Understanding wind conditions is critical for the NASA Advanced Air Mobility (AAM) mission. The types of aircraft, and the region of the atmosphere they operate in, make them highly susceptible to wind effects. We demonstrate the feasibility of using wind lidar to measure wind dynamics for the AAM mission. Wind vector measurements from two Doppler wind lidars using dual-Doppler techniques are compared with in situ measurements from a ground-based sonic anemometer and small uninhabited aircraft systems (sUAS). Both lidar beams intersected directly above a sonic anemometer and measurements were compared. The resulting root mean square error values between the two instruments’ speed and direction measurements were 1.72 m/s and 23.05 deg, respectively. Following this test, a dual-Doppler scan pattern which measured wind vectors along a vertical column was performed while a sUAS measured wind vectors along the scanned volume for comparison. The wind profiles from the two measurement techniques are consistent and demonstrate the potential of using Doppler lidar for AAM.
A coherent Doppler lidar at 2μm wavelength has been built with higher output energy (300 mJ) than previously available. The laser transmitter is based on the solid-state Ho:Tm:LuLiF, a NASA Langley Research Center invented laser material for higher extraction efficiency. This diode pumped injection seeded MOPA has a transform limited line width and diffraction limited beam quality. NASA Langley Research Center is developing coherent wind lidar transmitter technology at eye-safe wavelength for satellite-based observation of wind on a global scale. The ability to profile wind is a key measurement for understanding and predicting atmospheric dynamics and is a critical measurement for improving weather forecasting and climate modeling. We would describe the development and performance of an engineering hardened 2μm laser transmitter for coherent Doppler wind measurement from ground/aircraft/space platform.
A ground-based 2-micron Differential Absorption Lidar (DIAL) CO2 profiling system for atmospheric boundary layer studies and validation of space-based CO2 sensors is being developed and tested at NASA Langley Research Center as part of the NASA Instrument Incubator Program. To capture the variability of CO2 in the lower troposphere a precision of 1-2 ppm of CO2 ( <0.5%) with 0.5 to 1 km vertical resolution from near surface to free troposphere (4-5 km) is one of the goals of this program. In addition, a 1% (3 ppm) absolute accuracy with a 1 km resolution over 0.5 km to free troposphere (4-5 km) is also a goal of the program. This DIAL system leverages 2-micron laser technology developed under NASA’s Laser Risk Reduction Program (LRRP) and other NASA programs to develop new solid-state laser technology that provides high pulse energy, tunable, wavelength-stabilized, and double-pulsed lasers that are operable over pre-selected temperature insensitive strong CO2 absorption lines suitable for profiling of lower tropospheric CO2. It also incorporates new high quantum efficiency, high gain, and relatively low noise phototransistors, and a new receiver/signal processor system to achieve high precision DIAL measurements. This presentation describes the capabilities of this system for atmospheric CO2 and aerosol profiling. Examples of atmospheric measurements in the lidar and DIAL mode will be presented.
Knowledge derived from global tropospheric wind measurement is an important constituent of our overall understanding of climate behavior [1]. Accurate weather prediction saves lives and protects properties from destructions. High-energy 2-micron laser is the transmitter of choice for coherent Doppler wind detection. In addition to the eye-safety, the wavelength of the transmitter suitably matches the aerosol size in the lower troposphere. Although the technology of the 2-micron laser has been maturing steadily, lidar derived wind data is still a void in the global weather database. In the last decade, researchers at NASA Langley Research Center (LaRC) have been engaged in this endeavor, contributing to the scientific database of 2-micron lidar transmitters. As part of this effort, an in depth analysis of the physics involved in the workings of the Ho: Tm laser systems have been published. In the last few years, we have demonstrated lidar transmitter with over1Joule output energy. In addition, a large body of work has been done in characterizing new laser materials and unique crystal configurations to enhance the efficiency and output energy of the 2-micron laser systems. At present 2-micron lidar systems are measuring wind from both ground and airborne platforms. This paper will provide an overview of the advancements made in recent years and the technology maturity levels attained.
The latest flight demonstration of Doppler Aerosol Wind Lidar (DAWN) at NASA Langley Research Center (LaRC) is presented. The goal of the campaign was to demonstrate the improvement of DAWN system since the previous flight campaign in 2012 and the capabilities of DAWN and the latest airborne wind profiling algorithm APOLO (Airborne Wind Profiling Algorithm for Doppler Wind Lidar) developed at LaRC. The comparisons of APOLO and another algorithm are discussed utilizing two and five line-of-sights (LOSs), respectively. Wind parameters from DAWN were compared with ground-based radar measurements for validation purposes. The campaign period was June – July in 2013 and the flight altitude was 8 km in inland toward Charlotte, NC, and offshores in Virginia Beach, VA and Ocean City, MD. The DAWN system was integrated into a UC12B with two operators onboard during the campaign.
