Abstract

Streak tube imaging lidar (STIL) is an active imaging system using a pulsed laser transmitter and a streak tube receiver to produce 3D range and intensity imagery. The STIL has recently attracted a great deal of interest and attention due to its advantages of wide azimuth field-of-view, high range and angle resolution, and high frame rate. This work investigates the signal-to-noise performance of STIL systems. A theoretical model for characterizing the signal-to-noise performance of the STIL system with an internal or external intensified streak tube receiver is presented, based on the linear cascaded systems theory of signal and noise propagation. The STIL system is decomposed into a series of cascaded imaging chains whose signal and noise transfer properties are described by the general (or the spatial-frequency dependent) noise factors (NFs). Expressions for the general NFs of the cascaded chains (or the main components) in the STIL system are derived. The work presented here is useful for the design and evaluation of STIL systems.

© 2012 Optical Society of America

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2010 (1)

J. Wei, Q. Wang, J. Sun, and J. Gao, “High-resolution imaging of a long-distance target with a single-slit streak-tube lidar,” J. Russ. Laser Res. 31, 307–312 (2010).
[CrossRef]

2009 (3)

J. Liu, Q. Wang, S. Li, Y. Cheng, and J. Wei, “Research on a flash imaging lidar based on a multiple-streak tube,” Laser Phys. 19, 115–120 (2009).
[CrossRef]

J. Sun and Q. Wang, “4-D image reconstruction for streak tube imaging lidar,” Laser Phys. 19, 502–504 (2009).
[CrossRef]

Q. Wang, J. Liu, and S. Li, “Analysis of detectable range of multiple-slit streak tube imaging lidar,” J. Russ. Laser Res. 30, 296–303 (2009).
[CrossRef]

2007 (2)

S. Li, Q. Wang, J. Lin, and Y. Guang, “Research of range resolution of streak tube imaging system,” Proc. SPIE 6279, 62790C (2007).
[CrossRef]

Y. Cheng, S. Xiang, and H. Shi, “Theoretical model for resolution calculation of third generation image intensifiers,” J. Appl. Opt. 28, 578–581 (2007) (in Chinese).

2005 (1)

V. B. Lebedev, G. G. Feldman, O. V. Aleksander, A. A. Nazaryan, A. A. Tsovyan, Y. A. Yedigaryan, and S. S. Melikyan, “Application of K008 camera within lidar for laser sounding of water width from air,” Proc. SPIE 5580, 282–292 (2005).
[CrossRef]

2004 (1)

D. Dussault and P. Hoess, “Noise performance comparison of ICCD with CCD and EMCCD cameras,” Proc. SPIE 5563, 195–204 (2004).
[CrossRef]

2003 (1)

R. T. Eagleton and S. F. James, “Dynamic range measurements on streak imaging tubes with internal and external microchannel plate image amplification,” Rev. Sci. Instrum. 74, 2215–2219 (2003).
[CrossRef]

2002 (1)

A. Gelbart, B. C. Redman, R. S. Light, C. A. Schwartzlow, and A. J. Griffis, “Flash lidar based on multiple-slit streak tube imaging lidar,” Proc. SPIE 4723, 9–18 (2002).
[CrossRef]

2001 (2)

A. D. Gleckler, A. Gelbart, and J. M. Bowden, “Multispectral and hyperspectral 3D imaging lidar based upon the multiple slit streak tube imaging lidar,” Proc. SPIE 4377, 328–335 (2001).
[CrossRef]

A. D. Gleckler and A. Gelbart, “Three-dimensional imaging polarimetry,” Proc. SPIE 4377, 175–185 (2001).
[CrossRef]

2000 (1)

A. D. Gleckler, “Multiple-slit streak tube imaging lidar (MS-STIL) applications,” Proc. SPIE 4035, 266–278 (2000).
[CrossRef]

1999 (5)

J. W. McLean, “High resolution 3-D underwater imaging,” Proc. SPIE 3761, 10–19 (1999).
[CrossRef]

M. J. DeWeert, S. E. Moran, B. L. Ulich, and R. N. Keeler, “Numerical simulations of the relative performance of streak-tube, range-gated, and PMT-based airborne imaging lidar systems with realistic sea surfaces,” Proc. SPIE 3761, 115–129 (1999).
[CrossRef]

I. A. Cunningham and R. Shaw, “Signal-to-noise optimization of medical imaging systems,” J. Opt. Soc. Am. 16, 621–632 (1999).
[CrossRef]

M. B. Williams, P. U. Simoni, L. Smilowitz, M. Stanton, W. Phillips, and A. Stewart, “Analysis of the detective quantum efficiency of a developmental detector for digital mammography,” Med. Phys. 26, 2273–2285 (1999).
[CrossRef]

G. Zanell and R. Zannoni, “DQE of imaging detectors in terms of spatial frequency,” Nucl. Instrum. Methods 437, 163–167 (1999).
[CrossRef]

1997 (6)

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

S. Hejazi and D. P. Trauernicht, “System considerations in CCD-based x-ray imaging for digital chest radiography and digital mammography,” Med. Phys. 24, 287–297 (1997).
[CrossRef]

J. P. Bissonette, I. A. Cunningham, D. A. Jaffray, A. Fenster, and P. Munro, “A quantum accounting and detective quantum efficiency analysis for video-based portal imaging,” Med. Phys. 24, 815–826 (1997).
[CrossRef]

J. H. Siewerdsen, L. E. Antonuk, Y. El-Mohri, J. Yorkston, W. Huang, J. M. Boudry, and I. A. Cunningham, “Empirical and theoretical investigation of the noise performance of indirect detection, active matrix flat-panel imagers (AMFPIs) for diagnostic radiology,” Med. Phys. 24, 71–89 (1997).
[CrossRef]

W. Zhao and J. A. Rowlands, “Digital radiology using active matrix readout of amorphous selenium: theoretical analysis of detective quantum efficiency,” Med. Phys. 24, 1819–1833 (1997).
[CrossRef]

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

1996 (2)

A. D. A. Maidment and M. J. Yaffe, “Analysis of signal propagation in optically coupled detectors for digital mammography: II. Lens and fiber optics,” Phys. Med. Biol. 41, 475–493 (1996).
[CrossRef]

H. Liu, L. L. Fajardo, and B. C. Penny, “Signal-to-noise ratio and detective quantum efficiency analysis of optically coupled CCD mammography imaging systems,” Acad. Radiol. 3, 799–805 (1996).
[CrossRef]

1994 (1)

I. A. Cunningham, M. S. Westmore, and A. Fenster, “A spatial-frequency dependent quantum accounting diagram and detective quantum efficiency model of signal and noise propagation in cascaded imaging systems,” Med. Phys. 21, 417–427 (1994).
[CrossRef]

1990 (1)

A. Whiteson, “Streak tube modulation transfer functions,” Proc. SPIE 1155, 344–355 (1990).
[CrossRef]

1989 (1)

1987 (2)

1981 (1)

E. H. Eberhardt, “An operational model for microchannel plate devices,” IEEE Trans. Nucl. Sci. 28, 712–717(1981).
[CrossRef]

1980 (1)

1979 (1)

Abshire, J. B.

