Abstract

We propose a novel and simple method for generating optical vortex with high topological charge (TC), merely using an asymmetrical pinhole plate illuminated by plane wave. N pinholes are arranged along a particular spiral line around the plate origin, with constant azimuth angle increment and varied radial distances. The radial differences introduce a constant variation of m/N wavelength to the optical paths from the N pinholes to the observation plane origin, and this increases the phases of the transmitting waves by progressively 2mπ/Nand totally2mπ. We numerically calculate the transmitted light field according to the Fresnel diffraction theory, and find the vortex with TC m around the observation plane origin. The experimental verifications are performed using some self-made asymmetrical pinhole plates fabricated by a femtosecond laser, with the high TC vortices both generated and detected in a Mach-Zehnder type interferometer. The experimental results coincide with the theoretical simulations well.

© 2013 OSA

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2012 (6)

2011 (2)

A. Mourka, J. Baumgartl, C. Shanor, K. Dholakia, and E. M. Wright, “Visualization of the birth of an optical vortex using diffraction from a triangular aperture,” Opt. Express19(7), 5760–5771 (2011).
[CrossRef] [PubMed]

G. X. Wei, P. Wang, and Y. Y. Liu, “Phase retrieval and coherent diffraction imaging by a linear scanning pinhole sampling array,” Opt. Commun.284(12), 2720–2725 (2011).
[CrossRef]

2010 (3)

A. Bekshaev, O. Orlinska, and M. Vasnetsov, “Optical vortex generation with a ‘fork’ hologram under conditions of high-angle diffraction,” Opt. Commun.283(10), 2006–2016 (2010).

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature464(7289), 737–739 (2010).
[CrossRef] [PubMed]

G. C. G. Berkhout and M. W. Beijersbergen, “Measuring optical vortices in a speckle pattern using a multi-pinhole interferometer,” Opt. Express18(13), 13836–13841 (2010).
[CrossRef] [PubMed]

2009 (1)

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A, Pure Appl. Opt.11(9), 094021 (2009).
[CrossRef]

2008 (3)

2007 (3)

2005 (1)

2004 (4)

K. Ladavac and D. G. Grier, “Microoptomechanical pumps assembled and driven by holographic optical vortex arrays,” Opt. Express12(6), 1144–1149 (2004).
[CrossRef] [PubMed]

W. M. Lee, X.-C. Yuan, and W. C. Cheong, “Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optical micromanipulation,” Opt. Lett.29(15), 1796–1798 (2004).
[CrossRef] [PubMed]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt.6(2), 259–268 (2004).
[CrossRef]

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

2003 (1)

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

2002 (1)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

1999 (2)

1997 (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett.78(25), 4713–4716 (1997).
[CrossRef]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

1992 (2)

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett.17(3), 221–223 (1992).
[CrossRef] [PubMed]

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt.39, 291–372 (1999).
[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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Almazov, A. A.

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt.39, 291–372 (1999).
[CrossRef]

Barnett, S. M.

Baumgartl, J.

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, “Measuring optical vortices in a speckle pattern using a multi-pinhole interferometer,” Opt. Express18(13), 13836–13841 (2010).
[CrossRef] [PubMed]

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A, Pure Appl. Opt.11(9), 094021 (2009).
[CrossRef]

G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett.101(10), 100801 (2008).
[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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Bekshaev, A.

A. Bekshaev, O. Orlinska, and M. Vasnetsov, “Optical vortex generation with a ‘fork’ hologram under conditions of high-angle diffraction,” Opt. Commun.283(10), 2006–2016 (2010).

Bekshaev, A. Y.

A. Y. Bekshaev, S. V. Sviridova, A. Y. Popov, and A. V. Tyurin, “Generation of optical vortex light beams by volume holograms with embedded phase singularity,” Opt. Commun.285(20), 4005–4014 (2012).

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, “Measuring optical vortices in a speckle pattern using a multi-pinhole interferometer,” Opt. Express18(13), 13836–13841 (2010).
[CrossRef] [PubMed]

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A, Pure Appl. Opt.11(9), 094021 (2009).
[CrossRef]

G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett.101(10), 100801 (2008).
[CrossRef] [PubMed]

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt.6(2), 259–268 (2004).
[CrossRef]

Chen, X. F.

Chen, X. Y.

Cheng, C. F.

Cheong, W. C.

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

Dholakia, K.

Elfstrom, H.

Flossmann, F.

Franke-Arnold, S.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Gahagan, K. T.

Götte, J. B.

Grier, D. G.

