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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 22 — Oct. 27, 2008
  • pp: 18288–18295
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All semiconductor laser Doppler anemometer at 1.55 µm

René Skov Hansen and Christian Pedersen  »View Author Affiliations


Optics Express, Vol. 16, Issue 22, pp. 18288-18295 (2008)
http://dx.doi.org/10.1364/OE.16.018288


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Abstract

We report to our best knowledge the first all semiconductor Laser Doppler Anemometer (LIDAR) for wind speed determination. We will present the design and first experimental results on a focusing coherent cw laser Doppler anemometer for measuring atmospheric wind velocities in the 10 meters to 300 meters distance range. Especially, we will demonstrate that both the output power as well as the demanding coherence properties required from the laser source can be accomplished by an all semiconductor laser. Preliminary tests at a distance of 40 meters indicate a typical signal to noise ratio of 9 dB. This result is obtained at a clear day with an up-date rate of 12 Hz.

© 2008 Optical Society of America

1. Introduction

During the past decade, both pulsed and focused continuous wave (cw) coherent mid range laser Doppler anemometers has been developed to a high level of sophistication and are now available as commercial products [1]. Continuous wave anemometers, which we will concentrate on in the present paper, focuses an output laser beam at the point in the atmosphere where the radial wind velocity shall be measured. The back-scattered light from the aerosols in the wind flow is Doppler shifted and collected by the anemometer optics. The velocity dependent Doppler shift of the back-scattered light is detected using an optical autodyne or heterodyne detection scheme where the collected light is mixed with local reference wave on a semiconductor photo detector. This measurement scheme requires the back-scattered and the reference wave to be temporally correlated. Two ways of obtaining this correlation has been employed; using a laser source with a sufficiently long coherence length and creating the local oscillator within a short path in the set-up, or using a low coherence laser and creating the local oscillator through path-length compensating optics [2

2. G. G. Matvienko, S. N. Polyakov, and V. K. Oshlakov, “Low-coherence doppler lidar with multiple time coherence of reference and probe waves,” Laser Phys. 17, p 1327–1332 (2007) [CrossRef]

5

5. K. W. Fischer, “High spectral resolution, low-coherence technique for daytime Doppler wind measurements with lidar,” IGARSS ′96. 1996 International Geoscience and Remote Sensing Symposium. Remote Sensing for a Sustainable Future 1, (Cat. No.96CH35875), 694-6, (1996)

]. In this paper we will be concentrating on the long coherence scheme since it yields the most compact and simple set-up and it is able to dynamically change the measuring distance.

The first suggestions for a compact LIDAR system were based on waveguide CO2 lasers [6

6. R. Frehlich, “Comparison of 2- and 10-µm Coherent Doppler Lidar Performance,” J. Atmos. Oceanic Technol. 12, 415–420 (1995). [CrossRef]

]. Note however that LIDAR systems based on bulk optics have also been demonstrated [7

7. T. J. Kane, W. J. Kozlovsky, R. L. Byer, and C. E. Byvik, “Coherent laser radar at 1.06 mm using Nd:YAG lasers,” Opt. Lett. 12, 239–241, (1987). [CrossRef] [PubMed]

]. CO2 systems have proven to operate stable, but since the operating wavelength of the CO2 laser lies in the far infrared region of the spectrum, specially cooled detectors are needed. Furthermore the size and the special materials needed for optics in this wavelength range forces the cost price of these LIDAR instruments up to a level which prevents mass production. More recently, systems based on a fiber laser master oscillator/fiber amplifier combination and using communication fiber technology throughout the instrument have been successfully constructed [1]. Still the complexity and price is high, i.e. in the order of 100.000 Euros. The fiber lasers operate with a wavelength equal to 1550nm. The benefits of using this near infrared wavelength are threefold; the wavelength is considered as being eye-safe at the power levels required for atmospheric anemometry applications, conventional glass-optics and standard communication fiber optics can be employed for the optical components in the anemometer, and a conventional un-cooled GaAs detector can be employed as the detection means.

Common for the coherent laser Doppler anemometers are the extensive requirements on the laser source with respect to overall stability, the relative intensity noise (RIN) [8

8. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Second Edition), Springer (1993).

