Abstract

Transient, high repetition pulse laser can be applied to test numerous physical parameters, where in situ, real time measurement and isolation of vibration is highly demanded. Because of its short half-width, high power, high repetition, and even large distortion, the laser presents unique challenges to conventional diagnosing methods. A system based on a novel cyclic radial shearing interferometer is proposed to diagnose the transient, high repetition pulse laser with common path, no reference plane, and high precision. With the spatial-carrier methods, the system needs only one interferogram to reconstruct amplitude and wavefront of the laser. The theories of amplitude and wavefront reconstruction have been validated by computer simulation, and errors less than 1/1000λ are obtained for both. Comparing with the results of the ZYGO interferometer, an error less than 1/20λ for both peak–valley and root-mean-square values is gained with good repeatability for the wavefront. The calibration process and real time diagnosis of a high repetition pulse laser are presented then. Finally, the error consideration and system optimization are discussed in detail.

© 2007 Optical Society of America

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References

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  1. D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer," Opt. Commun. 275, 173-178 (2007).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. J. T. Salmon, E. S. Bliss, J. L. Byrd, M. Feldman, M. W. Kartz, J. S. Toeppen, B. M. Van Wonterghem, and S. Winters, "Adaptive optics system for solid state laser systems used in inertial confinement fusion," Proc. SPIE 2633, 105-113 (1995).
    [CrossRef]
  4. M. Strojnik, G. Paez, and M. Mantravadi, "Lateral shear interferometers," in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 122-184.
    [CrossRef]
  5. Y. Yang, Y. Lu, Y. Chen, Y. Zhuo, X. Zhang, B. Chen, and X. Qing, "A radial-shearing interference system of testing laser-pulse wavefront distortion and the original wavefront reconstructing," Proc. SPIE 5638, 200-204 (2005).
    [CrossRef]
  6. Y. Yang, Y. Lu, Y. Zhuo, J. Chen, X. Zhang, and B. Chen, "Wavefront sensing technique with a radial shearing interferometry applied to an adaptive optic system," Proc. SPIE 4926, 132-139 (2002).
    [CrossRef]
  7. T. Kohno, D. Matsumoto, T. Yazawa, and Y. Uda, "Radial shearing interferometer for in-process measurement of diamond turning," Opt. Eng. 39, 2696-2699 (2000).
    [CrossRef]
  8. P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. Williams, and B. M. Van Wonterghem, "Wavefront and divergence of the Beamlet prototype laser," Proc. SPIE 3492, 1019-1030 (1999).
    [CrossRef]
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    [CrossRef]
  10. D.Malacara, M.Servin, and Z.Malcacara, eds., "Spatial linear and circular carrier analysis," in Interferogram Analysis for Optical Testing (Wiley, 2005), pp. 396-450.
  11. J. Liang, Y. Yang, D. Liu, Y. Zhuo, J. Hui, and J. Weng, "Research of transient flow field real time interferogram acquisition system," Proc. SPIE 6279, 62794K (2007).
    [CrossRef]
  12. Y. Lu, Y. Yang, Y. Chen, and Y. Zhuo, "Calculating Strehl ratio through radial shearing method," Proc. SPIE 5638, 428-437 (2005).
    [CrossRef]
  13. A. Fernández, G. H. Kaufmann, Á. F. Doval, J. Blanco-García, and J. L. Fernández, "Comparison of carrier removal methods in the analysis of TV holography fringes by the Fourier transform method," Opt. Eng. 37, 2899-2905 (1998).
    [CrossRef]
  14. D. Malacara, "Mathematical interpretation of radial shearing interferometers," Appl. Opt. 13, 1781-1784 (1974).
    [CrossRef] [PubMed]
  15. M. Takeda, "Spatial carrier heterodyne techniques for precision interferometry and profilometry: an overview," Proc. SPIE 1121, 73-88 (1989).
  16. J. Schmit, K. Creath, and M. Kujawinska, "Spatial and temporal phase-measurement techniques: a comparison of major error sources in one dimension," Proc. SPIE 1755, 202-211 (1992).
    [CrossRef]
  17. D. Malacara, M. Servin, and Z. Malcacara, eds., "Digital image processing," in Interferogram Analysis for Optical Testing (Wiley, 2005), pp. 93-124.

