Abstract

In-line digital holography based on two-intensity measurements [Zhang et al. Opt. Lett. 29, 1787 (2004)], is modified by introducing a π shifting in the reference phase. Such an improvement avoids the assumption that the object beam must be much weaker than the reference beam in strength and results in a simplified experimental implementation. Computer simulations and optical experiments are carried out to validate the method, which we refer to as position-phase-shifting digital holography.

© 2008 Optical Society of America

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2007 (3)

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
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[Crossref] [PubMed]

2006 (4)

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2004 (1)

2003 (1)

2002 (2)

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[Crossref]

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[Crossref]

2001 (1)

2000 (4)

1999 (3)

D. Mas, J. Carcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithm for free-space diffraction patterns calculation,” Opt. Commun. 164, 233-245 (1999).
[Crossref]

S. Lai, B. Kemper, and G. von Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37-43 (1999).
[Crossref]

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257-268 (1999).
[Crossref]

1998 (2)

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104-115 (1998).
[Crossref]

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[Crossref]

1997 (3)

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[Crossref]

M. Adams, T. Kreis, and W. Jüptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234-240 (1997).
[Crossref]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).
[Crossref] [PubMed]

1994 (2)

1992 (1)

1987 (1)

1983 (1)

1968 (1)

1951 (1)

W. L. Bragg and G. L. Rogers, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, 190-191 (1951).
[Crossref] [PubMed]

Absil, E.

Adams, M.

M. Adams, T. Kreis, and W. Jüptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234-240 (1997).
[Crossref]

Alfieri, D.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[Crossref]

Atlan, M.

Bernardo, L. M.

D. Mas, J. Carcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithm for free-space diffraction patterns calculation,” Opt. Commun. 164, 233-245 (1999).
[Crossref]

Boyer, K.

Bragg, W. L.

W. L. Bragg and G. L. Rogers, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, 190-191 (1951).
[Crossref] [PubMed]

Burow, R.

Cai, L. Z.

Carcia, J.

D. Mas, J. Carcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithm for free-space diffraction patterns calculation,” Opt. Commun. 164, 233-245 (1999).
[Crossref]

Charriére, F.

Chen, J. W.

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[Crossref]

Colomb, T.

Cuche, E.

Cullen, D.

Darakis, E.

De Petrocellis, L.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[Crossref]

Depeursinge, C.

Dong, G. Y.

Elssner, K.-E.

Ferraro, P.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[Crossref]

Ferreira, C.

D. Mas, J. Carcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithm for free-space diffraction patterns calculation,” Opt. Commun. 164, 233-245 (1999).
[Crossref]

Finizio, A.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[Crossref]

Fröning, P.

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257-268 (1999).
[Crossref]

Garcia-Sucerquia, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2004).

Gopinathan, U.

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, “Three dimensional object recognition from digital Fresnel hologram by wavelength matched filtering,” Opt. Commun. 259, 499-506 (2006).
[Crossref]

Grilli, S.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[Crossref]

Gross, M.

Grzanna, J.

Guo, C. S.

Haddad, W.

Hayashi, K.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[Crossref]

Hennelly, B. M.

Ishikawa, T.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[Crossref]

Javidi, B.

Jericho, M. H.

Jericho, S. K.

Joseph, J.

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, “Three dimensional object recognition from digital Fresnel hologram by wavelength matched filtering,” Opt. Commun. 259, 499-506 (2006).
[Crossref]

Jüptner, W.

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104-115 (1998).
[Crossref]

M. Adams, T. Kreis, and W. Jüptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234-240 (1997).
[Crossref]

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179-181 (1994).
[Crossref] [PubMed]

Kato, J.

Kemper, B.

S. Lai, B. Kemper, and G. von Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37-43 (1999).
[Crossref]

King, B.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[Crossref]

Klages, P.

Konforti, N.

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[Crossref]

Kreis, T.

M. Adams, T. Kreis, and W. Jüptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234-240 (1997).
[Crossref]

Kreuzer, H. J.

Lai, S.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[Crossref]

S. Lai, B. Kemper, and G. von Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37-43 (1999).
[Crossref]

Lalor, Ê.

Liao, J.

Liu, G.

Longworth, J. M.

Marinho, F.

D. Mas, J. Carcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithm for free-space diffraction patterns calculation,” Opt. Commun. 164, 233-245 (1999).
[Crossref]

Marquet, P.

Mas, D.

