Abstract

In this paper a new method to evaluate gated viewing systems and range-gated imaging sequences, using a Lissajous-type eye pattern, is presented. This approach enables the comparison of gated viewing systems and defines clear criteria for depth resolution and depth mapping capabilities of an active imaging system. A distinct parameter can be depicted and sensed within a single chart. Therefore, this approach is a first proposal for an evaluation procedure of gated viewing systems and an enhanced analysis tool in the means of 3D capabilities.

© 2010 Optical Society of America

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References

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  1. R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng.  42, 738–746 (2003).
    [CrossRef]
  2. R. L. Espinola, E. L. Jacobs, C. E. Halford, R. Vollmerhausen, and D. H. Tofsted, “Modeling the target acquisition performance of active imaging systems,” Opt. Express  15, 3816–3832 (2007).
    [CrossRef] [PubMed]
  3. O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE.  3707, 432–448 (1999).
    [CrossRef]
  4. E. Belin, F. Christnacher, F. Taillade, and M. Laurenzis, “Display of an analytical model for backscattered luminance and a full-field range gated imaging system for vision in fog,” Proc. SPIE.  7088, 708800 (2008).
    [CrossRef]
  5. G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng.  32, 2185–2190 (1993).
    [CrossRef]
  6. H. M. Tulldahl, P. Andersson, A. Olsson, and A. Andersson, “Experimental evaluation of underwater range-gated viewing in natural waters,” Proc. SPIE.  6395, 639506 (2006).
    [CrossRef]
  7. J. Busck, “Underwater 3-D optical imaging with a gated viewing laser radar,” Opt. Eng.  44, 116001 (2005).
    [CrossRef]
  8. J. Busck and H. Heiselberg, “Gated viewing and high-accuracy three dimensional laser radar,” Appl. Opt.  43, 4705–4710(2004).
    [CrossRef] [PubMed]
  9. J. F. Andersen, J. Busck, and H. Heiselberg, “Pulsed Raman fiber laser and multispectral imaging in three dimensions,” Appl. Opt.  45, 6198–6204 (2006).
    [CrossRef] [PubMed]
  10. M. A. Albota, R. M. Heinrich, D. G. Kocher, D. G. Fouche, B. E. Player, M. E. O’Brien, B. F. Aull, J. J. Zayhowski, J. Mooney, B. C. Willard, and R. R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt.  41, 7671–7678 (2002).
    [CrossRef]
  11. P. Andersson, “Long-range three dimensional imaging using range-gated laser radar images,” Opt. Eng.  45, 034301(2006).
    [CrossRef]
  12. M. Laurenzis, F. Christnacher, and D. Monnin, “Long-range three-dimensional active imaging with superresolution depth mapping,” Opt. Lett.  32, 3146–3148 (2007).
    [CrossRef] [PubMed]
  13. M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3D range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE.  7298, 729833 (2009).
    [CrossRef]
  14. D. Monnin, A. L. Schneider, F. Christnacher, and Y. Lutz, “A 3D outdoor scene scanner based on a night-vision range-gated active imaging system,” in Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (IEEE, 2006) pp. 938–945.
    [CrossRef]
  15. E. Repasi, P. Lutzmann, O. Steinvall, M. Elmquist, B. Goehler, and G. Anstett, “Advanced short-wavelength infrared range-gated imaging for ground application in monostatic and bistatic configuration,” Appl. Opt.  48, 5956–5969 (2009).
    [CrossRef] [PubMed]
  16. G. C. Holst, Testing and Evaluation of Infrared Imaging Systems (JCD Publishing, 1993).
  17. G. C. Holst, Electro-Optical Imaging System Performance (JCD, 1995).
  18. D. Bonnier, S. Chatigny, Y. Lutz, B. Labranche, M. Levesque, and P. Galarneau, “Modelling of active TV system for surveillance operations,” Proc. SPIE.  3698, 217–228 (1999).
    [CrossRef]
  19. N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998).
  20. J. A. Jargon, C. M. Wang, and P. D. Hale, “A robust algorithm for eye-diagram analysis,” J. Lightwave Technol.  26, 3592–3600 (2008).
    [CrossRef]
  21. M. Hart, C. Duff, and S. Hinch, “Firmware measurement algorithms for the HP 83480 digital communications analyzer,” Hewlett-Packard J.  47, 13–21 (1996).

