Abstract

The conventional theory of image transfer through a scattering medium treats objects located upon reflecting surfaces. It is shown that, when an object is located inside a scattering medium and shields a part of space, ignoring the shadowing leads to incorrect results, especially for modern time-gating systems. We develop a general theory of image formation including the shadowing effect when an object is located inside a scattering medium. The example of the observation of a submerged object through a windy ocean surface is chosen to illustrate this theory. A few unexpected effects in imaging of a submerged object are found and discussed, including contrast conversion for a sinking object and higher contrast in the shadow image than in the image of the object itself. The conclusion that using the shadow image for detection of a submerged object can be more efficient than using the image of the object itself is of practical significance.

© 1999 Optical Society of America

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References

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  1. E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991).
    [CrossRef]
  2. L. S. Dolin, I. M. Levin, Theory of Underwater Vision (Gidrometeoizdat, Leningrad, 1991).
  3. I. L. Katsev, E. P. Zege, A. S. Prikhach, I. N. Polonsky, “Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems,” J. Opt. Soc. Am. A 14, 1338–1346 (1997).
    [CrossRef]
  4. S. E. Moran, B. L. Ulich, M. J. DeWeert, R. L. Strittmatter, R. N. Keeler, E. P. Zege, I. L. Katsev, A. S. Prikhach, “A comparative analysis of the signal-to-noise ratio and resolving power of laser line scan, streak tube, and range-gated underwater imaging lidar systems,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).
  5. V. V. Barun, “Detection of a small target against bottom of water reservoir,” in Signal and Data Processing of Small Targets 1996, O. E. Drummond, ed., Proc. SPIE2759, 490–501 (1996).
    [CrossRef]
  6. E. P. Zege, I. L. Katsev, A. S. Prikhach, “Range of vision in ocean and atmosphere,” Atmos. Oceanic Opt. 8, 510–523 (1992).

1997 (1)

1992 (1)

E. P. Zege, I. L. Katsev, A. S. Prikhach, “Range of vision in ocean and atmosphere,” Atmos. Oceanic Opt. 8, 510–523 (1992).

Barun, V. V.

V. V. Barun, “Detection of a small target against bottom of water reservoir,” in Signal and Data Processing of Small Targets 1996, O. E. Drummond, ed., Proc. SPIE2759, 490–501 (1996).
[CrossRef]

DeWeert, M. J.

S. E. Moran, B. L. Ulich, M. J. DeWeert, R. L. Strittmatter, R. N. Keeler, E. P. Zege, I. L. Katsev, A. S. Prikhach, “A comparative analysis of the signal-to-noise ratio and resolving power of laser line scan, streak tube, and range-gated underwater imaging lidar systems,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).

Dolin, L. S.

L. S. Dolin, I. M. Levin, Theory of Underwater Vision (Gidrometeoizdat, Leningrad, 1991).

Ivanov, A. P.

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991).
[CrossRef]

Katsev, I. L.

I. L. Katsev, E. P. Zege, A. S. Prikhach, I. N. Polonsky, “Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems,” J. Opt. Soc. Am. A 14, 1338–1346 (1997).
[CrossRef]

E. P. Zege, I. L. Katsev, A. S. Prikhach, “Range of vision in ocean and atmosphere,” Atmos. Oceanic Opt. 8, 510–523 (1992).

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991).
[CrossRef]

S. E. Moran, B. L. Ulich, M. J. DeWeert, R. L. Strittmatter, R. N. Keeler, E. P. Zege, I. L. Katsev, A. S. Prikhach, “A comparative analysis of the signal-to-noise ratio and resolving power of laser line scan, streak tube, and range-gated underwater imaging lidar systems,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).

Keeler, R. N.

S. E. Moran, B. L. Ulich, M. J. DeWeert, R. L. Strittmatter, R. N. Keeler, E. P. Zege, I. L. Katsev, A. S. Prikhach, “A comparative analysis of the signal-to-noise ratio and resolving power of laser line scan, streak tube, and range-gated underwater imaging lidar systems,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).

Levin, I. M.

L. S. Dolin, I. M. Levin, Theory of Underwater Vision (Gidrometeoizdat, Leningrad, 1991).

Moran, S. E.

S. E. Moran, B. L. Ulich, M. J. DeWeert, R. L. Strittmatter, R. N. Keeler, E. P. Zege, I. L. Katsev, A. S. Prikhach, “A comparative analysis of the signal-to-noise ratio and resolving power of laser line scan, streak tube, and range-gated underwater imaging lidar systems,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).

Polonsky, I. N.

Prikhach, A. S.

I. L. Katsev, E. P. Zege, A. S. Prikhach, I. N. Polonsky, “Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems,” J. Opt. Soc. Am. A 14, 1338–1346 (1997).
[CrossRef]

E. P. Zege, I. L. Katsev, A. S. Prikhach, “Range of vision in ocean and atmosphere,” Atmos. Oceanic Opt. 8, 510–523 (1992).

