Abstract

We describe a concept of detecting the piston and tilt errors with a Shack-Hartmann sensor and correcting them simultaneously via a segmented deformable mirror (DM) in a two-dimensional laser array. The concept in coherent beam combination (CBC) is demonstrated by both simulation and experiment. The simulative results show only two iterations are enough to correct the random initial phase errors in the steady condition. The experimental results confirm that this method works effectively in a dynamic condition. The study represents that the Shack-Hartmann sensor can extract any piston error in –π ~π, which means the concept is an arbitrary phasing technique for a laser array.

© 2012 OSA

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References

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  4. G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
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    [Crossref]
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    [Crossref]
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  10. M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, “Efficient coherent addition of fiber lasers in free space,” Opt. Lett. 32(7), 790–792 (2007).
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  15. P. Zhou, Y. Ma, X. Wang, H. Ma, X. Xu, and Z. Liu, “Coherent beam combination of three two-tone fiber amplifiers using stochastic parallel gradient descent algorithm,” Opt. Lett. 34(19), 2939–2941 (2009).
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  16. S. Esposito, E. Pinna, A. Puglisi, A. Tozzi, and P. Stefanini, “Pyramid sensor for segmented mirror alignment,” Opt. Lett. 30(19), 2572–2574 (2005).
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  17. K. L. Baker, D. Homoelle, E. Utterback, and S. M. Jones, “Phasing rectangular apertures,” Opt. Express 17(22), 19551–19565 (2009).
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  18. S. C. West, “Interferometric hartmann wave-front sensing for active optics at the 6.5-m conversion of the multiple mirror telescope,” Appl. Opt. 41(19), 3781–3789 (2002).
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  19. G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, and D. Kirkman, “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37(1), 140–155 (1998).
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  20. P. Yang, R. Yang, L. Dong, X. Lei, and B. Xu, “Hartmann phase pick-up method for detection and correction of piston aberrations in a multi-beam coherent combination system,” Appl. Phys. B 98(2-3), 465–469 (2010).
    [Crossref]
  21. X. Wang and F. Shen, “Application of DBPIP to phase errors detection in coherent beam combination,” Proc. SPIE 7656, 76564Q, 76564Q-9 (2010).
    [Crossref]
  22. D. R. Neal, T. G. Smith, G. R. Eisler, J. L. Wilcoxen, and R. R. Rosenthal, “Multiple laser beam combining and phasing using closed-loop control,” Proc. SPIE 1920, 9–19 (1993).
    [Crossref]
  23. D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
    [Crossref]
  24. D. R. Neal, D. J. Armstrong, and W. T. Turner, “Wavefront sensors for control and process monitoring in optics manufacture,” Proc. SPIE 2993, 211–220 (1997).
    [Crossref]
  25. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company Publishers, Greenwood Village, 2004).

2011 (1)

2010 (3)

Y. Zheng, X. Wang, F. Shen, and X. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express 18(26), 26946–26958 (2010).
[Crossref] [PubMed]

P. Yang, R. Yang, L. Dong, X. Lei, and B. Xu, “Hartmann phase pick-up method for detection and correction of piston aberrations in a multi-beam coherent combination system,” Appl. Phys. B 98(2-3), 465–469 (2010).
[Crossref]

X. Wang and F. Shen, “Application of DBPIP to phase errors detection in coherent beam combination,” Proc. SPIE 7656, 76564Q, 76564Q-9 (2010).
[Crossref]

2009 (5)

P. Zhou, Y. Ma, X. Wang, H. Ma, X. Xu, and Z. Liu, “Coherent beam combination of three two-tone fiber amplifiers using stochastic parallel gradient descent algorithm,” Opt. Lett. 34(19), 2939–2941 (2009).
[Crossref] [PubMed]

B. Wang, E. Mies, M. Minden, and A. Sanchez, “All-fiber 50 W coherently combined passive laser array,” Opt. Lett. 34(7), 863–865 (2009).
[Crossref] [PubMed]

K. L. Baker, D. Homoelle, E. Utterback, and S. M. Jones, “Phasing rectangular apertures,” Opt. Express 17(22), 19551–19565 (2009).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 231106 (2009).
[Crossref]

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

2007 (4)

M. Fridman, V. Eckhouse, N. Davidson, and A. A. Friesem, “Efficient coherent addition of fiber lasers in free space,” Opt. Lett. 32(7), 790–792 (2007).
[Crossref] [PubMed]

