Abstract

The clipped speckle autocorrelation (CSA) metric is proposed for estimating the laser beam energy concentration on a remote diffuse target in a laser beam projection system with feedback information. Using the second order statistics of the intensity distribution of the fully developed speckle and the relation of the autocorrelation functions for the clipped and unclipped speckles, we present the theoretical expression of this metric as a function of the normalized CSA function. The simulation technique based on the equivalence of the spatial average and the ensemble time average is provided. Based on this simulation technique, we analyze the influence of the surface roughness of the target on this metric and then show the influencing factors of the metric performance, for example the finite sample effect and aperture size of the observation system. Experimental results are illustrated to examine the capability of this metric and the correctness of the discussion about the metric performance.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Speckle pattern sequential extraction metric for estimating the focus spot size on a remote diffuse target

Zhan Yu, Yuanyang Li, Lisheng Liu, Jin Guo, Tingfeng Wang, and Guoqing Yang
Appl. Opt. 56(32) 8941-8949 (2017)

Statistical properties of dynamic speckles in application to laser focusing systems

Zhan Yu, Jin Guo, Lisheng Liu, Tingfeng Wang, and Yuanyang Li
Appl. Opt. 58(12) 3310-3316 (2019)

Adaptive phase distortion correction in strong speckle-modulation conditions

M. A. Vorontsov and G. W. Carhart
Opt. Lett. 27(24) 2155-2157 (2002)

References

  • View by:
  • |
  • |
  • |

  1. T. Yoshimura, M. Zhou, K. Yamahai, and Z. Liyan, “Optimum determination of speckle size to be used in electronic speckle pattern interferometry,” Appl. Opt. 34(1), 87–91 (1995).
    [Crossref] [PubMed]
  2. S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, “Noise in laser speckle correlation and imaging techniques,” Opt. Express 18(14), 14519–14534 (2010).
    [PubMed]
  3. D. V. Semenov, S. V. Miridonov, E. Nippolainen, and A. A. Kamshilin, “Statistical properties of dynamic speckles formed by a deflecting laser beam,” Opt. Express 16(2), 1238–1249 (2008).
    [Crossref] [PubMed]
  4. J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 1975).
  5. P. Piatrou and M. Roggemann, “Beaconless stochastic parallel gradient descent laser beam control: numerical experiments,” Appl. Opt. 46(27), 6831–6842 (2007).
    [Crossref] [PubMed]
  6. M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. 22(12), 907–909 (1997).
    [Crossref] [PubMed]
  7. X. Lei, S. Wang, H. Yan, W. Liu, L. Dong, P. Yang, and B. Xu, “Double-deformable-mirror adaptive optics system for laser beam cleanup using blind optimization,” Opt. Express 20(20), 22143–22157 (2012).
    [Crossref] [PubMed]
  8. T. Sawatari and A. C. Elek, “Image plane detection using laser speckle patterns,” Appl. Opt. 12(4), 881–883 (1973).
    [Crossref] [PubMed]
  9. M. A. Vorontsov and G. W. Carhart, “Adaptive phase distortion correction in strong speckle-modulation conditions,” Opt. Lett. 27(24), 2155–2157 (2002).
    [Crossref] [PubMed]
  10. D. Li, D. P. Kelly, and J. T. Sheridan, “Three-dimensional static speckle fields. Part I. Theory and numerical investigation,” J. Opt. Soc. Am. A 28(9), 1896–1903 (2011).
    [Crossref]
  11. R. Barakat, “Clipped correlation functions of aperture integrated laser speckle,” Appl. Opt. 25(21), 3885–3888 (1986).
    [Crossref] [PubMed]
  12. M. B. Priestley, Spectral Analysis and Time Series (Academic, 1981).
  13. A. D. Ducharme, G. D. Boreman, and D. R. Snyder, “Effects of intensity thresholding on the power spectrum of laser speckle,” Appl. Opt. 33(13), 2715–2720 (1994).
    [Crossref] [PubMed]
  14. H. M. Pedersen, “Theory of speckle-correlation measurements using nonlinear detectors,” J. Opt. Soc. Am. A 1(8), 850–855 (1984).
    [Crossref]
  15. A. J. Lambert and D. Fraser, “Linear systems approach to simulation of optical diffraction,” Appl. Opt. 37(34), 7933–7939 (1998).
    [Crossref] [PubMed]
  16. A. K. Fung and M. F. Chen, “Numerical simulation of scattering from simple and composite random surfaces,” J. Opt. Soc. Am. A 2(12), 2274–2284 (1985).
    [Crossref]
  17. J. W. Goodman, Statistical Optics (John Wiley & Sons, 2000).

