Abstract

Using the theory developed in Part 1, the receiving efficiency as a function of range, η(z), is calculated under different conditions for the NOAA/ERL/Wave Propagation Laboratory CO2 Doppler lidar. Theoretical analyses, numerical calculations, and experimental measurements are carried out to quantify the sensitivity of η(z) to transmitted laser beam quality, telescope focal setting, telescope power, scanner astigmatism, LO beam divergence, and system misalignment. These results bring insight to the design of practical coherent lidar systems.

© 1990 Optical Society of America

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  1. Y. Zhao, M. J. Post, R. M. Hardesty, “Receiving Efficiency of Monostatic Pulsed Coherent Lidars. 1: Theory,” Appl. Opt. 00, 000–000 (1990).
  2. M. J. Post, “Atmospheric Infrared Backscattering Profiles: Interpretation of Statistical and Temporal Properties,” NOAA Technical Memorandum ERL WPL-122 (1985).
  3. T. R. Lawrence, R. M. Hardesty, M. J. Post, R. A. Richter, R. M. Huffaker, F. F. Hall, “Performance characteristics of the NOAA Pulsed Doppler Lidar and Its Application to Atmospheric Measurements,” in Proceedings, Fifth Symposium on Meteorological Observations and Instrumentation, (Toronto, Canada, (April 11–15, 1983) p. 481.
  4. F. F. Hall, R. E. Cupp, R. M. Hardesty, T. R. Lawrence, M. J. Post, R. A. Richter, B. F. Weber, “Six Years of Pulsed-Doppler Lidar Field Experiments at NOAA/WPL,” in Proceedings, Sixth Symposium on Meteorological Observations and Instrumentation, New Orleans, (January 12–16, 1987) p. 11.
  5. M. J. Post, Richard Cupp, “Optimizing a Pulsed Doppler Lidar,” Submitted to Appl. Opt.28, 4145–4158 (1990).
    [CrossRef]
  6. E. A. Sziklas, A. E. Siegman, “Mode Calculations in Unstable Resonators with Flowing Saturable Gain. 2: Fast Fourier Transform Method,” Appl. Opt. 14, 1874–1889 (1975).
    [CrossRef] [PubMed]
  7. Y. Zhao, M. J. Post, T. R. Lawrence, “The Effects of Injection Pinhole, Mirror. Tilt, and Reflectivity Function of the Tapered Output Mirror on the Performance of a CO2 TEA Laser with Unstable Resonator,” to be published.
  8. A. E. Siegman, Lasers (University Science Books, Mill Valley, CA1986).
  9. British Association for the Advancement of Science: Mathematical Tables, Vol. 6: Bessel Functions, Part I, Functions of Order Zero and Unity (University Press, Cambridge, 1950).

1990 (1)

Y. Zhao, M. J. Post, R. M. Hardesty, “Receiving Efficiency of Monostatic Pulsed Coherent Lidars. 1: Theory,” Appl. Opt. 00, 000–000 (1990).

1985 (1)

M. J. Post, “Atmospheric Infrared Backscattering Profiles: Interpretation of Statistical and Temporal Properties,” NOAA Technical Memorandum ERL WPL-122 (1985).

1975 (1)

Cupp, R. E.

F. F. Hall, R. E. Cupp, R. M. Hardesty, T. R. Lawrence, M. J. Post, R. A. Richter, B. F. Weber, “Six Years of Pulsed-Doppler Lidar Field Experiments at NOAA/WPL,” in Proceedings, Sixth Symposium on Meteorological Observations and Instrumentation, New Orleans, (January 12–16, 1987) p. 11.

Cupp, Richard

M. J. Post, Richard Cupp, “Optimizing a Pulsed Doppler Lidar,” Submitted to Appl. Opt.28, 4145–4158 (1990).
[CrossRef]

Hall, F. F.

T. R. Lawrence, R. M. Hardesty, M. J. Post, R. A. Richter, R. M. Huffaker, F. F. Hall, “Performance characteristics of the NOAA Pulsed Doppler Lidar and Its Application to Atmospheric Measurements,” in Proceedings, Fifth Symposium on Meteorological Observations and Instrumentation, (Toronto, Canada, (April 11–15, 1983) p. 481.

