Abstract

Advanced technological developments have stimulated renewed interest in volume holography for applications such as information storage and wavelength multiplexing for communications and laser beam shaping. In these and many other applications, the information-carrying wave fronts usually possess narrow spatial-frequency bands, although they may propagate at large angles with respect to each other or a preferred optical axis. Conventional analytic methods are not capable of properly analyzing the optical architectures involved. For mitigation of the analytic difficulties, a novel approximation is introduced to treat narrow spatial-frequency band wave fronts propagating at large angles. This approximation is incorporated into the analysis of volume holography based on a plane-wave decomposition and Fourier analysis. As a result of the analysis, the recently introduced generalized Bragg selectivity is rederived for this more general case and is shown to provide enhanced performance for the above indicated applications. The power of the new theoretical description is demonstrated with the help of specific examples and computer simulations. The simulations reveal some interesting effects, such as coherent motion blur, that were predicted in an earlier publication.

© 2005 Optical Society of America

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2004 (2)

2003 (3)

2002 (1)

2000 (3)

1999 (2)

X. M. Yi, P. Yeh, C. Gu, and S. Campbell, "Crosstalk in volume holographic memory," Proc. IEEE 87, 1912-1930 (1999).
[CrossRef]

P. C. Sun, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, "Space-time processing with photorefractive volume holography," Proc. IEEE 87, 2086-2097 (1999).
[CrossRef]

1998 (1)

1992 (1)

1982 (1)

1980 (1)

Barbastathis, G.

Bianco, B.

Boffi, P.

Boyd, C.

W. L. Wilson, K. Curtis, M. Tackitt, A. Hill, A. Hale, M. Schilling, C. Boyd, S. Campbell, L. Dhar, and A. Harris, "High density, high performance optical data storage via volume holography: viability at last?," Opt. Quantum Electron. 32, 393-404 (2000).
[CrossRef]

Campbell, S.

W. L. Wilson, K. Curtis, M. Tackitt, A. Hill, A. Hale, M. Schilling, C. Boyd, S. Campbell, L. Dhar, and A. Harris, "High density, high performance optical data storage via volume holography: viability at last?," Opt. Quantum Electron. 32, 393-404 (2000).
[CrossRef]

X. M. Yi, P. Yeh, C. Gu, and S. Campbell, "Crosstalk in volume holographic memory," Proc. IEEE 87, 1912-1930 (1999).
[CrossRef]

Chevallier, R.

J.-L. Kaiser, E. Quertemont, and R. Chevallier, "Light propagation in the pseudo-paraxial Fresnel approximation," Opt. Commun. 233, 261-269 (2004).
[CrossRef]

Cook, D. J.

L. Solymar and D. J. Cook, Volume Holography and Volume Gratings (Academic, New York, 1981).

Curtis, K.

W. L. Wilson, K. Curtis, M. Tackitt, A. Hill, A. Hale, M. Schilling, C. Boyd, S. Campbell, L. Dhar, and A. Harris, "High density, high performance optical data storage via volume holography: viability at last?," Opt. Quantum Electron. 32, 393-404 (2000).
[CrossRef]

Delen, N.

Dhar, L.

W. L. Wilson, K. Curtis, M. Tackitt, A. Hill, A. Hale, M. Schilling, C. Boyd, S. Campbell, L. Dhar, and A. Harris, "High density, high performance optical data storage via volume holography: viability at last?," Opt. Quantum Electron. 32, 393-404 (2000).
[CrossRef]

Endo, M.

Fainman, S. Y.

P. C. Sun, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, "Space-time processing with photorefractive volume holography," Proc. IEEE 87, 2086-2097 (1999).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, Calif., 1996).

Griffiths, L.

Gu, C.

X. M. Yi, P. Yeh, C. Gu, and S. Campbell, "Crosstalk in volume holographic memory," Proc. IEEE 87, 1912-1930 (1999).
[CrossRef]

Hale, A.

