Abstract

The precision of departure angle detection for the laser beam can be improved by optimizing algorithms by which the high precision and stability of the laser beam pointing and tracking would be obtained, namely, improving the performance and accommodation of the free space optical communications. Atmospheric turbulence-induced optical intensity scintillations have a strong impact on the location precision of the laser spot through the atmospheric channels. Consequently, new requests come into view for the optimization of the algorithms. In the paper, the advantages and disadvantages of the traditional centroid method are analyzed. In terms of variations of laser spot, combined with the requests for real-time detection of departure angle, we proposed a new detection method. The edge of the laser spot on the detection sensor was redefined, and then the redefined spot was used to calculate the departure angle of the laser beam. The results of the simulations and experiments show that the precision of departure angle detection has been improved by more than 16%, which could reduce the effect of detection errors on the tracking procedure.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010

J. Ma, Y. Jiang, S. Yu, L. Tan, and W. Du, “Packet error rate analysis of OOK, DPIM and PPM modulation schemes for ground-to-satellite optical communications,” Opt. Commun. 283, 237–242 (2010).
[CrossRef]

2008

J.-J. Ying, Y. He, and Z.-L. Zhou, “High speed gradient Hough transform algorithm for laser spot location,” Proc. SPIE 6625, 66250J1–66250J6 (2008).

2007

S. Yu, Q. Han, J. Ma, L. Tan, and J. Ming, “Size selection of dispersive spot imaging on CCD in a satellite optical communication terminal,” Chin. J. Lasers 34, 67–71 (2007).

2006

H. Zhang and X.-Y. Li, “Numerical simulation of wavefront phase screen distorted by atmospheric turbulence,” Opto-Electron. Eng. 33, 14–19 (2006).

2003

C. Rusu, M. Tico, P. Kuosmanen, and E. J. Delp, “Classical geometrical approach to circle fitting—review and new developments,” J. Electron. Imaging 12, 179–193 (2003).
[CrossRef]

J. E. Hill, C. Cheruvu, and T. F. Abbey, R. A. AmbrosiD. N. Burrows, A. T. Short, A. A. Wells, and J. A. Nousek,, “An algorithm for locating PSF-like events and computing the centroid in X-ray images,” Proc. SPIE 4851, 1347–1355 (2003).
[CrossRef]

1999

Y.-Q. Yui, R. Shi, X.-N. Yu, and T.-N. Gao, “An algorithm to raise the locating precision of laser spot center based on Hough transform,” Acta Opt. Sin. 19, 1655–1660 (1999).

1998

1992

Z. Li and Z. Shen, “A new filtering method for precision target tracking,” Proc. SPIE 1697, 198–207 (1992).
[CrossRef]

1990

N. Roddier, “Atmospheric wave-front simulation using Zernike polynomial,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

F. Anderson, W. Christensen, and B. Kortegaard, “Real time, video image centroid tracker,” Proc. SPIE 1304, 82–91 (1990).
[CrossRef]

1976

Abbey, T. F.

J. E. Hill, C. Cheruvu, and T. F. Abbey, R. A. AmbrosiD. N. Burrows, A. T. Short, A. A. Wells, and J. A. Nousek,, “An algorithm for locating PSF-like events and computing the centroid in X-ray images,” Proc. SPIE 4851, 1347–1355 (2003).
[CrossRef]

Ambrosi, R. A.

J. E. Hill, C. Cheruvu, and T. F. Abbey, R. A. AmbrosiD. N. Burrows, A. T. Short, A. A. Wells, and J. A. Nousek,, “An algorithm for locating PSF-like events and computing the centroid in X-ray images,” Proc. SPIE 4851, 1347–1355 (2003).
[CrossRef]

Anderson, F.

F. Anderson, W. Christensen, and B. Kortegaard, “Real time, video image centroid tracker,” Proc. SPIE 1304, 82–91 (1990).
[CrossRef]

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Optical Engineering, 1998).

Bruno, T. L.

Burrows, D. N.

J. E. Hill, C. Cheruvu, and T. F. Abbey, R. A. AmbrosiD. N. Burrows, A. T. Short, A. A. Wells, and J. A. Nousek,, “An algorithm for locating PSF-like events and computing the centroid in X-ray images,” Proc. SPIE 4851, 1347–1355 (2003).
[CrossRef]

Cheruvu, C.

