Abstract

Recently, Fourier-domain (FD) optical delay lines (ODLs) were introduced for high-speed scanning and dispersion compensation in imaging interferometry. We investigate the effect of first- and second-order dispersion on the photocurrent signal associated with an optical coherence imaging system implemented with a single-mode fiber, a superluminescent diode centered at 950 nm ± 35 nm, a FD ODL, a mirror, and a layered LiTAO3 that has suitable dispersion characteristics to model a skin specimen. We present a practical and useful method to minimize the effect of dispersion through the interferometer and the specimen combined, as well as to quantify the results using two general metrics for resolution. Theoretical and associated experimental results show that, under the optimum solution, the maximum broadening of the point-spread function through a 1-mm-deep specimen is limited to 57% of its original rms width value (i.e., 8.1 µm optimal, 12.7 µm at maximum broadening) compared with approximately 110% when compensation is performed without the specimen taken into account.

© 2005 Optical Society of America

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  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, J. F. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express 12, 2435–2447 (2004), www.opticsexpress.org .
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    [CrossRef] [PubMed]
  16. Y. Wang, J. Stuart Nelson, Z. Chen, B. J. Reiser, R. S. Chuck, R. S. Windeler, “Optimal wavelength for ultrahigh-resolution optical coherence tomography,” Opt. Express 11, 1411–1417 (2003), www.opticsexpress.org .
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    [CrossRef] [PubMed]
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2004 (4)

2003 (6)

2002 (2)

2001 (2)

2000 (1)

1999 (1)

1998 (1)

1997 (1)

1996 (2)

1993 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Abedin, K. S.

K. S. Abedin, H. Ito, “Temperature-dependent dispersion relation of ferroelectric lithium tantalite,” J. Appl. Phys. 80, 6561–6563 (1996).
[CrossRef]

Agrawal, G. P.

Akcay, C.

Bajraszewski, T.

Boppart, S. A.

Bop-part, S. A.

Bouma, B. E.

Brabec, T.

Brezinski, M. E.

Cense, B.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chen, T. C.

Chen, Z.

Chiang, C.

Chu, K. C.

Chuck, R. S.

de Boer, J. F.

Dienes, A.

Drexler, W.

Duker, J. S.

Fercher, A. F.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

Golubovic, B.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Heritage, J. P.

Hermann, B.

Hitzenberger, C. K.

Hsu, I.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Ito, H.

K. S. Abedin, H. Ito, “Temperature-dependent dispersion relation of ferroelectric lithium tantalite,” J. Appl. Phys. 80, 6561–6563 (1996).
[CrossRef]

Izatt, J. A.

Ko, T. H.

Kowalczyk, A.

Kulkarni, M. D.

Kwong, K. F.

Lakoba, T. I.

Le, T.

Leitgeb, R. A.

Lin, C.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Liu, B.

Lu, C.

Marks, D. L.

Nasr, M. B.

Nassif, N. A.

Niblack, W. K.

Oldenburg, A. L.

Park, B. H.

Parrein, P.

Pierce, M. C.

Pulifito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Reiser, B. J.

Reynolds, J. J.

Rolland, J. P.

Rollins, A. M.

Saleh, B. E. A.

Sampson, D. D.

Schenk, J. O.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Sergienko, A. V.

Smith, E. D. J.

Sorokin, E.

Srinivasan, V. J.

Sticker, M.

Stingl, A.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Stuart Nelson, J.

Sun, C.

Swanson, E. A.

G. J. Tearney, B. E. Bouma, S. A. Boppart, B. Golubovic, E. A. Swanson, J. G. Fujimoto, “Rapid acquisition of in vivo biological images by use of optical coherence tomography,” Opt. Lett. 21, 1408–1410 (1996).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

Teich, M.

Tempea, G.

Thennadil, S. N.

T. L. Troy, S. N. Thennadil, “Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm,” J. Biomed. Opt. 6, 167–176 (2001).
[CrossRef] [PubMed]

Troy, T. L.

T. L. Troy, S. N. Thennadil, “Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm,” J. Biomed. Opt. 6, 167–176 (2001).
[CrossRef] [PubMed]

Ungarunyawee, R.

Unterhuber, A.

Wang, Y.

Windeler, R. S.

Wojtkowski, M.

Yang, C. C.

Yankelevich, D.

Yazdanafar, S.

Yun, S.

Zawadzki, R.

Zvyagin, A. V.

