Abstract

The CCD-based point source centroid computation (PSCC) error under the background light is analyzed integrally in theory, numerical simulation and experiment. Furthermore, a comprehensive formula of the PSCC error caused by the diversified error sources is put forward. The optimum threshold to reduce the effects of all the error sources to a minimum is selected. The best threshold level is NB+3σB, where NB is the average value of the error sources and σB is the mean-square value of the fluctuation of the error sources. The simulation and experiment results are in great accordance with the theoretical analysis.

© 2009 Optical Society of America

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  1. D.-g.  Jia, P.-s.  Zhang, W.-c.  Jing, J.  Tan, H.-x.  Zhang, and Y.  Zhang, "Design of a multi-channel free space optical interconnection component," Optoelectron. Lett. 4, 407-409 (2008).
    [CrossRef]
  2. R. G. Dorsch, G. Hausler, and J. M. Herrmann, "Laser triangulation: fundamental uncertainty in distance measurement," Appl. Opt. 33, 1306-1314 (1994).
    [CrossRef] [PubMed]
  3. L. Chunyan, X. Hua, L. Huafeng, and S. Caihong, "Centroiding algorithm for high-accuracy star tracker," Opto-Electron.Engin. 33, 41-44 (2006).
  4. J. Ares, "Position and displacement sensing with Shack-Hartmann wavefront sensors," Appl. Opt. 39, 1511-1520 (2000).
    [CrossRef]
  5. C. H. Rao, W. H. Jiang, and N. Ling, "Atmospheric characterization with Shack-Hartmann wavefront sensors for non-Kolmogorov turbulence," Opt. Eng. 41, 534-541 (2002).
    [CrossRef]
  6. G. A. Tyler and D. L. Fried, "Image-position error associated with a quadrant detector," J. Opt. Soc. Am. 6, 804-808 (1982).
    [CrossRef]
  7. C. Genrui and Y. Xin, "Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object," Opt. Eng. 33, 2321-2335 (1994).
  8. W. Jiang, H. Xian, and S. Feng, "Detecting error of Shack-Hartmann wavefront sensor," Proc. SPIE 3126, 534-544 (1997).
    [CrossRef]
  9. M. Xiaoyu, R. Changhui, and Z. Xuejun, "Performance comparison of Photon-Multiplier-Tube-Based and CCD-Based photon-electronic devices," Acta Opt. Sin. 5, 882-888 (2007).
  10. Z. Ang, R. Changhui, Z. Yudong, and J. Wenhan, "Performance analysis of Shack-Hartmann wavefront sensor with variable sub-aperture pixels," Porc. SPIE 5490, 1268-1277 (2004).
    [CrossRef]
  11. Z. Zhicheng, "On the Subject of Gauss Approximation of Poisson Distribution," Acta Scicentiarum Naturalum Universitis Pekinesis 5, 605-619 (1988).
  12. B. F. Aull, M. J. Renzi, A. H. Loomis, D. J. Young, B. J. Felton, T. A. Lind, and D. M. Craig, "Geiger-mode Quad-cell array for adaptive optics," CLEO/QELS, (2008).

2008 (1)

D.-g.  Jia, P.-s.  Zhang, W.-c.  Jing, J.  Tan, H.-x.  Zhang, and Y.  Zhang, "Design of a multi-channel free space optical interconnection component," Optoelectron. Lett. 4, 407-409 (2008).
[CrossRef]

2007 (1)

M. Xiaoyu, R. Changhui, and Z. Xuejun, "Performance comparison of Photon-Multiplier-Tube-Based and CCD-Based photon-electronic devices," Acta Opt. Sin. 5, 882-888 (2007).

2006 (1)

L. Chunyan, X. Hua, L. Huafeng, and S. Caihong, "Centroiding algorithm for high-accuracy star tracker," Opto-Electron.Engin. 33, 41-44 (2006).