J. E. Hill, C. Cheruvu, and T. F. Abbey, R. A. AmbrosiD. N. Burrows, A. T. Short, A. A. Wells, and J. A. Nousek,, “An algorithm for locating PSF-like events and computing the centroid in X-ray images,” Proc. SPIE 4851, 1347–1355 (2003).
[CrossRef]

Christensen, W.

F. Anderson, W. Christensen, and B. Kortegaard, “Real time, video image centroid tracker,” Proc. SPIE 1304, 82–91 (1990).
[CrossRef]

Delp, E. J.

C. Rusu, M. Tico, P. Kuosmanen, and E. J. Delp, “Classical geometrical approach to circle fitting—review and new developments,” J. Electron. Imaging 12, 179–193 (2003).
[CrossRef]

Du, W.

J. Ma, Y. Jiang, S. Yu, L. Tan, and W. Du, “Packet error rate analysis of OOK, DPIM and PPM modulation schemes for ground-to-satellite optical communications,” Opt. Commun. 283, 237–242 (2010).
[CrossRef]

Gao, T.-N.

Y.-Q. Yui, R. Shi, X.-N. Yu, and T.-N. Gao, “An algorithm to raise the locating precision of laser spot center based on Hough transform,” Acta Opt. Sin. 19, 1655–1660 (1999).

Han, Q.

S. Yu, Q. Han, J. Ma, L. Tan, and J. Ming, “Size selection of dispersive spot imaging on CCD in a satellite optical communication terminal,” Chin. J. Lasers 34, 67–71 (2007).

He, Y.

J.-J. Ying, Y. He, and Z.-L. Zhou, “High speed gradient Hough transform algorithm for laser spot location,” Proc. SPIE 6625, 66250J1–66250J6 (2008).

Hill, J. E.

J. E. Hill, C. Cheruvu, and T. F. Abbey, R. A. AmbrosiD. N. Burrows, A. T. Short, A. A. Wells, and J. A. Nousek,, “An algorithm for locating PSF-like events and computing the centroid in X-ray images,” Proc. SPIE 4851, 1347–1355 (2003).
[CrossRef]

Jankevics, A.

Jiang, Y.

J. Ma, Y. Jiang, S. Yu, L. Tan, and W. Du, “Packet error rate analysis of OOK, DPIM and PPM modulation schemes for ground-to-satellite optical communications,” Opt. Commun. 283, 237–242 (2010).
[CrossRef]

Kortegaard, B.

F. Anderson, W. Christensen, and B. Kortegaard, “Real time, video image centroid tracker,” Proc. SPIE 1304, 82–91 (1990).
[CrossRef]

Kuosmanen, P.

C. Rusu, M. Tico, P. Kuosmanen, and E. J. Delp, “Classical geometrical approach to circle fitting—review and new developments,” J. Electron. Imaging 12, 179–193 (2003).
[CrossRef]

Landers, F.

Levine, B. M.

Li, X.-Y.

H. Zhang and X.-Y. Li, “Numerical simulation of wavefront phase screen distorted by atmospheric turbulence,” Opto-Electron. Eng. 33, 14–19 (2006).

Li, Z.

Z. Li and Z. Shen, “A new filtering method for precision target tracking,” Proc. SPIE 1697, 198–207 (1992).
[CrossRef]

Ma, J.

J. Ma, Y. Jiang, S. Yu, L. Tan, and W. Du, “Packet error rate analysis of OOK, DPIM and PPM modulation schemes for ground-to-satellite optical communications,” Opt. Commun. 283, 237–242 (2010).
[CrossRef]

S. Yu, Q. Han, J. Ma, L. Tan, and J. Ming, “Size selection of dispersive spot imaging on CCD in a satellite optical communication terminal,” Chin. J. Lasers 34, 67–71 (2007).

Martinsen, E. A.

Ming, J.

S. Yu, Q. Han, J. Ma, L. Tan, and J. Ming, “Size selection of dispersive spot imaging on CCD in a satellite optical communication terminal,” Chin. J. Lasers 34, 67–71 (2007).

Noll, R. J.

Nousek, J. A.