W. L. Wilson, K. Curtis, M. Tackitt, A. Hill, A. Hale, M. Schilling, C. Boyd, S. Campbell, L. Dhar, and A. Harris, "High density, high performance optical data storage via volume holography: viability at last?," Opt. Quantum Electron. 32, 393-404 (2000).
[CrossRef]

Harris, A.

W. L. Wilson, K. Curtis, M. Tackitt, A. Hill, A. Hale, M. Schilling, C. Boyd, S. Campbell, L. Dhar, and A. Harris, "High density, high performance optical data storage via volume holography: viability at last?," Opt. Quantum Electron. 32, 393-404 (2000).
[CrossRef]

Hill, A.

W. L. Wilson, K. Curtis, M. Tackitt, A. Hill, A. Hale, M. Schilling, C. Boyd, S. Campbell, L. Dhar, and A. Harris, "High density, high performance optical data storage via volume holography: viability at last?," Opt. Quantum Electron. 32, 393-404 (2000).
[CrossRef]

Hooker, B.

Imai, T.

Kaiser, J.-L.

J.-L. Kaiser, E. Quertemont, and R. Chevallier, "Light propagation in the pseudo-paraxial Fresnel approximation," Opt. Commun. 233, 261-269 (2004).
[CrossRef]

Kim, J. D.

Kiruluta, A.

Kraut, S.

Kriehn, G.

Kurihara, T.

Kurokawa, Y.

Lee, B.

Lee, S.

Martinelli, M.

Mazurenko, Y. T.

P. C. Sun, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, "Space-time processing with photorefractive volume holography," Proc. IEEE 87, 2086-2097 (1999).
[CrossRef]

Nazarathy, M.

Oba, K.

P. C. Sun, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, "Space-time processing with photorefractive volume holography," Proc. IEEE 87, 2086-2097 (1999).
[CrossRef]

Osmond, J.

Pati, G. S.

Piccinin, D.

Quertemont, E.

J.-L. Kaiser, E. Quertemont, and R. Chevallier, "Light propagation in the pseudo-paraxial Fresnel approximation," Opt. Commun. 233, 261-269 (2004).
[CrossRef]

Sarto, A. W.

Schilling, M.

W. L. Wilson, K. Curtis, M. Tackitt, A. Hill, A. Hale, M. Schilling, C. Boyd, S. Campbell, L. Dhar, and A. Harris, "High density, high performance optical data storage via volume holography: viability at last?," Opt. Quantum Electron. 32, 393-404 (2000).
[CrossRef]

Shamir, J.

J. Shamir and K. Wagner, "Generalized Bragg effect in volume holography," Appl. Opt. 41, 6773-6785 (2002).
[CrossRef] [PubMed]

M. Nazarathy and J. Shamir, "First-order optics--a canonical operator representation: lossless systems," J. Opt. Soc. Am. 72, 356-364 (1982).
[CrossRef]

M. Nazarathy and J. Shamir, "Fourier optics described by operator algebra," J. Opt. Soc. Am. 70, 150-159 (1980).
[CrossRef]

J. Shamir, "Holograms of volumes and volume holograms," in The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk, H.J.Caulfield, ed., Vol. PM124 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 2004), pp. 239-260.

J. Shamir, Optical Systems and Processes, Vol. PM65 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1999).
[CrossRef]

J. Shamir and K. Wagner, "New look at volume holography," in Holography: A Tribute to Yuri Denisyuk and Emmett Leith, H.J.Caulfield, ed., Proc. SPIE 4737, 64-76 (2002).

Silveira, P. E. X.

Sinha, A.

Solymar, L.

L. Solymar and D. J. Cook, Volume Holography and Volume Gratings (Academic, New York, 1981).

Sommerfeld, A.

A. Sommerfeld, Optics: Lectures in Theoretical Physics (Academic, New York, 1964).

Sun, P. C.

P. C. Sun, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, "Space-time processing with photorefractive volume holography," Proc. IEEE 87, 2086-2097 (1999).
[CrossRef]

Syms, R. R. A.

R. R. A. Syms, Practical Volume Holography (Clarendon, Oxford, UK, 1990).

Tackitt, M.