], the beam quality, the temporal and spatial coherency and the necessary output power. The causes of these constrains are briefly discussed here; the measurement volume in the atmosphere, from which the anemometer receives signal, is given by the intensity distribution of the focused laser beam. The optimum Doppler signal is achieved when the phase fronts of the reference wave and the back-scattered wave are perfectly matched and the intensity distribution within the measurement volume is Gaussian. Thus the optimum performance is obtained with a Gaussian intensity distribution from the laser. In order to perform the autodyne or heterodyne detection of the Doppler frequency of the back-scattered light, the coherence length of the laser source has to be at least twice the distance between the instrument and the measurement volume. At altitudes ranging from 0 to 1km, the collected reflection coefficient of the aerosols in the volume along the Rayleigh length of the focused beam is in the order of 10-12. This implies that relatively high output power is needed to have sufficient back reflected light for detection. Our LIDAR system requires in the range from 0.5-1Watt (CW) to obtain a reliable Doppler signal. Considerable development effort and special care has to be put into laser unit in order to meet these requirements. This has until now limited the possibility for substantial price reductions. Consequently the laser unit is the most delicate and expensive component in today’s LIDAR systems.

This paper demonstrates a possible way to construct a low cost laser anemometer based on a newly developed all-semiconductor Master-Oscillator-Power-Amplifier (MOPA). The laser consists of a Distributed Feed-Back (DFB) master oscillator section followed by a tapered amplifier section. Both sections are manufactured on a single chip. With some considerations on the anemometer optics design, the laser has been found to be able to meet the demanding requirements for coherent laser Doppler anemometer applications.

2 The all semiconductor MOPA laser

The semiconductor laser employed in our laser Doppler anemometer is an edge emitting laser which consist of two sections: A low-power distributed feed-back master oscillator followed by a tapered power amplifier. Each section is driven by its own current supply. The two sections are laid out on a single semiconductor chip see Fig. 1 [9

9. M. L. Osayuki, W. Hu, R. M. Lammert, T. Liu, Y. Ma, S. W. Oh, C. Panja, P. T. Rudy, T. Stakelon, and J. E. Unga, “High brightness semiconductor lasers,” SPIE Photonics West, LASE Conference 6456, 64560D.1-64560D.7, (2007)

].

Fig. 1. The MOPA semiconductor unit including a first, single-frequency, DFB laser and a tapered power amplifier.

The MOPA unit is able to deliver approximately 0.9 Watt of optical power from the power amplifier. This is power level is necessary in our LIDAR system. Of particular importance is the line-width of the laser unit. The line-width of the output from the DFB-laser/amplifier combination is determined from the RF-frequency spectrum of the photo-current in a standard Mac-Zender interferometer set-up. In this interferometer one part of the laser beam is coupled to a 2.5 km fiber and subsequently mix with a non-delayed part to produce a self heterodyned signal at the detector. The non-delayed beam is frequency-shifted by approximately 80MHz using an acoustic-optic modulator so as to eliminate low frequency noise sources. Under typical stabilized conditions, the FWHM line width of this laser is found to be 100kHz. This line-width is appropriate for an anemometer operating at distances up to about 300 meters. A collection of typical detector RF-spectra is shown in Fig. 2. Note that the MOPA device is temperature controlled to within ±0.05°C using a thermoelectric cooler.

Fig. 2. A collection of RF power spectra of the photocurrent obtained from the Mac-Zender interferometer. The operating conditions for the MOPA laser is: Drive current for the DFBsection is 460mA, and the drive current for the amplifier section=4.0A, and the temperature of the laser C-mount=22°C. The FWHM line with of the laser optical output is equal to the HWHM (3-dB level) of the power spectrum of the photo current. Horisontal axis: 600Khz/div, vertical axis: 3 dB/div.

The laser output has a Gaussian intensity distribution with small variations along the fast axis. However, along the slow axis the intensity shows a random fringe pattern within a Gaussian envelope, see Fig. 3.

Fig. 3. The intensity distribution from the naked laser shown by a viewer-card. The fast axis is the vertical direction and the slow axis is aligned horizontally. The intensity profile along the slow axis shows a line structure.

3 The laser anemometer

The optical set-up for the monostatic laser anemometer demonstrated is shown in Fig. 4.