2004 (1)

Z. Ang, R. Changhui, Z. Yudong, and J. Wenhan, "Performance analysis of Shack-Hartmann wavefront sensor with variable sub-aperture pixels," Porc. SPIE 5490, 1268-1277 (2004).
[CrossRef]

2002 (1)

C. H. Rao, W. H. Jiang, and N. Ling, "Atmospheric characterization with Shack-Hartmann wavefront sensors for non-Kolmogorov turbulence," Opt. Eng. 41, 534-541 (2002).
[CrossRef]

2000 (1)

1997 (1)

W. Jiang, H. Xian, and S. Feng, "Detecting error of Shack-Hartmann wavefront sensor," Proc. SPIE 3126, 534-544 (1997).
[CrossRef]

1994 (2)

C. Genrui and Y. Xin, "Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object," Opt. Eng. 33, 2321-2335 (1994).

R. G. Dorsch, G. Hausler, and J. M. Herrmann, "Laser triangulation: fundamental uncertainty in distance measurement," Appl. Opt. 33, 1306-1314 (1994).
[CrossRef] [PubMed]

1988 (1)

Z. Zhicheng, "On the Subject of Gauss Approximation of Poisson Distribution," Acta Scicentiarum Naturalum Universitis Pekinesis 5, 605-619 (1988).

1982 (1)

G. A. Tyler and D. L. Fried, "Image-position error associated with a quadrant detector," J. Opt. Soc. Am. 6, 804-808 (1982).
[CrossRef]

Ang, Z.

Z. Ang, R. Changhui, Z. Yudong, and J. Wenhan, "Performance analysis of Shack-Hartmann wavefront sensor with variable sub-aperture pixels," Porc. SPIE 5490, 1268-1277 (2004).
[CrossRef]

Ares, J.

Caihong, S.

L. Chunyan, X. Hua, L. Huafeng, and S. Caihong, "Centroiding algorithm for high-accuracy star tracker," Opto-Electron.Engin. 33, 41-44 (2006).

Changhui, R.

M. Xiaoyu, R. Changhui, and Z. Xuejun, "Performance comparison of Photon-Multiplier-Tube-Based and CCD-Based photon-electronic devices," Acta Opt. Sin. 5, 882-888 (2007).

Z. Ang, R. Changhui, Z. Yudong, and J. Wenhan, "Performance analysis of Shack-Hartmann wavefront sensor with variable sub-aperture pixels," Porc. SPIE 5490, 1268-1277 (2004).
[CrossRef]

Chunyan, L.

L. Chunyan, X. Hua, L. Huafeng, and S. Caihong, "Centroiding algorithm for high-accuracy star tracker," Opto-Electron.Engin. 33, 41-44 (2006).

Dorsch, R. G.

Feng, S.

W. Jiang, H. Xian, and S. Feng, "Detecting error of Shack-Hartmann wavefront sensor," Proc. SPIE 3126, 534-544 (1997).
[CrossRef]

Fried, D. L.

G. A. Tyler and D. L. Fried, "Image-position error associated with a quadrant detector," J. Opt. Soc. Am. 6, 804-808 (1982).
[CrossRef]

Genrui, C.

C. Genrui and Y. Xin, "Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object," Opt. Eng. 33, 2321-2335 (1994).

Hausler, G.

Herrmann, J. M.

Hua, X.

L. Chunyan, X. Hua, L. Huafeng, and S. Caihong, "Centroiding algorithm for high-accuracy star tracker," Opto-Electron.Engin. 33, 41-44 (2006).

Huafeng, L.

L. Chunyan, X. Hua, L. Huafeng, and S. Caihong, "Centroiding algorithm for high-accuracy star tracker," Opto-Electron.Engin. 33, 41-44 (2006).

Jia, D.-g.

D.-g.  Jia, P.-s.  Zhang, W.-c.  Jing, J.  Tan, H.-x.  Zhang, and Y.  Zhang, "Design of a multi-channel free space optical interconnection component," Optoelectron. Lett. 4, 407-409 (2008).
[CrossRef]

Jiang, W.

W. Jiang, H. Xian, and S. Feng, "Detecting error of Shack-Hartmann wavefront sensor," Proc. SPIE 3126, 534-544 (1997).
[CrossRef]

Jiang, W. H.

C. H. Rao, W. H. Jiang, and N. Ling, "Atmospheric characterization with Shack-Hartmann wavefront sensors for non-Kolmogorov turbulence," Opt. Eng. 41, 534-541 (2002).
[CrossRef]

Jing, W.-c.