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 480–486 (2007).
[Crossref]

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

2006 (2)

2005 (2)

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005).
[Crossref]

S. Esposito, E. Pinna, A. Puglisi, A. Tozzi, and P. Stefanini, “Pyramid sensor for segmented mirror alignment,” Opt. Lett. 30(19), 2572–2574 (2005).
[Crossref] [PubMed]

2002 (1)

1998 (1)

1997 (1)

D. R. Neal, D. J. Armstrong, and W. T. Turner, “Wavefront sensors for control and process monitoring in optics manufacture,” Proc. SPIE 2993, 211–220 (1997).
[Crossref]

1996 (1)

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

1994 (1)

N. M. Lyndin, V. A. Sychugov, and A. Y. Tikhomirov, “Coherent coupling of two Nd3-doped single-mode waveguide lasers using Y-junction,” Proc. SPIE 2212, 564–570 (1994).
[Crossref]

1993 (1)

D. R. Neal, T. G. Smith, G. R. Eisler, J. L. Wilcoxen, and R. R. Rosenthal, “Multiple laser beam combining and phasing using closed-loop control,” Proc. SPIE 1920, 9–19 (1993).
[Crossref]

Alford, W. J.

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

Anderegg, J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U, 61020U-5 (2006).
[Crossref]

Armstrong, D. J.

D. R. Neal, D. J. Armstrong, and W. T. Turner, “Wavefront sensors for control and process monitoring in optics manufacture,” Proc. SPIE 2993, 211–220 (1997).
[Crossref]

Asman, C. P.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Augst, S. J.

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

Baker, J. T.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 480–486 (2007).
[Crossref]

Baker, K. L.

Benham, V.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 480–486 (2007).
[Crossref]

Beresnev, L. A.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).

Brosnan, S.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U, 61020U-5 (2006).
[Crossref]

Chanan, G.

Chann, B.

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

Cheung, E.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U, 61020U-5 (2006).
[Crossref]

Cheung, E. C.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
[Crossref] [PubMed]

Connors, M. K.

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

Davidson, N.

Dekens, F.

Deng, L.

Dong, L.

P. Yang, R. Yang, L. Dong, X. Lei, and B. Xu, “Hartmann phase pick-up method for detection and correction of piston aberrations in a multi-beam coherent combination system,” Appl. Phys. B 98(2-3), 465–469 (2010).
[Crossref]

Donnelly, J. P.

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

Dorsch, F.

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

Eckhouse, V.

Eisler, G. R.

D. R. Neal, T. G. Smith, G. R. Eisler, J. L. Wilcoxen, and R. R. Rosenthal, “Multiple laser beam combining and phasing using closed-loop control,” Proc. SPIE 1920, 9–19 (1993).
[Crossref]

Epp, P.

Esposito, S.

Fan, T. Y.

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005).
[Crossref]

Fridman, M.

Friesem, A. A.

Goodno, G. D.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
[Crossref] [PubMed]

Gruetzner, J. K.

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

Hammons, D.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U, 61020U-5 (2006).
[Crossref]

Homoelle, D.

Hostetler, J. L.

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

Howland, D.

Huang, R. K.

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

Injeyan, H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
[Crossref] [PubMed]

Jones, S. M.

Kirkman, D.

Komine, H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
[Crossref] [PubMed]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U, 61020U-5 (2006).
[Crossref]

Lei, X.

P. Yang, R. Yang, L. Dong, X. Lei, and B. Xu, “Hartmann phase pick-up method for detection and correction of piston aberrations in a multi-beam coherent combination system,” Appl. Phys. B 98(2-3), 465–469 (2010).
[Crossref]

Li, X.

Liu, L.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).

Liu, Z.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 231106 (2009).
[Crossref]

P. Zhou, Y. Ma, X. Wang, H. Ma, X. Xu, and Z. Liu, “Coherent beam combination of three two-tone fiber amplifiers using stochastic parallel gradient descent algorithm,” Opt. Lett. 34(19), 2939–2941 (2009).
[Crossref] [PubMed]

Long, W.

Long, W. H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Lu, C. A.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 480–486 (2007).
[Crossref]

Lyndin, N. M.