D. Mas, J. Carcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithm for free-space diffraction patterns calculation,” Opt. Commun. 164, 233-245 (1999).
[Crossref]

Massig, J. H.

Matsubara, E.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[Crossref]

McPherson, A.

Mendlovic, D.

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[Crossref]

Meng, X. F.

Merkel, K.

Miccio, L.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[Crossref]

Mizuno, J.

Montfort, F.

Naughton, T. J.

Neifeld, M. A.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[Crossref]

Nelleri, A.

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, “Three dimensional object recognition from digital Fresnel hologram by wavelength matched filtering,” Opt. Commun. 259, 499-506 (2006).
[Crossref]

Nicola, S. D.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[Crossref]

Nishino, Y.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[Crossref]

Nomura, T.

Ohta, S.

Osten, W.

Pedrini, G.

Rhodes, C. K.

Rogers, G. L.

G. L. Rogers, “In-line soft-x-ray holography: the unwanted image,” Opt. Lett. 19, 67-67 (1994).
[Crossref] [PubMed]

W. L. Bragg and G. L. Rogers, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, 190-191 (1951).
[Crossref] [PubMed]

Santoyo, F. M.

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257-268 (1999).
[Crossref]

Schnars, U.

Schwider, J.

Scott, P. D.

Seebacher, S.

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104-115 (1998).
[Crossref]

Shen, X. X.

Sheridan, J. T.

B. M. Hennelly and J. T. Sheridan, “Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms,” J. Opt. Soc. Am. A 22, 917-927 (2005).
[Crossref]

B. M. Hennelly and J. T. Sheridan, “Fast numerical algorithm for the linear canonical transform,” J. Opt. Soc. Am. A 22, 928-937 (2005).
[Crossref]

G. Situ and J. T. Sheridan, “A new reconstruction algorithm for in-line digital holography,” in European Conference on Lasers and Electro-Optics, 2007 and the International Quantum Electronics, Conference (CLEOE-IQEC 2007) (IEEE, 2007), digital OID: 4386033.
[Crossref] [PubMed]

Singh, K.

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, “Three dimensional object recognition from digital Fresnel hologram by wavelength matched filtering,” Opt. Commun. 259, 499-506 (2006).
[Crossref]

Situ, G.

G. Situ and J. T. Sheridan, “A new reconstruction algorithm for in-line digital holography,” in European Conference on Lasers and Electro-Optics, 2007 and the International Quantum Electronics, Conference (CLEOE-IQEC 2007) (IEEE, 2007), digital OID: 4386033.
[Crossref] [PubMed]

Solem, J. C.

Soraghan, J. J.

Spolaczyk, R.

Stadelmaier, A.

Tajahuerce, E.

Takahashi, Y.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[Crossref]

Tiziani, H.

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257-268 (1999).
[Crossref]

Tiziani, H. J.

von Bally, G.

S. Lai, B. Kemper, and G. von Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37-43 (1999).
[Crossref]

Wang, H. T.

Xiao, T. Q.

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[Crossref]

Xu, H. J.

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[Crossref]

Xu, W.

Xu, X. F.

Xu, Z. Z.

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[Crossref]

Yamaguchi, I.

Zalevsky, Z.

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[Crossref]

Zhang, L.

Zhang, T.

Zhang, Y.

Zhang, Y. J.

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[Crossref]

Zhu, Y. Y.

Appl. Opt. (7)

Appl. Phys. Lett. (1)

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[Crossref]

J. Mod. Opt. (2)

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[Crossref]

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Nature (1)

W. L. Bragg and G. L. Rogers, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, 190-191 (1951).
[Crossref] [PubMed]

Opt. Commun. (5)

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[Crossref]

D. Mas, J. Carcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithm for free-space diffraction patterns calculation,” Opt. Commun. 164, 233-245 (1999).
[Crossref]

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, “Three dimensional object recognition from digital Fresnel hologram by wavelength matched filtering,” Opt. Commun. 259, 499-506 (2006).
[Crossref]

S. Lai, B. Kemper, and G. von Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37-43 (1999).
[Crossref]

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257-268 (1999).
[Crossref]

Opt. Lett. (9)

Phys. Rev. B (1)

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[Crossref]

Proc. SPIE (2)

M. Adams, T. Kreis, and W. Jüptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234-240 (1997).
[Crossref]

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104-115 (1998).
[Crossref]

Other (3)

G. Situ and J. T. Sheridan, “A new reconstruction algorithm for in-line digital holography,” in European Conference on Lasers and Electro-Optics, 2007 and the International Quantum Electronics, Conference (CLEOE-IQEC 2007) (IEEE, 2007), digital OID: 4386033.
[Crossref] [PubMed]

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2004).

http://www.edmundoptics.com/onlinecatalog/displayproduct.cfm?productID=1790.