Appl. Opt. (5)

J. Appl. Phys. (1)

K. S. Abedin, H. Ito, “Temperature-dependent dispersion relation of ferroelectric lithium tantalite,” J. Appl. Phys. 80, 6561–6563 (1996).
[CrossRef]

J. Biomed. Opt. (1)

T. L. Troy, S. N. Thennadil, “Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm,” J. Biomed. Opt. 6, 167–176 (2001).
[CrossRef] [PubMed]

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

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

Opt. Express (7)

A. M. Rollins, M. D. Kulkarni, S. Yazdanafar, R. Ungarunyawee, J. A. Izatt, “In vivo video rate optical coherence tomography,” Opt. Express 3, 219–229 (1998), www.opticsex-press.org .
[CrossRef] [PubMed]

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, M. Teich, “Dispersion-cancelled and dispersion-sensitive quantum optical coherence tomography,” Opt. Express 12, 1353–1362 (2004), www.opticsexpress.org .
[CrossRef] [PubMed]

Y. Wang, J. Stuart Nelson, Z. Chen, B. J. Reiser, R. S. Chuck, R. S. Windeler, “Optimal wavelength for ultrahigh-resolution optical coherence tomography,” Opt. Express 11, 1411–1417 (2003), www.opticsexpress.org .
[CrossRef] [PubMed]

R. A. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, A. F. Fercher, “Ultrahigh resolution Fourier domain optical coherence tomography,” Opt. Express 12, 2156–2165 (2004), www.opticsexpress.org .
[CrossRef] [PubMed]

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, J. S. Duker, “Ultrahigh-resolution, highspeed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12, 2404–2422 (2004), www.opticsexpress.org .
[CrossRef] [PubMed]

B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, J. F. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express 12, 2435–2447 (2004), www.opticsexpress.org .
[CrossRef] [PubMed]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, “Numerical dispersion compensation for partial coherence interferometry and optical coherence tomography,” Opt. Express 9, 610–615 (2001), www.opticsexpress.org .
[CrossRef] [PubMed]

Opt. Lett. (4)

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Pulifito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Other (3)

H. H. Barrett, K. J. Myers, B. E. A. Saleh, eds., Foundations of Image Science, Wiley Series in Pure and Applied Optics (Wiley, Hoboken, N.J., 2004).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of a fiber-optic imaging interferometer with a frequency-domain ODL in the reference arm.

Fig. 2
Fig. 2

(a) Measured power spectral density of the SLD, (b) corresponding ideal photocurrent signal.

Fig. 3
Fig. 3

(a) Experimental result corresponding to the parameters listed in (b); (b) simulation result for Δz = 0.06 mm, Δd = 3.6 mm, and x0 = 0.4 mm.

Fig. 4
Fig. 4

(a) Experimental result with an additional 0.07-mm axial grating shift from the initial 0.06 mm; (b) simulation result for Δz = 0.13 mm, Δd = 3.6 mm, and x0 = 0.4 mm; (c) isolated effect of first-order dispersion; (d) isolated effect of second-order dispersion.

Fig. 5
Fig. 5

(a) Schematic of two layers of 0.5-mm LiTaO3 separated by an air gap; (b) two-dimensional image of the specimen when the first-order dispersion compensation is set for the signal reflected off the front surface A of the specimen; (c) single depth scan through the line S shown in (b) of the specimen image; (d)–(f) solid curves are zoomed photocurrent signal envelopes and the dashed curves are simulated photocurrent signal envelopes for light reflected off of (d) the front surface A, (e) the second surface (i.e., from layer B), and (f) the back surface C of the specimen for Δz = 0.06 mm, Δd = 3.6 mm, and x0 = 3 mm.

Fig. 6
Fig. 6

Schematic of two layers of 0.5-mm LiTaO3 separated by an air gap; (b) two-dimensional image of the specimen when the first-order dispersion compensation is set for the signal reflected off of the middle surface B of the specimen; (c) single depth scan through the line S shown in (b) of the specimen image; (d)–(f) solid curves are zoomed photocurrent signal envelopes and the dashed curves are simulated photocurrent signal envelopes for light reflected off of (d) the front surface A, (e) the second surface (i.e., from layer B), and (f) the back surface C of the specimen for Δz = 0.005 mm, Δd = 3.6 mm, and x0 = 3 mm.

Fig. 7
Fig. 7

Schematic of two layers of 0.5-mm LiTaO3 separated by an air gap; (b) two-dimensional image of the specimen when the first-order dispersion compensation is set for the signal reflected off of the back surface C of the specimen; (c) single depth scan through the line S shown in (b) of the specimen image; (d)–(f) solid curves are zoomed photocurrent signal envelopes and the dashed curves are simulated photocurrent signal envelopes for light reflected off (d) the front surface A, (e) the second surface (i.e., from layer B), and (f) the back surface C of the specimen for Δz = − 0.055 mm, Δd = 3.6 mm, and x0 = 3 mm.