2009 (2)

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3D range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE.  7298, 729833 (2009).
[CrossRef]

E. Repasi, P. Lutzmann, O. Steinvall, M. Elmquist, B. Goehler, and G. Anstett, “Advanced short-wavelength infrared range-gated imaging for ground application in monostatic and bistatic configuration,” Appl. Opt.  48, 5956–5969 (2009).
[CrossRef] [PubMed]

2008 (2)

J. A. Jargon, C. M. Wang, and P. D. Hale, “A robust algorithm for eye-diagram analysis,” J. Lightwave Technol.  26, 3592–3600 (2008).
[CrossRef]

E. Belin, F. Christnacher, F. Taillade, and M. Laurenzis, “Display of an analytical model for backscattered luminance and a full-field range gated imaging system for vision in fog,” Proc. SPIE.  7088, 708800 (2008).
[CrossRef]

2007 (2)

2006 (3)

P. Andersson, “Long-range three dimensional imaging using range-gated laser radar images,” Opt. Eng.  45, 034301(2006).
[CrossRef]

H. M. Tulldahl, P. Andersson, A. Olsson, and A. Andersson, “Experimental evaluation of underwater range-gated viewing in natural waters,” Proc. SPIE.  6395, 639506 (2006).
[CrossRef]

J. F. Andersen, J. Busck, and H. Heiselberg, “Pulsed Raman fiber laser and multispectral imaging in three dimensions,” Appl. Opt.  45, 6198–6204 (2006).
[CrossRef] [PubMed]

2005 (1)

J. Busck, “Underwater 3-D optical imaging with a gated viewing laser radar,” Opt. Eng.  44, 116001 (2005).
[CrossRef]

2004 (1)

2003 (1)

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng.  42, 738–746 (2003).
[CrossRef]

2002 (1)

1999 (2)

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE.  3707, 432–448 (1999).
[CrossRef]

D. Bonnier, S. Chatigny, Y. Lutz, B. Labranche, M. Levesque, and P. Galarneau, “Modelling of active TV system for surveillance operations,” Proc. SPIE.  3698, 217–228 (1999).
[CrossRef]

1996 (1)

M. Hart, C. Duff, and S. Hinch, “Firmware measurement algorithms for the HP 83480 digital communications analyzer,” Hewlett-Packard J.  47, 13–21 (1996).

1993 (1)

G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng.  32, 2185–2190 (1993).
[CrossRef]

Albota, M. A.

Andersen, J. F.

Andersson, A.

H. M. Tulldahl, P. Andersson, A. Olsson, and A. Andersson, “Experimental evaluation of underwater range-gated viewing in natural waters,” Proc. SPIE.  6395, 639506 (2006).
[CrossRef]

Andersson, P.

H. M. Tulldahl, P. Andersson, A. Olsson, and A. Andersson, “Experimental evaluation of underwater range-gated viewing in natural waters,” Proc. SPIE.  6395, 639506 (2006).
[CrossRef]

P. Andersson, “Long-range three dimensional imaging using range-gated laser radar images,” Opt. Eng.  45, 034301(2006).
[CrossRef]

Anstett, G.

Aull, B. F.

Bacher, E.

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3D range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE.  7298, 729833 (2009).
[CrossRef]

Barnard, K. J.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng.  42, 738–746 (2003).
[CrossRef]

Belin, E.

E. Belin, F. Christnacher, F. Taillade, and M. Laurenzis, “Display of an analytical model for backscattered luminance and a full-field range gated imaging system for vision in fog,” Proc. SPIE.  7088, 708800 (2008).
[CrossRef]

Bolander, G.

