Abstract

We present what we believe to be a new computational algorithm for complex frequency domain optical coherence tomography that can effectively suppress artifacts that are caused by uncertainty in phase shift due to sample motion and errors in reference phases. The algorithm treats the phase-shifting values as additional unknowns, and we can determine their exact values by analyzing interference fringes using the numerical least-squares technique. A series of simulations and experiments prove that this algorithm can effectively remove strong mirror-image artifacts because it is unaffected by random phase fluctuation.

© 2006 Optical Society of America

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  1. D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
    [CrossRef]
  2. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometer," Opt. Commun. 117, 43-48 (1995).
    [CrossRef]
  3. G. Hausler and M. W. Linder, "Coherence radar and spectral radar--new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
    [CrossRef]
  4. M. Wojtkowski, T. Bajraszewski, P. Targowski, and A. Kowalczyk, "Real time in vivo imaging by high-speed spectral coherence tomography," Opt. Lett. 28, 1745-1747 (2003).
    [CrossRef] [PubMed]
  5. S. H. Yun, G. J. Tearney, B. E. Bouma, B. H. Park, and J. F. de Boer, "High-speed spectral domain optical coherence tomography at 1.3 μm wavelength," Opt. Express 11, 3598-3604 (2003).
    [CrossRef] [PubMed]
  6. S. R. Chinn, E. Swanson, and J. G. Fujimoto, "Optical coherence tomography using a frequency-tunable optical source," Opt. Lett. 22, 340-342 (1997).
    [CrossRef] [PubMed]
  7. S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, "High-speed optical frequency-domain imaging," Opt. Express 11, 2953-2963 (2003).
    [CrossRef] [PubMed]
  8. M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, "Full range complex spectral optical coherence tomography," Opt. Lett. 27, 1415-1417 (2002).
    [CrossRef]
  9. R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, "Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography," Op. Lett. 28, 2201-2203 (2003).
    [CrossRef]
  10. S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, "Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting," Opt. Express 12, 4822-4828 (2004).
    [CrossRef] [PubMed]
  11. J. Zhang, J. S. Nelson, and Z. Chen, "Removal of a mirror image and enhancement of the signal-to-noise ratio in Fourier-domain optical coherence tomography using an electro-optic phase modulator," Opt. Lett. 30, 147-149 (2005).
    [CrossRef] [PubMed]
  12. M. V. Sarunic, M. A. Choma, C. Yang, and J. A. Izatt, "Instantaneous complex conjugate resolved spectral domain and swept-source OCT using 3 × 3 fiber couplers," Opt. Express 13, 957-967 (2005).
    [CrossRef] [PubMed]
  13. G. S. Han and S. W. Kim, "Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting," Appl. Opt. 33, 7321-7325 (1994).
    [CrossRef] [PubMed]
  14. P. J. de Groot, "Vibration in phase-shifting interferometer," J. Opt. Soc. Am. A 12, 354-365 (1995).
    [CrossRef]
  15. W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, "Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source," J. Opt. Soc. Am. B 19, 2148-2155 (2002).
    [CrossRef]
  16. N. R. Newbury, B. R. Washburn, and K. L. Corwin, "Noise amplification during supercontinuum generation in microstructure fiber," Opt. Lett. 28, 944-946 (2003).
    [CrossRef] [PubMed]

2005 (2)

2004 (1)

2003 (5)

2002 (2)

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, "Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source," J. Opt. Soc. Am. B 19, 2148-2155 (2002).
[CrossRef]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, "Full range complex spectral optical coherence tomography," Opt. Lett. 27, 1415-1417 (2002).
[CrossRef]

1998 (1)

G. Hausler and M. W. Linder, "Coherence radar and spectral radar--new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
[CrossRef]

1997 (1)

1995 (2)

P. J. de Groot, "Vibration in phase-shifting interferometer," J. Opt. Soc. Am. A 12, 354-365 (1995).
[CrossRef]

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometer," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

1994 (1)

1991 (1)

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

Bajraszewski, T.

R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, "Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography," Op. Lett. 28, 2201-2203 (2003).
[CrossRef]

M. Wojtkowski, T. Bajraszewski, P. Targowski, and A. Kowalczyk, "Real time in vivo imaging by high-speed spectral coherence tomography," Opt. Lett. 28, 1745-1747 (2003).
[CrossRef] [PubMed]

Birks, T. A.

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, "Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source," J. Opt. Soc. Am. B 19, 2148-2155 (2002).
[CrossRef]

Bouma, B. E.

Chang, W.

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

Chen, Z.

Chinn, S. R.

Choma, M. A.

Corwin, K. L.

de Boer, J. F.

de Groot, P. J.

P. J. de Groot, "Vibration in phase-shifting interferometer," J. Opt. Soc. Am. A 12, 354-365 (1995).
[CrossRef]

El-Zaiat, S. Y.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometer," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Fercher, A. F.

R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, "Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography," Op. Lett. 28, 2201-2203 (2003).
[CrossRef]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, "Full range complex spectral optical coherence tomography," Opt. Lett. 27, 1415-1417 (2002).
[CrossRef]

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometer," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Flotte, T.