S. E. Moran, B. L. Ulich, M. J. DeWeert, R. L. Strittmatter, R. N. Keeler, E. P. Zege, I. L. Katsev, A. S. Prikhach, “A comparative analysis of the signal-to-noise ratio and resolving power of laser line scan, streak tube, and range-gated underwater imaging lidar systems,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).

Strittmatter, R. L.

S. E. Moran, B. L. Ulich, M. J. DeWeert, R. L. Strittmatter, R. N. Keeler, E. P. Zege, I. L. Katsev, A. S. Prikhach, “A comparative analysis of the signal-to-noise ratio and resolving power of laser line scan, streak tube, and range-gated underwater imaging lidar systems,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).

Ulich, B. L.

S. E. Moran, B. L. Ulich, M. J. DeWeert, R. L. Strittmatter, R. N. Keeler, E. P. Zege, I. L. Katsev, A. S. Prikhach, “A comparative analysis of the signal-to-noise ratio and resolving power of laser line scan, streak tube, and range-gated underwater imaging lidar systems,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).

Zege, E. P.

I. L. Katsev, E. P. Zege, A. S. Prikhach, I. N. Polonsky, “Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems,” J. Opt. Soc. Am. A 14, 1338–1346 (1997).
[CrossRef]

E. P. Zege, I. L. Katsev, A. S. Prikhach, “Range of vision in ocean and atmosphere,” Atmos. Oceanic Opt. 8, 510–523 (1992).

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991).
[CrossRef]

S. E. Moran, B. L. Ulich, M. J. DeWeert, R. L. Strittmatter, R. N. Keeler, E. P. Zege, I. L. Katsev, A. S. Prikhach, “A comparative analysis of the signal-to-noise ratio and resolving power of laser line scan, streak tube, and range-gated underwater imaging lidar systems,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).

Atmos. Oceanic Opt. (1)

E. P. Zege, I. L. Katsev, A. S. Prikhach, “Range of vision in ocean and atmosphere,” Atmos. Oceanic Opt. 8, 510–523 (1992).

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

Other (4)

S. E. Moran, B. L. Ulich, M. J. DeWeert, R. L. Strittmatter, R. N. Keeler, E. P. Zege, I. L. Katsev, A. S. Prikhach, “A comparative analysis of the signal-to-noise ratio and resolving power of laser line scan, streak tube, and range-gated underwater imaging lidar systems,” in Ocean Optics XIV CD-ROM (Office of Naval Research, Washington, D.C., 1998).

V. V. Barun, “Detection of a small target against bottom of water reservoir,” in Signal and Data Processing of Small Targets 1996, O. E. Drummond, ed., Proc. SPIE2759, 490–501 (1996).
[CrossRef]

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991).
[CrossRef]

L. S. Dolin, I. M. Levin, Theory of Underwater Vision (Gidrometeoizdat, Leningrad, 1991).

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Figures (4)

Fig. 1
Fig. 1

Geometric schematic of observation of the object.

Fig. 2
Fig. 2

Relative irradiance distributions over the image of an object shadow, computed through an approximate solution [Eq. (46); solid curve 1] and through a rigorous solution [Eqs. (38) and (34); dashed curves] for depths of z = 20.1 m (curve 2), 24 m (curve 3), 30 m (curve 4), and 50 m (curve 5). Clean ocean water with extinction coefficient σ e and scattering coefficient σ s of 0.1 and 0.06 m-1, respectively; L ob = 20 m; object diameter D ob = 5 m.

Fig. 3
Fig. 3

Contrast in the image of a submerged object in turbid shallow water (σ e = 1 m-1, σ s = 0.83 m-1) observed by a pulse time-gating system as a function of gating start L g . L bot = 5 m, A bot = 0.3, A ob = 0.1, D ob = 0.5 m, and object depths L ob = 3 m (curves 1) and L ob = 4 m (curves 2). Data for the observation through a smooth surface are given by dashed curves; those for the observation through a rough sea surface at the wind velocity 3m/s are depicted by solid curves.

Fig. 4
Fig. 4

Contrast in the image of a submerged object as a function of object depth at gating start L g with values of 2 m (curves 1), 5 m (curves 2), and 9 m (curves 3) at L bot = 10 m. All characteristics of system, water, and object are the same as for Fig. 3. Data for the observation through a smooth surface are given by dashed curves; those for the observation through a rough sea surface at a wind velocity of 3 m/s are depicted by solid curves.