F. F. Hall, R. E. Cupp, R. M. Hardesty, T. R. Lawrence, M. J. Post, R. A. Richter, B. F. Weber, “Six Years of Pulsed-Doppler Lidar Field Experiments at NOAA/WPL,” in Proceedings, Sixth Symposium on Meteorological Observations and Instrumentation, New Orleans, (January 12–16, 1987) p. 11.

Hardesty, R. M.

Y. Zhao, M. J. Post, R. M. Hardesty, “Receiving Efficiency of Monostatic Pulsed Coherent Lidars. 1: Theory,” Appl. Opt. 00, 000–000 (1990).

T. R. Lawrence, R. M. Hardesty, M. J. Post, R. A. Richter, R. M. Huffaker, F. F. Hall, “Performance characteristics of the NOAA Pulsed Doppler Lidar and Its Application to Atmospheric Measurements,” in Proceedings, Fifth Symposium on Meteorological Observations and Instrumentation, (Toronto, Canada, (April 11–15, 1983) p. 481.

F. F. Hall, R. E. Cupp, R. M. Hardesty, T. R. Lawrence, M. J. Post, R. A. Richter, B. F. Weber, “Six Years of Pulsed-Doppler Lidar Field Experiments at NOAA/WPL,” in Proceedings, Sixth Symposium on Meteorological Observations and Instrumentation, New Orleans, (January 12–16, 1987) p. 11.

Huffaker, R. M.

T. R. Lawrence, R. M. Hardesty, M. J. Post, R. A. Richter, R. M. Huffaker, F. F. Hall, “Performance characteristics of the NOAA Pulsed Doppler Lidar and Its Application to Atmospheric Measurements,” in Proceedings, Fifth Symposium on Meteorological Observations and Instrumentation, (Toronto, Canada, (April 11–15, 1983) p. 481.

Lawrence, T. R.

T. R. Lawrence, R. M. Hardesty, M. J. Post, R. A. Richter, R. M. Huffaker, F. F. Hall, “Performance characteristics of the NOAA Pulsed Doppler Lidar and Its Application to Atmospheric Measurements,” in Proceedings, Fifth Symposium on Meteorological Observations and Instrumentation, (Toronto, Canada, (April 11–15, 1983) p. 481.

F. F. Hall, R. E. Cupp, R. M. Hardesty, T. R. Lawrence, M. J. Post, R. A. Richter, B. F. Weber, “Six Years of Pulsed-Doppler Lidar Field Experiments at NOAA/WPL,” in Proceedings, Sixth Symposium on Meteorological Observations and Instrumentation, New Orleans, (January 12–16, 1987) p. 11.

Y. Zhao, M. J. Post, T. R. Lawrence, “The Effects of Injection Pinhole, Mirror. Tilt, and Reflectivity Function of the Tapered Output Mirror on the Performance of a CO2 TEA Laser with Unstable Resonator,” to be published.

Post, M. J.

Y. Zhao, M. J. Post, R. M. Hardesty, “Receiving Efficiency of Monostatic Pulsed Coherent Lidars. 1: Theory,” Appl. Opt. 00, 000–000 (1990).

M. J. Post, “Atmospheric Infrared Backscattering Profiles: Interpretation of Statistical and Temporal Properties,” NOAA Technical Memorandum ERL WPL-122 (1985).

T. R. Lawrence, R. M. Hardesty, M. J. Post, R. A. Richter, R. M. Huffaker, F. F. Hall, “Performance characteristics of the NOAA Pulsed Doppler Lidar and Its Application to Atmospheric Measurements,” in Proceedings, Fifth Symposium on Meteorological Observations and Instrumentation, (Toronto, Canada, (April 11–15, 1983) p. 481.

F. F. Hall, R. E. Cupp, R. M. Hardesty, T. R. Lawrence, M. J. Post, R. A. Richter, B. F. Weber, “Six Years of Pulsed-Doppler Lidar Field Experiments at NOAA/WPL,” in Proceedings, Sixth Symposium on Meteorological Observations and Instrumentation, New Orleans, (January 12–16, 1987) p. 11.