J. E. Hill, C. Cheruvu, and T. F. Abbey, R. A. AmbrosiD. N. Burrows, A. T. Short, A. A. Wells, and J. A. Nousek,, “An algorithm for locating PSF-like events and computing the centroid in X-ray images,” Proc. SPIE 4851, 1347–1355 (2003).
[CrossRef]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Optical Engineering, 1998).

Rao, R.

R. Rao, Light Propagation in the Turbulent Atmosphere (Anhui Science & Technology, 2005).

Roddier, N.

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

N. Roddier, “Atmospheric wave-front simulation using Zernike polynomial,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Rusu, C.

C. Rusu, M. Tico, P. Kuosmanen, and E. J. Delp, “Classical geometrical approach to circle fitting—review and new developments,” J. Electron. Imaging 12, 179–193 (2003).
[CrossRef]

Shen, Z.

Z. Li and Z. Shen, “A new filtering method for precision target tracking,” Proc. SPIE 1697, 198–207 (1992).
[CrossRef]

Shi, R.

Y.-Q. Yui, R. Shi, X.-N. Yu, and T.-N. Gao, “An algorithm to raise the locating precision of laser spot center based on Hough transform,” Acta Opt. Sin. 19, 1655–1660 (1999).

Short, A. T.

J. E. Hill, C. Cheruvu, and T. F. Abbey, R. A. AmbrosiD. N. Burrows, A. T. Short, A. A. Wells, and J. A. Nousek,, “An algorithm for locating PSF-like events and computing the centroid in X-ray images,” Proc. SPIE 4851, 1347–1355 (2003).
[CrossRef]

Tan, L.

J. Ma, Y. Jiang, S. Yu, L. Tan, and W. Du, “Packet error rate analysis of OOK, DPIM and PPM modulation schemes for ground-to-satellite optical communications,” Opt. Commun. 283, 237–242 (2010).
[CrossRef]

S. Yu, Q. Han, J. Ma, L. Tan, and J. Ming, “Size selection of dispersive spot imaging on CCD in a satellite optical communication terminal,” Chin. J. Lasers 34, 67–71 (2007).

Tico, M.

C. Rusu, M. Tico, P. Kuosmanen, and E. J. Delp, “Classical geometrical approach to circle fitting—review and new developments,” J. Electron. Imaging 12, 179–193 (2003).
[CrossRef]

Toledo-Quinones, M.

Wells, A. A.

J. E. Hill, C. Cheruvu, and T. F. Abbey, R. A. AmbrosiD. N. Burrows, A. T. Short, A. A. Wells, and J. A. Nousek,, “An algorithm for locating PSF-like events and computing the centroid in X-ray images,” Proc. SPIE 4851, 1347–1355 (2003).
[CrossRef]

Wirth, A.

Yang, X.

X. Zhu, X. Yang, J. Zhu, Y. Zhang, and J. Zhou, “An analytical method of determining the plane based on dual ellipse equations,” presented at the Artificial Intelligence and Computational Intelligence (AICI), International Conference, China, 2010.

Ying, J.-J.

J.-J. Ying, Y. He, and Z.-L. Zhou, “High speed gradient Hough transform algorithm for laser spot location,” Proc. SPIE 6625, 66250J1–66250J6 (2008).

Yu, S.

J. Ma, Y. Jiang, S. Yu, L. Tan, and W. Du, “Packet error rate analysis of OOK, DPIM and PPM modulation schemes for ground-to-satellite optical communications,” Opt. Commun. 283, 237–242 (2010).
[CrossRef]

S. Yu, Q. Han, J. Ma, L. Tan, and J. Ming, “Size selection of dispersive spot imaging on CCD in a satellite optical communication terminal,” Chin. J. Lasers 34, 67–71 (2007).

Yu, X.-N.

Y.-Q. Yui, R. Shi, X.-N. Yu, and T.-N. Gao, “An algorithm to raise the locating precision of laser spot center based on Hough transform,” Acta Opt. Sin. 19, 1655–1660 (1999).

Yui, Y.-Q.

Y.-Q. Yui, R. Shi, X.-N. Yu, and T.-N. Gao, “An algorithm to raise the locating precision of laser spot center based on Hough transform,” Acta Opt. Sin. 19, 1655–1660 (1999).

Zhang, H.