2012 (1)

2011 (1)

2010 (1)

2008 (1)

2007 (1)

2002 (1)

1998 (1)

1997 (1)

1995 (1)

1994 (1)

1986 (1)

1985 (1)

1984 (1)

1973 (1)

Barakat, R.

Boreman, G. D.

Carhart, G. W.

Cerbino, R.

Chen, M. F.

Dong, L.

Ducharme, A. D.

Elek, A. C.

Fraser, D.

Fung, A. K.

Kamshilin, A. A.

Kelly, D. P.

Lambert, A. J.

Lei, X.

Li, D.

Liu, W.

Liyan, Z.

Miridonov, S. V.

Nippolainen, E.

Pedersen, H. M.

Peuser, J.

Piatrou, P.

Ricklin, J. C.

Roggemann, M.

Sawatari, T.

Scheffold, F.

Semenov, D. V.

Sheridan, J. T.

Skipetrov, S. E.

Snyder, D. R.

Vorontsov, M. A.

Wang, S.

Weber, B.

Xu, B.

Yamahai, K.

Yan, H.

Yang, P.

Yoshimura, T.

Zakharov, P.

Zhou, M.

Appl. Opt. (6)

J. Opt. Soc. Am. A (3)

Opt. Express (3)

Opt. Lett. (2)

Other (3)

J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 1975).

M. B. Priestley, Spectral Analysis and Time Series (Academic, 1981).

J. W. Goodman, Statistical Optics (John Wiley & Sons, 2000).

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 (11)

Fig. 1
Fig. 1 An unfolded representation of the laser beam projection system
Fig. 2
Fig. 2 (a) The clipped autocorrelation function Rbr) changes against the continuous normalized autocorrelation function Rnr) when the threshold parameter b has the values from 0.5 to 3. (b) The relation of the function Rnr) and unbiased version of the clipped autocorrelation function ψr).
Fig. 3
Fig. 3 Error analysis for taking the place of curves in Fig. 2(b) by the fitting result Eq. (12) when the threshold parameter b is in the range of 1 to 2. PV error (left vertical axis) and RMS error (right vertical axis) are both given.
Fig. 4
Fig. 4 Detail configuration of the observation system
Fig. 5
Fig. 5 The speckle intensity distributions are given in (a), (b) and (c) for the focusing spot size of 1 mm, 2 mm and 3 mm, respectively. The CSA functions ψr) calculated by the simulation method are compared with the theoretical ones in (d). Solid lines are theoretical results and markers stand for the numerical ones.
Fig. 6
Fig. 6 (a) The central bright spot caused by the specular reflection of the slightly rough surface. (b) The non-uniform distribution of the average speckle intensity produced by the slightly rough surface. (c) The CSA functions for the two kinds of intensity distributions in (a) and (b) respectively, and the deviations introduced by the slightly rough surfaces can be found by comparing with the theoretical result.
Fig. 7
Fig. 7 The CSA metric is shown as a function of the focusing spot size ω0. The simulation results are calculated by the parameters in Section 3.1 and the theoretical result for comparing is calculated by Eq. (16).
Fig. 8
Fig. 8 The simulations of the CSA metric Me using one hundred different realizations of the diffuse target. Every point in this figure stands for a simulation result. The thick lines on the top and bottom are the deviations calculated by Eq. (29). The solid and dot lines in the center are the mean values of the theory Eq. (16) and the simulation respectively. The focusing spot sizes are (a) 0.5 mm and (b) 1.0 mm.
Fig. 9
Fig. 9 (a) The deviation range of the CSA metric calculated by Eq. (29) and Eq. (30). The dash lines are the upper and lower boundary of the range. (b) The accuracy Δω0 of the metric changes against the value of Me.
Fig. 10
Fig. 10 The experimental setup for examining the CSA metric and its performance.
Fig. 11
Fig. 11 (a) The CSA function derived from experimental data. The areas between the dash lines stand for the deviation range predicted by Eq. (29). (b) The experimental result for CSA metric Me. The error bars are the deviation ranges for the corresponding spot size.