2007

J. Liang, Y. Yang, D. Liu, Y. Zhuo, J. Hui, and J. Weng, "Research of transient flow field real time interferogram acquisition system," Proc. SPIE 6279, 62794K (2007).
[CrossRef]

D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer," Opt. Commun. 275, 173-178 (2007).
[CrossRef]

2005

Y. Lu, Y. Yang, Y. Chen, and Y. Zhuo, "Calculating Strehl ratio through radial shearing method," Proc. SPIE 5638, 428-437 (2005).
[CrossRef]

Y. Yang, Y. Lu, Y. Chen, Y. Zhuo, X. Zhang, B. Chen, and X. Qing, "A radial-shearing interference system of testing laser-pulse wavefront distortion and the original wavefront reconstructing," Proc. SPIE 5638, 200-204 (2005).
[CrossRef]

2002

Y. Yang, Y. Lu, Y. Zhuo, J. Chen, X. Zhang, and B. Chen, "Wavefront sensing technique with a radial shearing interferometry applied to an adaptive optic system," Proc. SPIE 4926, 132-139 (2002).
[CrossRef]

2000

T. Kohno, D. Matsumoto, T. Yazawa, and Y. Uda, "Radial shearing interferometer for in-process measurement of diamond turning," Opt. Eng. 39, 2696-2699 (2000).
[CrossRef]

1999

P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. Williams, and B. M. Van Wonterghem, "Wavefront and divergence of the Beamlet prototype laser," Proc. SPIE 3492, 1019-1030 (1999).
[CrossRef]

1998

A. Fernández, G. H. Kaufmann, Á. F. Doval, J. Blanco-García, and J. L. Fernández, "Comparison of carrier removal methods in the analysis of TV holography fringes by the Fourier transform method," Opt. Eng. 37, 2899-2905 (1998).
[CrossRef]

1995

J. T. Salmon, E. S. Bliss, J. L. Byrd, M. Feldman, M. W. Kartz, J. S. Toeppen, B. M. Van Wonterghem, and S. Winters, "Adaptive optics system for solid state laser systems used in inertial confinement fusion," Proc. SPIE 2633, 105-113 (1995).
[CrossRef]

1992

J. Schmit, K. Creath, and M. Kujawinska, "Spatial and temporal phase-measurement techniques: a comparison of major error sources in one dimension," Proc. SPIE 1755, 202-211 (1992).
[CrossRef]

1989

M. Takeda, "Spatial carrier heterodyne techniques for precision interferometry and profilometry: an overview," Proc. SPIE 1121, 73-88 (1989).

1987

1982

1974

Appl. Opt.

J. Opt. Soc. Am.

Opt. Commun.

D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer," Opt. Commun. 275, 173-178 (2007).
[CrossRef]

Opt. Eng.

A. Fernández, G. H. Kaufmann, Á. F. Doval, J. Blanco-García, and J. L. Fernández, "Comparison of carrier removal methods in the analysis of TV holography fringes by the Fourier transform method," Opt. Eng. 37, 2899-2905 (1998).
[CrossRef]

T. Kohno, D. Matsumoto, T. Yazawa, and Y. Uda, "Radial shearing interferometer for in-process measurement of diamond turning," Opt. Eng. 39, 2696-2699 (2000).
[CrossRef]

Proc. SPIE

P. J. Wegner, M. A. Henesian, J. T. Salmon, L. G. Seppala, T. L. Weiland, W. H. Williams, and B. M. Van Wonterghem, "Wavefront and divergence of the Beamlet prototype laser," Proc. SPIE 3492, 1019-1030 (1999).
[CrossRef]

J. T. Salmon, E. S. Bliss, J. L. Byrd, M. Feldman, M. W. Kartz, J. S. Toeppen, B. M. Van Wonterghem, and S. Winters, "Adaptive optics system for solid state laser systems used in inertial confinement fusion," Proc. SPIE 2633, 105-113 (1995).
[CrossRef]