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

Fujimoto, J. G.

S. R. Chinn, E. Swanson, and J. G. Fujimoto, "Optical coherence tomography using a frequency-tunable optical source," Opt. Lett. 22, 340-342 (1997).
[CrossRef] [PubMed]

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

Gregory, K.

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

Han, G. S.

Haung, D.

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

Hausler, G.

G. Hausler and M. W. Linder, "Coherence radar and spectral radar--new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
[CrossRef]

Hee, M. R.

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

Hitzenberger, C. K.

R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, "Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography," Op. Lett. 28, 2201-2203 (2003).
[CrossRef]

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometer," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Iftimia, N.

Izatt, J. A.

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometer," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Kim, S. W.

Knight, J. C.

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, "Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source," J. Opt. Soc. Am. B 19, 2148-2155 (2002).
[CrossRef]

Kowalczyk, A.

Leitgeb, R.

Leitgeb, R. A.

R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, "Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography," Op. Lett. 28, 2201-2203 (2003).
[CrossRef]

Lin, C. P.

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

Linder, M. W.

G. Hausler and M. W. Linder, "Coherence radar and spectral radar--new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
[CrossRef]

Man, T.-P. M.

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, "Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source," J. Opt. Soc. Am. B 19, 2148-2155 (2002).
[CrossRef]

Nelson, J. S.

Newbury, N. R.

Ortigosa-Blanch, A.

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, "Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source," J. Opt. Soc. Am. B 19, 2148-2155 (2002).
[CrossRef]

Park, B. H.

Puliafito, C. A.

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

Russell, P. St. J.

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, "Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source," J. Opt. Soc. Am. B 19, 2148-2155 (2002).
[CrossRef]

Sarunic, M. V.

Schuman, J. S.

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

Stinson, W. G.

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

Swabson, E. A.

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

Swanson, E.

Targowski, P.

Tearney, G. J.

Wadsworth, W. J.

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, "Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source," J. Opt. Soc. Am. B 19, 2148-2155 (2002).
[CrossRef]

Washburn, B. R.

Wojtkowski, M.

Yang, C.

Yun, S. H.

Zhang, J.

Appl. Opt. (1)

J. Biomed. Opt. (1)

G. Hausler and M. W. Linder, "Coherence radar and spectral radar--new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

P. J. de Groot, "Vibration in phase-shifting interferometer," J. Opt. Soc. Am. A 12, 354-365 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, "Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source," J. Opt. Soc. Am. B 19, 2148-2155 (2002).
[CrossRef]

Op. Lett. (1)

R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, "Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography," Op. Lett. 28, 2201-2203 (2003).
[CrossRef]

Opt. Commun. (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometer," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Opt. Express (4)

Opt. Lett. (5)

Science (1)

D. Haung, E. A. Swabson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic of complex FD-OCT configured for testing new algorithm. The source power spectrum after spectral broadening is in the upper left inset. NBS, nonpolarizing beam splitter; SMF, single-mode fiber.

Fig. 2
Fig. 2

Simulation results for artifact removal under random sample motion condition. Upper figure, comparison between before and after applying this algorithm. Lower figure, convergence path of δ 0j .

Fig. 3
Fig. 3

Simulation result for artifact removal under the phase-shifting transducer calibration error. Upper figure, comparison between before and after applying this algorithm. Lower figure, convergence path of δ 0j .

Fig. 4
Fig. 4

Experimental result for mirror-image artifact removal for the attenuated reflecting surface. The position of the surface is −0.7 mm.

Fig. 5
Fig. 5

Effect of the FD-OCT system imperfections in the artifact removal algorithm. Displayed are the simulation results of artifact removal under (a) the ideal system conditions, (b) source intensify noise, (c) CCD detector nonlinearity, and (d) quantization error. The same random sample motion for Fig. 3 is applied to all cases.

Fig. 6
Fig. 6

Artifact removal for complex FD-OCT image of the rat skin in vitro: (a) before compensation and (b) after compensation. The arrow in image (a) indicates artifacts caused by random motion of the sample. The physical size of each image is 1.5 mm (depth) × 2.4 mm (width).

Tables (2)

Tables Icon

Table 1 Simulation Parameters

Tables Icon

Table 2 Fluctuation of Phase-Shift Values Caused by Random Sample Motion in the In Vitro Measurement

Equations (45)

Equations on this page are rendered with MathJax. Learn more.