W. L. Wilson, K. Curtis, M. Tackitt, A. Hill, A. Hale, M. Schilling, C. Boyd, S. Campbell, L. Dhar, and A. Harris, "High density, high performance optical data storage via volume holography: viability at last?," Opt. Quantum Electron. 32, 393-404 (2000).
[CrossRef]

Tanabe, T.

Tommasi, T.

Ubaldi, M. Chiara

Wagner, K.

Weaver, S.

Weverka, R. T.

Wilson, W. L.

W. L. Wilson, K. Curtis, M. Tackitt, A. Hill, A. Hale, M. Schilling, C. Boyd, S. Campbell, L. Dhar, and A. Harris, "High density, high performance optical data storage via volume holography: viability at last?," Opt. Quantum Electron. 32, 393-404 (2000).
[CrossRef]

Yagi, S.

Yeh, P.

X. M. Yi, P. Yeh, C. Gu, and S. Campbell, "Crosstalk in volume holographic memory," Proc. IEEE 87, 1912-1930 (1999).
[CrossRef]

Yi, X. M.

X. M. Yi, P. Yeh, C. Gu, and S. Campbell, "Crosstalk in volume holographic memory," Proc. IEEE 87, 1912-1930 (1999).
[CrossRef]

Appl. Opt. (5)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

J.-L. Kaiser, E. Quertemont, and R. Chevallier, "Light propagation in the pseudo-paraxial Fresnel approximation," Opt. Commun. 233, 261-269 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

W. L. Wilson, K. Curtis, M. Tackitt, A. Hill, A. Hale, M. Schilling, C. Boyd, S. Campbell, L. Dhar, and A. Harris, "High density, high performance optical data storage via volume holography: viability at last?," Opt. Quantum Electron. 32, 393-404 (2000).
[CrossRef]

Proc. IEEE (2)

X. M. Yi, P. Yeh, C. Gu, and S. Campbell, "Crosstalk in volume holographic memory," Proc. IEEE 87, 1912-1930 (1999).
[CrossRef]

P. C. Sun, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, "Space-time processing with photorefractive volume holography," Proc. IEEE 87, 2086-2097 (1999).
[CrossRef]

Other (7)

J. Shamir, "Holograms of volumes and volume holograms," in The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk, H.J.Caulfield, ed., Vol. PM124 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 2004), pp. 239-260.

L. Solymar and D. J. Cook, Volume Holography and Volume Gratings (Academic, New York, 1981).

R. R. A. Syms, Practical Volume Holography (Clarendon, Oxford, UK, 1990).

A. Sommerfeld, Optics: Lectures in Theoretical Physics (Academic, New York, 1964).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, Calif., 1996).

J. Shamir, Optical Systems and Processes, Vol. PM65 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1999).
[CrossRef]

J. Shamir and K. Wagner, "New look at volume holography," in Holography: A Tribute to Yuri Denisyuk and Emmett Leith, H.J.Caulfield, ed., Proc. SPIE 4737, 64-76 (2002).

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Figures (5)

Fig. 1
Fig. 1

Defining parameters for the NB approximation. A narrow spatial-frequency band modulation δ is imposed on the average (carrier) spatial frequency ν.

Fig. 2
Fig. 2

Recording in a plane-parallel slab of thickness d. (a) The recording process with two waves that are assumed to be nondepleted. (b) Reconstruction with wave u r showing the undepleted transmitted wave and the the first-order reconstructed wave.

Fig. 3
Fig. 3

Configuration for the simulations:  ν 1 and ν 2 are the recording spatial-frequency vectors, and u r is the reconstructing Gaussian beam possessing a waist size w 0 focused at a distance z 0 from the front surface of the recording medium with thickness d.

Fig. 4
Fig. 4

Simulated intensity distribution of the diffracted field over the output surface due to illumination of volume grating with an on-axis Gaussian beam. In each frame the hologram thickness d and focus distance z 0 from the entrance surface are noted. All dimensions are in micrometers with the intensity (vertical axis) given in arbitrary units. See text for more detail on the other system parameters.