D.-g.  Jia, P.-s.  Zhang, W.-c.  Jing, J.  Tan, H.-x.  Zhang, and Y.  Zhang, "Design of a multi-channel free space optical interconnection component," Optoelectron. Lett. 4, 407-409 (2008).
[CrossRef]

Ling, N.

C. H. Rao, W. H. Jiang, and N. Ling, "Atmospheric characterization with Shack-Hartmann wavefront sensors for non-Kolmogorov turbulence," Opt. Eng. 41, 534-541 (2002).
[CrossRef]

Rao, C. H.

C. H. Rao, W. H. Jiang, and N. Ling, "Atmospheric characterization with Shack-Hartmann wavefront sensors for non-Kolmogorov turbulence," Opt. Eng. 41, 534-541 (2002).
[CrossRef]

Tan, J.

D.-g.  Jia, P.-s.  Zhang, W.-c.  Jing, J.  Tan, H.-x.  Zhang, and Y.  Zhang, "Design of a multi-channel free space optical interconnection component," Optoelectron. Lett. 4, 407-409 (2008).
[CrossRef]

Tyler, G. A.

G. A. Tyler and D. L. Fried, "Image-position error associated with a quadrant detector," J. Opt. Soc. Am. 6, 804-808 (1982).
[CrossRef]

Wenhan, J.

Z. Ang, R. Changhui, Z. Yudong, and J. Wenhan, "Performance analysis of Shack-Hartmann wavefront sensor with variable sub-aperture pixels," Porc. SPIE 5490, 1268-1277 (2004).
[CrossRef]

Xian, H.

W. Jiang, H. Xian, and S. Feng, "Detecting error of Shack-Hartmann wavefront sensor," Proc. SPIE 3126, 534-544 (1997).
[CrossRef]

Xiaoyu, M.

M. Xiaoyu, R. Changhui, and Z. Xuejun, "Performance comparison of Photon-Multiplier-Tube-Based and CCD-Based photon-electronic devices," Acta Opt. Sin. 5, 882-888 (2007).

Xin, Y.

C. Genrui and Y. Xin, "Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object," Opt. Eng. 33, 2321-2335 (1994).

Xuejun, Z.

M. Xiaoyu, R. Changhui, and Z. Xuejun, "Performance comparison of Photon-Multiplier-Tube-Based and CCD-Based photon-electronic devices," Acta Opt. Sin. 5, 882-888 (2007).

Yudong, Z.

Z. Ang, R. Changhui, Z. Yudong, and J. Wenhan, "Performance analysis of Shack-Hartmann wavefront sensor with variable sub-aperture pixels," Porc. SPIE 5490, 1268-1277 (2004).
[CrossRef]

Zhang, H.-x.

D.-g.  Jia, P.-s.  Zhang, W.-c.  Jing, J.  Tan, H.-x.  Zhang, and Y.  Zhang, "Design of a multi-channel free space optical interconnection component," Optoelectron. Lett. 4, 407-409 (2008).
[CrossRef]

Zhang, P.-s.

D.-g.  Jia, P.-s.  Zhang, W.-c.  Jing, J.  Tan, H.-x.  Zhang, and Y.  Zhang, "Design of a multi-channel free space optical interconnection component," Optoelectron. Lett. 4, 407-409 (2008).
[CrossRef]

Zhang, Y.

D.-g.  Jia, P.-s.  Zhang, W.-c.  Jing, J.  Tan, H.-x.  Zhang, and Y.  Zhang, "Design of a multi-channel free space optical interconnection component," Optoelectron. Lett. 4, 407-409 (2008).
[CrossRef]

Zhicheng, Z.

Z. Zhicheng, "On the Subject of Gauss Approximation of Poisson Distribution," Acta Scicentiarum Naturalum Universitis Pekinesis 5, 605-619 (1988).

Acta Opt. Sin. (1)

M. Xiaoyu, R. Changhui, and Z. Xuejun, "Performance comparison of Photon-Multiplier-Tube-Based and CCD-Based photon-electronic devices," Acta Opt. Sin. 5, 882-888 (2007).

Acta Scicentiarum Naturalum Universitis Pekinesis (1)

Z. Zhicheng, "On the Subject of Gauss Approximation of Poisson Distribution," Acta Scicentiarum Naturalum Universitis Pekinesis 5, 605-619 (1988).