Aleksander, O. V.

V. B. Lebedev, G. G. Feldman, O. V. Aleksander, A. A. Nazaryan, A. A. Tsovyan, Y. A. Yedigaryan, and S. S. Melikyan, “Application of K008 camera within lidar for laser sounding of water width from air,” Proc. SPIE 5580, 282–292 (2005).
[CrossRef]

Antonuk, L. E.

J. H. Siewerdsen, L. E. Antonuk, Y. El-Mohri, J. Yorkston, W. Huang, J. M. Boudry, and I. A. Cunningham, “Empirical and theoretical investigation of the noise performance of indirect detection, active matrix flat-panel imagers (AMFPIs) for diagnostic radiology,” Med. Phys. 24, 71–89 (1997).
[CrossRef]

Bebris, J.

Bissonette, J. P.

J. P. Bissonette, I. A. Cunningham, D. A. Jaffray, A. Fenster, and P. Munro, “A quantum accounting and detective quantum efficiency analysis for video-based portal imaging,” Med. Phys. 24, 815–826 (1997).
[CrossRef]

Boreman, G. D.

G. D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE, 2001), Chap. 1.

Boudry, J. M.

J. H. Siewerdsen, L. E. Antonuk, Y. El-Mohri, J. Yorkston, W. Huang, J. M. Boudry, and I. A. Cunningham, “Empirical and theoretical investigation of the noise performance of indirect detection, active matrix flat-panel imagers (AMFPIs) for diagnostic radiology,” Med. Phys. 24, 71–89 (1997).
[CrossRef]

Bowden, J. M.

A. D. Gleckler, A. Gelbart, and J. M. Bowden, “Multispectral and hyperspectral 3D imaging lidar based upon the multiple slit streak tube imaging lidar,” Proc. SPIE 4377, 328–335 (2001).
[CrossRef]

Bunch, P. C.

Chen, C.

L. Wu, X. Wang, H. Yang, B. Yu, C. Chen, B. Yang, L. Yuan, L. Wu, Z. Xue, G. Li, and B. Wu, “Signal-to-noise performance analysis of streak tube imaging lidar systems. II. Theoretical analysis and discussion,” Appl. Opt.51, 8836–8847 (2012).

Cheng, Y.

J. Liu, Q. Wang, S. Li, Y. Cheng, and J. Wei, “Research on a flash imaging lidar based on a multiple-streak tube,” Laser Phys. 19, 115–120 (2009).
[CrossRef]

Y. Cheng, S. Xiang, and H. Shi, “Theoretical model for resolution calculation of third generation image intensifiers,” J. Appl. Opt. 28, 578–581 (2007) (in Chinese).

Cunningham, I. A.

I. A. Cunningham and R. Shaw, “Signal-to-noise optimization of medical imaging systems,” J. Opt. Soc. Am. 16, 621–632 (1999).
[CrossRef]

J. P. Bissonette, I. A. Cunningham, D. A. Jaffray, A. Fenster, and P. Munro, “A quantum accounting and detective quantum efficiency analysis for video-based portal imaging,” Med. Phys. 24, 815–826 (1997).
[CrossRef]

J. H. Siewerdsen, L. E. Antonuk, Y. El-Mohri, J. Yorkston, W. Huang, J. M. Boudry, and I. A. Cunningham, “Empirical and theoretical investigation of the noise performance of indirect detection, active matrix flat-panel imagers (AMFPIs) for diagnostic radiology,” Med. Phys. 24, 71–89 (1997).
[CrossRef]

I. A. Cunningham, M. S. Westmore, and A. Fenster, “A spatial-frequency dependent quantum accounting diagram and detective quantum efficiency model of signal and noise propagation in cascaded imaging systems,” Med. Phys. 21, 417–427 (1994).
[CrossRef]

I. A. Cunningham, “Applied linear-systems theory,” in Handbook of Medical Imaging, J. Beutel, H. L. Kundel, and R. L. Van Metter, eds. Vol. 1: Physics and Psychophysics (SPIE, Bellingham, 2010), Chap. 2.

DeWeert, M. J.

M. J. DeWeert, S. E. Moran, B. L. Ulich, and R. N. Keeler, “Numerical simulations of the relative performance of streak-tube, range-gated, and PMT-based airborne imaging lidar systems with realistic sea surfaces,” Proc. SPIE 3761, 115–129 (1999).
[CrossRef]

Dussault, D.

D. Dussault and P. Hoess, “Noise performance comparison of ICCD with CCD and EMCCD cameras,” Proc. SPIE 5563, 195–204 (2004).
[CrossRef]

Eagleton, R. T.

R. T. Eagleton and S. F. James, “Dynamic range measurements on streak imaging tubes with internal and external microchannel plate image amplification,” Rev. Sci. Instrum. 74, 2215–2219 (2003).
[CrossRef]

Eberhardt, E. H.

E. H. Eberhardt, “An operational model for microchannel plate devices,” IEEE Trans. Nucl. Sci. 28, 712–717(1981).
[CrossRef]

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

Elkins, W. P.

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

El-Mohri, Y.

J. H. Siewerdsen, L. E. Antonuk, Y. El-Mohri, J. Yorkston, W. Huang, J. M. Boudry, and I. A. Cunningham, “Empirical and theoretical investigation of the noise performance of indirect detection, active matrix flat-panel imagers (AMFPIs) for diagnostic radiology,” Med. Phys. 24, 71–89 (1997).
[CrossRef]

Fajardo, L. L.

H. Liu, L. L. Fajardo, and B. C. Penny, “Signal-to-noise ratio and detective quantum efficiency analysis of optically coupled CCD mammography imaging systems,” Acad. Radiol. 3, 799–805 (1996).
[CrossRef]

Feldman, G. G.

V. B. Lebedev, G. G. Feldman, O. V. Aleksander, A. A. Nazaryan, A. A. Tsovyan, Y. A. Yedigaryan, and S. S. Melikyan, “Application of K008 camera within lidar for laser sounding of water width from air,” Proc. SPIE 5580, 282–292 (2005).
[CrossRef]

Fenster, A.

J. P. Bissonette, I. A. Cunningham, D. A. Jaffray, A. Fenster, and P. Munro, “A quantum accounting and detective quantum efficiency analysis for video-based portal imaging,” Med. Phys. 24, 815–826 (1997).
[CrossRef]

I. A. Cunningham, M. S. Westmore, and A. Fenster, “A spatial-frequency dependent quantum accounting diagram and detective quantum efficiency model of signal and noise propagation in cascaded imaging systems,” Med. Phys. 21, 417–427 (1994).
[CrossRef]

Frenkel, A.