Fig. 5
Fig. 5

Similar to Fig. 4 but here all waves involved are axially propagating Gaussian beams with a waist radius of 1 μ m . In addition to the hologram thickness d, the waist distances from the hologram surface are also marked. See text for additional details.

Equations (69)

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F u ( x , y , 0 ) = exp [ j 2 π ( ν x x + ν y y ) ] u ( x , y , 0 ) d x d y ,
x ̂ ν x + y ̂ ν y ν x y
2 π ν x y = k x y .
F u ( x , y , z ) = exp ( j k z z ) exp [ j 2 π ( ν x x + ν y y ) ] u ( x , y , 0 ) d x d y = exp ( j k z z ) F u ( x , y , 0 ) ,
k z = ± ( k 2 k x 2 k y 2 ) 1 2 = ± k [ 1 λ 2 ( ν x 2 + ν y 2 ) ] 1 2 ,
F u ( x , y , z ) = O ν F u ( x , y , 0 ) ,
O ν exp { j k z [ 1 λ 2 ( ν x 2 + ν y 2 ) ] 1 2 }
λ 2 ( ν z 2 + ν x 2 + ν y 2 ) = 1 λ ν z = ( 1 λ 2 ν x y 2 ) 1 2 ; λ 2 ν x y 2 1
u ( x , y , z ) = F 1 O ν F u ( x , y , 0 ) .
R ̃ [ z ] = F 1 O ν F ,
u ( x , y , z ) = R ̃ [ z ] u ( x , y , 0 ) .
u ( x , y , z ) = exp ( j k 0 r ) f ( x , y , z ) ,
u ( x , y , z ) = R ̃ [ z ] exp ( j k 0 r ) f ( x , y , 0 ) = F 1 O ν F exp [ j 2 π ( ν 0 , x x + ν 0 , y y ) ] f ( x , y , 0 ) .
G [ λ ν 0 , x y ] exp [ j 2 π ( ν 0 , x x + ν 0 , y y ) ] = exp ( j 2 π ν 0 , x y ρ ) ,
F G [ s ] = S [ s λ ] F ,
S [ s ] f ( x , y ) f ( x s x , y s y ) .
u ( x , y , z ) = F 1 O ν F G [ λ ν 0 , x y ] f ( x , y , 0 ) = F 1 O ν S ( ν 0 , x y ) F f ( x , y , 0 ) = F 1 S [ ν 0 , x y ] { S [ ν 0 , x y ] O ν } F f ( x , y , 0 ) = G [ λ ν 0 , x y ] F 1 { S [ ν 0 , x y ] O ν } F f ( x , y , 0 ) ,
S [ m 1 ] S [ m 2 ] = S [ m 1 + m 2 ] .
S [ ν 0 , x y ] O ν = exp [ j k z ( 1 λ 2 ν x y + ν 0 , x y 2 ) 1 2 ] ,
O δ ν 0 = exp [ j k z ( 1 λ 2 δ x y + ν 0 , x y 2 ) 1 2 ] = exp [ j k z ( 1 λ 2 ν 0 , x y 2 ) 1 2 ( 1 λ 2 2 ν 0 , x y δ x y + δ x y 2 1 λ 2 ν 0 , x y 2 ) 1 2 ] = exp [ j k z λ ν 0 , z ( 1 2 ν 0 x y δ x y + δ x y 2 ν 0 , z 2 ) 1 2 ] ,
O δ ν 0 exp [ j k 0 , z z ( 1 2 ν 0 , x y δ x y + δ x y 2 2 ν 0 , z 2 ) ] = exp ( j k 0 , z z ) exp ( j k 0 z λ 2 ν 0 , x y δ x y + δ x y 2 2 ν 0 , z ) .
Q δ [ a ] exp ( j k a 2 δ x y 2 ) , Q ρ [ a ] exp ( j k a 2 ρ 2 )
O δ ν 0 exp ( j k 0 , z z ) G δ [ λ z ν 0 , x y ν 0 , z ] Q δ [ λ z ν 0 , z ] .