M. J. Post, Richard Cupp, “Optimizing a Pulsed Doppler Lidar,” Submitted to Appl. Opt.28, 4145–4158 (1990).
[CrossRef]

Y. Zhao, M. J. Post, T. R. Lawrence, “The Effects of Injection Pinhole, Mirror. Tilt, and Reflectivity Function of the Tapered Output Mirror on the Performance of a CO2 TEA Laser with Unstable Resonator,” to be published.

Richter, R. A.

F. F. Hall, R. E. Cupp, R. M. Hardesty, T. R. Lawrence, M. J. Post, R. A. Richter, B. F. Weber, “Six Years of Pulsed-Doppler Lidar Field Experiments at NOAA/WPL,” in Proceedings, Sixth Symposium on Meteorological Observations and Instrumentation, New Orleans, (January 12–16, 1987) p. 11.

T. R. Lawrence, R. M. Hardesty, M. J. Post, R. A. Richter, R. M. Huffaker, F. F. Hall, “Performance characteristics of the NOAA Pulsed Doppler Lidar and Its Application to Atmospheric Measurements,” in Proceedings, Fifth Symposium on Meteorological Observations and Instrumentation, (Toronto, Canada, (April 11–15, 1983) p. 481.

Siegman, A. E.

Sziklas, E. A.

Weber, B. F.

F. F. Hall, R. E. Cupp, R. M. Hardesty, T. R. Lawrence, M. J. Post, R. A. Richter, B. F. Weber, “Six Years of Pulsed-Doppler Lidar Field Experiments at NOAA/WPL,” in Proceedings, Sixth Symposium on Meteorological Observations and Instrumentation, New Orleans, (January 12–16, 1987) p. 11.

Zhao, Y.

Y. Zhao, M. J. Post, R. M. Hardesty, “Receiving Efficiency of Monostatic Pulsed Coherent Lidars. 1: Theory,” Appl. Opt. 00, 000–000 (1990).

Y. Zhao, M. J. Post, T. R. Lawrence, “The Effects of Injection Pinhole, Mirror. Tilt, and Reflectivity Function of the Tapered Output Mirror on the Performance of a CO2 TEA Laser with Unstable Resonator,” to be published.

Appl. Opt. (2)

Y. Zhao, M. J. Post, R. M. Hardesty, “Receiving Efficiency of Monostatic Pulsed Coherent Lidars. 1: Theory,” Appl. Opt. 00, 000–000 (1990).

E. A. Sziklas, A. E. Siegman, “Mode Calculations in Unstable Resonators with Flowing Saturable Gain. 2: Fast Fourier Transform Method,” Appl. Opt. 14, 1874–1889 (1975).
[CrossRef] [PubMed]

NOAA Technical Memorandum ERL WPL-122 (1)

M. J. Post, “Atmospheric Infrared Backscattering Profiles: Interpretation of Statistical and Temporal Properties,” NOAA Technical Memorandum ERL WPL-122 (1985).

Other (6)

T. R. Lawrence, R. M. Hardesty, M. J. Post, R. A. Richter, R. M. Huffaker, F. F. Hall, “Performance characteristics of the NOAA Pulsed Doppler Lidar and Its Application to Atmospheric Measurements,” in Proceedings, Fifth Symposium on Meteorological Observations and Instrumentation, (Toronto, Canada, (April 11–15, 1983) p. 481.

F. F. Hall, R. E. Cupp, R. M. Hardesty, T. R. Lawrence, M. J. Post, R. A. Richter, B. F. Weber, “Six Years of Pulsed-Doppler Lidar Field Experiments at NOAA/WPL,” in Proceedings, Sixth Symposium on Meteorological Observations and Instrumentation, New Orleans, (January 12–16, 1987) p. 11.