K. Ladavac and D. G. Grier, “Microoptomechanical pumps assembled and driven by holographic optical vortex arrays,” Opt. Express12(6), 1144–1149 (2004).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett.17(3), 221–223 (1992).
[CrossRef] [PubMed]

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett.78(25), 4713–4716 (1997).
[CrossRef]

Jennewein, T.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

Joseph, J.

Khonina, S. N.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

Kotlyar, V. V.

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett.78(25), 4713–4716 (1997).
[CrossRef]

Ladavac, K.

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), (2004).

Lee, W. M.

Li, H. X.

Li, Z. H.

Liu, Y. Y.

G. X. Wei, P. Wang, and Y. Y. Liu, “Phase retrieval and coherent diffraction imaging by a linear scanning pinhole sampling array,” Opt. Commun.284(12), 2720–2725 (2011).
[CrossRef]

Löffler, W.

McDuff, R.

Mourka, A.

O’Holleran, K.

Orlinska, O.

A. Bekshaev, O. Orlinska, and M. Vasnetsov, “Optical vortex generation with a ‘fork’ hologram under conditions of high-angle diffraction,” Opt. Commun.283(10), 2006–2016 (2010).

Padgett, M. J.

J. B. Götte, K. O’Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express16(2), 993–1006 (2008).
[CrossRef] [PubMed]

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

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt.39, 291–372 (1999).
[CrossRef]

Paganin, D. M.

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(6), 066613 (2007).
[CrossRef] [PubMed]

Pan, J. W.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

Popov, A. Y.

A. Y. Bekshaev, S. V. Sviridova, A. Y. Popov, and A. V. Tyurin, “Generation of optical vortex light beams by volume holograms with embedded phase singularity,” Opt. Commun.285(20), 4005–4014 (2012).

Preece, D.

Ricci, F.

Ruben, G.

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(6), 066613 (2007).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett.78(25), 4713–4716 (1997).
[CrossRef]

Scipioni, M.

Senthilkumaran, P.

Shanor, C.

Shi, L.

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett.78(25), 4713–4716 (1997).
[CrossRef]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett.78(25), 4713–4716 (1997).
[CrossRef]

Singh, R. P.

Smith, C. P.

Soifer, V. A.

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Sviridova, S. V.

A. Y. Bekshaev, S. V. Sviridova, A. Y. Popov, and A. V. Tyurin, “Generation of optical vortex light beams by volume holograms with embedded phase singularity,” Opt. Commun.285(20), 4005–4014 (2012).

Swartzlander, G. A.

Tian, L. H.

Tonomura, A.

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature464(7289), 737–739 (2010).
[CrossRef] [PubMed]

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett.78(25), 4713–4716 (1997).
[CrossRef]

Turunen, J.

Tyson, R. K.

Tyurin, A. V.

A. Y. Bekshaev, S. V. Sviridova, A. Y. Popov, and A. V. Tyurin, “Generation of optical vortex light beams by volume holograms with embedded phase singularity,” Opt. Commun.285(20), 4005–4014 (2012).

Uchida, M.

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature464(7289), 737–739 (2010).
[CrossRef] [PubMed]

Vaity, P.

van Exter, M. P.

Vasnetsov, M.

A. Bekshaev, O. Orlinska, and M. Vasnetsov, “Optical vortex generation with a ‘fork’ hologram under conditions of high-angle diffraction,” Opt. Commun.283(10), 2006–2016 (2010).

Vaziri, A.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

Viegas, J.

Vyas, S.

Wang, P.

G. X. Wei, P. Wang, and Y. Y. Liu, “Phase retrieval and coherent diffraction imaging by a linear scanning pinhole sampling array,” Opt. Commun.284(12), 2720–2725 (2011).
[CrossRef]

Wei, G. X.

G. X. Wei, P. Wang, and Y. Y. Liu, “Phase retrieval and coherent diffraction imaging by a linear scanning pinhole sampling array,” Opt. Commun.284(12), 2720–2725 (2011).
[CrossRef]

Weihs, G.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

White, A. G.

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Wright, E. M.

Xavier, J.

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), (2004).

Yuan, X.-C.

Zeilinger, A.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

Zhang, M. N.

Appl. Opt. (4)

Chin. Opt. Lett. (1)

J. Opt. A, Pure Appl. Opt. (2)

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A, Pure Appl. Opt.11(9), 094021 (2009).
[CrossRef]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt.6(2), 259–268 (2004).
[CrossRef]

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

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

Nature (1)

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature464(7289), 737–739 (2010).
[CrossRef] [PubMed]

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), (2004).