Appl. Opt. (2)

Engin. (1)

L. Chunyan, X. Hua, L. Huafeng, and S. Caihong, "Centroiding algorithm for high-accuracy star tracker," Opto-Electron.Engin. 33, 41-44 (2006).

J. Opt. Soc. Am. (1)

G. A. Tyler and D. L. Fried, "Image-position error associated with a quadrant detector," J. Opt. Soc. Am. 6, 804-808 (1982).
[CrossRef]

Opt. Eng. (2)

C. Genrui and Y. Xin, "Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object," Opt. Eng. 33, 2321-2335 (1994).

C. H. Rao, W. H. Jiang, and N. Ling, "Atmospheric characterization with Shack-Hartmann wavefront sensors for non-Kolmogorov turbulence," Opt. Eng. 41, 534-541 (2002).
[CrossRef]

Optoelectron. Lett. (1)

D.-g.  Jia, P.-s.  Zhang, W.-c.  Jing, J.  Tan, H.-x.  Zhang, and Y.  Zhang, "Design of a multi-channel free space optical interconnection component," Optoelectron. Lett. 4, 407-409 (2008).
[CrossRef]

Porc. SPIE (1)

Z. Ang, R. Changhui, Z. Yudong, and J. Wenhan, "Performance analysis of Shack-Hartmann wavefront sensor with variable sub-aperture pixels," Porc. SPIE 5490, 1268-1277 (2004).
[CrossRef]

Proc. SPIE (1)

W. Jiang, H. Xian, and S. Feng, "Detecting error of Shack-Hartmann wavefront sensor," Proc. SPIE 3126, 534-544 (1997).
[CrossRef]

Other (1)

B. F. Aull, M. J. Renzi, A. H. Loomis, D. J. Young, B. J. Felton, T. A. Lind, and D. M. Craig, "Geiger-mode Quad-cell array for adaptive optics," CLEO/QELS, (2008).

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Figures (13)

Fig. 1.
Fig. 1.

Schematic diagram of CCD-based PSCC

Fig. 2.
Fig. 2.

The curves of the PSCC error that change along with threshold

Fig. 3.
Fig. 3.

The images of ideal spot (a) and sampling spot (b)

Fig. 4.
Fig. 4.

One of the spot imaged by simulation

Fig. 5.
Fig. 5.

The PSCC error changing with threshold when position of spot is different

Fig. 6.
Fig. 6.

The PSCC error changing with threshold when background noise is different

Fig. 7.
Fig. 7.

The PSCC error changing with threshold when the size of aperture is different

Fig. 8.
Fig. 8.

The PSCC error changing with threshold when readout noise is different

Fig. 9.
Fig. 9.

The PSCC error changing with threshold when background level is different

Fig. 10.
Fig. 10.

Schematic diagram of experimental system

Fig. 11.
Fig. 11.

The zones of signal and the 1st class error source

Fig. 12.
Fig. 12.

Spot and noise in single aperture

Fig. 13.
Fig. 13.

The curves of the PSCC error in theory and by experiment

Tables (4)

Tables Icon

Table 1. The list of symbols and their explanations

Tables Icon

Table 2. The error sources of CCD-based PSCC and their distributions

Tables Icon

Table 3. The relationship between the threshold and xB

Tables Icon

Table 4. The relationship between the threshold and the PSCC error

Equations (50)