Y. Yang, Y. Lu, Y. Chen, Y. Zhuo, X. Zhang, B. Chen, and X. Qing, "A radial-shearing interference system of testing laser-pulse wavefront distortion and the original wavefront reconstructing," Proc. SPIE 5638, 200-204 (2005).
[CrossRef]

Y. Yang, Y. Lu, Y. Zhuo, J. Chen, X. Zhang, and B. Chen, "Wavefront sensing technique with a radial shearing interferometry applied to an adaptive optic system," Proc. SPIE 4926, 132-139 (2002).
[CrossRef]

J. Liang, Y. Yang, D. Liu, Y. Zhuo, J. Hui, and J. Weng, "Research of transient flow field real time interferogram acquisition system," Proc. SPIE 6279, 62794K (2007).
[CrossRef]

Y. Lu, Y. Yang, Y. Chen, and Y. Zhuo, "Calculating Strehl ratio through radial shearing method," Proc. SPIE 5638, 428-437 (2005).
[CrossRef]

M. Takeda, "Spatial carrier heterodyne techniques for precision interferometry and profilometry: an overview," Proc. SPIE 1121, 73-88 (1989).

J. Schmit, K. Creath, and M. Kujawinska, "Spatial and temporal phase-measurement techniques: a comparison of major error sources in one dimension," Proc. SPIE 1755, 202-211 (1992).
[CrossRef]

Other

D. Malacara, M. Servin, and Z. Malcacara, eds., "Digital image processing," in Interferogram Analysis for Optical Testing (Wiley, 2005), pp. 93-124.

M. Strojnik, G. Paez, and M. Mantravadi, "Lateral shear interferometers," in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 122-184.
[CrossRef]

D.Malacara, M.Servin, and Z.Malcacara, eds., "Spatial linear and circular carrier analysis," in Interferogram Analysis for Optical Testing (Wiley, 2005), pp. 396-450.

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Figures (9)

Fig. 1
Fig. 1

System layout and process of image grabbing.

Fig. 2
Fig. 2

Layout of the CRSI and the procedure of optical processing.

Fig. 3
Fig. 3

Filter the zeroth-order and plus one order spectra; (a) separated Fourier spectra of a interferogram, (b) filter the A ( f , y ) , and (c) filter the C ( f f 0 , y ) and shift it to the origin.

Fig. 4
Fig. 4

(Color online) Simulated wave; (a) original amplitude of the simulated wave, and (b) original wavefront of the simulated wave.

Fig. 5
Fig. 5

Simulated radial shearing interferogram and its Fourier spectrum; (a) radial shearing interferogram, and (b) frequency spectrum of radial shearing interferogram.

Fig. 6
Fig. 6

(Color online) Reconstructed wave; (a) reconstructed amplitude of the simulated wave, and (b) reconstructed wavefront of the simulated wave.

Fig. 7
Fig. 7

(Color online) Reconstruction error; (a) error of amplitude reconstruction, and (b) error of wavefront reconstruction.

Fig. 8
Fig. 8

Radial shearing interferogram of the pulse laser under diagnosis.

Fig. 9
Fig. 9

(Color online) Diagnosing results of high repetition pulse laser; (a) amplitude of the diagnosing pulse laser, and (b) wavefront of the diagnosing pulse laser.

Tables (3)

Tables Icon

Table 1 Simulation Results of Amplitude and Wavefront Reconstruction in RSI

Tables Icon

Table 2 Parameters Summary of the CRSI

Tables Icon

Table 3 Comparison of the CRSI and ZYGO Interferometer (Φ100 mm)

Equations (33)

