Abstract

An intensified high dynamic star tracker (IHDST) is a photoelectric instrument and stably outputs three-axis attitude for a spacecraft at very high angular velocity. The IHDST uses an image intensifier to multiply the incident starlight. Thus, high sensitivity of the star detection is achieved under short exposure time such that extremely high dynamic performance is achieved. The IHDST differs from a traditional star tracker in terms of the imaging process. Therefore, we establish a quantum transfer model of IHDST based on stochastic process theory. By this model, the probability distribution of the output quantum number is obtained accurately. Then, we introduce two-dimensional Lorentz functions to describe the spatial spreading process of the IHDST. Considering the interaction of these two processes, a complete star imaging model of IHDST is provided. Using this model, the centroiding accuracy of the IHDST is analyzed in detail. Accordingly, a working parameter optimizing strategy is developed for high centroiding accuracy and improved dynamic performance. Finally, the laboratory tests and the night sky experiment support the conclusions.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  20. R. A. Kronmal and A. V. Peterson, “On the Alias Method for Generating Random Variables from a Discrete Distribution,” Am. Stat. 33(4), 214–218 (1979).
  21. H. Deschout, F. Cella Zanacchi, M. Mlodzianoski, A. Diaspro, J. Bewersdorf, S. T. Hess, and K. Braeckmans, “Precisely and accurately localizing single emitters in fluorescence microscopy,” Nat. Methods 11(3), 253–266 (2014).
    [Crossref] [PubMed]

2016 (1)

2015 (1)

2014 (1)

H. Deschout, F. Cella Zanacchi, M. Mlodzianoski, A. Diaspro, J. Bewersdorf, S. T. Hess, and K. Braeckmans, “Precisely and accurately localizing single emitters in fluorescence microscopy,” Nat. Methods 11(3), 253–266 (2014).
[Crossref] [PubMed]

2012 (2)

2010 (2)

J. Shen, G. Zhang, and X. Wei, “Simulation analysis of dynamic working performance for star trackers,” J. Opt. Soc. Am. A 27(12), 2638–2647 (2010).
[Crossref] [PubMed]

E. Bodegom, A. Katake, V. Nguyen, and C. Bruccoleri, “StarCam SG100: a high-update rate, high-sensitivity stellar gyroscope for spacecraft,” Proc. SPIE 7536, 753608 (2010).
[Crossref]

2009 (1)

P. Embrechts and M. Frei, “Panjer recursion versus FFT for compound distributions,” Math. Methods Oper. Res. 69(3), 497–508 (2009).
[Crossref]

2004 (1)

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27(1), 91–99 (2004).
[Crossref]

2002 (1)

C. C. Liebe, “Accuracy performance of star trackers-a tutorial,” IEEE T. Aero. Elec. Sys. 38(2), 587–599 (2002).
[Crossref]

1997 (2)

A. Frenkel, M. A. Sartor, and M. S. Wlodawski, “Photon-noise-limited operation of intensified CCD cameras,” Appl. Opt. 36(22), 5288–5297 (1997).
[Crossref] [PubMed]

S. E. Moran, B. L. Ulich, W. P. Elkins, R. J. Strittmatter, and M. J. DeWeert, “Intensified CCD (ICCD) dynamic range and noise performance,” Proc. SPIE 3173, 430–457 (1997).
[Crossref]

1993 (1)

M. S. Westmore and I. A. Cunningham, “Analysis of the detective quantum efficiency of coupling a CCD to a scintillating phosphor for x-ray microtomographic imaging,” Proc. SPIE 1896, 82–92 (1993).
[Crossref]

1990 (1)

J. N. Hollenhorst, “A theory of multiplication noise,” IEEE Trans. Electron Dev. 37(3), 781–788 (1990).
[Crossref]

1979 (2)

R. A. Kronmal and A. V. Peterson, “On the Alias Method for Generating Random Variables from a Discrete Distribution,” Am. Stat. 33(4), 214–218 (1979).

E. H. Eberhardt, “Gain model for microchannel plates,” Appl. Opt. 18(9), 1418–1423 (1979).
[Crossref] [PubMed]

1977 (1)

Bewersdorf, J.