Tables (1)

Tables Icon

Table 1 Curve fitting result of Eq. (12)

Equations (31)

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

R( r 1 , r 2 )= I( r 1 )I( r 2 ) .
R( r 1 , r 2 )= I( r 1 ) I( r 2 ) + | J( r 1 , r 2 ) | 2 ,
J( r 1 , r 2 )= U( r 1 ) U ( r 2 ) .
U(r)= 1 jλB U 0 (ρ)exp[ jk 2B (A ρ 2 2rρ+D r 2 ) ] d 2 ρ ,
J( r 1 , r 2 )= 1 λ 2 B 2 exp[ jk 2B ( r 1 2 r 2 2 ) ] d 2 ρ 1 d 2 ρ 2 J 0 ( ρ 1 , ρ 2 ) ×exp{ jk 2B [ A( ρ 1 2 ρ 2 2 )2( r 1 ρ 1 r 2 ρ 2 ) ] },
J 0 ( ρ 1 , ρ 2 )=κP( ρ 1 ) P ( ρ 2 ) μ 0 (Δρ)κ | P( ρ 1 ) | 2 μ 0 (Δρ),
J( r 1 , r 2 )= κ λ 2 B 2 exp[ jk 2B ( r 1 2 r 2 2 ) ] d 2 ρ 1 d 2 Δρ | P( ρ 1 ) | 2 μ 0 (Δρ) ×exp{ jk 2B [ A(2 ρ 1 ΔρΔ ρ 2 )2( r 1 ρ 1 r 2 ρ 1 r 2 Δρ) ] }.
J(Δr)= κ λ 2 B 2 exp( jk 2B Δ r 2 ) d 2 ρ 1 | P( ρ 1 ) | 2 exp( jk B ρ 1 Δr ) ,
R(Δr)= I 2 [ 1+ | | P(ρ) | 2 exp( jk B ρΔr ) d 2 ρ | P(ρ) | 2 d 2 ρ | 2 ].
R b (Δr)exp(b){ 1+ b 2 n=1 [ L n1 ( 1 ) (b) ] 2 n 2 [ R n (Δr) ] n }.
ψ(Δr)= R b (Δr)exp(b) max{ R b (Δr)exp(b) } .
R n (Δr)= i=0 m a i [ψ(Δr)] i .
P(ρ)=exp( ρ 2 ω 0 2 ),
R n (Δr)= R(Δr) I(r) 2 1=exp( π 2 ω 0 2 λ 2 B 2 | Δr | 2 ).
M e =| Δr |= λB π ω 0 [ ln( 1 R n (Δr) ) ] 1/2 .
M e = λB π ω 0 [ ln i=0 m a i [ψ(Δr)] i ] 1/2 .
( A im B im C im D im )=( 1 z 3 0 1 )( 1 0 1/f 1 )( 1 z 2 0 1 ).
z 2 =f( 1 1 A im ),
z 3 =f(1 A im ).
( A B C D )=( 1 z 3 0 1 )( 1 0 1/f 1 )( 1 z 2 0 1 )( 1 z 1 0 1 ).
ϕ eff = ϕ imag | A im | = A im z 1 ϕ A im z 1 +f( A im 1) ,
H surf (ξ,η)=FF T 1 [ FFT[ Ω(ξ,η) ] FFT[ X(ξ,η) ] ],
Ω(ξ,η)= h rms 2 exp( ξ 2 + η 2 l c 2 ).
U 0 (ξ,η)=P(ξ,η)exp[ ik H surf (ξ,η) ],
J( r 1 , r 2 )K(Δr)G(r) | P(ρ) | 2 exp( jk B ρΔr ) d 2 ρ=J(r,Δr),
K(Δr)= κ λ 2 B 2 exp( jk 2B Δ r 2 ); G(r)= μ 0 (Δρ)exp( jk B rΔρ ) d 2 Δρ .
μ 0 (Δρ)=exp{ k 2 h rms 2 [ 1exp( | Δρ | 2 / l c 2 ) ] },
μ 1 (Δρ)= μ 0 (Δρ)exp( k 2 h rms 2 ) 1exp( k 2 h rms 2 ) ,
ω e 2 =2 0 ρ| μ 1 ( ρ ) | dρ l c 2 / ( k 2 h rms 2 ) .
var{ ψ ^ (s) } 1 N m= [ ψ 2 (m)+ψ(m+s)ψ(ms) +2 ψ 2 (s) ψ 2 (m)4ψ(s)ψ(m)ψ(ms)+ κ 4 (m,s,0)].
N = N 2 i j ψ( | r i r j | ) = N 2 N+2 k=1 N1 ( Nk )ψ( k )

Metrics