Abstract

The transmitted energy required for an airborne laser radar system to be able to image a target at 20 km is investigated. Because direct detection is being considered, two methods of enhancing the received signal are discussed: (1) using an avalanche photodiode (APD) as the detector and (2) using a commercial fiber amplifier as a preamplifier before a photodetector. For this analysis a specified signal-to-noise ratio was used in conjunction with the radar range equation, which includes the effects of atmospheric transmission and turbulence. Theoretical analysis reveals that a system with a fiber amplifier performs nearly the same as a system incorporating an APD.

© 1995 Optical Society of America

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References

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  1. A. V. Jelalian, Laser Radar Systems (Artech, Boston, 1992), pp. 3–19.
  2. A. Yariv, Optical Electronics (Holt, Rinehart & Winston, New York, 1985), pp. 315, 317, 375, 379.
  3. B. E. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), pp. 673–681.
  4. J. E. Pederson, M. C. Brierley, R. A. Lobbett, “Noise characterization of a neodymium-doped fluoride fiber amplifier and its performance in a 2.4 Gb/s system,” IEEE Photon. Technol. Lett. 2, 750–752 (1990).
    [CrossRef]
  5. M. S. Salisbury, “Sensitivity and signal to noise ratio improvements of a one micron ladar system incorporating a neodymium doped optical fiber preamplifier,” M.S. thesis (University of Dayton, Dayton, Ohio, 1993).
  6. M. S. Salisbury, “Sensitivity improvement of a 1 μm ladar system incorporating an optical fiber preamplifier,” Opt. Eng. 32, 2671–2680 (1993).
    [CrossRef]
  7. G. Anderson, FASCODE, version, GEO-Physics Directorate Phillips Laboratory (Hanscomb Air Force Base, Mass., 1992).
  8. J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 12, 3292–3313 (1981).
    [CrossRef]

1993 (1)

M. S. Salisbury, “Sensitivity improvement of a 1 μm ladar system incorporating an optical fiber preamplifier,” Opt. Eng. 32, 2671–2680 (1993).
[CrossRef]

1990 (1)

J. E. Pederson, M. C. Brierley, R. A. Lobbett, “Noise characterization of a neodymium-doped fluoride fiber amplifier and its performance in a 2.4 Gb/s system,” IEEE Photon. Technol. Lett. 2, 750–752 (1990).
[CrossRef]

1981 (1)

J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 12, 3292–3313 (1981).
[CrossRef]

Anderson, G.

G. Anderson, FASCODE, version, GEO-Physics Directorate Phillips Laboratory (Hanscomb Air Force Base, Mass., 1992).

Brierley, M. C.

J. E. Pederson, M. C. Brierley, R. A. Lobbett, “Noise characterization of a neodymium-doped fluoride fiber amplifier and its performance in a 2.4 Gb/s system,” IEEE Photon. Technol. Lett. 2, 750–752 (1990).
[CrossRef]

Capron, B. A.

J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 12, 3292–3313 (1981).
[CrossRef]

Harney, R. C.

J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 12, 3292–3313 (1981).
[CrossRef]

Jelalian, A. V.

A. V. Jelalian, Laser Radar Systems (Artech, Boston, 1992), pp. 3–19.

Lobbett, R. A.

J. E. Pederson, M. C. Brierley, R. A. Lobbett, “Noise characterization of a neodymium-doped fluoride fiber amplifier and its performance in a 2.4 Gb/s system,” IEEE Photon. Technol. Lett. 2, 750–752 (1990).
[CrossRef]

Pederson, J. E.

J. E. Pederson, M. C. Brierley, R. A. Lobbett, “Noise characterization of a neodymium-doped fluoride fiber amplifier and its performance in a 2.4 Gb/s system,” IEEE Photon. Technol. Lett. 2, 750–752 (1990).
[CrossRef]

Saleh, B. E.