H. Deschout, F. Cella Zanacchi, M. Mlodzianoski, A. Diaspro, J. Bewersdorf, S. T. Hess, and K. Braeckmans, “Precisely and accurately localizing single emitters in fluorescence microscopy,” Nat. Methods 11(3), 253–266 (2014).
[Crossref] [PubMed]

Bodegom, E.

E. Bodegom, A. Katake, V. Nguyen, and C. Bruccoleri, “StarCam SG100: a high-update rate, high-sensitivity stellar gyroscope for spacecraft,” Proc. SPIE 7536, 753608 (2010).
[Crossref]

Braeckmans, K.

H. Deschout, F. Cella Zanacchi, M. Mlodzianoski, A. Diaspro, J. Bewersdorf, S. T. Hess, and K. Braeckmans, “Precisely and accurately localizing single emitters in fluorescence microscopy,” Nat. Methods 11(3), 253–266 (2014).
[Crossref] [PubMed]

Bruccoleri, C.

E. Bodegom, A. Katake, V. Nguyen, and C. Bruccoleri, “StarCam SG100: a high-update rate, high-sensitivity stellar gyroscope for spacecraft,” Proc. SPIE 7536, 753608 (2010).
[Crossref]

Cella Zanacchi, F.

H. Deschout, F. Cella Zanacchi, M. Mlodzianoski, A. Diaspro, J. Bewersdorf, S. T. Hess, and K. Braeckmans, “Precisely and accurately localizing single emitters in fluorescence microscopy,” Nat. Methods 11(3), 253–266 (2014).
[Crossref] [PubMed]

Chen, C.

Csorba, I. P.

Cunningham, I. A.

M. S. Westmore and I. A. Cunningham, “Analysis of the detective quantum efficiency of coupling a CCD to a scintillating phosphor for x-ray microtomographic imaging,” Proc. SPIE 1896, 82–92 (1993).
[Crossref]

Cunningham, T. J.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy,” in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

Da, L.

Deschout, H.

H. Deschout, F. Cella Zanacchi, M. Mlodzianoski, A. Diaspro, J. Bewersdorf, S. T. Hess, and K. Braeckmans, “Precisely and accurately localizing single emitters in fluorescence microscopy,” Nat. Methods 11(3), 253–266 (2014).
[Crossref] [PubMed]

DeWeert, M. J.

S. E. Moran, B. L. Ulich, W. P. Elkins, R. J. Strittmatter, and M. J. DeWeert, “Intensified CCD (ICCD) dynamic range and noise performance,” Proc. SPIE 3173, 430–457 (1997).
[Crossref]

Diaspro, A.

H. Deschout, F. Cella Zanacchi, M. Mlodzianoski, A. Diaspro, J. Bewersdorf, S. T. Hess, and K. Braeckmans, “Precisely and accurately localizing single emitters in fluorescence microscopy,” Nat. Methods 11(3), 253–266 (2014).
[Crossref] [PubMed]

Eberhardt, E. H.

Elkins, W. P.

S. E. Moran, B. L. Ulich, W. P. Elkins, R. J. Strittmatter, and M. J. DeWeert, “Intensified CCD (ICCD) dynamic range and noise performance,” Proc. SPIE 3173, 430–457 (1997).
[Crossref]

Embrechts, P.

P. Embrechts and M. Frei, “Panjer recursion versus FFT for compound distributions,” Math. Methods Oper. Res. 69(3), 497–508 (2009).
[Crossref]

Frankel, K. A.

J. M. Holton, C. Nielsen, and K. A. Frankel, “The point-spread function of fiber-coupled area detectors,” J. Synchrotron Radiat. 19(6), 1006–1011 (2012).
[Crossref] [PubMed]

Frei, M.

P. Embrechts and M. Frei, “Panjer recursion versus FFT for compound distributions,” Math. Methods Oper. Res. 69(3), 497–508 (2009).
[Crossref]

Frenkel, A.

Gromov, K.

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27(1), 91–99 (2004).
[Crossref]

Hancock, B. R.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy,” in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

Hess, S. T.