Gao, J.

J. Wei, Q. Wang, J. Sun, and J. Gao, “High-resolution imaging of a long-distance target with a single-slit streak-tube lidar,” J. Russ. Laser Res. 31, 307–312 (2010).
[CrossRef]

Gelbart, A.

A. Gelbart, B. C. Redman, R. S. Light, C. A. Schwartzlow, and A. J. Griffis, “Flash lidar based on multiple-slit streak tube imaging lidar,” Proc. SPIE 4723, 9–18 (2002).
[CrossRef]

A. D. Gleckler, A. Gelbart, and J. M. Bowden, “Multispectral and hyperspectral 3D imaging lidar based upon the multiple slit streak tube imaging lidar,” Proc. SPIE 4377, 328–335 (2001).
[CrossRef]

A. D. Gleckler and A. Gelbart, “Three-dimensional imaging polarimetry,” Proc. SPIE 4377, 175–185 (2001).
[CrossRef]

Gleckler, A. D.

A. D. Gleckler and A. Gelbart, “Three-dimensional imaging polarimetry,” Proc. SPIE 4377, 175–185 (2001).
[CrossRef]

A. D. Gleckler, A. Gelbart, and J. M. Bowden, “Multispectral and hyperspectral 3D imaging lidar based upon the multiple slit streak tube imaging lidar,” Proc. SPIE 4377, 328–335 (2001).
[CrossRef]

A. D. Gleckler, “Multiple-slit streak tube imaging lidar (MS-STIL) applications,” Proc. SPIE 4035, 266–278 (2000).
[CrossRef]

Griffis, A. J.

A. Gelbart, B. C. Redman, R. S. Light, C. A. Schwartzlow, and A. J. Griffis, “Flash lidar based on multiple-slit streak tube imaging lidar,” Proc. SPIE 4723, 9–18 (2002).
[CrossRef]

B. C. Redman, A. J. Griffis, and E. B. Schibley, “Streak tube imaging lidar (STIL) for 3-D imaging of terrestrial targets,” Tech. Report (Arête Associates, Tucson, Ariz., 2000).

Guang, Y.

S. Li, Q. Wang, J. Lin, and Y. Guang, “Research of range resolution of streak tube imaging system,” Proc. SPIE 6279, 62790C (2007).
[CrossRef]

Hejazi, S.

S. Hejazi and D. P. Trauernicht, “System considerations in CCD-based x-ray imaging for digital chest radiography and digital mammography,” Med. Phys. 24, 287–297 (1997).
[CrossRef]

Hoess, P.

D. Dussault and P. Hoess, “Noise performance comparison of ICCD with CCD and EMCCD cameras,” Proc. SPIE 5563, 195–204 (2004).
[CrossRef]

Huang, W.

J. H. Siewerdsen, L. E. Antonuk, Y. El-Mohri, J. Yorkston, W. Huang, J. M. Boudry, and I. A. Cunningham, “Empirical and theoretical investigation of the noise performance of indirect detection, active matrix flat-panel imagers (AMFPIs) for diagnostic radiology,” Med. Phys. 24, 71–89 (1997).
[CrossRef]

Huff, K. E.

Hunkler, L. T.

C. B. Johnson, L. T. Hunkler, S. A. Letzring, and P. Jaanimagi, Streak tube camera receiver definition studies, Tech. Report (ITT Electro-Optical Products Div, 1990).

Ientilucci, E. J.

E. J. Ientilucci, “Synthetic simulation and modeling of image intensified CCDs (IICCD),” MS. thesis, Rochester Institute of Technology, 2000.

Jaanimagi, P.

C. B. Johnson, L. T. Hunkler, S. A. Letzring, and P. Jaanimagi, Streak tube camera receiver definition studies, Tech. Report (ITT Electro-Optical Products Div, 1990).

Jaffray, D. A.

J. P. Bissonette, I. A. Cunningham, D. A. Jaffray, A. Fenster, and P. Munro, “A quantum accounting and detective quantum efficiency analysis for video-based portal imaging,” Med. Phys. 24, 815–826 (1997).
[CrossRef]

James, S. F.

R. T. Eagleton and S. F. James, “Dynamic range measurements on streak imaging tubes with internal and external microchannel plate image amplification,” Rev. Sci. Instrum. 74, 2215–2219 (2003).
[CrossRef]

Johnson, C. B.

C. B. Johnson, S. Nevin, J. Bebris, and J. B. Abshire, “Circular-scan streak tube with solid-state readout,” Appl. Opt. 19, 3491–3495 (1980).
[CrossRef]

C. B. Johnson and L. D. Owen, “Image tube intensified electronic imaging,” in Handbook of Optics, 3rd ed. Vol. II. Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill Companies, 2010), Chap. 31.

C. B. Johnson, L. T. Hunkler, S. A. Letzring, and P. Jaanimagi, Streak tube camera receiver definition studies, Tech. Report (ITT Electro-Optical Products Div, 1990).

Keeler, R. N.

M. J. DeWeert, S. E. Moran, B. L. Ulich, and R. N. Keeler, “Numerical simulations of the relative performance of streak-tube, range-gated, and PMT-based airborne imaging lidar systems with realistic sea surfaces,” Proc. SPIE 3761, 115–129 (1999).
[CrossRef]

Lebedev, V. B.

V. B. Lebedev, G. G. Feldman, O. V. Aleksander, A. A. Nazaryan, A. A. Tsovyan, Y. A. Yedigaryan, and S. S. Melikyan, “Application of K008 camera within lidar for laser sounding of water width from air,” Proc. SPIE 5580, 282–292 (2005).
[CrossRef]

Letzring, S. A.

C. B. Johnson, L. T. Hunkler, S. A. Letzring, and P. Jaanimagi, Streak tube camera receiver definition studies, Tech. Report (ITT Electro-Optical Products Div, 1990).

Li, G.

L. Wu, X. Wang, H. Yang, B. Yu, C. Chen, B. Yang, L. Yuan, L. Wu, Z. Xue, G. Li, and B. Wu, “Signal-to-noise performance analysis of streak tube imaging lidar systems. II. Theoretical analysis and discussion,” Appl. Opt.51, 8836–8847 (2012).

Li, S.

Q. Wang, J. Liu, and S. Li, “Analysis of detectable range of multiple-slit streak tube imaging lidar,” J. Russ. Laser Res. 30, 296–303 (2009).
[CrossRef]

J. Liu, Q. Wang, S. Li, Y. Cheng, and J. Wei, “Research on a flash imaging lidar based on a multiple-streak tube,” Laser Phys. 19, 115–120 (2009).
[CrossRef]

S. Li, Q. Wang, J. Lin, and Y. Guang, “Research of range resolution of streak tube imaging system,” Proc. SPIE 6279, 62790C (2007).
[CrossRef]

Light, R. S.