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE.  3707, 432–448 (1999).
[CrossRef]

Bonnier, D.

D. Bonnier, S. Chatigny, Y. Lutz, B. Labranche, M. Levesque, and P. Galarneau, “Modelling of active TV system for surveillance operations,” Proc. SPIE.  3698, 217–228 (1999).
[CrossRef]

G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng.  32, 2185–2190 (1993).
[CrossRef]

Busck, J.

Carlson, R. R.

Carlsson, C.

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE.  3707, 432–448 (1999).
[CrossRef]

Chatigny, S.

D. Bonnier, S. Chatigny, Y. Lutz, B. Labranche, M. Levesque, and P. Galarneau, “Modelling of active TV system for surveillance operations,” Proc. SPIE.  3698, 217–228 (1999).
[CrossRef]

Christnacher, F.

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3D range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE.  7298, 729833 (2009).
[CrossRef]

E. Belin, F. Christnacher, F. Taillade, and M. Laurenzis, “Display of an analytical model for backscattered luminance and a full-field range gated imaging system for vision in fog,” Proc. SPIE.  7088, 708800 (2008).
[CrossRef]

M. Laurenzis, F. Christnacher, and D. Monnin, “Long-range three-dimensional active imaging with superresolution depth mapping,” Opt. Lett.  32, 3146–3148 (2007).
[CrossRef] [PubMed]

D. Monnin, A. L. Schneider, F. Christnacher, and Y. Lutz, “A 3D outdoor scene scanner based on a night-vision range-gated active imaging system,” in Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (IEEE, 2006) pp. 938–945.
[CrossRef]

Devitt, N.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng.  42, 738–746 (2003).
[CrossRef]

Driggers, R. G.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng.  42, 738–746 (2003).
[CrossRef]

Duff, C.

M. Hart, C. Duff, and S. Hinch, “Firmware measurement algorithms for the HP 83480 digital communications analyzer,” Hewlett-Packard J.  47, 13–21 (1996).

Elmquist, M.

Espinola, R. L.

Forand, J. L.

G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng.  32, 2185–2190 (1993).
[CrossRef]

Fouche, D. G.

Fournier, G. R.

G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng.  32, 2185–2190 (1993).
[CrossRef]

Galarneau, P.

D. Bonnier, S. Chatigny, Y. Lutz, B. Labranche, M. Levesque, and P. Galarneau, “Modelling of active TV system for surveillance operations,” Proc. SPIE.  3698, 217–228 (1999).
[CrossRef]

Goehler, B.

Hale, P. D.

Halford, C.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng.  42, 738–746 (2003).
[CrossRef]

Halford, C. E.

Hart, M.

M. Hart, C. Duff, and S. Hinch, “Firmware measurement algorithms for the HP 83480 digital communications analyzer,” Hewlett-Packard J.  47, 13–21 (1996).

Heinrich, R. M.

Heiselberg, H.

Hinch, S.

M. Hart, C. Duff, and S. Hinch, “Firmware measurement algorithms for the HP 83480 digital communications analyzer,” Hewlett-Packard J.  47, 13–21 (1996).

Holst, G. C.

G. C. Holst, Testing and Evaluation of Infrared Imaging Systems (JCD Publishing, 1993).

G. C. Holst, Electro-Optical Imaging System Performance (JCD, 1995).

Jacobs, E. L.

Jargon, J. A.

Kocher, D. G.

Kopeika, N. S.

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998).

Labranche, B.

D. Bonnier, S. Chatigny, Y. Lutz, B. Labranche, M. Levesque, and P. Galarneau, “Modelling of active TV system for surveillance operations,” Proc. SPIE.  3698, 217–228 (1999).
[CrossRef]

Laurenzis, M.