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Figures (6)

Fig. 1
Fig. 1

(Color online) Setup of the in-line DH recording system. HWP, half-wave plate; BS, beam splitter.

Fig. 2
Fig. 2

(Color online) Schematic for computer simulations. BS, beam splitter; reference, reference beam. The object volume is used to simulate a 3D object.

Fig. 3
Fig. 3

Simulation results of the reconstruction of the three letters at the best focus distance of (a) U, 140   mm ; (b) C, 120   mm ; (c) D, 100   mm from the CCD plane.

Fig. 4
Fig. 4

(Color online) Experimental setup of the proposed technique. BS, beam splitter; LP, linear polarizer.

Fig. 5
Fig. 5

Experimental results of the reconstruction image with the proposed technique: (a) magnitude, (b) phase, and (c) the cross section of the phase map as indicated with a dot–dash cross line in (b). Note that those marked with dot ellipses are associating the transparent area.

Fig. 6
Fig. 6

Reconstruction with a twin image superposition: (a) amplitude, (b) phase component.

Tables (1)

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Table 1 Statistic Properties of the Phase Patterns (in Radians)

Equations (18)

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I 11 ( x 1 , y 1 ) = | r + u 1 ( x 1 , y 1 ) | 2 ,
I 21 ( x 2 , y 2 ) = | r + u 2 ( x 2 , y 2 ) | 2 ,
u i ( x i , y i ) = P { u 0 ( x 0 , y 0 ) ; z i } , = 1 2 π u 0 ( x 0 , y 0 ) z i [ exp [ j k r i ] r i ] d x 0 d y 0 ,
I 12 ( x 1 , y 1 ) = | r + u 1 ( x 1 , y 1 ) | 2 ,
I 22 ( x 2 , y 2 ) = | r + u 2 ( x 2 , y 2 ) | 2 .
Δ I 1 ( x 1 , y 1 ) = u 1 ( x 1 , y 1 ) + u 1 * ( x 1 , y 1 ) ,
Δ I 2 ( x 2 , y 2 ) = u 2 ( x 2 , y 2 ) + u 2 * ( x 2 , y 2 ) .
u 1 * ( x 1 , y 1 ) = P { u 2 * ( x 2 , y 2 ) ; Δ z } .
δ I ( x 1 , y 1 ) = Δ I 1 ( x 1 , y 1 ) P { Δ I 2 ( x 2 , y 2 ) ; Δ z } = u 1 ( x 1 , y 1 ) + u 1 * ( x 1 , y 1 ) P { u 2 ( x 2 , y 2 ) ; Δ z } P { u 2 * ( x 2 , y 2 ) ; Δ z } = u 1 ( x 1 , y 1 ) P { u 2 ( x 2 , y 2 ) ; Δ z } = u 1 ( x 1 , y 1 ) P { u 1 ( x 1 , y 1 ) ; 2 Δ z } .
δ ( ξ , η ) = U 1 ( ξ , η ) [ 1 ( ξ , η ; 2 Δ z ) ] ,
u 1 ( x 1 , y 1 ) = 1 { δ ( ξ , η ) 1 ( ξ , η ; 2 Δ z ) } ,
h ( x 0 , y 0 ; x i , y i ; z i ) = 1 2 π z i [ exp [ j k r i ] r i ] .
( ξ , η ; z i ) = { h ( x 0 , y 0 ; x i , y i ; z i ) } = exp { j k z i [ 1 ( λ ξ ) 2 ( λ η ) 2 ] 1 / 2 } .
( m , n ; z i ) = exp { j k z i [ 1 ( λ m M δ x ) 2 ( λ n N δ y ) 2 ] 1 / 2 } ,
1 ( ξ , η , 2 Δ z ) 0 .
k 2 Δ z [ 1 λ 2 ( ξ 2 + η 2 ) ] 1 / 2 2 l π ,
Δ z λ 2 l 1 λ 2 ( ξ 2 + η 2 ) .
Δ z λ 2 l N δ N 2 δ 2 λ 2 ( m 2 + n 2 ) ,

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