Opt. Commun. (4)

G. X. Wei, P. Wang, and Y. Y. Liu, “Phase retrieval and coherent diffraction imaging by a linear scanning pinhole sampling array,” Opt. Commun.284(12), 2720–2725 (2011).
[CrossRef]

A. Bekshaev, O. Orlinska, and M. Vasnetsov, “Optical vortex generation with a ‘fork’ hologram under conditions of high-angle diffraction,” Opt. Commun.283(10), 2006–2016 (2010).

A. Y. Bekshaev, S. V. Sviridova, A. Y. Popov, and A. V. Tyurin, “Generation of optical vortex light beams by volume holograms with embedded phase singularity,” Opt. Commun.285(20), 4005–4014 (2012).

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Opt. Lett. (3)

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. A45(11), 8185–8189 (1992).
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Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

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[CrossRef] [PubMed]

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[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Scheme of an asymmetrical pinhole screen. (a). Spiral distributed (solid red line) pinholes on a asymmetrical screen. The azimuth angle of the nth pinhole is uniformly α n =2nπ/N , and the starting pinhole P0 with α 0 =0 is also equivalent to α N =2π . The radial distance d n to the screen origin increases (or decreases) with n non-uniformly. (b) shows the phase variation of transmitting waves via the propagation, with the lines in red, yellow, green and blue respectively represent four different phase change of the incident plane wave. The observation plane is z away from the screen, with l n being the distance between its origin and the nth pinhole P n .

Fig. 2
Fig. 2

Simulated distributions of the intensities and the phases of the light fields on the observation plane with the pinhole size neglected. For all calculations, the propagation distances are 10cm, the radial distances of the original pinholes are 1mm, and the observation areas are all 140 μm × 140 μm .

Fig. 3
Fig. 3

Simulated intensity and phase distributions on the observation plane. (a) shows the vortex with opposite sign to the one for N = 6, m = 2, with similar intensity pattern. (b) shows that no traditional phase vortex is found in N = 2m case.

Fig. 4
Fig. 4

Simulated light fields with pinhole size considered in. For all, the original radial distance is 1mm, pinhole number is 16, and m is 2. The calculated areas are 140 μm × 140 μm in (a), and 680 μm × 680 μm in the other three cases. The obvious deformation in (d) indicates a case with a too big pinhole diameter.

Fig. 5
Fig. 5

Asymmetrical pinhole plates punched on aluminium plates. (a) 72-pinhole plate for m = 2, with pinhole radius approximately 26μm . (b) Plate for N = 16, m = 3 with pinhole radius r18μm . The radial distances of the original pinholes in both are all 1mm, and the observation planes are set to be 1m away.

Fig. 6
Fig. 6

Schematic diagram of the experimental setup for generating and detecting phase vortices. M1-3 are mirrors, BS1 and BS2 are beam splitters. The spatial filters SF1 and SF2 are used to filter and expand the reference and the object beams respectively, and the lens L1 and L2 are used to convert the two beams to plane wave. A1 and A2 are neutral attenuators that adjust the light powers; Pin-P is the asymmetrical pinhole plate which is mounted on a 3D transmission stage.

Fig. 7
Fig. 7

The Interferograms, the extracted intensity patterns and phase patterns on the observation plane that is 1m behind the asymmetrical pinhole plates. (a). N = 16, m = 1. (b). N = 72, m = 2. (c). N = 16, m = 3.

Fig. 8
Fig. 8

(a) Light intensities along the vertical line passing through the vortex cores. (b) Phase distributions around the origins. The curves for Figs. 7(a3-c3) are depicted by circle rings, squares and triangles represent respectively, and the linear-fits are shown by colored lines. Note that the phase regions are not (π,π) , for clear indication of the total phase variation.

Equations (5)

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U(X,Y)= n=0 N1 exp{iπ[ (X x n ) 2 + (Y y n ) 2 ]/λz} = n=0 N1 exp [iπ( X 2 + Y 2 )/λz]exp[i2π(X x n +Y y n )/λz]exp[iπ( x n 2 + y n 2 )/λz],
U(X,Y)= n=0 N1 exp [i2π(X x n +Y y n )/λz]exp(i2nmπ/N),
U(X,Y)= U 0 (x,y)exp{i2π[ (Xx) 2 + (Yy) 2 ]/λz}dxdy,
I(X,Y)= | U(X,Y)+r(X,Y) | 2 = | U(X,Y) | 2 + | r(X,Y) | 2 +U(X,Y) r * (X,Y)+ U * (X,Y)r(X,Y),
I f ( f X , f Y )= B f ( f X , f Y )+ U f ( f X + f 0X , f Y + f 0Y )+ U f * ( f X f 0X , f Y f 0Y ),

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