H. Zhang and X.-Y. Li, “Numerical simulation of wavefront phase screen distorted by atmospheric turbulence,” Opto-Electron. Eng. 33, 14–19 (2006).

Zhang, Y.

X. Zhu, X. Yang, J. Zhu, Y. Zhang, and J. Zhou, “An analytical method of determining the plane based on dual ellipse equations,” presented at the Artificial Intelligence and Computational Intelligence (AICI), International Conference, China, 2010.

Zhou, J.

X. Zhu, X. Yang, J. Zhu, Y. Zhang, and J. Zhou, “An analytical method of determining the plane based on dual ellipse equations,” presented at the Artificial Intelligence and Computational Intelligence (AICI), International Conference, China, 2010.

Zhou, Z.-L.

J.-J. Ying, Y. He, and Z.-L. Zhou, “High speed gradient Hough transform algorithm for laser spot location,” Proc. SPIE 6625, 66250J1–66250J6 (2008).

Zhu, J.

X. Zhu, X. Yang, J. Zhu, Y. Zhang, and J. Zhou, “An analytical method of determining the plane based on dual ellipse equations,” presented at the Artificial Intelligence and Computational Intelligence (AICI), International Conference, China, 2010.

Zhu, X.

X. Zhu, X. Yang, J. Zhu, Y. Zhang, and J. Zhou, “An analytical method of determining the plane based on dual ellipse equations,” presented at the Artificial Intelligence and Computational Intelligence (AICI), International Conference, China, 2010.

Acta Opt. Sin.

Y.-Q. Yui, R. Shi, X.-N. Yu, and T.-N. Gao, “An algorithm to raise the locating precision of laser spot center based on Hough transform,” Acta Opt. Sin. 19, 1655–1660 (1999).

Appl. Opt.

Chin. J. Lasers

S. Yu, Q. Han, J. Ma, L. Tan, and J. Ming, “Size selection of dispersive spot imaging on CCD in a satellite optical communication terminal,” Chin. J. Lasers 34, 67–71 (2007).

J. Electron. Imaging

C. Rusu, M. Tico, P. Kuosmanen, and E. J. Delp, “Classical geometrical approach to circle fitting—review and new developments,” J. Electron. Imaging 12, 179–193 (2003).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

J. Ma, Y. Jiang, S. Yu, L. Tan, and W. Du, “Packet error rate analysis of OOK, DPIM and PPM modulation schemes for ground-to-satellite optical communications,” Opt. Commun. 283, 237–242 (2010).
[CrossRef]

Opt. Eng.

N. Roddier, “Atmospheric wave-front simulation using Zernike polynomial,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Opto-Electron. Eng.

H. Zhang and X.-Y. Li, “Numerical simulation of wavefront phase screen distorted by atmospheric turbulence,” Opto-Electron. Eng. 33, 14–19 (2006).

Proc. SPIE

J. E. Hill, C. Cheruvu, and T. F. Abbey, R. A. AmbrosiD. N. Burrows, A. T. Short, A. A. Wells, and J. A. Nousek,, “An algorithm for locating PSF-like events and computing the centroid in X-ray images,” Proc. SPIE 4851, 1347–1355 (2003).
[CrossRef]

F. Anderson, W. Christensen, and B. Kortegaard, “Real time, video image centroid tracker,” Proc. SPIE 1304, 82–91 (1990).
[CrossRef]

Z. Li and Z. Shen, “A new filtering method for precision target tracking,” Proc. SPIE 1697, 198–207 (1992).
[CrossRef]

J.-J. Ying, Y. He, and Z.-L. Zhou, “High speed gradient Hough transform algorithm for laser spot location,” Proc. SPIE 6625, 66250J1–66250J6 (2008).

Other

X. Zhu, X. Yang, J. Zhu, Y. Zhang, and J. Zhou, “An analytical method of determining the plane based on dual ellipse equations,” presented at the Artificial Intelligence and Computational Intelligence (AICI), International Conference, China, 2010.

R. Rao, Light Propagation in the Turbulent Atmosphere (Anhui Science & Technology, 2005).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Optical Engineering, 1998).

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Figures (13)

Fig. 1
Fig. 1

Receiving image of the beam through atmospheric turbulence.

Fig. 2
Fig. 2

Detection of departure angle.

Fig. 3
Fig. 3

The principle for detection of departure angle.