H. Deschout, F. Cella Zanacchi, M. Mlodzianoski, A. Diaspro, J. Bewersdorf, S. T. Hess, and K. Braeckmans, “Precisely and accurately localizing single emitters in fluorescence microscopy,” Nat. Methods 11(3), 253–266 (2014).
[Crossref] [PubMed]

Hollenhorst, J. N.

J. N. Hollenhorst, “A theory of multiplication noise,” IEEE Trans. Electron Dev. 37(3), 781–788 (1990).
[Crossref]

Holton, J. M.

J. M. Holton, C. Nielsen, and K. A. Frankel, “The point-spread function of fiber-coupled area detectors,” J. Synchrotron Radiat. 19(6), 1006–1011 (2012).
[Crossref] [PubMed]

Jiang, J.

Jun, Z.

Katake, A.

E. Bodegom, A. Katake, V. Nguyen, and C. Bruccoleri, “StarCam SG100: a high-update rate, high-sensitivity stellar gyroscope for spacecraft,” Proc. SPIE 7536, 753608 (2010).
[Crossref]

Kronmal, R. A.

R. A. Kronmal and A. V. Peterson, “On the Alias Method for Generating Random Variables from a Discrete Distribution,” Am. Stat. 33(4), 214–218 (1979).

Li, G.

Li, W.

Liebe, C. C.

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27(1), 91–99 (2004).
[Crossref]

C. C. Liebe, “Accuracy performance of star trackers-a tutorial,” IEEE T. Aero. Elec. Sys. 38(2), 587–599 (2002).
[Crossref]

Meller, D. M.

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27(1), 91–99 (2004).
[Crossref]

Mlodzianoski, M.

H. Deschout, F. Cella Zanacchi, M. Mlodzianoski, A. Diaspro, J. Bewersdorf, S. T. Hess, and K. Braeckmans, “Precisely and accurately localizing single emitters in fluorescence microscopy,” Nat. Methods 11(3), 253–266 (2014).
[Crossref] [PubMed]

Moran, S. E.

S. E. Moran, B. L. Ulich, W. P. Elkins, R. J. Strittmatter, and M. J. DeWeert, “Intensified CCD (ICCD) dynamic range and noise performance,” Proc. SPIE 3173, 430–457 (1997).
[Crossref]

Nguyen, V.

E. Bodegom, A. Katake, V. Nguyen, and C. Bruccoleri, “StarCam SG100: a high-update rate, high-sensitivity stellar gyroscope for spacecraft,” Proc. SPIE 7536, 753608 (2010).
[Crossref]

Nielsen, C.

J. M. Holton, C. Nielsen, and K. A. Frankel, “The point-spread function of fiber-coupled area detectors,” J. Synchrotron Radiat. 19(6), 1006–1011 (2012).
[Crossref] [PubMed]

Pain, B.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy,” in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

Peterson, A. V.

R. A. Kronmal and A. V. Peterson, “On the Alias Method for Generating Random Variables from a Discrete Distribution,” Am. Stat. 33(4), 214–218 (1979).

Ringold, P. G.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy,” in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

Sartor, M. A.

Shen, J.

Stirbl, R. C.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy,” in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

Strittmatter, R. J.

S. E. Moran, B. L. Ulich, W. P. Elkins, R. J. Strittmatter, and M. J. DeWeert, “Intensified CCD (ICCD) dynamic range and noise performance,” Proc. SPIE 3173, 430–457 (1997).
[Crossref]

Ulich, B. L.

S. E. Moran, B. L. Ulich, W. P. Elkins, R. J. Strittmatter, and M. J. DeWeert, “Intensified CCD (ICCD) dynamic range and noise performance,” Proc. SPIE 3173, 430–457 (1997).
[Crossref]

Wang, X.

Wei, X.

Westmore, M. S.

M. S. Westmore and I. A. Cunningham, “Analysis of the detective quantum efficiency of coupling a CCD to a scintillating phosphor for x-ray microtomographic imaging,” Proc. SPIE 1896, 82–92 (1993).
[Crossref]

Wlodawski, M. S.

Wrigley, C. J.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy,” in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

Wu, B.

Wu, L.

Xue, Z.

Yan, J.

Yang, B.

Yang, H.

Yu, B.

Yuan, L.

Yuncai, H.

Zhang, G.