Fig. 4. The optical set-up for the laser anemometer using the MOPA semiconductor laser

The set-up is based on the MOPA semiconductor laser whose optical output is collimated and made circular symmetric using a high numerical lens followed by a 40mm focal length cylindrical lens, see Fig 4. The 1/e2 diameter of the collimated output beam is 2.5mm. The output from the laser is linearly TM-polarized and is fully transmitted through the polarizing beam splitter. The quarter wave plate changes the transmitted optical output into a circular polarization state. The quarter wave plate is slightly tilted to avoid any back-reflected TM-polarized laser light to the laser. The detector is a InGaAs PIN photodiode. The local oscillator needed for autodyne detection of the Doppler frequency of the received backscattered light is established by back-reflecting a small fraction of the circularly polarized laser output towards the detector. For this purpose, a 0.3% reflecting reference window is inserted after the quarter wave plate. The back-reflected light takes a second transit through the quarter wave plate and end up as TE-polarized light. This TE-polarized wave is fully reflected by the polarizing beam splitter and forms the local oscillator in the detection process. The wave front disturbances exiting inherently in the output from the laser are thus also transmitted towards the detector. When this wave front is used for the heterodyne mixing with the received back-scattered light, having a smooth wave front, the areas of varying phase may attenuate the detected Doppler signal [12

12. Z. Yanzeng, J. P. Madison, and R. M. Hardesty, “Receiving efficiency of monostatic pulsed coherent lidars. 1: Theory,” Appl. Opt.29, (1990).

]. Therefore, in order to clean-up the wave front of the reference wave, the detector is positioned at the focal plane of a Fourier transforming lens. The size of the detector area and the size of the Gaussian part of the reference beam are chosen to match. Thereby the detector area/lens combination serves as a spatial filter, filtering out unwanted spatial components and phase-front disturbances of the reference wave front. The collected back-scattered signal is likewise focused onto the small detector area making the two wave fronts match, thus maximizing the heterodyne mixing efficiency. The detector radius is chosen to be equal to the 1/e2 intensity radius of the focused Gaussian waves. The detector thus collects most of the optical power contained in the Gaussian part of the waves. Approximately 3mW of the back-reflected local oscillator power is focused onto the detector surface. The detector is slightly tilted to avoid any back reflections towards the laser.

Due to the low loss beam splitter arrangement, most of the laser power is transmitted as circularly polarized light through the reference window. The telescope subsequently expands and focuses the transmitted beam to form the focused measuring volume at the desired measuring distance. We note that also the optical telescope also acts as a spatial filter. Only the pure Gaussian and plane wave part of the laser output contributes to the central spot and forms the focused remote measurement volume. All other higher spatial frequencies in the intensity distribution are focused outside the measuring volume. The intensity distribution across the focus plane in the measuring volume is seen in Fig. 5. The imperfections of the laser wave front are filtered out as the non-Gaussian spatial frequencies are clearly observed outside the Gaussian spot. The total output power from the laser is 0.9Watt. We estimate that approximately P transmit=0.6Watt is within the central spot, forming the measuring volume. A 3inch diameter lens with 200mm focal length is employed as the transmitting lens for the telescope. In order to avoid diffraction effects from the edges of the telescope lenses, the 1/e2 radius of the Gaussian part of the output beam is chosen to be 3 times smaller than the radius of telescope lenses.

Fig. 5. An image of the intensity distribution across the measuring volume. The higher non-Gaussian spatial frequencies are clearly seen outside the Gaussian focus spot. These unwanted spatial frequencies will be not be imaged and thus mixed efficiently with the reference beam at the detector surface.

The back-scattered optical wave from the aerosols is received by the same telescope as used in the transmitter part. The Fourier transforming lens focuses the two waves onto the detector unit. The detector size is matched so as to receive light only from the Gaussian part of the two waves. The detection is shot-noise limited. The detected Doppler signal is further amplified and Fourier analyzed by the signal processing electronics. A running bin-wise averaging of the detector power spectrum is performed to extract the Doppler spectrum from the noisy detector signal. Typically, 2048 spectra, each with 1024 sample points, are averaged with 75% time overlap between each calculated Fourier-power spectrum.