A. Gelbart, B. C. Redman, R. S. Light, C. A. Schwartzlow, and A. J. Griffis, “Flash lidar based on multiple-slit streak tube imaging lidar,” Proc. SPIE 4723, 9–18 (2002).
[CrossRef]

Lin, J.

S. Li, Q. Wang, J. Lin, and Y. Guang, “Research of range resolution of streak tube imaging system,” Proc. SPIE 6279, 62790C (2007).
[CrossRef]

Liu, H.

H. Liu, L. L. Fajardo, and B. C. Penny, “Signal-to-noise ratio and detective quantum efficiency analysis of optically coupled CCD mammography imaging systems,” Acad. Radiol. 3, 799–805 (1996).
[CrossRef]

Liu, J.

J. Liu, Q. Wang, S. Li, Y. Cheng, and J. Wei, “Research on a flash imaging lidar based on a multiple-streak tube,” Laser Phys. 19, 115–120 (2009).
[CrossRef]

Q. Wang, J. Liu, and S. Li, “Analysis of detectable range of multiple-slit streak tube imaging lidar,” J. Russ. Laser Res. 30, 296–303 (2009).
[CrossRef]

J. Sun, J. Liu, and Q. Wang, “A multiple-slit streak tube imaging lidar and its detection ability analysis by flash lidar equation,” Optik (to be published).
[CrossRef]

Maidment, A. D. A.

A. D. A. Maidment and M. J. Yaffe, “Analysis of signal propagation in optically coupled detectors for digital mammography: II. Lens and fiber optics,” Phys. Med. Biol. 41, 475–493 (1996).
[CrossRef]

McLean, J. W.

J. W. McLean, “High resolution 3-D underwater imaging,” Proc. SPIE 3761, 10–19 (1999).
[CrossRef]

Melikyan, S. S.

V. B. Lebedev, G. G. Feldman, O. V. Aleksander, A. A. Nazaryan, A. A. Tsovyan, Y. A. Yedigaryan, and S. S. Melikyan, “Application of K008 camera within lidar for laser sounding of water width from air,” Proc. SPIE 5580, 282–292 (2005).
[CrossRef]

Moran, S. E.

M. J. DeWeert, S. E. Moran, B. L. Ulich, and R. N. Keeler, “Numerical simulations of the relative performance of streak-tube, range-gated, and PMT-based airborne imaging lidar systems with realistic sea surfaces,” Proc. SPIE 3761, 115–129 (1999).
[CrossRef]

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

Munro, P.

J. P. Bissonette, I. A. Cunningham, D. A. Jaffray, A. Fenster, and P. Munro, “A quantum accounting and detective quantum efficiency analysis for video-based portal imaging,” Med. Phys. 24, 815–826 (1997).
[CrossRef]

Nazaryan, A. A.

V. B. Lebedev, G. G. Feldman, O. V. Aleksander, A. A. Nazaryan, A. A. Tsovyan, Y. A. Yedigaryan, and S. S. Melikyan, “Application of K008 camera within lidar for laser sounding of water width from air,” Proc. SPIE 5580, 282–292 (2005).
[CrossRef]

Nevin, S.

Ni, G.

S. Xiang and G. Ni, The Principle of Photoelectronic Imaging Devices (National Defence Industry, Beijing, 1999).

Owen, L. D.

C. B. Johnson and L. D. Owen, “Image tube intensified electronic imaging,” in Handbook of Optics, 3rd ed. Vol. II. Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill Companies, 2010), Chap. 31.

Penny, B. C.

H. Liu, L. L. Fajardo, and B. C. Penny, “Signal-to-noise ratio and detective quantum efficiency analysis of optically coupled CCD mammography imaging systems,” Acad. Radiol. 3, 799–805 (1996).
[CrossRef]

Phillips, W.

M. B. Williams, P. U. Simoni, L. Smilowitz, M. Stanton, W. Phillips, and A. Stewart, “Analysis of the detective quantum efficiency of a developmental detector for digital mammography,” Med. Phys. 26, 2273–2285 (1999).
[CrossRef]

Rabbani, M.

Redman, B. C.

A. Gelbart, B. C. Redman, R. S. Light, C. A. Schwartzlow, and A. J. Griffis, “Flash lidar based on multiple-slit streak tube imaging lidar,” Proc. SPIE 4723, 9–18 (2002).
[CrossRef]

B. C. Redman, A. J. Griffis, and E. B. Schibley, “Streak tube imaging lidar (STIL) for 3-D imaging of terrestrial targets,” Tech. Report (Arête Associates, Tucson, Ariz., 2000).

Rowlands, J. A.

W. Zhao and J. A. Rowlands, “Digital radiology using active matrix readout of amorphous selenium: theoretical analysis of detective quantum efficiency,” Med. Phys. 24, 1819–1833 (1997).
[CrossRef]

Sartor, M. A.

Schibley, E. B.

B. C. Redman, A. J. Griffis, and E. B. Schibley, “Streak tube imaging lidar (STIL) for 3-D imaging of terrestrial targets,” Tech. Report (Arête Associates, Tucson, Ariz., 2000).

Schwartzlow, C. A.

A. Gelbart, B. C. Redman, R. S. Light, C. A. Schwartzlow, and A. J. Griffis, “Flash lidar based on multiple-slit streak tube imaging lidar,” Proc. SPIE 4723, 9–18 (2002).
[CrossRef]

Shaw, R.

I. A. Cunningham and R. Shaw, “Signal-to-noise optimization of medical imaging systems,” J. Opt. Soc. Am. 16, 621–632 (1999).
[CrossRef]

M. Rabbani and R. Shaw, “Analysis of signal and noise propagation for several imaging mechanisms,” J. Opt. Soc. Am. A 6, 1156–1164 (1989).
[CrossRef]

Shaw, R. L.

Shi, H.

Y. Cheng, S. Xiang, and H. Shi, “Theoretical model for resolution calculation of third generation image intensifiers,” J. Appl. Opt. 28, 578–581 (2007) (in Chinese).

Siewerdsen, J. H.

J. H. Siewerdsen, L. E. Antonuk, Y. El-Mohri, J. Yorkston, W. Huang, J. M. Boudry, and I. A. Cunningham, “Empirical and theoretical investigation of the noise performance of indirect detection, active matrix flat-panel imagers (AMFPIs) for diagnostic radiology,” Med. Phys. 24, 71–89 (1997).
[CrossRef]

Simoni, P. U.

M. B. Williams, P. U. Simoni, L. Smilowitz, M. Stanton, W. Phillips, and A. Stewart, “Analysis of the detective quantum efficiency of a developmental detector for digital mammography,” Med. Phys. 26, 2273–2285 (1999).
[CrossRef]

Smilowitz, L.