N. M. Lyndin, V. A. Sychugov, and A. Y. Tikhomirov, “Coherent coupling of two Nd3-doped single-mode waveguide lasers using Y-junction,” Proc. SPIE 2212, 564–570 (1994).
[Crossref]

Ma, H.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 231106 (2009).
[Crossref]

P. Zhou, Y. Ma, X. Wang, H. Ma, X. Xu, and Z. Liu, “Coherent beam combination of three two-tone fiber amplifiers using stochastic parallel gradient descent algorithm,” Opt. Lett. 34(19), 2939–2941 (2009).
[Crossref] [PubMed]

Ma, Y.

P. Zhou, Y. Ma, X. Wang, H. Ma, X. Xu, and Z. Liu, “Coherent beam combination of three two-tone fiber amplifiers using stochastic parallel gradient descent algorithm,” Opt. Lett. 34(19), 2939–2941 (2009).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 231106 (2009).
[Crossref]

Mast, T.

McClellan, M.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
[Crossref] [PubMed]

McNaught, S. J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
[Crossref] [PubMed]

Michaels, S.

Mies, E.

Miester, C.

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

Minden, M.

Missaggia, L. J.

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

Neal, D. R.

D. R. Neal, D. J. Armstrong, and W. T. Turner, “Wavefront sensors for control and process monitoring in optics manufacture,” Proc. SPIE 2993, 211–220 (1997).
[Crossref]

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

D. R. Neal, T. G. Smith, G. R. Eisler, J. L. Wilcoxen, and R. R. Rosenthal, “Multiple laser beam combining and phasing using closed-loop control,” Proc. SPIE 1920, 9–19 (1993).
[Crossref]

Nelson, J.

Pilkington, D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 480–486 (2007).
[Crossref]

Pinna, E.

Polnau, E.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).

Puglisi, A.

Redmond, S.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
[Crossref] [PubMed]

Rosenthal, R. R.

D. R. Neal, T. G. Smith, G. R. Eisler, J. L. Wilcoxen, and R. R. Rosenthal, “Multiple laser beam combining and phasing using closed-loop control,” Proc. SPIE 1920, 9–19 (1993).
[Crossref]

Sanchez, A.

Sanchez, A. D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 480–486 (2007).
[Crossref]

Sanchez-Rubio, A.

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

Shay, T. M.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 480–486 (2007).
[Crossref]

Shen, F.

Simpson, R.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
[Crossref] [PubMed]

Smith, T. G.

D. R. Neal, T. G. Smith, G. R. Eisler, J. L. Wilcoxen, and R. R. Rosenthal, “Multiple laser beam combining and phasing using closed-loop control,” Proc. SPIE 1920, 9–19 (1993).
[Crossref]

Sollee, J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
[Crossref] [PubMed]

Stefanini, P.

Sychugov, V. A.

N. M. Lyndin, V. A. Sychugov, and A. Y. Tikhomirov, “Coherent coupling of two Nd3-doped single-mode waveguide lasers using Y-junction,” Proc. SPIE 2212, 564–570 (1994).
[Crossref]

Tikhomirov, A. Y.

N. M. Lyndin, V. A. Sychugov, and A. Y. Tikhomirov, “Coherent coupling of two Nd3-doped single-mode waveguide lasers using Y-junction,” Proc. SPIE 2212, 564–570 (1994).
[Crossref]

Tozzi, A.

Troy, M.

Turner, G. W.

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

Turner, W. T.

D. R. Neal, D. J. Armstrong, and W. T. Turner, “Wavefront sensors for control and process monitoring in optics manufacture,” Proc. SPIE 2993, 211–220 (1997).
[Crossref]

Utterback, E.

Vorontsov, M. A.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).

Wang, B.

Wang, X.

Warren, M. E.

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

Weber, M.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U, 61020U-5 (2006).
[Crossref]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
[Crossref] [PubMed]

Weiss, S. B.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
[Crossref] [PubMed]

West, S. C.

Weyrauch, T.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).

Wickham, M.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U, 61020U-5 (2006).
[Crossref]

Wilcoxen, J. L.

D. R. Neal, T. G. Smith, G. R. Eisler, J. L. Wilcoxen, and R. R. Rosenthal, “Multiple laser beam combining and phasing using closed-loop control,” Proc. SPIE 1920, 9–19 (1993).
[Crossref]

Xu, B.