I ( k ) = S ( k ) + R e { S ( k ) n m α n α m exp [ 2 i k ( z n z m ) ] } + 2 R e { S ( k ) n α n exp [ 2 i k ( z n z r ) ] } ,
Ψ ( k ) = S ( k ) n α n exp [ 2 i k ( z n z r ) ] = ψ ( k ) [ i ϕ ( k ) ] .
FT 1 [ Ψ ( k ) ] = n α n Γ [ z ( z n z r ) ] ,
I j ( k ) = D ( k ) + Ψ ( k ) cos [ ϕ ( k ) + δ j ( k ) ] ,
ϕ ( k ) = tan 1 { [ j = 1 m I j ( k ) sin δ j ] / [ j = 1 m I j ( k ) cos δ j ] } ,
ψ ( k ) = 1 4 { [ j = 1 m I j ( k ) sin δ j ] 2 + [ j = 1 m I j ( k ) cos δ j ] 2 } 1 / 2 .
ϕ ˜ ( k ) = 2 k ( z n z r ) + β n cos [ 4 k ( z n z r ) ] ,
ψ ˜ ( k ) α n S ( k ) { 1 β n sin [ 4 k ( z n z r ) ] } .
Ψ ˜ ( k ) = α n S ( k ) { 1 β n sin [ 4 k ( z n z r ) ] } [ exp ( i { 2 k ( z n z r ) + β n cos [ 4 k ( z n z r ) ] } ) ] .
Ψ ˜ ( k ) α n S ( k ) { 1 β n sin [ 4 k ( z n z r ) ] } ( exp { i [ 2 k ( z n z r ) ] } ) ( J 0 ( β n ) + i J 1 ( β n ) exp { i [ 4 k ( z n z r ) ] } + i J 1 ( β n ) exp { i [ 4 k ( z n z r ) ] } ) .
FT 1 [ Ψ ˜ ( k ) ] α n Γ [ z ( z n z r ) ] + α n β n Γ [ z + ( z n z r ) ] .
I i j = [ D i + D i V i cos ( ϕ i + δ i j ) ] ,
δ i j = 2 k i Δ z j = δ 0 j [ 1 + ( k i k 0 ) / k 0 ] ,
I i j = [ D i + D i V i cos ( ϕ i + δ i j ) ]
= D i + D i V i cos ϕ i cos δ i j D i V i sin ϕ i sin δ i j
= D i + C i cos δ i j S i sin δ i j .
d m d 3 d + m 1   or   d 1 + 3 ( m 4 ) .
ε = i = 1 d j = 1 m ( I i j I ^ i j ) 2 ,
ε = i = 1 d ε i = j = 1 m ε j ,
ε j = j = 1 m ( D i + C i cos δ i j S i sin δ i j I ^ i j ) 2 ,
ε i = i = 1 d ( D i + C i cos δ i j S i sin δ i j I ^ i j ) 2 .
ε D i = ε C i = ε S i = 0   or   ε i D i = ε i C i = ε i S i = 0 ,
ε δ 0 j = ε j δ 0 j = 0.
I ( ϕ , δ ) = D + Ψ cos ( ϕ + δ ) ,
I ( ϕ , δ ) = D + ψ cos [ ϕ + δ n ( δ ) ] ,
Δ I = I I D ψ n ( δ ) sin ( ϕ + δ ) .
Δ φ = φ ( ϕ , ) ϕ .
φ ( ϕ ) = tan 1 [ s ( ϕ ) / c ( ϕ ) ] ,
ψ ( ϕ ) = κ s 2 ( ϕ ) + c 2 ( ϕ ) ,
s ( ϕ ) = f s ( δ ) I ( ϕ , δ ) d δ ,
c ( ϕ ) = f c ( δ ) I ( ϕ , δ ) d δ ,
s ( ϕ ) D ψ q sin ( ϕ ) , c ( ϕ ) D ψ q cos ( ϕ ) ,
q = f s ( δ ) sin ( δ ) d δ = f c ( δ ) cos ( δ ) d δ ,
Δφ [ Δs ( ϕ ) d s | φ = ϕ + Δc ( ϕ ) d s | φ = ϕ ] ,
Δψ [ Δs ( ϕ ) d s | φ = ϕ + Δc ( ϕ ) d s | φ = ϕ ] .
Δφ 1 D ψ q [ Δ s ( ϕ ) cos ( ϕ ) Δ c ( ϕ ) sin ( ϕ ) ] ,
Δψ 1 D ψ q [ Δ s ( ϕ ) sin ( ϕ ) Δ c ( ϕ ) cos ( ϕ ) ] .
Δ s ( ϕ ) = D ψ f s ( δ ) n ( δ ) sin ( δ + ϕ ) d δ ,
Δ c ( ϕ ) = D ψ f c ( δ ) n ( δ ) sin ( δ + ϕ ) d δ .
Δφ P 0 + P 1 cos ( 2 ϕ ) + P 2 sin ( 2 ϕ ) ,
Δψ P 0 * + P 2 cos ( 2 ϕ ) P 1 sin ( 2 ϕ ) ,
P 0 = 1 2 q [ f s ( δ ) n ( δ ) sin ( δ ) d δ f c ( δ ) n ( δ ) cos ( δ ) d δ ] ,
P 0 * = 1 2 q [ f s ( δ ) n ( δ ) cos ( δ ) d δ + f c ( δ ) n ( δ ) sin ( δ ) d δ ] ,
P 1 = 1 2 q [ f s ( δ ) n ( δ ) sin ( δ ) d δ + f c ( δ ) n ( δ ) cos ( δ ) d δ ] ,
P 2 = 1 2 q [ f s ( δ ) n ( δ ) cos ( δ ) d δ f c ( δ ) n ( δ ) sin ( δ ) d δ ] .

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