M. B. Williams, P. U. Simoni, L. Smilowitz, M. Stanton, W. Phillips, and A. Stewart, “Analysis of the detective quantum efficiency of a developmental detector for digital mammography,” Med. Phys. 26, 2273–2285 (1999).
[CrossRef]

Stanton, M.

M. B. Williams, P. U. Simoni, L. Smilowitz, M. Stanton, W. Phillips, and A. Stewart, “Analysis of the detective quantum efficiency of a developmental detector for digital mammography,” Med. Phys. 26, 2273–2285 (1999).
[CrossRef]

Stewart, A.

M. B. Williams, P. U. Simoni, L. Smilowitz, M. Stanton, W. Phillips, and A. Stewart, “Analysis of the detective quantum efficiency of a developmental detector for digital mammography,” Med. Phys. 26, 2273–2285 (1999).
[CrossRef]

Sun, J.

J. Wei, Q. Wang, J. Sun, and J. Gao, “High-resolution imaging of a long-distance target with a single-slit streak-tube lidar,” J. Russ. Laser Res. 31, 307–312 (2010).
[CrossRef]

J. Sun and Q. Wang, “4-D image reconstruction for streak tube imaging lidar,” Laser Phys. 19, 502–504 (2009).
[CrossRef]

J. Sun, J. Liu, and Q. Wang, “A multiple-slit streak tube imaging lidar and its detection ability analysis by flash lidar equation,” Optik (to be published).
[CrossRef]

Trauernicht, D. P.

S. Hejazi and D. P. Trauernicht, “System considerations in CCD-based x-ray imaging for digital chest radiography and digital mammography,” Med. Phys. 24, 287–297 (1997).
[CrossRef]

Tsovyan, A. A.

V. B. Lebedev, G. G. Feldman, O. V. Aleksander, A. A. Nazaryan, A. A. Tsovyan, Y. A. Yedigaryan, and S. S. Melikyan, “Application of K008 camera within lidar for laser sounding of water width from air,” Proc. SPIE 5580, 282–292 (2005).
[CrossRef]

Ulich, B. L.

M. J. DeWeert, S. E. Moran, B. L. Ulich, and R. N. Keeler, “Numerical simulations of the relative performance of streak-tube, range-gated, and PMT-based airborne imaging lidar systems with realistic sea surfaces,” Proc. SPIE 3761, 115–129 (1999).
[CrossRef]

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

Van Metter, R.

Van Metter, R. L.

Vedantham, S.

S. Vedantham, “Design and characterization of a high-resolution cardiovascular imager,” Ph.D. thesis, Worcester Polytechnic Institute, 2002.

Wang, Q.

J. Wei, Q. Wang, J. Sun, and J. Gao, “High-resolution imaging of a long-distance target with a single-slit streak-tube lidar,” J. Russ. Laser Res. 31, 307–312 (2010).
[CrossRef]

J. Liu, Q. Wang, S. Li, Y. Cheng, and J. Wei, “Research on a flash imaging lidar based on a multiple-streak tube,” Laser Phys. 19, 115–120 (2009).
[CrossRef]

J. Sun and Q. Wang, “4-D image reconstruction for streak tube imaging lidar,” Laser Phys. 19, 502–504 (2009).
[CrossRef]

Q. Wang, J. Liu, and S. Li, “Analysis of detectable range of multiple-slit streak tube imaging lidar,” J. Russ. Laser Res. 30, 296–303 (2009).
[CrossRef]

S. Li, Q. Wang, J. Lin, and Y. Guang, “Research of range resolution of streak tube imaging system,” Proc. SPIE 6279, 62790C (2007).
[CrossRef]

J. Sun, J. Liu, and Q. Wang, “A multiple-slit streak tube imaging lidar and its detection ability analysis by flash lidar equation,” Optik (to be published).
[CrossRef]

Wang, X.

L. Wu, X. Wang, H. Yang, B. Yu, C. Chen, B. Yang, L. Yuan, L. Wu, Z. Xue, G. Li, and B. Wu, “Signal-to-noise performance analysis of streak tube imaging lidar systems. II. Theoretical analysis and discussion,” Appl. Opt.51, 8836–8847 (2012).

Wei, J.

J. Wei, Q. Wang, J. Sun, and J. Gao, “High-resolution imaging of a long-distance target with a single-slit streak-tube lidar,” J. Russ. Laser Res. 31, 307–312 (2010).
[CrossRef]

J. Liu, Q. Wang, S. Li, Y. Cheng, and J. Wei, “Research on a flash imaging lidar based on a multiple-streak tube,” Laser Phys. 19, 115–120 (2009).
[CrossRef]

Westmore, M. S.

I. A. Cunningham, M. S. Westmore, and A. Fenster, “A spatial-frequency dependent quantum accounting diagram and detective quantum efficiency model of signal and noise propagation in cascaded imaging systems,” Med. Phys. 21, 417–427 (1994).
[CrossRef]

Whiteson, A.

A. Whiteson, “Streak tube modulation transfer functions,” Proc. SPIE 1155, 344–355 (1990).
[CrossRef]

Williams, M. B.

M. B. Williams, P. U. Simoni, L. Smilowitz, M. Stanton, W. Phillips, and A. Stewart, “Analysis of the detective quantum efficiency of a developmental detector for digital mammography,” Med. Phys. 26, 2273–2285 (1999).
[CrossRef]

Wlodawski, M. S.

Wu, B.

L. Wu, X. Wang, H. Yang, B. Yu, C. Chen, B. Yang, L. Yuan, L. Wu, Z. Xue, G. Li, and B. Wu, “Signal-to-noise performance analysis of streak tube imaging lidar systems. II. Theoretical analysis and discussion,” Appl. Opt.51, 8836–8847 (2012).

Wu, L.

L. Wu, X. Wang, H. Yang, B. Yu, C. Chen, B. Yang, L. Yuan, L. Wu, Z. Xue, G. Li, and B. Wu, “Signal-to-noise performance analysis of streak tube imaging lidar systems. II. Theoretical analysis and discussion,” Appl. Opt.51, 8836–8847 (2012).

L. Wu, X. Wang, H. Yang, B. Yu, C. Chen, B. Yang, L. Yuan, L. Wu, Z. Xue, G. Li, and B. Wu, “Signal-to-noise performance analysis of streak tube imaging lidar systems. II. Theoretical analysis and discussion,” Appl. Opt.51, 8836–8847 (2012).

Xiang, S.

Y. Cheng, S. Xiang, and H. Shi, “Theoretical model for resolution calculation of third generation image intensifiers,” J. Appl. Opt. 28, 578–581 (2007) (in Chinese).

S. Xiang and G. Ni, The Principle of Photoelectronic Imaging Devices (National Defence Industry, Beijing, 1999).

Xue, Z.

L. Wu, X. Wang, H. Yang, B. Yu, C. Chen, B. Yang, L. Yuan, L. Wu, Z. Xue, G. Li, and B. Wu, “Signal-to-noise performance analysis of streak tube imaging lidar systems. II. Theoretical analysis and discussion,” Appl. Opt.51, 8836–8847 (2012).