Am. Stat. (1)

R. A. Kronmal and A. V. Peterson, “On the Alias Method for Generating Random Variables from a Discrete Distribution,” Am. Stat. 33(4), 214–218 (1979).

Appl. Opt. (5)

IEEE T. Aero. Elec. Sys. (1)

C. C. Liebe, “Accuracy performance of star trackers-a tutorial,” IEEE T. Aero. Elec. Sys. 38(2), 587–599 (2002).
[Crossref]

IEEE Trans. Electron Dev. (1)

J. N. Hollenhorst, “A theory of multiplication noise,” IEEE Trans. Electron Dev. 37(3), 781–788 (1990).
[Crossref]

J. Guid. Control Dyn. (1)

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27(1), 91–99 (2004).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Synchrotron Radiat. (1)

J. M. Holton, C. Nielsen, and K. A. Frankel, “The point-spread function of fiber-coupled area detectors,” J. Synchrotron Radiat. 19(6), 1006–1011 (2012).
[Crossref] [PubMed]

Math. Methods Oper. Res. (1)

P. Embrechts and M. Frei, “Panjer recursion versus FFT for compound distributions,” Math. Methods Oper. Res. 69(3), 497–508 (2009).
[Crossref]

Nat. Methods (1)

H. Deschout, F. Cella Zanacchi, M. Mlodzianoski, A. Diaspro, J. Bewersdorf, S. T. Hess, and K. Braeckmans, “Precisely and accurately localizing single emitters in fluorescence microscopy,” Nat. Methods 11(3), 253–266 (2014).
[Crossref] [PubMed]

Opt. Express (1)

Proc. SPIE (3)

E. Bodegom, A. Katake, V. Nguyen, and C. Bruccoleri, “StarCam SG100: a high-update rate, high-sensitivity stellar gyroscope for spacecraft,” Proc. SPIE 7536, 753608 (2010).
[Crossref]

S. E. Moran, B. L. Ulich, W. P. Elkins, R. J. Strittmatter, and M. J. DeWeert, “Intensified CCD (ICCD) dynamic range and noise performance,” Proc. SPIE 3173, 430–457 (1997).
[Crossref]

M. S. Westmore and I. A. Cunningham, “Analysis of the detective quantum efficiency of coupling a CCD to a scintillating phosphor for x-ray microtomographic imaging,” Proc. SPIE 1896, 82–92 (1993).
[Crossref]

Other (4)

Y. Zou, Electrically Vacuum Imaging Devices and Theoretical Analysis (National Defense Industry, 1989).

S. M. Ross, Introduction to Probability Models (Tenth Edition) (2011).

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy,” in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

A. B. Katake, “Modeling, image processing and attitude estimation of high speed star sensors,” (Diss. Texas A&M University, 2006).

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Figures (18)

Fig. 1
Fig. 1 Schematic of the IHDST imaging.
Fig. 2
Fig. 2 Electron multiplication of MCP.
Fig. 3
Fig. 3 PDFs of different gains.
Fig. 4
Fig. 4 PDF and histogram of the star energy. (a) Theoretical PDF vs. λ1; (b) Theoretical PDF vs. r.
Fig. 5
Fig. 5 IHDST star image and its locating accuracy. (xe,i, ye,i) is the centroid of the i-th star image. σx and σy are the star locating accuracy in the x- and y-directions, respectively.
Fig. 6
Fig. 6 Centroiding error in the x-direction vs. Uc and T under static conditions.
Fig. 7
Fig. 7 Centroiding error vs. exposure time under the dynamic condition.
Fig. 8
Fig. 8 Centroiding error vs. Uc under the dynamic condition.
Fig. 9
Fig. 9 Smearing effect of a star spot.
Fig. 10
Fig. 10 IHDST exposure time vs. angular velocity.
Fig. 11
Fig. 11 Star intensity vs. angular velocity. (a) PSFs of star spots; (b) Brightest pixel grayscale.
Fig. 12
Fig. 12 Settings of Uc vs. angular velocity for different stellar magnitudes.
Fig. 13
Fig. 13 Laboratory test setup.
Fig. 14
Fig. 14 Experimental and theoretical PDFs of the IHDST.
Fig. 15
Fig. 15 Spatial spreading of the IHDST.
Fig. 16
Fig. 16 Validation of the IHDST imaging model. (a) Experimental star spots; (b) Simulated star spots based on our model; (c) Simulated star spots based on the model in [9].
Fig. 17
Fig. 17 Centroiding error vs. Uc under different exposure times.
Fig. 18
Fig. 18 Night sky experiment for dynamic tracking performance.