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3D range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE.  7298, 729833 (2009).
[CrossRef]

E. Belin, F. Christnacher, F. Taillade, and M. Laurenzis, “Display of an analytical model for backscattered luminance and a full-field range gated imaging system for vision in fog,” Proc. SPIE.  7088, 708800 (2008).
[CrossRef]

M. Laurenzis, F. Christnacher, and D. Monnin, “Long-range three-dimensional active imaging with superresolution depth mapping,” Opt. Lett.  32, 3146–3148 (2007).
[CrossRef] [PubMed]

Letalick, D.

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE.  3707, 432–448 (1999).
[CrossRef]

Levesque, M.

D. Bonnier, S. Chatigny, Y. Lutz, B. Labranche, M. Levesque, and P. Galarneau, “Modelling of active TV system for surveillance operations,” Proc. SPIE.  3698, 217–228 (1999).
[CrossRef]

Lutz, Y.

D. Bonnier, S. Chatigny, Y. Lutz, B. Labranche, M. Levesque, and P. Galarneau, “Modelling of active TV system for surveillance operations,” Proc. SPIE.  3698, 217–228 (1999).
[CrossRef]

D. Monnin, A. L. Schneider, F. Christnacher, and Y. Lutz, “A 3D outdoor scene scanner based on a night-vision range-gated active imaging system,” in Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (IEEE, 2006) pp. 938–945.
[CrossRef]

Lutzmann, P.

Metzger, N.

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3D range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE.  7298, 729833 (2009).
[CrossRef]

Monnin, D.

M. Laurenzis, F. Christnacher, and D. Monnin, “Long-range three-dimensional active imaging with superresolution depth mapping,” Opt. Lett.  32, 3146–3148 (2007).
[CrossRef] [PubMed]

D. Monnin, A. L. Schneider, F. Christnacher, and Y. Lutz, “A 3D outdoor scene scanner based on a night-vision range-gated active imaging system,” in Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (IEEE, 2006) pp. 938–945.
[CrossRef]

Mooney, J.

O’Brien, M. E.

Olsson, A.

H. M. Tulldahl, P. Andersson, A. Olsson, and A. Andersson, “Experimental evaluation of underwater range-gated viewing in natural waters,” Proc. SPIE.  6395, 639506 (2006).
[CrossRef]

Olsson, H.

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE.  3707, 432–448 (1999).
[CrossRef]

Pace, P. W.

G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng.  32, 2185–2190 (1993).
[CrossRef]

Player, B. E.

Repasi, E.

Schneider, A. L.

D. Monnin, A. L. Schneider, F. Christnacher, and Y. Lutz, “A 3D outdoor scene scanner based on a night-vision range-gated active imaging system,” in Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (IEEE, 2006) pp. 938–945.
[CrossRef]

Steinvall, O.

Taillade, F.

E. Belin, F. Christnacher, F. Taillade, and M. Laurenzis, “Display of an analytical model for backscattered luminance and a full-field range gated imaging system for vision in fog,” Proc. SPIE.  7088, 708800 (2008).
[CrossRef]

Tofsted, D. H.

Tulldahl, H. M.

H. M. Tulldahl, P. Andersson, A. Olsson, and A. Andersson, “Experimental evaluation of underwater range-gated viewing in natural waters,” Proc. SPIE.  6395, 639506 (2006).
[CrossRef]

Vollmerhausen, R.

Vollmerhausen, R. H.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng.  42, 738–746 (2003).
[CrossRef]

Wang, C. M.

Willard, B. C.

Zayhowski, J. J.

Zielenski, I.

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3D range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE.  7298, 729833 (2009).
[CrossRef]

Appl. Opt. (4)

Hewlett-Packard J. (1)

M. Hart, C. Duff, and S. Hinch, “Firmware measurement algorithms for the HP 83480 digital communications analyzer,” Hewlett-Packard J.  47, 13–21 (1996).