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I * * = | A ( r / β 1 / 2 , ϕ ) exp { i k [ W ( r / β 1 / 2 , ϕ ) ] + A ( β 1 / 2 r , ϕ ) exp { i k [ W ( β 1 / 2 r , ϕ ) ] } | 2 = A 2 ( r / β 1 / 2 , ϕ ) + A 2 ( β 1 / 2 r , ϕ ) + 2 A ( r / β 1 / 2 , ϕ ) × A ( β 1 / 2 r , ϕ ) cos { k [ W ( r / β 1 / 2 , ϕ ) W ( β 1 / 2 r , ϕ ) ] } = a ( r , ϕ ) + b ( r , ϕ ) cos ( k W * * ) .
k = 2 π / λ
a ( r , ϕ ) = A 2 ( r / β 1 / 2 , ϕ ) + A 2 ( β 1 / 2 r , ϕ ) ,
b ( r , ϕ ) = 2 A ( r / β 1 / 2 , ϕ ) A ( β 1 / 2 r , ϕ ) ,
W * * = W ( r / β 1 / 2 , ϕ ) W ( β 1 / 2 r , ϕ ) ,
I * * = a ( x , y ) + b ( x , y ) cos [ 2 π f 0 x + W * * ] ,
i ( x , y ) = a ( x , y ) + c ( x , y ) exp ( i 2 π f 0 x ) + c * ( x , y ) exp ( i 2 π f 0 x ) ,
c ( x , y ) = 1 2 b ( x , y ) exp [ i W * * ] ,
I ( f , y ) = A ( f , y ) + C ( f f 0 , y ) + C * ( f + f 0 , y ) ,
a ( x , y ) = F 1 { A ( f , y ) } .
a ( β 1 / 2 r , ϕ ) = A 2 ( r , ϕ ) + A 2 ( β r , ϕ ) .
a ( β 3 / 2 r , ϕ ) = A 2 ( β r , ϕ ) + A 2 ( β 2 r , ϕ ) ,
a ( β 5 / 2 r , ϕ ) = A 2 ( β 2 r , ϕ ) + A 2 ( β 3 r , ϕ ) ,
a ( β 7 / 2 r , ϕ ) = A 2 ( β 3 r , ϕ ) + A 2 ( β 4 r , ϕ ) ,
a ( β ( 2 n 1 ) / 2 r , ϕ ) = A 2 ( β n 1 r , ϕ ) + A 2 ( β n r , ϕ ) ,
a ( β ( 2 n + 1 ) / 2 r , ϕ ) = A 2 ( β n r , ϕ ) + A 2 ( β n + 1 r , ϕ ) ,
a ( β 1 / 2 r , ϕ ) a ( β 3 / 2 r , ϕ ) = A 2 ( r , ϕ ) A 2 ( β 2 r , ϕ ) ,
a ( β 5 / 2 r , ϕ ) a ( β 7 / 2 r , ϕ ) = A 2 ( β 2 r , ϕ ) A 2 ( β 4 r , ϕ ) ,
a ( β ( 2 n 1 ) / 2 r , ϕ ) a ( β ( 2 n + 1 ) / 2 r , ϕ ) = A 2 ( β n 1 r , ϕ ) A 2 ( β n + 1 r , ϕ ) .
i = 1 n [ a ( β ( 2 i 1 ) / 2 r , ϕ ) a ( β ( 2 i + 1 ) / 2 r , ϕ ) ] = A 2 ( r , ϕ ) A 2 ( β n + 1 r , ϕ ) .
A ( r , ϕ ) = i = 1 n [ a ( β ( 2 i 1 ) / 2 r , ϕ ) a ( β ( 2 i + 1 ) / 2 r , ϕ ) ] + A 2 ( β n + 1 r , ϕ ) .
c ( x , y ) = F 1 { C ( f , y ) } .
W * * = tan 1 { Im [ c ( x , y ) ] Re [ c ( x , y ) ] } ,
W ( β 1 / 2 r ) = W ( r , ϕ ) W ( β r , ϕ ) .
j = 1 m ϕ OPD ( β ( 2 j 1 ) / 2 r , θ ) = W ( r , θ ) W ( β m r , θ ) .
W ( r , θ ) = i = 1 m ϕ OPD ( β ( 2 j 1 ) / 2 r , θ ) + W ( β m r , θ ) ,
W = W 0 + W ,
sin   θ > ( OPD ( x , y ) x ) max ,
f 0 = sin   θ λ > 1 λ ( W ( x , y ) x ) max = Δ f max ,
P ( x , y ) = { ( 1 | x | a ) ( 1 | y | b ) , for   ( | x | a , | y | b ) 0 , elsewhere ,
γ τ = ( f 2 f 1 ) 2 .

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