Tables (5)

Tables Icon

Table 1 Typical stochastic processes

Tables Icon

Table 2 Centroiding errors of the three static cases

Tables Icon

Table 3 IHDST hardware configurations

Tables Icon

Table 4 Simulation and experiment results of the centroiding error

Tables Icon

Table 5 Tracking state under different conditions

Equations (34)

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

g MCP = λ 1 δ M .
G( s )= i=0 p( i ) s i ,
G S ( s )= G N ( G g ( s ) ).
p S ( n )= 1 n! d n G S ( s ) d s n | s=0 = 1 n! G S ( n ) ( 0 ).
p S ( n )= 1 1a p g ( 0 ) j=1 n ( a+ bj n ) p g ( j ) p S ( nj ),n1.
μ S = G S ( 1 ) ( 1 )= μ N μ g ,
σ S 2 = G S ( 2 ) ( 1 )+ G S ( 1 ) ( 1 ) [ G S ( 1 ) ( 1 )] 2 = μ N σ g 2 + σ N 2 μ g 2 .
G( s )= G 1 { G 2 [ G n ( s ) ] }.
μ= μ 1 μ 2 μ n ,
λ in = E 0 / ε λ 2.512 Mv π D 2 /4 ,
G eq1 ( s )=exp( λ 0 s λ 0 ).
G MCP2 ( s )=G( G M1 ( s ) ) = p r / [ 1( 1p ) G M1 ( s ) ] r ,
G MCP ( s )= G MCP1 [ G MCP2 ( s ) ] =exp[ λ 1 G MCP2 ( s ) λ 1 ].
G eq2 ( s )=exp( λ 2 τ 2 η 2 s λ 2 τ 2 η 2 ).
G ST ( s )= G eq1 { G MCP [ G eq2 ( s ) ] } =exp{ λ 0 exp{ λ 1 G MCP2 [ exp( λ 2 τ 2 η 2 s λ 2 τ 2 η 2 ) ] λ 1 } λ 0 }.
p k = q k q k+1 p ST ( x ) ,
g ST = τ 1 η 1 λ 1 δ M λ 2 τ 2 η 2 K.
S= λ in g ST T.
( λ 1 ,r)= arg λ 1 ,r { min x=1 [ p ex ( x ) p th ( x; λ 1 ,δ,r ) ] 2 }.
f OL (x,y; ρ OL )= 1 2π ρ OL 2 exp( x 2 + y 2 2 ρ OL 2 ),
f 1 (x,y; ρ 1 )= 1 2π ρ 1 2 exp( x 2 + y 2 2 ρ 1 2 ),
f B (x,y; ρ B )= ρ B 2π ( x 2 + y 2 + ρ B 2 ) 3/2 ,
f out (x,y)= λ 0 T f in f 1 f B f FOT g ST ,
J ij = j0.5 j+0.5 i0.5 i+0.5 f out (x,y)dx dy.
v k = λ 0 A k f in f 1 ( x,y; ρ 1 )dxdy .
n k = f Poisson ( v k T),k=1,2,,N,
m i = f Alias ( p MCP ),i=1,2,, n k ,
N k = i=1 n k m i .
I= f Poisson ( λ 2 τ 2 η 2 I MCP f B ) f FOT K.
x e = k=1 n x k I k / k=1 n I k , y e = k=1 n y k I k / k=1 n I k ,
σ x = ( i=1 n ( x i x ¯ ) 2 σ Ii 2 + 2 I tot 2 1i<j n ρ ij ( x i x ¯ )( x j x ¯ ) σ Ii σ Ij ) 1/2 ,
σ x = 1 N1 i=1 N ( x e,i x ¯ e ) 2 .
σ c = σ x 2 + σ y 2 .
T= 2r v = 2r ω tan( θ FOV /2 ) N pix /2 ,

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