Equations (59)

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Wb=WBSI+Wsur+Wbot.
WBSI=WBSIw+WBSIa.
Wrr=Wsur+Wobrr+WBSIrr+Wbotrr,
Wvsrr=Wrr-Wb.
Wvsrr=Wobrr-Wshrr,
Wshrr=WBSIshrr+Wbotshrr=WBSI-WBSIrr+Wbot-Wbotrr.
 fstdt=1.
W=W0  fgtdt  Ptfst-tdt,
W=W0  PtFsgtdt,
Fsgt= fgtfst-tdt.
W=W0  Ptfgtdt.
t=2H+nz/c,
Pvsrr, t=Pobrr, t-Pshrr, t.
WBSIrr=W0  PBSIrr, tFsgtdt.
PBSIrr, t=ξσsz  dr  Jsrcr, z, n; rs×Pπz, n, nJrecr, z, n; rr×dndn,
Pbotrr, t=ξδz-Lbot  dr  Jsrcr, Lbot, n; rs×Abotr, n, nJrecr, Lbot, n; rr×dndn,
Pobrr, t=ξδz-Lob  dr  Jsrcr, Lob, n; rs×Aobr, n, nJrecr, Lob, n; rr×dndn,
ξ=W0 Σrec Ωrecπc2n.
Aobr, n, n=Aobr,  Abotr, n, n=Abotr,  Pπz, n, n=Pπz,
PBSIrr, t=ξσszPπz  Esrcr, z; rs×Erecr, z; rrdr,
Pbotrr, t=ξδz-Lbot  AbotrEsrcr, Lob; rs×Erecr, Lob; rrdr,
Pobrr, t=ξδz-Lob  AobrEsrcr, Lob; rs×Erecr, Lob; rrdr,
Ejr, z; rj= Jjr, z, n; rjdn,  j=src, rec
Jjq, z, p; rj= Jjr, z, n; rjexp-iqr-ipndrdn,
Ejq, z; rj= Ejr, z; rjexp-iqrdr,
Jjq, z, p; rj=Jjq, Lob+0, p+qz-Lob; rjIq, z-Lob, p,
Iq, z, p=exp-σez+σs0z Pp+qξdξ,
Jjq, Lob+0, p; rj=14π2  Jjq, Lob-0, p; rj×Tobq-qdq,
Jjq, Lob-0, p; rj=J0jq, p/n+qZob; rjTsurp+qLobIq, Lob, p,
Z=H+z/n,  Zob=H+Lob/n,
Jjq, z, p; rj=Iq, z-Lob, p4π2 J0jq, p/n+qZob+qz-Lob/n; rjTsurp+qLob+qz-LobIq, Lob, p+qz-LobTobq-qdq.
Ejr, z; rj= Jjr, z, n; rjdn,
Ejq, z; rj=Jjq, z, p=0; rj,
Ejq, z; rj=Iq, z-Lob, 04π2  J0jq, qZob+qz-Lob/n; rjTsurqLob+qz-LobIq, Lob, qz-LobTobq-qdq.
J0jq, p; rj=φjpexpiprj/Zob.
Ejq, z; rj=Iq, z-Lob, 04π2 φjqZob+qz-Lob/nTsurqLob+qz-LobIq, Lob, qz-LobTobq-qexpiqZob+qz-Lob/nrjZobdq,
Ejq, z; rj=φjqZIq, z, 0TsurqzexpiqZ rjZob.
Iq, z-L, 0Iq, L, qz-L=Iq, z, 0.
Ejq, z; rj=Iq, z, 0Z2 4π2δq×TsurqzexpiqZrj/Zob.
Ejr, z; rj=1H+z/n2 exp-σe-σsz.
Pbotrr, t=ξδz-LbotAbot14π2× Esrc*q, Lbot; rsErecq, Lbot; rrdq,
Pbotrr, t=ξδz-Lbot  AbotrEsrcr, Lob; rs×Erecr, Lob; rrdr.
Pbotrr, t=ξδz-LbotAbotEsrcLbotErecLbot, rr,
ErecLbot, rr= Erecr, Lbot; rrdr.
Erecshz, rr=Erecz, rr-Erecz, rr,
ψrr=Erecshz, rr/Erecz, rr=ErecshLob+0, rr/ErecLob+0, rr.
Tobr=1-Σobr,
ψrr= ΣobrErecr, Lob; rrdrErecLob=14π2  Σob*qErecq, Lob; rrdqErecq=0, Lob; rr.
Pbotrr, t=ξδz-LbotAbotEsrcLbotErecLbot1-ψrr.
Wrr=WBSI+Wbot+Wobrr-Wbotshrr-WBSIshrr.
Wbotshrr=Wbotψrr,  WBSIshrr=WBSILob, Lbotψrr,
Wrr=R1-ηLbot+AbotηLbot+AobηLob-AbotηLbot-RηLob-ηLbotψrr,
ηz=exp-2σe-σsz.
k=Wrr=0-Wrr=Wrr==Aob-RηLob-Abot-RηLbotAbotηLbot+R1-ηLbot ψrr=0.
Aob-RAbot-R<ηLbotηLob=exp-2σe-σsLbot-Lob,
ψrr=0=exp-σeLob/exp-σe-σsLob=exp-σsLob.
k=Wrr=0-Wrr=Wrr=0+Wrr=.
Ejr, Lob; rj=Ejr-rj, Lob,  j=src, rec.
Qr-rj, Lob=Esrcr-rj, LobErecr-rj, Lob,

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