Fig. 4
Fig. 4

Algorithm processing sketches of the input images.

Fig. 5
Fig. 5

Flow chat of the reconstructive geometric-centroid algorithm.

Fig. 6
Fig. 6

Variance of incident departure angle for satellite-to-ground laser downlinks.

Fig. 7
Fig. 7

Variance of incident departure angle for horizontal links.

Fig. 8
Fig. 8

An aerial picture of the optical path (data from maps. Google.com).

Fig. 9
Fig. 9

Configuration of the experimental setup.

Fig. 10
Fig. 10

Photograph of the transmitting and receiving optical elements for this experiment.

Fig. 11
Fig. 11

Standard deviation of departure angle as a function of scintillation index.

Fig. 12
Fig. 12

Incident beam locations vibrating following the sine wave versus time, (a) centroid algorithms, (b) reconstructive geometric-centroid algorithms, (c) sine waves.

Fig. 13
Fig. 13

Incident beam locations vibrating following the spire patterns versus time, (a) centroid algorithms, (b) reconstructive geometric-centroid algorithms, (c) spire patterns.

Equations (21)

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

t g φ = ( x i x ¯ ) 2 + ( y i y ¯ ) 2 f · a M = r i f · a M ,
φ r i f · a M .
x c = i = 1 m j = 1 n i I ( i , j ) / i = 1 m j = 1 n I ( i , j ) y c = i = 1 m j = 1 n j I ( i , j ) / i = 1 m j = 1 n I ( i , j ) .
T = i = 1 2 ( W 1 + W 2 ) 4 I i 2 ( W 1 + W 2 ) 4 ,
I ( i , j ) = { 1 , ( i , j ) A 0 , ( i , j ) A ,
x r g c = i , j A i I ( i , j ) / i , j A I ( i , j ) , y r g c = i , j A j I ( i , j ) / i , j A I ( i , j ) .
u ( ρ , θ , L i ) exp [ i 2 k L i 1 L i 2 d L ] exp [ i ϕ ( ρ , θ ) ] u ( ρ , θ , L i 1 ) ,
u ( ρ , θ , L i ) = F 1 { exp [ i Δ L 2 k ( K x 2 + K y 2 ) ] F [ e i ϕ ( ρ , θ ) u ( ρ , θ , L i ) ] } .
ϕ ( ρ , θ ) = q = 1 a q · Z q ( ρ , θ ) ,
Z q = { n + 1 R n 0 ( ρ ) , m = 0 2 ( n + 1 ) R n m ( ρ ) cos m θ q   is even   m 0 2 ( n + 1 ) R n m ( ρ ) sin m θ q     is odd   m 0 ,
R n m ( ρ ) = s = 0 n m 2 ( 1 ) s ( n s ) ! s ! ( n + m 2 s ) ! ( n m 2 s ) ! ρ n 2 s ,
E ( a q a q ) = { 0 , q q   is odd ( D r 0 ) 5 / 3 2.246 ( 1 ) ( n q + n q 2 m q ) / 2 [ ( n q + 1 ) ( n q + 1 ) ] 1 / 2 Γ ( 14 / 3 ) Γ [ ( n q + n q 5 / 3 ) / 2 ] δ m q m q Γ [ ( n q n q + 17 / 3 ) / 2 ] Γ [ ( n q n q + 17 / 3 ) / 2 ] Γ [ ( n q + n q + 23 / 3 ) / 2 ] , q q   is even .
Γ a = G · V · G T .
ϕ ( ρ , θ ) = q = 1 b q K q ( ρ , θ ) ,
Γ a = E [ a · a T ] .
E { b · b T } = E { G · a · a T · G T } = G · E { a · a T } · G T = V .
a = G 1 · b = G T · b .
ϕ ( ρ , θ ) = q = 1 b q · q = 1 G q q Z q ( ρ , θ ) .
r 0 = 2.1 ( 1.45 h 0 H 0 C n 2 ( h ) d h ) 3 / 5 ,
C n 2 ( h ) = 0.00594 ( υ / 27 ) 2 ( 10 5 h ) 10 exp ( h / 1000 ) + 2.7 × 10 16 exp ( h / 1500 ) + C exp ( h / 100 ) ,
σ I 2 = I 2 I 2 I 2 = I 2 I 2 1 ,

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