Yaffe, M. J.

A. D. A. Maidment and M. J. Yaffe, “Analysis of signal propagation in optically coupled detectors for digital mammography: II. Lens and fiber optics,” Phys. Med. Biol. 41, 475–493 (1996).
[CrossRef]

Yang, B.

L. Wu, X. Wang, H. Yang, B. Yu, C. Chen, B. Yang, L. Yuan, L. Wu, Z. Xue, G. Li, and B. Wu, “Signal-to-noise performance analysis of streak tube imaging lidar systems. II. Theoretical analysis and discussion,” Appl. Opt.51, 8836–8847 (2012).

Yang, H.

L. Wu, X. Wang, H. Yang, B. Yu, C. Chen, B. Yang, L. Yuan, L. Wu, Z. Xue, G. Li, and B. Wu, “Signal-to-noise performance analysis of streak tube imaging lidar systems. II. Theoretical analysis and discussion,” Appl. Opt.51, 8836–8847 (2012).

Yedigaryan, Y. A.

V. B. Lebedev, G. G. Feldman, O. V. Aleksander, A. A. Nazaryan, A. A. Tsovyan, Y. A. Yedigaryan, and S. S. Melikyan, “Application of K008 camera within lidar for laser sounding of water width from air,” Proc. SPIE 5580, 282–292 (2005).
[CrossRef]

Yorkston, J.

J. H. Siewerdsen, L. E. Antonuk, Y. El-Mohri, J. Yorkston, W. Huang, J. M. Boudry, and I. A. Cunningham, “Empirical and theoretical investigation of the noise performance of indirect detection, active matrix flat-panel imagers (AMFPIs) for diagnostic radiology,” Med. Phys. 24, 71–89 (1997).
[CrossRef]

Yu, B.

L. Wu, X. Wang, H. Yang, B. Yu, C. Chen, B. Yang, L. Yuan, L. Wu, Z. Xue, G. Li, and B. Wu, “Signal-to-noise performance analysis of streak tube imaging lidar systems. II. Theoretical analysis and discussion,” Appl. Opt.51, 8836–8847 (2012).

Yuan, L.

L. Wu, X. Wang, H. Yang, B. Yu, C. Chen, B. Yang, L. Yuan, L. Wu, Z. Xue, G. Li, and B. Wu, “Signal-to-noise performance analysis of streak tube imaging lidar systems. II. Theoretical analysis and discussion,” Appl. Opt.51, 8836–8847 (2012).

Zanell, G.

G. Zanell and R. Zannoni, “DQE of imaging detectors in terms of spatial frequency,” Nucl. Instrum. Methods 437, 163–167 (1999).
[CrossRef]

Zannoni, R.

G. Zanell and R. Zannoni, “DQE of imaging detectors in terms of spatial frequency,” Nucl. Instrum. Methods 437, 163–167 (1999).
[CrossRef]

Zhao, W.

W. Zhao and J. A. Rowlands, “Digital radiology using active matrix readout of amorphous selenium: theoretical analysis of detective quantum efficiency,” Med. Phys. 24, 1819–1833 (1997).
[CrossRef]

Acad. Radiol. (1)

H. Liu, L. L. Fajardo, and B. C. Penny, “Signal-to-noise ratio and detective quantum efficiency analysis of optically coupled CCD mammography imaging systems,” Acad. Radiol. 3, 799–805 (1996).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Nucl. Sci. (1)

E. H. Eberhardt, “An operational model for microchannel plate devices,” IEEE Trans. Nucl. Sci. 28, 712–717(1981).
[CrossRef]

J. Appl. Opt. (1)

Y. Cheng, S. Xiang, and H. Shi, “Theoretical model for resolution calculation of third generation image intensifiers,” J. Appl. Opt. 28, 578–581 (2007) (in Chinese).

J. Opt. Soc. Am. (1)

I. A. Cunningham and R. Shaw, “Signal-to-noise optimization of medical imaging systems,” J. Opt. Soc. Am. 16, 621–632 (1999).
[CrossRef]

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

J. Russ. Laser Res. (2)

J. Wei, Q. Wang, J. Sun, and J. Gao, “High-resolution imaging of a long-distance target with a single-slit streak-tube lidar,” J. Russ. Laser Res. 31, 307–312 (2010).
[CrossRef]

Q. Wang, J. Liu, and S. Li, “Analysis of detectable range of multiple-slit streak tube imaging lidar,” J. Russ. Laser Res. 30, 296–303 (2009).
[CrossRef]

Laser Phys. (2)

J. Liu, Q. Wang, S. Li, Y. Cheng, and J. Wei, “Research on a flash imaging lidar based on a multiple-streak tube,” Laser Phys. 19, 115–120 (2009).
[CrossRef]

J. Sun and Q. Wang, “4-D image reconstruction for streak tube imaging lidar,” Laser Phys. 19, 502–504 (2009).
[CrossRef]

Med. Phys. (6)

I. A. Cunningham, M. S. Westmore, and A. Fenster, “A spatial-frequency dependent quantum accounting diagram and detective quantum efficiency model of signal and noise propagation in cascaded imaging systems,” Med. Phys. 21, 417–427 (1994).
[CrossRef]

J. P. Bissonette, I. A. Cunningham, D. A. Jaffray, A. Fenster, and P. Munro, “A quantum accounting and detective quantum efficiency analysis for video-based portal imaging,” Med. Phys. 24, 815–826 (1997).
[CrossRef]

J. H. Siewerdsen, L. E. Antonuk, Y. El-Mohri, J. Yorkston, W. Huang, J. M. Boudry, and I. A. Cunningham, “Empirical and theoretical investigation of the noise performance of indirect detection, active matrix flat-panel imagers (AMFPIs) for diagnostic radiology,” Med. Phys. 24, 71–89 (1997).
[CrossRef]

W. Zhao and J. A. Rowlands, “Digital radiology using active matrix readout of amorphous selenium: theoretical analysis of detective quantum efficiency,” Med. Phys. 24, 1819–1833 (1997).
[CrossRef]

M. B. Williams, P. U. Simoni, L. Smilowitz, M. Stanton, W. Phillips, and A. Stewart, “Analysis of the detective quantum efficiency of a developmental detector for digital mammography,” Med. Phys. 26, 2273–2285 (1999).
[CrossRef]

S. Hejazi and D. P. Trauernicht, “System considerations in CCD-based x-ray imaging for digital chest radiography and digital mammography,” Med. Phys. 24, 287–297 (1997).
[CrossRef]

Nucl. Instrum. Methods (1)

G. Zanell and R. Zannoni, “DQE of imaging detectors in terms of spatial frequency,” Nucl. Instrum. Methods 437, 163–167 (1999).
[CrossRef]

Phys. Med. Biol. (1)