u ( x , y , z ) = G [ λ ν 0 , x y ] exp ( j k 0 , z z ) F 1 G δ [ λ z ν 0 , x y ν 0 , z ] Q δ [ λ z ν 0 , z ] F f ( x , y , 0 ) .
F 1 = V [ 1 ] F ,
V [ a ] f ( x , y ) = f ( a x , a y ) .
u ( x , y , z ) = G [ λ ν 0 , x y ] S x y [ z ν 0 , x y ν 0 , z ] exp ( j k 0 , z z ) F 1 Q δ [ λ z ν 0 , z ] F f ( x , y , 0 ) .
u ( x , y , z ) = R [ z ] f ( x , y , 0 ) ,
R [ z ] = exp ( j k z ) F 1 Q δ [ λ 2 z ] F exp ( j k z ) R ¯ [ z ] .
u ( x , y , z ) = G [ λ ν 0 , x y ] S x y [ z ν 0 , x y ν 0 , z ] exp ( j k 0 , z z ) R ¯ [ z λ ν 0 , z ] f ( x , y , 0 ) = exp ( j k 0 r ) S x y [ z ν 0 , x y ν 0 , z ] R ¯ [ z λ ν 0 , z ] f ( x , y , 0 ) ,
I ( z ) = u 1 ( z ) + u 2 ( z ) 2 = [ u 1 ( z ) 2 + u 2 ( z ) 2 ] + u 1 ( z ) u 2 * ( z ) + u 1 * ( z ) u 2 ( z ) .
d u ( z ; z ) = u r ( z ) u 1 * ( z ) u 2 ( z ) d z ,
u 2 ( x , y , z ) = R ̃ [ z ] u 2 ( x , y , 0 ) ,
u 1 ( x , y , z ) = R ̃ b [ z d ] u 1 ( x , y , d ) ,
u r ( x , y , z ) = R ̃ r b [ z d ] u r ( x , y , d )
d u ( z ; d ) = R r [ d z ] { R ̃ r b [ z d ] u r ( x , y , d ) } { R ̃ b [ z d ] u 1 ( x , y , d ) } * { R ̃ [ z ] u 2 ( x , y , 0 ) } d z .
u out ( x , y , d ) = 0 d R ̃ r [ d z ] { R ̃ r b [ z d ] u r ( x , y , d ) } { R ̃ b [ z d ] u 1 ( x , y , d ) } * { R ̃ [ z ] u 2 ( x , y , 0 ) } d z .
u 2 ( x , y , z ) = G [ λ ν 2 , x y ] S x y [ z ν 2 , x y ν 2 , z ] exp ( j k 2 , z z ) R ¯ [ z λ ν 2 , z ] f 2 ( x , y , 0 ) ,
u 1 ( x , y , z ) = G [ λ ν 1 , x y ] S x y [ ( z d ) ν 1 , x y ν 1 , ν ] exp [ j k 1 , z ( z d ) ] R ¯ b [ z d λ ν 1 , z ] f 1 ( x , y , d ) ,
u r ( x , y , z ) = G r [ λ r ν r , x y ] S x y [ ( z d ) ν r , x y ν r , z ] exp [ j k r , z ( z d ) ] R ¯ r b [ z d λ ν r , z ] f r ( x , y , d ) ,
s 1 ( z d ) ν 1 , x y ν 1 , z , s 2 z ν 2 , x y ν 2 , z ,
s 3 ( d z ) ν 3 , x y ν 3 , z , s r ( z d ) ν r , x y ν r , z ,
b 1 z d λ ν 1 , z , b 2 z λ ν 2 , z ,
b 3 d z λ r ν 3 , z , b r z d λ r ν r , z ,
d u ( z ; z ) = { G [ λ ν 2 , x y ] S [ s 2 ] exp ( j k 2 , z z ) R ¯ [ b 2 ] f 2 ( x , y , 0 ) } × { G [ λ ν 1 , x y ] S [ s 1 ] exp [ j k 1 , z ( z d ) ] R ¯ b [ b 1 ] f 1 ( x , y , d ) } * × { G r [ λ r ν r , x y ] S [ s r ] exp [ j k r , z ( z d ) ] R ¯ r b [ b r ] f r ( x , y , d ) } d z .