Fig. 8
Fig. 8

Schematic diagram of the double-pass FD ODL in the case of a grating tilted from the normal and offset from the focal plane.

Tables (3)

Tables Icon

Table 1 Parameters of the Single-Mode Optical Fiber and the FD ODL

Tables Icon

Table 2 Dispersion Coefficients of Skin and LiTaO3

Tables Icon

Table 3 Computed Axial Resolutions in LiTaO3

Equations (43)

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E s ( t ) = exp ( i ω t ) Ê s ( ω ) d ω ,
E ( t ) = α 1 exp [ i ϕ 1 ( ω , t ) + i ω t ] Ê s ( ω ) d ω + α ̂ 2 ( ω ) exp [ i ϕ 2 ( ω , t ) + i ω t ] Ê s ( ω ) d ω ,
m ( ω , t ) = α 1 exp [ i ϕ 1 ( ω , t ) ] + α ̂ 2 ( ω ) exp [ i ϕ 2 ( ω , t ) ] ,
E ( t ) = m ( ω , t ) exp ( i ω t ) Ê s ( ω ) d ω .
E s ( t ) = 0 ,
E ( t ) = 0 .
I ( t ) = e Δ t Δ t t N ( t ) d t = e Δ t r ( t t ) N ( t ) d t ,
r ( t ) = 1 for 0 t Δ t 0 otherwise .
N ( t ) = ρ E ( t ) E ( t ) ,
I ( t ) = e Δ t r ( t t ) N ( t ) d t .
N ( t ) = ρ m * ( ω , t ) m ( ω , t ) × exp [ i ( ω ω ) t ] Ê s ( ω ) Ê s ( ω ) d ω d ω .
G ( τ ) = Ê s ( t τ ) E s ( t ) .
G * ( τ ) = G ( τ ) ,
Ê s ( ω ) Ê s ( ω ) = 1 4 π 2 exp [ i ( ω t 2 ω t 1 ) ] × Ê s ( t 1 ) E s ( t 2 ) d t 1 d t 2 = 1 4 π 2 exp [ i ( ω t 2 ω t 1 ) ] × G ( t 2 t 1 ) d t 1 d t 2 .
ω t 2 ω t 1 = 1 2 ( ω ω ) ( t 2 + t 1 ) + 1 2 ( ω + ω ) ( t 2 t 1 ) ,
Ê s ( ω ) Ê s ( ω ) = 1 2 π δ ( ω ω ) × exp [ i ( ω + ω ) 2 s ] G ( s ) d s = δ ( ω ω ) Ĝ ( ω ) .
N ( t ) = ρ | m ( ω , t ) | 2 S ( ω ) d ω .
| m ( ω , t ) | 2 = α 1 2 + | α ̂ 2 ( ω ) | 2 + 2 α 1 Re { α ̂ 2 ( ω ) × exp [ i ϕ 1 ( ω , t ) + i ϕ 2 ( ω , t ) ] } .
I ( t ) = ρ e Δ t r ( t t ) × [ | m ( ω , t ) | 2 S ( ω ) d ω ] d t .
I ( t ) = ρ e Δ t | m ( ω , t ) | 2 S ( ω ) d ω .
| m ( ω , t ) | 2 = α 1 2 + α 2 2 + 2 α 1 α 2 Re { exp [ i ϕ 1 ( ω , t ) + i ϕ 2 ( ω , t ) ] } .
I ac ( t ) Re { exp i [ ϕ 2 ( ω , t ) ϕ 1 ( ω , t ) ] } S ( ω ) d ω Re [ exp i Δ ϕ ( ω , t ) ] S ( ω ) d ω .
Δ ϕ ( ω , t ) = ϕ 2 ( ω , t ) ϕ 1 ( ω , t ) = ω 0 t p ( t ) + ( ω ω 0 ) t g ( t ) + D ω ( t ) ( ω ω 0 ) 2 2 ! + D ω ( 1 ) ( t ) ( ω ω 0 ) 3 3 ! + ,
t p ( t ) Δ ϕ ( ω 0 , t ) / ω 0 , t g ( t ) [ Δ ϕ ( ω , t ) ] / ω | ω = ω 0 , D ω ( t ) 2 [ Δ ϕ ( ω , t ) ] / ω 2 | ω = ω 0 , D ω ( 1 ) ( t ) 3 [ Δ ϕ ( ω , t ) ] / ω 3 | ω = ω 0 .