B. E. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), pp. 673–681.

Salisbury, M. S.

M. S. Salisbury, “Sensitivity improvement of a 1 μm ladar system incorporating an optical fiber preamplifier,” Opt. Eng. 32, 2671–2680 (1993).
[CrossRef]

M. S. Salisbury, “Sensitivity and signal to noise ratio improvements of a one micron ladar system incorporating a neodymium doped optical fiber preamplifier,” M.S. thesis (University of Dayton, Dayton, Ohio, 1993).

Shapiro, J. H.

J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 12, 3292–3313 (1981).
[CrossRef]

Teich, M. C.

B. E. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), pp. 673–681.

Yariv, A.

A. Yariv, Optical Electronics (Holt, Rinehart & Winston, New York, 1985), pp. 315, 317, 375, 379.

Appl. Opt. (1)

J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 12, 3292–3313 (1981).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. E. Pederson, M. C. Brierley, R. A. Lobbett, “Noise characterization of a neodymium-doped fluoride fiber amplifier and its performance in a 2.4 Gb/s system,” IEEE Photon. Technol. Lett. 2, 750–752 (1990).
[CrossRef]

Opt. Eng. (1)

M. S. Salisbury, “Sensitivity improvement of a 1 μm ladar system incorporating an optical fiber preamplifier,” Opt. Eng. 32, 2671–2680 (1993).
[CrossRef]

Other (5)

G. Anderson, FASCODE, version, GEO-Physics Directorate Phillips Laboratory (Hanscomb Air Force Base, Mass., 1992).

M. S. Salisbury, “Sensitivity and signal to noise ratio improvements of a one micron ladar system incorporating a neodymium doped optical fiber preamplifier,” M.S. thesis (University of Dayton, Dayton, Ohio, 1993).

A. V. Jelalian, Laser Radar Systems (Artech, Boston, 1992), pp. 3–19.

A. Yariv, Optical Electronics (Holt, Rinehart & Winston, New York, 1985), pp. 315, 317, 375, 379.

B. E. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), pp. 673–681.

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Tables (2)

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Table 1 Atmospheric-Transmission Characteristics for a 20-km Slant Range from 4572 m (15,000 ft.) for Different Visibilities a

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Table 2 Energy Requirements for 1.54 mm Ladar to Image from 4572 m (15,000 ft) over a Slant Range of 20 km Using Direct Detection, an APD and a Fiber Amplifier a

Equations (47)

