Abstract

Based on moiré phenomena and the Talbot self-imaging effect, dual-spiral moiré fringes could be acquired with two spiral gratings. This kind of special moiré fringes could be used to test the collimation of the light beam, which was significant in many correlative applications. The characteristic parameter of the dual-spiral moiré fringes reflected the collimation condition directly. A method with two algorithms, which were respectively based on Fourier transform and the phase-shifting algorithm, was proposed and simulated to extract the characteristic parameter. The influence of the random noise on the extraction was also analyzed and discussed.

© 2008 Optical Society of America

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References

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  1. P. Latimer, Appl. Opt. 32, 1078 (1993).
    [CrossRef] [PubMed]
  2. C. Shakher, S. Prakash, D. Nand, and R. Kumar, Appl. Opt. 40, 1175 (2001).
    [CrossRef]
  3. M. Suzuki and M. Kanaya, Opt. Lasers Eng. 8, 171 (1988).
    [CrossRef]
  4. C. Quan, Y. Fu, and C. J. Tay, Opt. Commun. 230, 23 (2004).
    [CrossRef]
  5. C.-W. Chang and D.-C. Su, Opt. Lett. 16, 1783 (1991).
    [CrossRef] [PubMed]
  6. C.-W. Chang, D.-C. Su, and J.-T. Chang, Chin. J. Phys. (Taipei) 33, 339 (1995).
  7. M. Takeda and K. Mutoh, Appl. Opt. 22, 3977 (1983).
    [CrossRef] [PubMed]
  8. X. Su and W. Chen, Opt. Lasers Eng. 35, 263 (2001).
    [CrossRef]
  9. V. Srinivasan, H. C. Liu, and M. Halioua, Appl. Opt. 23, 3105 (1984).
    [CrossRef] [PubMed]
  10. X. Su, G. von Bally, and D. Vukicevic, Opt. Commun. 98, 141 (1993).
    [CrossRef]
  11. X. Su, W. Song, Y. Cao, and L. Xiang, Opt. Eng. 43, 708 (2004).
    [CrossRef]

2004 (2)

C. Quan, Y. Fu, and C. J. Tay, Opt. Commun. 230, 23 (2004).
[CrossRef]

X. Su, W. Song, Y. Cao, and L. Xiang, Opt. Eng. 43, 708 (2004).
[CrossRef]

2001 (2)

1995 (1)

C.-W. Chang, D.-C. Su, and J.-T. Chang, Chin. J. Phys. (Taipei) 33, 339 (1995).

1993 (2)

X. Su, G. von Bally, and D. Vukicevic, Opt. Commun. 98, 141 (1993).
[CrossRef]

P. Latimer, Appl. Opt. 32, 1078 (1993).
[CrossRef] [PubMed]

1991 (1)

1988 (1)

M. Suzuki and M. Kanaya, Opt. Lasers Eng. 8, 171 (1988).
[CrossRef]

1984 (1)

1983 (1)

Appl. Opt. (4)

Chin. J. Phys. (Taipei) (1)

C.-W. Chang, D.-C. Su, and J.-T. Chang, Chin. J. Phys. (Taipei) 33, 339 (1995).

Opt. Commun. (2)

C. Quan, Y. Fu, and C. J. Tay, Opt. Commun. 230, 23 (2004).
[CrossRef]

X. Su, G. von Bally, and D. Vukicevic, Opt. Commun. 98, 141 (1993).
[CrossRef]

Opt. Eng. (1)

X. Su, W. Song, Y. Cao, and L. Xiang, Opt. Eng. 43, 708 (2004).
[CrossRef]

Opt. Lasers Eng. (2)

M. Suzuki and M. Kanaya, Opt. Lasers Eng. 8, 171 (1988).
[CrossRef]

X. Su and W. Chen, Opt. Lasers Eng. 35, 263 (2001).
[CrossRef]

Opt. Lett. (1)

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Figures (6)

Fig. 1
Fig. 1

Optical arrangement for the collimation test: the light source S, the collimation lens CL, the observation plane OP, and the distance of the mth Talbot image Z m .

Fig. 2
Fig. 2

Simulation of dual-spiral moiré fringes and the observation is made on a Cartesian grid: (a) t 1 ( r , θ ) ( p 1 = 30 ) , (b) t 2 ( r , θ ) ( p 2 = 30 ) , (c) t ( r , θ ) ( p 1 = 25 ) , (d) t ( r , θ ) ( p 1 = 30 ) , and (e) t ( r , θ ) ( p 1 = 35 ) .

Fig. 3
Fig. 3

Sketch map to determine the divergence or convergence angle γ: (a) divergence angle, (b) convergence angle.

Fig. 4
Fig. 4

Original and filtered moiré fringes: (a) the original field amplitude t ( r , θ ) , (b) the spatial frequency spectrum of the original moiré fringes, and (c) the filtered moiré fringes f ( r , θ ) .

Fig. 5
Fig. 5

Relationship between the start phases and radii: (a) φ ( r n , θ 0 ) against r n by using FTA and (b) φ ( r n ) against r n by using SPSA.

Fig. 6
Fig. 6

Errors of p caused by noise with different levels.

Tables (1)

Tables Icon

Table 1 Mean Values and Standard Deviations of the Calculated p with the Noise Level Being 0.05 Times the Full Intensity in 20 Calculations

Equations (6)

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t i ( r , θ ) = 1 2 + 1 2 cos ( 2 π p i r N s θ ) ,
t ( r , θ ) = t 1 ( r , θ ) t 2 ( r , θ ) = 1 4 + 1 4 cos ( 2 π p 1 r N s θ ) + 1 4 cos ( 2 π p 2 r N s θ ) + 1 8 cos [ 2 π ( 1 p 1 + 1 p 2 ) r 2 N s θ ] + 1 8 cos [ 2 π ( 1 p 1 1 p 2 ) r ] .
1 p = 1 p 1 + 1 p 2 .
γ = arctan p 1 p 1 Z m λ 2 m p .
f ( r n , θ m ) = 1 4 + 1 8 cos ( 2 π r n p 2 N s θ m ) .
φ ( r n ) = arctan s = 0 S 1 f ( r n , θ m ) sin ( 2 π S s ) s = 0 S 1 f ( r n , θ m ) cos ( 2 π S s ) , m = s ( M ) 2 N s ( S ) .

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