M. J. Post, Richard Cupp, “Optimizing a Pulsed Doppler Lidar,” Submitted to Appl. Opt.28, 4145–4158 (1990).
[CrossRef]

Y. Zhao, M. J. Post, T. R. Lawrence, “The Effects of Injection Pinhole, Mirror. Tilt, and Reflectivity Function of the Tapered Output Mirror on the Performance of a CO2 TEA Laser with Unstable Resonator,” to be published.

A. E. Siegman, Lasers (University Science Books, Mill Valley, CA1986).

British Association for the Advancement of Science: Mathematical Tables, Vol. 6: Bessel Functions, Part I, Functions of Order Zero and Unity (University Press, Cambridge, 1950).

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Figures (24)

Fig. 1
Fig. 1

TEA laser output patterns (with injection pinhole): (a) intensity; (b) phase. Horizontal size: 1.89 × 1.89 cm2. Arbitrary scale for the intensity. Phase values (in radians): 0.0 at the center; −0.751 at the maximum; 0.32 at the edge.

Fig. 2
Fig. 2

TEA laser output patterns (without pinhole): (a) intensity; (b) phase. Horizontal size: 1.89 × 1.89 cm2. Arbitrary scale for the intensity. Phase values (in radians): 0.0 at the center; −0.114 at the maximum; 0.581 at the edge.

Fig. 3
Fig. 3

Transmitting laser patterns at telescope secondary: (a) intensity; (b) phase. Horizontal size: 3.06 × 3.06 cm2. Arbitrary scale for the intensity. Phase values (in radians): 0.0 at the center; −0.287 at the maximum; 3.02 at the edge.

Fig. 4
Fig. 4

Transmitting laser patterns at telescope primary (10×): (a) intensity; (b) phase. Horizontal size: 15 × 15 cm2. Arbitrary scale for the intensity. Phase values (in radians): 0.0 at the center; −0.225 at the maximum; 2.31 at the edge.

Fig. 5
Fig. 5

Transmitting laser patterns at telescope primary (20×): (a) intensity; (b) phase. Horizontal size: 15 × 15 cm2. Arbitrary scale for the intensity. Phase values (in radian): 0.0 at the center; −0.271 at the maximum; −0.115 at the edge.

Fig. 6
Fig. 6

Normalized intensity of the transmitted beam, Itn(r,z), as a function of range. Telescope power is 20×.

Fig. 7
Fig. 7

Optical layout of the receiving branch in WPL lidar.

Fig. 8
Fig. 8

Relative intensity of LO at the first wire grid polarizer WG1, where the aperture radius is 1.0 cm. Before WG1, the LO beam is first truncated at the output of the beam expander, where the aperture radius is 1.75 cm, and the e−2 size of the untruncated LO beam is 1.744 cm. At the center of WG1, the ratio of the LO intensity to the maximum intensity of the untruncated LO, indicated by Imax, is 1.663.

Fig. 9
Fig. 9

Relative intensity of LO at detector lens, where the aperture radius is 1.265 cm. At the center of the lens, the ratio of the LO intensity to the maximum intensity of the untruncated LO, Imax, is 1.473.

Fig. 10
Fig. 10

LO patterns in detector plane: (a) relative intensity I(r)/Imax, where Imax is the maximum intensity of the untruncated LO; (b) phase (in radian). The e−2 size of the untruncated LO at the detector is 19.3 μm, which is much smaller than the size of the Airy pattern of the truncated LO, ~46 μm.

Fig. 11
Fig. 11

BPLO patterns at detector lens: (a) intensity; (b) phase. Horizontal size: 2.53 × 2.53 cm2. Arbitrary scale for the intensity. Phase values (in radian): 0 at the center; −0.768 at the edge.

Fig. 12
Fig. 12

BPLO patterns at telescope secondary: (a) intensity; (b) phase. Horizontal size: 3.06 × 3.06 cm2. Arbitrary scale for the intensity. Phase values (in radian): 0.0 at the center; −0.342 at the maximum; 1.96 at the edge.

Fig. 13
Fig. 13

BPLO patterns at telescope primary (10×): (a) intensity; (b) phase. Horizontal size: 15 × 15 cm2. Arbitrary scale for the intensity. Phase values (in radian): 0 at the center; −0.358 at the maximum; and 1.52 at the edge.