A. D. A. Maidment and M. J. Yaffe, “Analysis of signal propagation in optically coupled detectors for digital mammography: II. Lens and fiber optics,” Phys. Med. Biol. 41, 475–493 (1996).
[CrossRef]

Proc. SPIE (11)

A. Whiteson, “Streak tube modulation transfer functions,” Proc. SPIE 1155, 344–355 (1990).
[CrossRef]

D. Dussault and P. Hoess, “Noise performance comparison of ICCD with CCD and EMCCD cameras,” Proc. SPIE 5563, 195–204 (2004).
[CrossRef]

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

A. D. Gleckler, “Multiple-slit streak tube imaging lidar (MS-STIL) applications,” Proc. SPIE 4035, 266–278 (2000).
[CrossRef]

A. D. Gleckler, A. Gelbart, and J. M. Bowden, “Multispectral and hyperspectral 3D imaging lidar based upon the multiple slit streak tube imaging lidar,” Proc. SPIE 4377, 328–335 (2001).
[CrossRef]

A. D. Gleckler and A. Gelbart, “Three-dimensional imaging polarimetry,” Proc. SPIE 4377, 175–185 (2001).
[CrossRef]

A. Gelbart, B. C. Redman, R. S. Light, C. A. Schwartzlow, and A. J. Griffis, “Flash lidar based on multiple-slit streak tube imaging lidar,” Proc. SPIE 4723, 9–18 (2002).
[CrossRef]

J. W. McLean, “High resolution 3-D underwater imaging,” Proc. SPIE 3761, 10–19 (1999).
[CrossRef]

M. J. DeWeert, S. E. Moran, B. L. Ulich, and R. N. Keeler, “Numerical simulations of the relative performance of streak-tube, range-gated, and PMT-based airborne imaging lidar systems with realistic sea surfaces,” Proc. SPIE 3761, 115–129 (1999).
[CrossRef]

V. B. Lebedev, G. G. Feldman, O. V. Aleksander, A. A. Nazaryan, A. A. Tsovyan, Y. A. Yedigaryan, and S. S. Melikyan, “Application of K008 camera within lidar for laser sounding of water width from air,” Proc. SPIE 5580, 282–292 (2005).
[CrossRef]

S. Li, Q. Wang, J. Lin, and Y. Guang, “Research of range resolution of streak tube imaging system,” Proc. SPIE 6279, 62790C (2007).
[CrossRef]

Rev. Sci. Instrum. (1)

R. T. Eagleton and S. F. James, “Dynamic range measurements on streak imaging tubes with internal and external microchannel plate image amplification,” Rev. Sci. Instrum. 74, 2215–2219 (2003).
[CrossRef]

Other (10)

B. C. Redman, A. J. Griffis, and E. B. Schibley, “Streak tube imaging lidar (STIL) for 3-D imaging of terrestrial targets,” Tech. Report (Arête Associates, Tucson, Ariz., 2000).

I. A. Cunningham, “Applied linear-systems theory,” in Handbook of Medical Imaging, J. Beutel, H. L. Kundel, and R. L. Van Metter, eds. Vol. 1: Physics and Psychophysics (SPIE, Bellingham, 2010), Chap. 2.

J. Sun, J. Liu, and Q. Wang, “A multiple-slit streak tube imaging lidar and its detection ability analysis by flash lidar equation,” Optik (to be published).
[CrossRef]

G. D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE, 2001), Chap. 1.

S. Xiang and G. Ni, The Principle of Photoelectronic Imaging Devices (National Defence Industry, Beijing, 1999).

S. Vedantham, “Design and characterization of a high-resolution cardiovascular imager,” Ph.D. thesis, Worcester Polytechnic Institute, 2002.

E. J. Ientilucci, “Synthetic simulation and modeling of image intensified CCDs (IICCD),” MS. thesis, Rochester Institute of Technology, 2000.

L. Wu, X. Wang, H. Yang, B. Yu, C. Chen, B. Yang, L. Yuan, L. Wu, Z. Xue, G. Li, and B. Wu, “Signal-to-noise performance analysis of streak tube imaging lidar systems. II. Theoretical analysis and discussion,” Appl. Opt.51, 8836–8847 (2012).

C. B. Johnson, L. T. Hunkler, S. A. Letzring, and P. Jaanimagi, Streak tube camera receiver definition studies, Tech. Report (ITT Electro-Optical Products Div, 1990).

C. B. Johnson and L. D. Owen, “Image tube intensified electronic imaging,” in Handbook of Optics, 3rd ed. Vol. II. Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill Companies, 2010), Chap. 31.

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Figures (3)

Fig. 1.
Fig. 1.

Principle of a STIL. (a) The scene is illuminated by a laser fan-beam. (b) The backscattered light from the scene is imaged on the photocathode of the streak tube. The photoelectron beam is swept in time across the vertical dimension of the streak tube’s phosphor screen, resulting in a continuous sequence of the slit images recorded at different time in the duration of the laser pulse. (c) The streak image at the phosphor screen of the streak tube is recorded by a CCD.

Fig. 2.
Fig. 2.

Imaging chains (main components) of (a) an external intensified STIL system and (b) an internal intensified STIL system.

Fig. 3.
Fig. 3.

Basic components of (a) a typical streak tube, (b) an internal intensified streak tube, and (c) an image intensifier tube.

Tables (3)

Tables Icon

Table 1. Summary of Amplification Statistics and Their Gain Variances and Gain Poisson Excesses

Tables Icon

Table 2. Summary of Cascaded Stages in the Internal Intensified Streak Tube

Tables Icon

Table 3. Summary of Cascaded Stages in the Image Intensifier Tube

Equations (54)