Our anemometer is operated in the focused mode and thus collects light from a measuring volume set by the Rayleigh length. Equation 24 of ref. 10 or equation 15 of ref. 11 gives the signal to noise ration of the detector output. When operating the anemometer with a tight focus the equations approximates [11

11. M. J. Kavaya and P. J. M. Suni, “Continuous wave coherent laser radar: calculation of measurement location and volume,” Appl. Opt. 30, 2634–2642 (1991). [CrossRef] [PubMed]

],

(SN)=πRdηa2PtransmitΓ(f)qeΔfbin.
(1)

Where Γ(f)=βλ is the collected reflection coefficient of the aerosols contained in the volume with radius given by the beam waist and a length equal to two times the Rayleigh length of the focused beam. β is the aerosol back-scatter coefficient. λ is the wavelength of the laser. ηa is added as the receiving efficiency of the anemometer given by the overlap integral between the detector surface, the reference wave front, and the received back-scattered wave front [12

12. Z. Yanzeng, J. P. Madison, and R. M. Hardesty, “Receiving efficiency of monostatic pulsed coherent lidars. 1: Theory,” Appl. Opt.29, (1990).

]. We do not have the accurate value for ηa. Since our focused cw set-up mainly collects light from finite range (the Rayleigh range) like a pulsed system, we employ a typical value of a pulsed system ηa≅0.4 [12

12. Z. Yanzeng, J. P. Madison, and R. M. Hardesty, “Receiving efficiency of monostatic pulsed coherent lidars. 1: Theory,” Appl. Opt.29, (1990).

]. Ptransmit is the Gaussian part of the transmitted power. Rd is the responsitivity of the detector, which is equal to 0.95 [A/W] in our case. qe is the charge of the electron, and Δfbin is the frequency bandwidth of each frequency-bin in the FFT-power spectrum of the detector signal. The bandwidth is given by Δfbin=fs/Q where fs is the sampling frequency and Q is the number of time-domain samples taken for calculating each FFT-spectrum. The volume and especially the Rayleigh length, i.e. the in-line resolution increases dramatically as the distance to the focus point increases. The distribution of wind velocities contained within the measuring volume also tends to smear out the measured Doppler spectrum. As the received signal can be considered a sum of all the back-scattered power contributions from the individual scatters in the measuring volume [10

10. C. M. Sonnenschein and F. A. Horrigan, “Signal-to-Noise Relationships for Coaxial Systems that Heterodyne Backscatter from the Atmosphere,” Appl. Opt. 10, 1600–1604 (1971). [CrossRef] [PubMed]

], the total back-scattered power received by the telescope must remain approximately constant. The measured Gaussian Doppler spectrum is modeled as a frequency-dependent reflection coefficient,

Γ(f)=βλe2αLΔfbinλ22πσwind2eλ2(ffDoppler)28σwind2
(2)

where λ is the wavelength of the laser, β and α are the back-scatter and the extension coefficients of the atmospheric air respectively. L is the distance from the instrument to the measuring volume, fDoppler is the centre Doppler frequency of the measured spectrum, and σwind is the standard derivation of the wind velocity along the measuring volume. By using the BETASPEC software model the back-scatter, β, and the extension, α, are found at an altitude of 1km for a laser wavelength of λ=1.55mm [13]: α=2.397*10-2 [km-1] and β=4.693*10-7 [(m*Sr)-1]. Using Ptransmit=0.5W, L=40m, ηa=0.4, Δfbin=48kHz, and σwind=0.3m/s, the signal to noise ratio in the FFT frequency-bin covering the centre of the Doppler spectrum (f=fDoppler) becomes -4.5dB. A different way to define the signal to noise ratio is to consider the ratio of the strength of the detected Doppler signal to the standard derivation of the bin height of the averaged FFT power spectrum,

SN=Sσsn=M2(SN)
(3)

where S is the peak power of the detected Doppler signal, σsn is the standard derivation of the bin-heights in the FFT power spectrum of the shot-noise, measured without Doppler signals, M is the number of power spectra averaged and (S/N) is the signal to noise ratio obtained from Eq. (1). Equation 3 tells the height of the signal peak with respect to the noise “grass” in the rest of the noisy spectrum. In other words how clearly the Doppler peak can be distinguished from the noise floor. Averaging 2048 spectra yields a <S/N>=14dB.

