Abstract

A new iterative algorithm to be used to precisely reconstruct near-field distribution from an interferogram of a laser output generated by a cyclic radial-shearing interferometer is proposed. First, by use of a window function around the zero-frequency part of the Fourier transform of the interferogram and calculation of the inverse Fourier transform of the zero-frequency part, we obtain the background intensity distribution of the interferogram. Then, according to the iterative algorithm, the near-field distribution of the laser output is precisely reconstructed from the background intensity distribution obtained in the first step. A numerical simulation and an actual experiment of the near-field reconstruction of the laser output with arbitrary amplitude distribution are implemented successfully.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. R. Barnes and L. C. Smith, Proc. SPIE 3492, 564 (1999).
    [Crossref]
  2. M. V. R. K. Murty, Appl. Opt. 3, 853 (1964).
    [Crossref]
  3. D. Malacara, Optical Shop Testing (Wiley, New York, 1978).
  4. J. D. Briers, Opt. Laser Technol. 4, 28 (1972).
    [Crossref]
  5. P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. William, and B. M. Van Wonterghem, Proc. SPIE 3492, 1019 (1999).
    [Crossref]
  6. D. H. Li, H. X. Chen, and Z. P. Chen, Opt. Eng. 41, 1893 (2002).
    [Crossref]

2002 (1)

D. H. Li, H. X. Chen, and Z. P. Chen, Opt. Eng. 41, 1893 (2002).
[Crossref]

1999 (2)

A. R. Barnes and L. C. Smith, Proc. SPIE 3492, 564 (1999).
[Crossref]

P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. William, and B. M. Van Wonterghem, Proc. SPIE 3492, 1019 (1999).
[Crossref]

1972 (1)

J. D. Briers, Opt. Laser Technol. 4, 28 (1972).
[Crossref]

1964 (1)

Barnes, A. R.

A. R. Barnes and L. C. Smith, Proc. SPIE 3492, 564 (1999).
[Crossref]

Briers, J. D.

J. D. Briers, Opt. Laser Technol. 4, 28 (1972).
[Crossref]

Chen, H. X.

D. H. Li, H. X. Chen, and Z. P. Chen, Opt. Eng. 41, 1893 (2002).
[Crossref]

Chen, Z. P.

D. H. Li, H. X. Chen, and Z. P. Chen, Opt. Eng. 41, 1893 (2002).
[Crossref]

Henesian, M. A.

P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. William, and B. M. Van Wonterghem, Proc. SPIE 3492, 1019 (1999).
[Crossref]

Li, D. H.

D. H. Li, H. X. Chen, and Z. P. Chen, Opt. Eng. 41, 1893 (2002).
[Crossref]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Murty, M. V. R. K.

Salmon, J. T.

P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. William, and B. M. Van Wonterghem, Proc. SPIE 3492, 1019 (1999).
[Crossref]

Seppala, L. G.

P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. William, and B. M. Van Wonterghem, Proc. SPIE 3492, 1019 (1999).
[Crossref]

Smith, L. C.

A. R. Barnes and L. C. Smith, Proc. SPIE 3492, 564 (1999).
[Crossref]

Van Wonterghem, B. M.

P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. William, and B. M. Van Wonterghem, Proc. SPIE 3492, 1019 (1999).
[Crossref]

Wegner, P. J.

P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. William, and B. M. Van Wonterghem, Proc. SPIE 3492, 1019 (1999).
[Crossref]

Weiland, T. L.

P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. William, and B. M. Van Wonterghem, Proc. SPIE 3492, 1019 (1999).
[Crossref]

William, W. H.

P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. William, and B. M. Van Wonterghem, Proc. SPIE 3492, 1019 (1999).
[Crossref]

Appl. Opt. (1)

Opt. Eng. (1)

D. H. Li, H. X. Chen, and Z. P. Chen, Opt. Eng. 41, 1893 (2002).
[Crossref]

Opt. Laser Technol. (1)

J. D. Briers, Opt. Laser Technol. 4, 28 (1972).
[Crossref]

Proc. SPIE (2)

P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. William, and B. M. Van Wonterghem, Proc. SPIE 3492, 1019 (1999).
[Crossref]

A. R. Barnes and L. C. Smith, Proc. SPIE 3492, 564 (1999).
[Crossref]

Other (1)

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Schematic of a CRS interferometer to be used to test a wave front. M1, M2, reflection mirrors.

Fig. 2
Fig. 2

Reconstruction of the near field of the CRS interference with s=1:2: (a) assumed near-field distribution to be tested; (b) intensity distribution of the expanded beam, (c) extracted background intensity distribution from a CRS interferogram with the Fourier-transform method, (d) retrieved near-field distribution from (c) with Eq. (13).

Fig. 3
Fig. 3

Experimental setup: BE, beam expander and spatial filter; T, transmission distribution of the GP. BS, beam splitter; M1, M2, mirrors.

Fig. 4
Fig. 4

Experimental study of an iterative algorithm: (a) transmission profile of the GP, (b) CRS fringe pattern of the GP, (c) extracted background intensity distribution from (b) with the Fourier-transform method, (d) the retrieved near-field distribution from (c) with Eq. (13).

Fig. 5
Fig. 5

Cross sections along the central column of the actual near field (solid curve), the reconstructed near field (dashed curve), and the background intensity distribution (dotted curve).

Equations (16)

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

Ir/s,ϕ=Ar/s,ϕexpikWr/s,ϕ+Ars,ϕexpikWrs,ϕ2=A2r/s,ϕ+A2rs,ϕ+2Ar/s,ϕArs,ϕ×coskWr/s,ϕ-Wrs,ϕ=I0r/s,ϕ+I0rs,ϕ+2Ar/s,ϕArs,ϕ×coskWr/s,ϕ-Wrs,ϕ.
Ibr/s,ϕ=I0r/s,ϕ+I0rs,ϕ.
Ibrs,ϕ=I0rs,ϕ+I0rs3,ϕ.
Ibrs3,ϕ=I0rs3,ϕ+I0rs5,ϕ,
Ibrs5,ϕ=I0rs5,ϕ+I0rs7,ϕ,
      
Ibrs2n-1,ϕ=I0rs2n-1,ϕ+I0rs2n+1,ϕ,
Ibrs2n+1,ϕ=I0rs2n+1,ϕ+I0rs2n+3,ϕ,
Ibr/s,ϕ-Ibrs,ϕ=I0r/s,ϕ-I0rs3,ϕ,
Ibrs3,ϕ-Ibrs5,ϕ=I0rs3,ϕ-I0rs7,ϕ,
      
Ibrs2n-1,ϕ-Ibrs2n+1,ϕ=I0rs2n-1,ϕ-I0rs2n+3,ϕ.
I0r/s,ϕ-I0rs2n+3,ϕ=Ibr/s,ϕ-Ibrs,ϕ+Ibrs3,ϕ-Ibrs5,ϕ++Ibrs2n-1,ϕ-Ibrs2n+1,ϕ,
I0r/s,ϕ=N=0nIbrs2N-1,ϕ-Ibrs2N+1,ϕ+I0rs2n+3,ϕ, N=0,1,2,,n.
I0r/s,ϕ=N=0nIbrs2N-1,ϕ-Ibrs2N+1,ϕ, N=0,1,2,,n.
I0x,y=7.168×108y5+3.584×107x4+2.24×104y2+1.12×104x2-2.8×102x×exp-1.6×103x2-1.6×103y2+3.4087.

Metrics