P. Yang, R. Yang, L. Dong, X. Lei, and B. Xu, “Hartmann phase pick-up method for detection and correction of piston aberrations in a multi-beam coherent combination system,” Appl. Phys. B 98(2-3), 465–469 (2010).
[Crossref]

Xu, X.

P. Zhou, Y. Ma, X. Wang, H. Ma, X. Xu, and Z. Liu, “Coherent beam combination of three two-tone fiber amplifiers using stochastic parallel gradient descent algorithm,” Opt. Lett. 34(19), 2939–2941 (2009).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 231106 (2009).
[Crossref]

Yang, P.

P. Yang, R. Yang, L. Dong, X. Lei, and B. Xu, “Hartmann phase pick-up method for detection and correction of piston aberrations in a multi-beam coherent combination system,” Appl. Phys. B 98(2-3), 465–469 (2010).
[Crossref]

Yang, R.

P. Yang, R. Yang, L. Dong, X. Lei, and B. Xu, “Hartmann phase pick-up method for detection and correction of piston aberrations in a multi-beam coherent combination system,” Appl. Phys. B 98(2-3), 465–469 (2010).
[Crossref]

Zheng, Y.

Zhou, P.

P. Zhou, Y. Ma, X. Wang, H. Ma, X. Xu, and Z. Liu, “Coherent beam combination of three two-tone fiber amplifiers using stochastic parallel gradient descent algorithm,” Opt. Lett. 34(19), 2939–2941 (2009).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 231106 (2009).
[Crossref]

Appl. Opt. (3)

Appl. Phys. B (1)

P. Yang, R. Yang, L. Dong, X. Lei, and B. Xu, “Hartmann phase pick-up method for detection and correction of piston aberrations in a multi-beam coherent combination system,” Appl. Phys. B 98(2-3), 465–469 (2010).
[Crossref]

Appl. Phys. Lett. (1)

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 231106 (2009).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (3)

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 480–486 (2007).
[Crossref]

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005).
[Crossref]

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
[Crossref]

Opt. Express (2)

Opt. Lett. (5)

Proc. SPIE (8)

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U, 61020U-5 (2006).
[Crossref]

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).

N. M. Lyndin, V. A. Sychugov, and A. Y. Tikhomirov, “Coherent coupling of two Nd3-doped single-mode waveguide lasers using Y-junction,” Proc. SPIE 2212, 564–570 (1994).
[Crossref]

R. K. Huang, B. Chann, L. J. Missaggia, S. J. Augst, M. K. Connors, G. W. Turner, A. Sanchez-Rubio, J. P. Donnelly, J. L. Hostetler, C. Miester, and F. Dorsch, “Coherent combination of slab-coupled optical waveguide lasers,” Proc. SPIE 7230, 72301G, 72301G-12 (2009).
[Crossref]

X. Wang and F. Shen, “Application of DBPIP to phase errors detection in coherent beam combination,” Proc. SPIE 7656, 76564Q, 76564Q-9 (2010).
[Crossref]

D. R. Neal, T. G. Smith, G. R. Eisler, J. L. Wilcoxen, and R. R. Rosenthal, “Multiple laser beam combining and phasing using closed-loop control,” Proc. SPIE 1920, 9–19 (1993).
[Crossref]

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

D. R. Neal, D. J. Armstrong, and W. T. Turner, “Wavefront sensors for control and process monitoring in optics manufacture,” Proc. SPIE 2993, 211–220 (1997).
[Crossref]

Other (2)

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

S. J. McNaught, C. P. Asman, H. Injeyan, A. Jankevics, A. M. Johnson, G. C. Jones, H. Komine, J. Machan, J. Marmo, and M. McClellan, “100-kW coherently combined Nd: YAG MOPA laser array,” in OSA Technical Digest, Frontiers in Optics (CD) (Optical Society of America, 2009), paper FThD2.

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Figures (13)

Fig. 1
Fig. 1

The arrangements between the seven-beam array (circle) and the 19-element Shack-Hartmann mirco-lens sensor (hexagon). Default unit: mm.

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Fig. 2
Fig. 2

The arrangement and parameters of two beams. (Default unit: mm)

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Fig. 3
Fig. 3

Intensity distributions of two beams’ interference patterns in different cases. The piston errors in (a)~(f) are -π,-0.6π,-0.2π, 0, 0.4π and 0.8π, respectively. The left side is the one dimensional intensity distribution of the patterns along the x axis. The dashed line marks the peak location in each case.