d u ( z ; z ) = exp [ j 2 π d ( ν 1 , z ν r , z ) ] exp ( j 2 π μ z z ) exp ( j 2 π μ x y ρ ) ϕ ( x , y , z ) d z ,
ϕ ( x , y , z ) = { S [ s 2 ] R ¯ [ b 2 ] f 2 ( x , y , 0 ) } × { S [ s 1 ] R ¯ b [ b 1 ] f 1 ( x , y , d ) } * { S [ s r ] R ¯ r b [ b r ] f r ( x , y , d ) }
μ ν 2 ν 1 + ν r .
λ r ν 3 , z = ( 1 λ r μ x y 2 ) 1 2 ,
ν 3 = μ x y + z ̂ ν 3 , z ( or ν 3 , x y = μ x y )
d u ( z ; d ) = G r [ λ r ν 3 , x y ] S [ s 3 ] exp [ j 2 π ν 3 , z ( d z ) ] × R ¯ r [ b 3 ] exp [ j 2 π d ( ν 1 , z ν r , z ) ] exp ( j 2 π μ z z ) ϕ ( x , y , z ) d z .
d u ( z ; d ) = exp [ j 2 π ( μ z ν 3 , z ) z ] G r [ λ r μ x y ] S [ s 3 ] R ¯ r [ b 3 ] ϕ ( x , y , z ) d z .
Δ = μ ν 3 = ν 2 ν 1 + ν r ν 3 , or 2 π Δ = k 2 k 1 + k r k 3
u out ( x , y , d ) = 0 d exp ( j 2 π Δ z z ) G r [ λ r μ x y ] S [ s 3 ] R ¯ r [ b 3 ] ϕ ( x , y , z ) d z .
u pw ( d ) = 0 d exp ( j 2 π Δ z z ) G r [ λ r μ x y ] d z = d exp ( j π Δ z d ) sinc ( Δ z d ) G r [ λ r μ x y ] .
ϕ grat ( x , y , z ) = S [ s r ] R ¯ r b [ b r ] f r ( x , y , d ) ,
u out ( x , y , d ) = 0 d exp ( j 2 π Δ z z ) G r [ λ r μ x y ] S [ s 3 + s r ] R ¯ r [ b 3 + b r ] f r ( x , y , d ) d z ,
f r ( x , y , z ) = Q r [ 1 q r ] ,
1 q r ( z ) z q 0 z 2 + q 0 2 1 R ( z ) + j λ π ω [ W ( z ) ] 2 .
R ¯ [ b ] Q [ 1 q ] = q b + q Q [ 1 ( b + q ) ] R ¯ [ b ( 1 + b q ) ] V [ 1 ( 1 + b q ) ] .
R ¯ [ b ] f r ( x , y , z ) = q r b + q r Q [ 1 ( b + q r ) ] ,
u out ( x , y , d ) = G r [ λ r μ x y ] 0 d exp ( j 2 π Δ z z ) S [ s 3 + s r ] q r b 3 + b r + q r Q [ 1 ( b 3 + b r + q r ) ] d z ,
k 1 = z ̂ k , k 2 = z ̂ k , k r = z ̂ k r , k 3 = z ̂ k r
u ax ( d ) = 0 d exp [ j 2 ( k k r ) z ] R ¯ r [ d z ] ϕ ax ( x , y , z ) d z ,
ϕ ax = { R ¯ [ z ] f 2 ( x , y , 0 ) } { R ¯ b [ d z ] f 1 * ( x , y , d ) } { R ¯ r b [ z d ] f r ( x , y , d ) } .
ϕ Gauss ( x , y , z ) = A Q r [ 1 q ] ,
1 q k k r ( b 2 + q 2 ) k k r ( b 1 + q 1 * ) + 1 b r + q r
A A q b 3 + q , A = q 2 b 2 + q 2 q 1 * b 1 + q 1 * q r b r + q r ,
u Gauss ( d ) = 0 d exp [ j 2 ( k k r ) z ] A Q r [ 1 q + d z ] d z .

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