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

xc=ijL,MxijNijijL,MNij=UV .
Nij=Nsij+Nbij+Nrij+Ndij=Nsij+NBij.
U=ijL,MxiNij=ijL,Mxi(Nsij+NBij)=Us+UB.
V=ijL,MNij=ijL,M(Nsij+NBij)=Vs+VB.
xc=UV=Us+UBVs+VB=VsVxs+VBVxB.
xs=xp+σs.
xc=VsV (xp+σs)+VBVxB.
σp=xpxc .
σp=VBV(xsxB)σS.
σS=i=0L1{[erf(i+1xp2σA)erf(ixp2σA)](i+0.5)}erf(Lxp2σA)+erf(xp2σA)xp.
σxc2=U2V4σV2+1V2σU22UV3σUV.
σxc2=U2i,jL,MSij2V4+i,jL,Mxi2Sij2V22Ui,jL,MxiSij2V3.
Sij2=σp2+σB2=Nsij+Nbij+σr2.
σxc2=U2i,jL,M(Nsij+Nbij+σr2)V4+i,jL,Mxi2(Nsij+Nbij+σr2)V22Ui,jL,Mxi(Nsij+Nbij+σr2)V3.
σxs2=i,jL,Mxi2NsijV2Us2V3=VsσA2V2+1Vsxs21Vxc2.
σxr2=U2i,jL,Mσr2V4+i,jL,Mxi2σr2V22Ui,jL,Mxiσr2V3=σr2LMV2 (L2112+xc2) .
σxb2=U2i,jL,MNbijV4+i,jL,Mxi2NbijV22Ui,jL,MxiNbijV3=VbV2 (L2112+xc2) .
σxc2=σxr2+σxs2+σxb2
=(σr2LM+Vb)V2(L2112+xc2)+VsσA2V2+1Vsxs21Vxc2.
σx2=σp2+σxc2
=σB2LMV2(L2112+xc2)+VsσA2V2+1Vsxs21Vxc2+[VBV(xsxB)σS]2.
σx2=σB2LMV2(L2112+xc2)+κVsσA2V2+κVsxs2κVxc2+[VBV(xsxB)σS]2.
σθ=π[(316)2+(n8)2]12SNRv λD .
σθ=3π16 1SNRv λD .
σx1=σAVs .
σx=1.37SNRvσA=0.97σAVs .
σx22=σr2LMVs2 (L2112+xc2)+κσA2Vs .
σx32=Vb2V2 [σr2LMVb2(L2112+xc2)+κVsVb2σA2+(xdxs)2]
σx42=1(1+sbr)2 [σr2LMVb2(L2112+xc2)+sbr2κσA2Vs+(xdxs)2] .
σx42=σb2LM(Vs+Vb)2 (L2112+xc2)+κVsσA2(Vs+Vb)2+κVsxs2κ(Vs+Vb)2xc2+[Vb(Vs+Vb)(xs+xb)]2.
P(NBij)=12πσB exp [(NBijNB)22σB2] .
NBij(T)=T [(NBijT)·P(NBij)] d NBij .
VB(T)=NBij (T) · LM .
NBij2(T)=T [(NBijT)2·P(NBij)] d NBij .
σB2(T)=T[(NBijT)2·P(NBij)]dNBij{T[(NBijT)·P(NBij)]dNBij}2.
xB=UBVB=VbVBxb+VbVBxd+VrVBxr.
xB(T)={0,T<NB3σBxB=lmσBVB(T)+lmσBxs,NB3σBTNB+3σBxs,T>NB+3σB
Nsij=Vs4 [erf(i+0.5xs2σA)erf(i0.5xs2σA)] · [erf(j+0.5xs2σA)erf(j0.5xs2σA)] .
Vs(T)={Vs,TNBi,j=1L,Mcheck[NsijT+NB],T>NB.
Nsij(T)=check(NsijT+NB).
xs(T)=ijL,Mxijcheck(NsijT+NB)ijL,Mcheck(NsijT+NB).
xs(T)=ijL,M[NsijT+NB]ijL,M[NsijT+NB]=ijL,M[xij·Nsij]ijL,M[xij·(TNB)]ijL,MNsijijL,M(TNB)
xs(T)=STRSTR1xp1STR1XT .
σS(T)=xpxc(T)=1STR1(xTxp).
σxc2=(STRSTR1)2σxp2 .
σxp2=4(σr2+NB)Vs(T)2[14xC2(T)]+κσA2Vs(T).
σxa2=MLσB2(T)[Vs+VB(T)]2[L2112+xc2(T)]+κVsσA2[Vs+VB(T)]2+κxs2Vsκxc2(T)Vs+VB(T)+{VB(T)Vs+VB(T)[xsxB(T)]σs}2
σxb2=MLσB2(T)[Vs(T)+VB(T)]2[L2112+xc2(T)]+κVs(T)σA2[Vs(T)+VB(T)]2+κxs2(T)Vsκxc2(T)Vs(T)+VB(T)+{VB(T)Vs(T)+VB(T)[xs(T)xB(T)]σs(T)}2
σxc2=1(STR1)2(xTxp)+4(σr2+NB)Vs2(T)[14xC2(T)]+κσA2Vs(T).
xp=2θp·f1SCCD(pixel).

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