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

ϕ¯i=g¯iϕ¯i1,
Si(u,v)=g¯i2Si1(u,v)+σgi2ϕ¯i1+Saddi(u,v),
εgi=σgi2g¯i1.
Φi(u,v)=Ti2(u,v)Φi1(u,v),
Si(u,v)=Ti2(u,v)Si1(u,v)+[1Ti2(u,v)]ϕ¯i1=Ti2(u,v)[Si1(u,v)ϕ¯i1]+ϕ¯i1,
Φi(u,v)=Ti2(u,v)Φi1(u,v),
Si(u,v)=Ti2(u,v)Si1(u,v).
DQE(u,v)=SNRout2(u,v)SNRin2(u,v)=Φout(u,v)/Sout(u,v)Φin(u,v)/Sin(u,v),
DQE(u,v)=(1+i=1M1+εgiTi2(u,v)+Saddi(u,v)/ϕ¯iPi(u,v))1,
NF(u,v)=1/DQE(u,v),
FG=1g¯2σout2σin2,
NF(u,v)=1+[NF1(u,v)1]+NF2(u,v)1G¯1(u,v)+NF3(u,v)1G¯1(u,v)G¯2(u,v)++NFM(u,v)1i=1M1G¯i(u,v),
G¯i(u,v)=g¯iTi2(u,v),
NFi(u,v)=1+(FiG1)+FiA(u,v)1g¯i+FiS(u,v)1g¯i=FiG+1Ti2(u,v)g¯iTi2(u,v)+Saddi(u,v)g¯iϕ¯i.
NFEI-STIL(u,v)=1+[NFRO(u,v)1]+NFST(u,v)1G¯RO(u,v)+NFCOA(u,v)1G¯RO(u,v)G¯ST(u,v)+NFII(u,v)1G¯RO(u,v)G¯ST(u,v)G¯COA(u,v)+NFCOB(u,v)1G¯RO(u,v)G¯ST(u,v)G¯COA(u,v)G¯II(u,v)+NFCCD(u,v)1G¯RO(u,v)G¯ST(u,v)G¯COA(u,v)G¯II(u,v)G¯COB(u,v),
NFII-STIL(u,v)=1+[NFRO(u,v)1]+NFIIST(u,v)1G¯RO(u,v)+NFCO(u,v)1G¯RO(u,v)G¯IIST(u,v)+NFCCD(u,v)1G¯RO(u,v)G¯IIST(u,v)G¯CO(u,v),
NFRO(u,v)=1+(FROG1)+1TRO2(u,v)g¯ROTRO2(u,v)=1G¯RO(u,v),
σ02=q¯0.
σ12=g¯12σ02+g¯1(1g¯1)q¯0=g¯1q¯0,
g¯1(λ)=τiwηpc(λ)=τiwhceλSλ.
g¯4(Vm)=δ¯1(Vm)δ¯2n1(Vm)=(nVpk+VmnVc)k(VmnVc)k(n1),
σ42=g¯42σ32+(1+bg¯4)g¯4q¯3=[g¯4+(1+bg¯4)]g¯1g¯2g¯3g¯4q¯0,
b=b1+1δ¯1+i=2M11Pi+b2δ¯2i=2M1Pi.
q¯5=g¯1g¯2g¯3g¯4g¯5q¯0=g¯IISTq¯0,
σ52=g¯52σ42+g¯5q¯4={1+[g¯4+(1+bg¯4)]g¯5}g¯1g¯2g¯3g¯4g¯5q¯0,
g¯5=(VaVd)ηps.
T6(f)=TST(f)=exp{(f/fST)nST},
FIISTG=1g¯IIST2σ52σ02=1+bg¯1g¯2g¯3+1g¯1g¯2g¯3g¯4+1g¯1g¯2g¯3g¯4g¯5.
q¯5=g¯5q¯2=g¯1g¯2g¯5q¯0=g¯STq¯0,
σ52=g¯52σ22+g¯5q¯2=(1+g¯5)g¯1g¯2g¯5q¯0,
FSTG=1g¯ST2σ52σ02=1g¯1g¯2+1g¯1g¯2g¯5.
NFIIST,ST(u,v)=FIIST,STG+1TIIST,ST2(u,v)g¯IIST,STTIIST,ST2(u,v).
q¯5=g¯IIq¯0=g¯1g¯2g¯3g¯4g¯5q¯0,
σ52={1+[g¯4+(1+bg¯4)]g¯5}g¯1g¯2g¯3g¯4g¯5q¯0,
FIIG=1g¯II2σ52σ02=1+bg¯1g¯2g¯3+1g¯1g¯2g¯3g¯4+1g¯1g¯2g¯3g¯4g¯5.
T6(ρ)=TII(ρ)=exp{(ρ/ρII)nII},
NFII(u,v)=1+(FIIG1)+FIIA(u,v)1g¯II+FIIS(u,v)1g¯II=FIIG+1TII2(u,v)g¯IITII2(u,v)+SIIadd(u,v)g¯IIϕ¯II_in,
NFCO(u,v)=1g¯CO+1TCO2(u,v)g¯COTCO2(u,v)=1G¯CO(u,v),
g¯OL=ηlens=τlens1+4F2(1+Dm)2,
g¯FO=ηFO=(1ηr)Fcτcni2sin2θi/M2,
TFO(ρ)=|SOMB(dρ)|=|2J1(2πdρ)2πdρ|,
FCCDG=1/g¯CCD,
TCCD(u,v)=|sin(πFbu)πFbu||sin(πFdv)πFdv|,
FCCDA(u,v)1+σCCDadd2/ϕ¯CCDin,
NFCCD(u,v)=1+(FCCDG1)+FCCDA(u,v)1g¯CCD+FCCDS1g¯CCD=1g¯CCD+σCCDadd2g¯CCDϕ¯CCDin.
SNRSTIL(u,v)=SNRin(u,v)NFSTIL(u,v),
NFEI-STIL(u,v)=NFST(u,v)G¯RO(u,v)1G¯RO(u,v)G¯ST(u,v)+NFII(u,v)G¯RO(u,v)G¯ST(u,v)G¯COA(u,v)1G¯RO(u,v)G¯ST(u,v)G¯COA(u,v)G¯II(u,v)+NFCCD(u,v)G¯RO(u,v)G¯ST(u,v)G¯COA(u,v)G¯II(u,v)G¯COB(u,v),
NFII-STIL(u,v)=NFIIST(u,v)G¯RO(u,v)1G¯RO(u,v)G¯IIST(u,v)+NFCCD(u,v)G¯RO(u,v)G¯IIST(u,v)G¯CO(u,v).
NFEI-STIL(0)=FSTGg¯RO1g¯ROg¯ST+FIIGg¯ROg¯STg¯COA1g¯ROg¯STg¯COAg¯II+FCCDGg¯ROg¯STg¯COAg¯IIg¯COB,
NFII-STIL(0)=FIISTGg¯RO1g¯ROg¯IIST+FCCDGg¯ROg¯IISTg¯CO.
FMCPG=1+i=1M1+εδiPi=1+(1+b1δ¯1δ¯1)+(1+b2δ¯2)i=2M1Pi=1+(b1+1δ¯1)+[(i=2M11Pi)+1δ¯11δ¯2M1]+b2δ¯2i=2M1Pi=1+1g¯mcp+(b1+1δ¯1+i=2M11Pi+b2δ¯2i=2M1Pi),
FMCPG=1+1+εgmcpg¯mcp=1+1g¯mcp+b.
b=b1+1δ¯1+i=2M11Pi+b2δ¯2i=2M1Pi={b1+(1+b2)(M1)δ¯1,δ¯2=1b1+1δ¯1+(1+b2)δ¯2(M2)δ¯1(1δ¯2)1+b2δ¯2δ¯1(1δ¯2),δ¯2<1b1+1δ¯1+1+b2δ¯2δ¯1(δ¯21)(1+b2)δ¯2(M2)δ¯1(δ¯21),δ¯2>1.
bb1+1δ¯1+1+b2δ¯2δ¯1(δ¯21),δ2>1,M1.

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