Fig. 14
Fig. 14

BPLO patterns at telescope primary (20×): (a) intensity; (b) phase. Horizontal size: 15 × 15 cm2. Arbitrary scale for the intensity. Phase values (in radian): 0 at the center; −0.356 at the maximum; −0.348 at the edge.

Fig. 15
Fig. 15

Single-point receiving efficiency η s (r,z) as a function of range. LO is collimated. Telescope power is 20×.

Fig. 16
Fig. 16

Signal diffraction patterns at the detector due to a single-point source at 30 km: (a) r = 0; (b) r = 0.5W; (c) r = 1.0W; (d) r = 1.5W. Horizontal size: 200 × 200 μm2. Arbitrary scale for the intensity.

Fig. 17
Fig. 17

Effect of injection pinhole on system receiving efficiency: (1) laser with injection pinhole; (2) laser without pinhole. LO is collimated and detector is at LO waist.

Fig. 18
Fig. 18

Effect of LO beam divergence on system receiving efficiency (20× telescope): (1) collimated LO; (2)–(5) uncollimated LO. Distance from focal plane to the detector: (2) 0.5 mm; (3) 1.0 mm; (4) 1.5 mm; (5) 2.0 mm; (6) −1.0 mm. Detector is at LO waist.

Fig. 19
Fig. 19

Effect of LO beam divergence on system receiving efficiency (10× telescope): (1) collimated LO; (2), (3) uncollimated LO. Distance from focal plane to the detector: (2) 0.5 mm; (3) 1.0 mm.

Fig. 20
Fig. 20

Focal setting effect: (a) 20× telescope: (1) focused at infinity; (2) focused at 2.4 km; (3) focused at 5 km; (4) focused at 10 km. (b) telescope 10×: (1) focused at 2.4 km; (2) focused at 3.5 km; (3) focused at 5 km; (4) focused at 10 km; (5) focused at infinity.

Fig. 21
Fig. 21

Misalignment effect: (a) telescope 20×; (b) telescope 10×. LO is collimated and detector is at LO waist. Solid lines: η(z) with misalignment. Angle of misalignment between transmitter and receiver: (1) 10 μrad; (2) 20 μrad; (3) 30 μrad; (4) 40 μrad; (5) 50 μrad. Dashed lines: η(z) with perfect alignment.

Fig. 22
Fig. 22

Scanner astigmatism effect: (a) 20× telescope; (b) 10× telescope. (1) η(z) with perfect scanning mirrors; (2) η(z) with astigmatic scanners.

Fig. 23
Fig. 23

Receiving efficiency at 30 km as a function of LO spot size at the detector. LO is Gaussian and collimated.

Fig. 24
Fig. 24

Signal diffraction pattern (from 30 km) at the detector: (1) total intensity of the incoherent signal; (2) intensity pattern due to an axial point source; (3) phase pattern due to an axial point source.

Tables (1)

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Table I The Spot Sze of the Untruncated Old Hybrid CO2 Laser Transmitted Through a 19.6× Telescope

Equations (5)

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η ( z ) = s I t n ( Q , z ) η s ( Q , z ) d Q ,
U ( r ) = 2 π p ( r ) λ z 0 a U 0 ( r 0 ) exp ( j π r 0 2 λ z ) p 0 ( r 0 ) J 0 ( 2 π r r 0 λ z ) r 0 d r 0 ,
η ( z ) = 2 π 0 I tn ( r , z ) η s ( r , z ) r d r .
η ( z , α ) = 0 η s ( r , z ) r d r 0 2 π I tn [ r ( z , α , r , ϕ ) ] d ϕ .
U ( r , ϕ ) = p ( r ) λ z 0 a U 0 ( r 0 ) exp ( j π r 0 2 λ z ) p 0 ( r 0 ) r 0 d r 0 × 0 2 π exp [ - j π ( r 0 cos θ ) 2 λ f x ] exp [ - j π ( r 0 sin θ ) 2 λ f y ] × exp [ - 2 π r r 0 cos ( θ - ϕ ) λ z ] d θ .

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