[Crossref]

Nano Lett. (1)

M. Khorasaninejad, Z. Shi, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, Nano Lett. 17, 1819 (2017).
[Crossref]

Nat. Commun. (1)

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, Nat. Commun. 7, 13682 (2016).
[Crossref]

Opt. Eng. (1)

M. R. Gordova, A. A. Lipovskii, V. V. Zhurihina, D. K. Tagantsev, B. V. Tatarintsev, and J. Turunen, Opt. Eng. 40, 1507 (2001).
[Crossref]

Opt. Express (2)

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

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, Proc. Natl. Acad. Sci. USA 113, 10473 (2016).
[Crossref]

Sci. Rep. (1)

Y. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, Sci. Rep. 6, 19885 (2016).
[Crossref]

Science (1)

N. Yu, P. Geneveet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[Crossref]

Other (7)

E. W. Marchand, Gradient Index Optics (Academic, 1978).

Z. L. Deng, X. Li, and G. P. Wang, “A multifunctional metasurface: from extraordinary optical transmission to extraordinary optical diffraction in a single structure,” arXiv:1705.10171 (2017).

P. McCarthy and D. T. Moore, Optical Fabrication and Testing (2012), OTu4D-2.

M. N. Polyanskiy, “Refractive index database,” 2017, https://refractiveindex.info .

J. P. Turpin, D. Brocker, and D. H. Werner, “Optimization of quasi-conformal transformation optics lenses with an arbitrary GRIN-capable ray tracer,” in IEEE AP-S Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, Orlando, Florida (IEEE, 2013), pp. 1898–1899.

W. J. Smith, Modern Optical Engineering (Tata McGraw-Hill Education, 2000).

S. D. Campbell, D. E. Brocker, D. H. Werner, C. Dupuy, S. K. Park, and P. Harmon, IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2015), 605.

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Figures (5)

Fig. 1.
Fig. 1. Cartoon examples of (a) a homogeneous lens showing chromatic aberrations and (b) an MS-GRIN lens exhibiting apochromatic performance.
Fig. 2.
Fig. 2. P-ν map for the MS-GRIN and refractive triplet.
Fig. 3.
Fig. 3. Ratio of MS-GRIN parameters predicted by analytical theory with those optimized by CMA-ES versus f/#: (a) Rf, (b) T, and (c) ϕm.
Fig. 4.
Fig. 4. Focal drift versus wavelength for the GRIN, MS-GRIN, refractive doublet and triplet. The shaded region corresponds to the diffraction-limited depth of focus.
Fig. 5.
Fig. 5. Comparison between optimized MS-GRIN and refractive triplet. (a) MTF at λd. (b) Strehl ratio versus wavelength.

Equations (9)

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ntsin(θt)=nisin(θi)+1kdϕdρ,
ϕ=2πλm[ρ2+fm2fm].
ϕm(λ)λλmfm,
νm=ϕ2ϕ1ϕ3=λ2λ1λ3,Pm=ϕ1ϕ2ϕ1ϕ3=λ1λ2λ1λ3,
n(r,z)=n0+Δnr(2D)2r2+Δnz(1T)z.
ϕG=Δnr2(2D)2T,νG=Δnr2Δnr1Δnr3,PG=Δnr1Δnr2Δnr1Δnr3,
ϕf=nf21Rf,νf=nf21nf1nf3,Pf=nf1nf2nf1nf3,
ϕf+ϕG+ϕm=ϕT,ϕfνf+ϕGνG+ϕmνm=0,Pfϕfνf+PGϕGνG+Pmϕmνm=0.
Xνf(PGPm)+νG(PmPf)+νm(PfPG),Rf=[(νf(PGPm)X)ϕTnf21]1,T=(D/2)22|αr|(νG(PmPf)nf21)ϕT,fm=[(νm(PfPG)X)ϕT]1.

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