I ac ( t ) Re ( S ( ω ω 0 ) exp { i [ D ω ( ω ω 0 ) 2 2 ! + D ω ( 1 ) ( t ) ( ω ω 0 ) 3 3 ! ] } ) exp ( i ω 0 t p ) exp [ i ( ω ω 0 ) t g ] d ω ,
Î ac ( ω ) S ( ω ) exp { i [ D ω ω 2 2 ! + D ω ( 1 ) ω 3 3 ! ] } exp ( i ω 0 t p ) ,
t p ODL ( t ) = 4 Δ z c + 4 Δ θ ( t ) x 0 c ,
t g ODL ( t ) = 4 Δ z c + 4 Δ θ ( t ) x 0 c + 8 π Δ θ ( t ) f p ω 0 cos θ g ,
D ω , ODL ( t ) = 16 π 2 c [ Δ z + f Δ θ ( t ) tan θ g ] p 2 ω 0 3 cos 2 θ g ,
D ω , ODL ( 1 ) ( t ) = 48 π 2 c [ Δ z + f Δ θ ( t ) tan θ g ] p 2 ω 0 4 cos 2 θ g × ( 1 + 2 π c sin θ g p ω 0 cos 2 θ g ) ,
t p ( t ) = t p ODL ( t ) + t p fiber ( t ) + t p sample ( t ) = 4 Δ z c + 4 Δ θ ( t ) x 0 c + 2 δ c 2 Δ d s ν p sample ,
t g ( t ) = t g ODL ( t ) + t g fiber ( t ) + t g sample ( t ) = 4 Δ z c + 4 Δ θ ( t ) x 0 c + 8 π θ ( t ) f p ω 0 cos θ g + 2 δ c 2 Δ d s ν g sample ,
D ω ( t ) = D ω ODL ( t ) + D ω fiber ( t ) + D ω sample ( t ) = 16 π 2 c [ Δ z + f Δ θ ( t ) tan θ g ] p 2 ω 0 3 cos 2 θ g + 2 β 2 fiber Δ d 2 β 2 sample Δ d s ,
D ω ( 1 ) ( t ) = D ω ODL ( 1 ) ( t ) + D w fiber ( 1 ) ( t ) + D w sample ( 1 ) ( t ) = 48 π 2 c [ Δ z + f Δ θ ( t ) tan θ g ] p 2 ω 0 4 cos 2 θ g ( 1 + 2 π c sin θ g p ω 0 cos 2 θ g ) + 2 β 3 fiber Δ d 2 β 3 sample Δ d s ,
D ω ( t ) = D ω ODL ( t ) + D ω fiber ( t ) = 16 π 2 c [ Δ z + f Δ θ ( t ) tan θ g ] p 2 ω 0 3 cos 2 θ g + 2 β 2 fiber Δ d .
Δ z Δ d = β 2 fiber p 2 ω 0 3 8 π 2 c .
Δ ϕ ( ω , t ) = 2 ω Δ z c cos β + 2 ω x 0 θ ( t ) c 2 ω θ ( t ) f c sin β ,
Δ ϕ ODL ( ω , t ) = 4 ω Δ z c cos β + 4 ω x 0 Δ θ ( t ) c 4 ω Δ θ ( t ) c sin β = 4 ω Δ z c 8 ω Δ z c sin 2 β 2 + 4 ω x 0 c Δ θ ( t ) 4 ω Δ θ ( t ) f c sin β ,
p [ sin ( β + θ g ) sin θ g ] = 2 π mc ( 1 ω 1 ω 0 ) .
t p ODL ( t ) Δ ϕ ODL ( ω 0 , t ) ω 0 = 4 Δ z c + 4 Δ θ ( t ) x 0 c ,
t g ODL ( t ) [ Δ ϕ ODL ( ω 0 , t ) ] ω 0 | ω = ω 0 = 4 Δ z c + 4 Δ θ ( t ) x 0 c + 8 π Δ θ ( t ) f p ω 0 cos θ g ,
D ω ODL ( t ) 2 [ Δ ϕ ODL ( ω , t ) ] ω 2 | ω = ω 0 = 16 π 2 c [ Δ z + f Δ θ ( t ) tan θ g p 2 ω 0 3 cos 2 θ g ,
D ω ODL ( 1 ) ( t ) 3 [ Δ ϕ ODL ( ω 0 , t ) ] ω 3 | ω = ω 0 = 48 π 2 c [ Δ z + f Δ θ ( t ) tan θ g ] p 2 ω 0 4 cos 2 θ g + ( 1 + 2 π c sin θ g p ω 0 cos 2 θ g ) .

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