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Fig. 4
Fig. 4

Calculated relation between the peak shift and the piston error. The circle points are the peak shifts calculated in different piston errors, and the line is the regression line of these points. The piston step is π/20. The max fitted error is about 0.04 rad (≈0.006*2π).

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Fig. 5
Fig. 5

Evolution of the wavefront and far-field in different states in the simulation. The first row is the wavefront evolution of the laser array, each pixel represents 32.25 μm. The second row is the evolution of the image spots created by the Shack-Hartmann sensor, each pixel represents 10.6 μm. The last row is the evolution of the far-field image of the laser array, each pixel represents 0.95 μm. (a) Images in the initial state; (b) images after the first iteration; (c) images after the second iteration.

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Fig. 6
Fig. 6

Evolution of the phase error in simulation. (a) Piston; (b) Tilt.

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Fig. 7
Fig. 7

Evolution of the peak shifts and Strehl ratio in simulation. (a) Peak shifts in the corresponding sub-micro-lenses’ focal plane; (b)the Strehl ratio of the far-field images.

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Fig. 8
Fig. 8

Schematic of the verification CBC testbed. BS, Beam Splitter, HRM, High Reflective Mirror, ASM, Active Segmented Mirror, HVA, High Voltage Amplifier. (Default unit: mm).

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Fig. 9
Fig. 9

Schematic of the Shack-Hartmann sensor system. MLA, Micro-lens Array. Lens3 and Lens4 compose a 1/8x beam reducing system.

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Fig. 10
Fig. 10

Experimental results. Focal spots created by MLA (a) before and (b) after the correction of the phase errors. (c) The measured peak shift varies with the piston error generated by the ASM. (λ = 632.8 nm, 1pixel = 10.6 μm).

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Fig. 11
Fig. 11

Evolution curves of the tilt error and piston error obtained in the experiment. (a) Curves of the tilt errors of three beams in open loop and close loop. (b) The curve of the piston error between the first beam and the third beam. To draw the curves clearly, only the last 3 seconds in open loop and the first 3 seconds in close loop are shown.

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Fig. 12
Fig. 12

Evolution of the long-exposure far-field image in different phases of the experiment. (a) Both the piston and tilt control loops are off. (b) Just the tilt control loop is on. (c) Both the piston and tilt control loops are on. (d) Theoretical.

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Fig. 13
Fig. 13

Evolution curve of the normalized power encircled in the area of the main lobe. The notes above or below the curve show the corresponding phases of the experiment. The white circle marks the area of the main lobe.

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Equations (12)

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

I(x,y)= ( λf ) −2 | G( x,y ) | 2 { 2+2cos{ φ− k f [ ( a 2 − a 1 )x+( b 2 − b 1 )y ] } },
G( x,y )=ℑ{ g(u,v) }={ π w 2 , x 2 + y 2 =0, wλf x 2 + y 2 J 1 ( 2πw x 2 + y 2 λf ), otherwise.
[ α β ]= 1 f [ C x C y ].
α= [ α 1 α 2 α 3 α 4 α 5 α 6 α 7 ] T , β= [ β 1 β 2 β 3 β 4 β 5 β 6 β 7 ] T , C x = [ c x 1 c x 8 c x 10 c x 12 c x 14 c x 16 c x 18 ] T , C y = [ c y 1 c y 8 c y 10 c y 12 c y 14 c y 16 c y 18 ] T .
P= k c ⋅S.
P= [ 0 p 2 p 3 p 4 p 5 p 6 p 7 ] T , S= [ 0 s 2 s 3 s 4 s 5 s 6 s 7 ] T ,
P=A⋅Γ,
Γ= [ ϕ 1 ϕ 2 ϕ 3 ϕ 4 ϕ 5 ϕ 6 ϕ 7 ] T ,
A=[ 1 1 0 −1 0 0 0 0 0 0 0 0 0 0 1 0 −1 0 0 0 0 1 0 0 −1 0 0 0 −1 0 0 0 1 0 0 −1 0 0 0 0 1 0 −1 0 0 0 0 0 1 ].
Γ= k c A −1 ⋅S.
U i (x,y)=exp{j ϕ i −jk[(x− a i ) α i +(y− b i ) β i ]}.
θ i = α i 2 + β i 2

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