Abstract

A detected laser signal backscattered from a tilted target is modeled with a laser-pulse shape as a response of a high-pass filter to an exponential input that describes the gain buildup within the laser cavity before a laser pulse is emitted and a single-pole low-pass RC filter for the electronic amplifier. The model is used to maximize the signal-to-noise ratio of the detected peak signal with a proper choice of the integration time constant τ as a function of the laser-pulse shape and the tilt angle of the backscattering target.

© 1996 Optical Society of America

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References

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  1. R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, New York, 1978).
  2. J. Millman, H. Taub, Pulse, Digital and Switching Waveforms (McGraw-Hill, New York, 1965).
  3. A. Zverev, Handbook of Filter Synthesis (Wiley, New York, 1967).
  4. Y. Zhao, T. K. Lea, R. M. Schotland, “Correction function for the lidar equation and some techniques for incoherent CO2 lidar data reduction,” Appl. Opt. 27, 2730–2740 (1988).
  5. L. L. Gurdev, T. N. Dreischuh, D. V. Stoyanov, “Deconvolution technique for improving the resolution of long-pulse lidars,” J. Opt. Soc. Am. A 10, 2296–2306 (1993).
  6. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 9.

1993 (1)

1988 (1)

Dreischuh, T. N.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 9.

Gurdev, L. L.

Kingston, R. H.

R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, New York, 1978).

Lea, T. K.

Millman, J.

J. Millman, H. Taub, Pulse, Digital and Switching Waveforms (McGraw-Hill, New York, 1965).

Schotland, R. M.

Stoyanov, D. V.

Taub, H.

J. Millman, H. Taub, Pulse, Digital and Switching Waveforms (McGraw-Hill, New York, 1965).

Zhao, Y.

Zverev, A.

A. Zverev, Handbook of Filter Synthesis (Wiley, New York, 1967).

Appl. Opt. (1)

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

Other (4)

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 9.

R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, New York, 1978).

J. Millman, H. Taub, Pulse, Digital and Switching Waveforms (McGraw-Hill, New York, 1965).

A. Zverev, Handbook of Filter Synthesis (Wiley, New York, 1967).

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Figures (3)

Fig. 1
Fig. 1

(a) CO2 laser pulse (10R20) measured with a 44-MHz amplifier and a photoconductive HgCdTe detector (time constant τ = 7 ns) and a laser pulse V L simulated with Eq. (1) (a = 0.91, τ1 = 35 ns, τ2 = 60 ns, τ3 = 800 ns). The pulse bandwidth is approximately 10 MHz (τ = 16 ns). (b) Simulated short pulse (a = 1, τ1 = 3 ns, τ2 = 4 ns) typical of a Nd:YAG laser. The pulse bandwidth is approximately 160 MHz (τ = 1 ns).

Fig. 2
Fig. 2

SNR p = V 0 ( τ ) τ , assuming a noise value of 1 at τ = 1 ns, and the detected peak signal V 0, for a laser pulse of a unit peak value backscattered from a Lambertian target, with reflectivity ρ = 1, perpendicular to the incident laser pulse (i.e., at ψ = 0). (a) Simulated CO2 laser pulse shown in Fig. 1(a). (b) Short laser pulse typical of a Nd:YAG laser pulse as shown in Fig. 1(b).

Fig. 3
Fig. 3

Optimal integration time τ for maximizing the SNR p of a detected peak signal, improvement of SNR p , reduction of the detected peak value when the integration time τ increased from a reference integration time τ [ τ = 16 ns in (a) and τ = 1 ns in (b)] to the optimal integration time τ, as well as target temporal broadening Δt as a function of the target tilt angle ψ. (a) Simulated CO2 laser pulse from Fig. 1(a) with a unit peak value with a full-width beam divergence θ = 2.8 mrad and a target distance of L = 10 km. For τ = 16 ns and ψ = 0 the peak detected signal V 0 (τ = 16 ns) = 95% of the peak incident laser pulse V L . (b) Short laser pulse typical of a Nd:YAG laser pulse as shown in Fig. 1(b) with a unit peak value with a full-width beam divergence θ = 0.5 mrad and a target distance of L = 10 km. For τ = 1 ns and ψ = 0 the peak detected signal V 0 (τ = 1 ns) = 95% of the peak incident laser pulse V L .

Equations (7)

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V L ( t ) = a   exp ( t / τ 2 ) + ( 1 a ) exp ( t / τ 3 ) exp ( t / τ 1 ) ,
V i ( t ) = ρ Δ t 0 t V L ( t ) d t t < Δ t , V i ( t ) = ρ Δ t t Δ t t V L ( t ) d t t Δ t .
V 0 ( t ) = τ 1 0 t ρ V i ( t ) exp [ ( t t ) / τ ] d t .
SNR E = 0 T V 0 ( t ) d t V n T ,
0 V L ( t ) d t = 0 T V 0 ( t ) ρ d t = τ 3 τ 1 a ( τ 3 τ 2 ) ,
SNR E SNE p = 0 T V 0 ( t ) d t T V 0 ( t 0 ) = ρ 0 V L ( t ) d t T V 0 ( t 0 ) = ρ τ 3 τ 1 a ( τ 3 τ 2 ) T V 0 ( t 0 ) .
ρ ( laser-pulse energy ) T ( laser-pulse peak pwoer ) SNR E SNR p 1 ,

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