A typical Doppler spectrum measured by our anemometer on a clear day is shown together with a Gaussian fit to the spectrum in Fig. 6. The anemometer is focused at distance of 40m. The Doppler peak is clearly identified in the spectrum. The DFB laser current is 430mA, and the tapered amplifier section is operated at 3A. The temperature of the laser unit is 19.9°C. The <S/N> in the spectrum shown is found to be 9dB which less than, but in somewhat good agreement with our theoretical calculations based on the BETASPEC model calculations. However the measurement shown is taken at a very low altitude, i.e. about 25m above the ground. We will therefore anticipate a higher backscatter coefficient as compared to the listed back scatter coefficient at an altitude of 1 km. Some improvements of the instrument is thus still to find. Any DC current and frequencies below 300kHz are removed before sampling the Doppler signal for the FFT process. Thus velocities below 0.3m/s can not be measured. The maximum velocity is set by the sampling rate, limited to 19m/s.

Fig. 6. A typical Doppler spectrum. A Gaussian fit to the Doppler spectrum is shown as the dotted curve.

4. Conclusion

Based on a single chip MOPA laser configuration, a coherent cw laser Doppler anemometer for measuring atmospheric wind velocities in the 10 meters to 200 meters distance range, has been demonstrated. A typical signal to noise ration of 9dB has been realised at 40 meters distance with an up-date frequency of 12Hz. Future research will be directed towards systematic field tests.

Both output power as well as the coherence properties required by the laser source can be accomplished by using an monolithic, all semiconductor laser unit. The laser unit operates at an wavelength of 1.55 mm and exploits an Master Oscillator – Power Amplifier (MOPA) configuration. Typically, a total output power of 0.8 Watt and a FWHM line width of 100kHz have been obtained. The wave front emitted by the MOPA laser is not ideal for the autodyne detection, however a spatial filtering technique has been demonstrated to circumvent this draw-back. In conclusion we believe to have demonstrated the first all semiconductor Doppler Laser Anemometer for operating over large distances for the wind speed determination application with the ability to dynamically change the measuring distance. Thus we show a route to low-cost and compact LIDAR systems for wind speed determination in the 40 –200 meter range.

Acknowledgments

We would like to acknowledge the Danish Research Council for supporting the work presented.

References and links

1.

ZephIR Laser Anemometer from Natural Power, http://www.naturalpower.com/products-and-services/zephir/zephir-product.html.

2.

G. G. Matvienko, S. N. Polyakov, and V. K. Oshlakov, “Low-coherence doppler lidar with multiple time coherence of reference and probe waves,” Laser Phys. 17, p 1327–1332 (2007) [CrossRef]

3.

J.-L. Shen, Kunnemeyer, “Amplified reference pulse storage for low-coherence pulsed Doppler lidar,” Appl. Opt. 45, p 8346-9 (2006) [CrossRef] [PubMed]

4.

A. A. Dorrington, R. Kunnemeyer, and P. M. Danehy, “Reference-beam storage for long-range lowcoherence pulsed Doppler lidar,” Appl. Opt. 40, 3076–81 (2001) [CrossRef]

5.

K. W. Fischer, “High spectral resolution, low-coherence technique for daytime Doppler wind measurements with lidar,” IGARSS ′96. 1996 International Geoscience and Remote Sensing Symposium. Remote Sensing for a Sustainable Future 1, (Cat. No.96CH35875), 694-6, (1996)

6.

R. Frehlich, “Comparison of 2- and 10-µm Coherent Doppler Lidar Performance,” J. Atmos. Oceanic Technol. 12, 415–420 (1995). [CrossRef]

7.

T. J. Kane, W. J. Kozlovsky, R. L. Byer, and C. E. Byvik, “Coherent laser radar at 1.06 mm using Nd:YAG lasers,” Opt. Lett. 12, 239–241, (1987). [CrossRef] [PubMed]

8.

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Second Edition), Springer (1993).

9.

M. L. Osayuki, W. Hu, R. M. Lammert, T. Liu, Y. Ma, S. W. Oh, C. Panja, P. T. Rudy, T. Stakelon, and J. E. Unga, “High brightness semiconductor lasers,” SPIE Photonics West, LASE Conference 6456, 64560D.1-64560D.7, (2007)

10.