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SNR UA = P sig P th + P a + P dark + P shot + P back ,
P sig = I 2 R L = ( Φ r R ) 2 R L ,
P th = 4 k T B ,
P a = 4 k T a B ,
P shot = 2 q Φ r R B R L .
P back = 2 q Φ B R B R L ,
Φ B = S IRR Δ λ Ω R ρ B ε opt A R ,
P dark = 2 q I dark B R L .
SNR UA = Φ r 2 R 2 R L 4 k B ( T + T a ) + 2 q B R L ( Φ r R + Φ B R + I dark ) ,
SNR UA = Φ r 2 2 q B R ( Φ r + Φ B + I dark R ) + 4 k B ( T + T a ) R 2 R L .
Φ r = q B SNR UA R ( 1 + { 1 + 2 SNR UA q B [ 2 k ( T a + T ) R L q + I dark + Φ B R ] } 1 / 2 ) .
SNR APD = P sig P th + P a + P dark + P shot + P back .
P sig = I 2 R L = ( M Φ r R ) 2 R L ,
P shot , APD = 2 q Φ r M 2 F ex R B R L .
P back , APD = 2 q Φ B M 2 F ex R B R L .
P dark , APD = 2 q I dark M 2 F ex B R L .
SNR APD = Φ r 2 R 2 R L M 2 4 k B ( T + T a ) + 2 q M 2 F ex B R L ( Φ r R + Φ B R + I dark ) ,
SNR APD = Φ r 2 2 q F ex B R ( Φ r + Φ B + I dark R ) + 4 k B ( T + T a ) M 2 R 2 R L .
Φ r = q B R SNR APD F ex ( 1 + { 1 + 1 SNR APD q B F ex + [ 2 Φ B R + 2 I dark + 4 k ( T + T a ) q R L M 2 F ex ] } 1 / 2 ) .
SNR FA = P sig P th + P a + P dark + P shot + P back + P fiber .
P sig = ( G Φ r R ) 2 R L ,
P shot , FA = 2 q Φ r G R B R L .
P back , FA = 2 q Φ B G R B R L .
P fiber = P spsn + P sigsp + P spsp ,
P spsn = 2 q R ρ sp B o B R L .
B o = c Δ λ / λ 2 ,
ρ sp = h ν F G ,
P sigsp = 2 G R 2 Φ tot ρ sp B R L ,
Φ tot = Φ r + Φ B .
P spsp = R 2 ρ sp 2 B o B R L = R 2 ( h ν ) 2 F 2 G 2 B o B R L .
SNR FA = G 2 Φ r 2 R 2 R L 2 R 2 Φ tot G ρ sp B R L + R 2 ρ sp 2 B o B R L + 4 k ( T + T a ) B ,
SNR FA = Φ r 2 2 h ν Φ r F B + 2 h ν Φ B F B + h 2 ν 2 F 2 B o B + 4 k ( T + T a ) B G 2 R 2 R L ,
Φ r = h ν F B SNR FA ( 1 + { 1 + 1 B SNR FA × [ B o + 2 B o G η F + 4 k ( T + T a ) ( η q F G ) 2 R L ] } 1 / 2 ) ,
Φ r = Φ t G t 4 π R 2 σ 4 π R 2 π D 2 4 η atm ε opt η scint η fiber ,
σ = πρ R 2 θ t 2 ,
Φ r = πρ D 2 E T B 16 R 2 η atm ε opt η scint η fiber ,
E T = Φ r πρ D 2 B 16 R 2 η atm ε opt η scint η fiber .
η scint = exp ( 4 σ χ 2 ) exp ( 2 σ 2 ) ,
σ χ 2 = 0 . 56 k 7 / 6 0 L d z C n 2 ( z ) ( z / L ) 5 / 6 ( L z ) 5 / 6 ,
C n 2 = C n 2 ( h 0 ) [ 1 + ( L z ) ( H h 0 ) L h 0 ] 4 / 3 ,
C n 2 ( 2 ) = 10 13 m 2 / 3 .
σ χ 2 = 0 . 56 k 7 / 6 0 L d z C n 2 ( h 0 ) [ 1 + ( L z ) ( H h 0 ) / ( L h 0 ) ] 4 / 3 ( z / L ) 5 / 6 ( L z ) 5 / 6 = 0 . 009757 .
σ 2 = 0 . 25 ln { λ L / D 2 1 + ( λ L / D 2 ) [ exp ( 16 σ χ 2 ) 1 ] + 1 } , = 0 . 0023289
η scint = 0 . 992 1 .
E T = q R SNR UA πρ D 2 16 R 2 ε opt η atm ( 1 + { 1 + 2 SNR UA q B × [ Φ B R + I dark + 2 k ( T + T a ) q R L ] } 1 / 2 ) .
E T = q R SNR APD F ex πρ D 2 16 R 2 ε opt η atm ( 1 + { 1 + 1 SNR APD q B F ex × [ 2 Φ B R + 2 I dark + 4 k ( T + T a ) q R L M 2 F ex ] } 1 / 2 ) ,
E T = h ν F SNR FA πρ D 2 16 R 2 ε opt η fiber η atm ( 1 + { 1 + 1 B SNR FA × [ B o + 4 k ( T + T a ) ( η q F G ) 2 R L + 2 B o G η F ] } 1 / 2 ) .

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