Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target

Barry J. Rye and Rod G. Frehlich

Barry J. Rye^{1} and Rod G. Frehlich^{1}

^{1}Cooperative Institute for Research in Environmental Sciences, University of Colorado–National Oceanic and Atmospheric Adminstration, Boulder, Colorado 80309-0449.

Barry J. Rye and Rod G. Frehlich, "Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target," Appl. Opt. 31, 2891-2899 (1992)

Two earlier computations of the optimal truncation of Gaussian beams for a simple, focused, coherent lidar that used an incoherent backscatter target with identical circular transmitter and receiver apertures differ because they refer to different receiver geometries. The definitions of heterodyne and system-antenna efficiencies are reviewed in light of the discrepancy and are used to compare the optical performance of systems with apertures illuminated by beam profiles that are not Gaussian. The heterodyne efficiency is less than 0.5 for all cases considered here.

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We used identical transmitter and receiver apertures and focused on an incoherent backscatter target. The parameters used in the studies by Rye3 and Wang4 can be compared as follows. Rye described the truncation using the ratio γ_{T} = b_{0}/b_{T} for the transmitter, where b_{0} is the 1/e^{2} irradiance radius of the Gaussian beam and b_{T} is the radius of the transmitter aperture (with a corresponding expression for the reciprocal receiver). Wang4 used α for the 1/e^{1} irradiance radius and described the transmitter truncation using the truncation ratio r_{trunc} = d_{1}/2α, where d_{1} is the diameter of the transmitter aperture. The relation between the two truncation parameters is therefore
$\mathrm{\gamma}=\sqrt{2}/{r}_{\text{trunc}}$. Tratt and Menzies7 (in their Figs. 2 and 3) described the truncation using the factor a/W = 1/γ which is not shown here. Zhao et al.8 (in their subsec. IIIB) used PM and “lm for Yh and la, respectively. DiMarzio’s calculation (Ref. 5, Figs. 4–10) is discussed at the end of Section III.
Ref. 18.
Ref 4.
Ref. 5.
Ref. 3.
Ref. 6.
Ref. 7.

Table II

Heterodyne and System-Antenna Efficiencies for Different Transmitter and Receiver Beam Profilesa

II, super-Gaussian transmitter (n = 16), Gaussian receiver

0.978

1.114

1.263

1.120

−3.36

47.7

−3.26

47.2

The difference of Gaussian profile, which is applicable to some unstable resonator laser outputs,7 is specified by the two values of γ and r_{trunc}, and by the reflectivity factor (R in Ref. 7). For a super-Gaussian beam of order n (see text), the product of γ (which is based on the 1/e^{2} irradiance radius) and r_{trunc;} (based on the 1/e irradiance radius) is the nth root of 2.
Ref. 7.

Tables (2)

Table 1

Recomputed Parameters for Maximum System Efficiency and the Corresponding Heterodyne Efficiency in a Truncated Gaussian Beam Lidara

We used identical transmitter and receiver apertures and focused on an incoherent backscatter target. The parameters used in the studies by Rye3 and Wang4 can be compared as follows. Rye described the truncation using the ratio γ_{T} = b_{0}/b_{T} for the transmitter, where b_{0} is the 1/e^{2} irradiance radius of the Gaussian beam and b_{T} is the radius of the transmitter aperture (with a corresponding expression for the reciprocal receiver). Wang4 used α for the 1/e^{1} irradiance radius and described the transmitter truncation using the truncation ratio r_{trunc} = d_{1}/2α, where d_{1} is the diameter of the transmitter aperture. The relation between the two truncation parameters is therefore
$\mathrm{\gamma}=\sqrt{2}/{r}_{\text{trunc}}$. Tratt and Menzies7 (in their Figs. 2 and 3) described the truncation using the factor a/W = 1/γ which is not shown here. Zhao et al.8 (in their subsec. IIIB) used PM and “lm for Yh and la, respectively. DiMarzio’s calculation (Ref. 5, Figs. 4–10) is discussed at the end of Section III.
Ref. 18.
Ref 4.
Ref. 5.
Ref. 3.
Ref. 6.
Ref. 7.

Table II

Heterodyne and System-Antenna Efficiencies for Different Transmitter and Receiver Beam Profilesa

II, super-Gaussian transmitter (n = 16), Gaussian receiver

0.978

1.114

1.263

1.120

−3.36

47.7

−3.26

47.2

The difference of Gaussian profile, which is applicable to some unstable resonator laser outputs,7 is specified by the two values of γ and r_{trunc}, and by the reflectivity factor (R in Ref. 7). For a super-Gaussian beam of order n (see text), the product of γ (which is based on the 1/e^{2} irradiance radius) and r_{trunc;} (based on the 1/e irradiance radius) is the nth root of 2.
Ref. 7.