C. M. Sonnenschein and F. A. Horrigan, “Signal-to-Noise Relationships for Coaxial Systems that Heterodyne Backscatter from the Atmosphere,” Appl. Opt. 10, 1600–1604 (1971). [CrossRef] [PubMed]

11.

M. J. Kavaya and P. J. M. Suni, “Continuous wave coherent laser radar: calculation of measurement location and volume,” Appl. Opt. 30, 2634–2642 (1991). [CrossRef] [PubMed]

12.

Z. Yanzeng, J. P. Madison, and R. M. Hardesty, “Receiving efficiency of monostatic pulsed coherent lidars. 1: Theory,” Appl. Opt.29, (1990).

13.

BETASPEC, http://www.cas.usf.edu/lidarlab/lidar_download.html.

OCIS Codes
(010.3640) Atmospheric and oceanic optics : Lidar
(010.3920) Atmospheric and oceanic optics : Meteorology
(140.2020) Lasers and laser optics : Diode lasers
(140.5960) Lasers and laser optics : Semiconductor lasers
(280.3340) Remote sensing and sensors : Laser Doppler velocimetry
(010.0280) Atmospheric and oceanic optics : Remote sensing and sensors

ToC Category:
Atmospheric and oceanic optics

History
Original Manuscript: July 28, 2008
Revised Manuscript: October 9, 2008
Manuscript Accepted: October 19, 2008
Published: October 23, 2008

Citation
René Skov Hansen and Christian Pedersen, "All semiconductor laser Doppler anemometer at 1.55 μm," Opt. Express 16, 18288-18295 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-22-18288


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References

  1. ZephIR  Laser Anemometer from Natural Power, http://www.naturalpower.com/products-and-services/zephir/zephir-product.html.
  2. G. G. Matvienko, S. N. Polyakov, and V. K. Oshlakov, "Low-coherence doppler lidar with multiple time coherence of reference and probe waves," Laser Phys. 17, 1327-1332 (2007). [CrossRef]
  3. J.-L. Shen, Kunnemeyer, "Amplified reference pulse storage for low-coherence pulsed Doppler lidar," Appl. Opt. 45, 8346-9 (2006). [CrossRef] [PubMed]
  4. A. A. Dorrington, R. Kunnemeyer, and P. M. Danehy, "Reference-beam storage for long-range low-coherence pulsed Doppler lidar," Appl. Opt. 40, 3076-81 (2001). [CrossRef]
  5. K. W. Fischer, "High spectral resolution, low-coherence technique for daytime Doppler wind measurements with lidar," IGARSS '96. 1996 International Geoscience and Remote Sensing Symposium. Remote Sensing for a Sustainable Future 1, (Cat. No.96CH35875), 694-6, (1996).
  6. R. Frehlich, "Comparison of 2- and 10-µm Coherent Doppler Lidar Performance," J. Atmos. Oceanic Technol. 12, 415-420 (1995). [CrossRef]
  7. T. J. Kane, W. J. Kozlovsky, R. L. Byer, and C. E. Byvik, "Coherent laser radar at 1.06 mm using Nd:YAG lasers," Opt. Lett. 12, 239-241(1987). [CrossRef] [PubMed]
  8. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Second Edition), Springer (1993).
  9. M. L. Osayuki, W. Hu, R. M. Lammert, T. Liu, Y. Ma, S. W. Oh, C. Panja, P. T. Rudy, T. Stakelon, and J. E. Unga, "High brightness semiconductor lasers," SPIE Photonics West, LASE Conference 6456, 64560D.1-64560D.7, (2007).
  10. C. M. Sonnenschein and F. A. Horrigan, "Signal-to-Noise Relationships for Coaxial Systems that Heterodyne Backscatter from the Atmosphere," Appl. Opt. 10, 1600-1604 (1971). [CrossRef] [PubMed]
  11. M. J. Kavaya, and P. J. M. Suni, "Continuous wave coherent laser radar: calculation of measurement location and volume," Appl. Opt. 30, 2634-2642 (1991). [CrossRef] [PubMed]
  12. Z. Yanzeng, J. P. Madison, and R. M. Hardesty, "Receiving efficiency of monostatic pulsed coherent lidars. 1: Theory," Appl. Opt. 29, 4111-4119 (1990).
  13. BETASPEC, http://www.cas.usf.edu/lidarlab/lidar_download.html.

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