J. Lightwave Technol. (1)

Opt. Eng. (4)

J. Busck, “Underwater 3-D optical imaging with a gated viewing laser radar,” Opt. Eng.  44, 116001 (2005).
[CrossRef]

G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging-system,” Opt. Eng.  32, 2185–2190 (1993).
[CrossRef]

P. Andersson, “Long-range three dimensional imaging using range-gated laser radar images,” Opt. Eng.  45, 034301(2006).
[CrossRef]

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng.  42, 738–746 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE. (5)

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3D range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE.  7298, 729833 (2009).
[CrossRef]

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE.  3707, 432–448 (1999).
[CrossRef]

E. Belin, F. Christnacher, F. Taillade, and M. Laurenzis, “Display of an analytical model for backscattered luminance and a full-field range gated imaging system for vision in fog,” Proc. SPIE.  7088, 708800 (2008).
[CrossRef]

H. M. Tulldahl, P. Andersson, A. Olsson, and A. Andersson, “Experimental evaluation of underwater range-gated viewing in natural waters,” Proc. SPIE.  6395, 639506 (2006).
[CrossRef]

D. Bonnier, S. Chatigny, Y. Lutz, B. Labranche, M. Levesque, and P. Galarneau, “Modelling of active TV system for surveillance operations,” Proc. SPIE.  3698, 217–228 (1999).
[CrossRef]

Other (4)

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998).

G. C. Holst, Testing and Evaluation of Infrared Imaging Systems (JCD Publishing, 1993).

G. C. Holst, Electro-Optical Imaging System Performance (JCD, 1995).

D. Monnin, A. L. Schneider, F. Christnacher, and Y. Lutz, “A 3D outdoor scene scanner based on a night-vision range-gated active imaging system,” in Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (IEEE, 2006) pp. 938–945.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Lissajous figures for two sinusoidal signals S 1 and S 2 [see Eq. (1)] with various phase shifts δ and frequency ratio ω 1 : ω 2 .

Fig. 2
Fig. 2

Eye pattern (eye diagram) generated by random overlay of digital signals depicting fundamental parameters (i.e., “1”-level, “0”-level, crossing level, and crossing time) to determine the signal quality or performance metrics, respectively.

Fig. 3
Fig. 3

Simulation of three gated viewing tomography signatures depicted as (a) time delay transients and (b) Lissajous-type eye pattern.

Fig. 4
Fig. 4

Scheme for identification of different parameters for the calculation of the gap between the lower and the upper paths.

Fig. 5
Fig. 5

Tomography data derived with the ISL SyLVi gated viewing system in a distance range of 900–1200 m: (a) image of the overall mean intensity of the sequence and (b) time delay transients (mean and RMS error) through S 1 S 4 .

Fig. 6
Fig. 6

Eye pattern of ISL tomography data: S 1 against S 2 , S 3 , and S 4 . The optical path difference is indicated as Δ z = c ( τ S i τ S 1 ) 2 .

Equations (10)

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

S 1 ( t ) = A sin ( ω 1 t ) ,           S 2 ( t ) = B sin ( ω 2 t + δ ) .
S = 1 N n = 1 N S n ,
σ = 1 N 1 n = 1 N ( S n S ) 2 .
S GV P ( t 2 z c ) G ( t τ Delay ) d t .
C i = High ( S i ) + Low ( S i ) 2 .
W EP ( S 1 , S 2 ) = ( S 1 ( C 2 ) σ S 1 ( C 2 ) ) ( S 1 ( C 2 ) + σ S 1 ( C 2 ) ) ,
H EP ( S 1 , S 2 ) = ( S 2 ( C 1 ) σ S 2 ( C 1 ) ) ( S 2 ( C 1 ) + σ S 2 ( C 1 ) ) ,
d EP ( S 1 , S 2 ) = 1 2 ( ( S 1 ( C 2 ) S 1 ( C 2 ) ) 2 + ( S 2 ( C 1 ) S 2 ( C 1 ) ) 2 ) 1 / 2 ,
σ d = σ S i ( C j ) 2 .
Q   factor : Q EP = d EP σ d .

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