A technique has been developed for imaging the wind field over offshore areas being considered for wind farming. This is accomplished with an eye-safe 2-μm wavelength coherent Doppler lidar installed in an aircraft. By raster scanning the aircraft over the wind energy area (WEA), a three-dimensional map of the wind vector can be made. This technique was evaluated in 11 flights over the Virginia and Maryland offshore WEAs. Heights above the ocean surface planned for wind turbines are shown to be within the marine boundary layer, and the wind vector is seen to show variation across the geographical area of interest at turbine heights.
Two versions of airborne wind profiling algorithms for the pulsed 2-micron coherent Doppler lidar system at NASA Langley Research Center in Virginia are presented. Each algorithm utilizes different number of line-of-sight (LOS) lidar returns while compensating the adverse effects of different coordinate systems between the aircraft and the Earth. One of the two algorithms APOLO (Airborne Wind Profiling Algorithm for Doppler Wind Lidar) estimates wind products using two LOSs. The other algorithm utilizes five LOSs. The airborne lidar data were acquired during the NASA’s Genesis and Rapid Intensification Processes (GRIP) campaign in 2010. The wind profile products from the two algorithms are compared with the dropsonde data to validate their results.
A field demonstration was done from Virginia Beach, Virginia, to show the use of high-energy (250-mJ) eyesafe Doppler lidar for measurements of offshore wind. The lidar is located onshore and pointed near-horizontally to reach a target area many kilometers away. In sample measurements, the lidar scan's hypothetical turbine is located 6 km away. For one beam elevation of interest, the horizontal wind vector is measured by scanning the beam in azimuth. The elevation can then be changed to profile the wind at many altitudes. An example measurement is shown in which wind vector is determined at six altitudes covering the height of a supposed turbine and above. In addition to the wind vector, wind shear is measured across a turbine blade span width. Over a two-week period in October 2011, range capability was found to vary from 4.5 to 17 km depending on weather and aerosol backscatter conditions. A comparison was made with an anemometer to validate the lidar's measurements.
KEYWORDS: LIDAR, Profiling, Signal to noise ratio, Data acquisition, Doppler effect, Control systems, Data processing, Digital signal processing, Data transmission, Fourier transforms
Two different noise whitening methods in airborne wind profiling with a pulsed 2-micron coherent Doppler lidar system
at NASA Langley Research Center in Virginia are presented. In order to provide accurate wind parameter estimates
from the airborne lidar data acquired during the NASA Genesis and Rapid Intensification Processes (GRIP) campaign in
2010, the adverse effects of background instrument noise must be compensated properly in the early stage of data
processing. The results of the two methods are presented using selected GRIP data and compared with the dropsonde
data for verification purposes.
A pulsed 2-micron coherent Doppler lidar system at NASA Langley Research Center in Virginia flew on the NASA's
DC-8 aircraft during the NASA Genesis and Rapid Intensification Processes (GRIP) during the summer of 2010. The
participation was part of the project Doppler Aerosol Wind Lidar (DAWN) Air. Selected results of airborne wind
profiling are presented and compared with the dropsonde data for verification purposes. Panoramic presentations of
different wind parameters over a nominal observation time span are also presented for selected GRIP data sets. The real-time
data acquisition and analysis software that was employed during the GRIP campaign is introduced with its unique
features.
Sustained research efforts at NASA Langley Research Center (LaRC) during last fifteen years have resulted in a
significant advancement in 2-micron diode-pumped, solid-state laser transmitter for wind and carbon dioxide
measurement from ground, air and space-borne platform. Solid-state 2-micron laser is a key subsystem for a
coherent Doppler lidar that measures the horizontal and vertical wind velocities with high precision and resolution.
The same laser, after a few modifications, can also be used in a Differential Absorption Lidar (DIAL) system for
measuring atmospheric CO2 concentration profiles. Researchers at NASA Langley Research Center have
developed a compact, flight capable, high energy, injection seeded, 2-micron laser transmitter for ground and
airborne wind and carbon dioxide measurements. It is capable of producing 250 mJ at 10 Hz by an oscillator and
one amplifier. This compact laser transmitter was integrated into a mobile trailer based coherent Doppler wind and
CO2 DIAL system and was deployed during field measurement campaigns. This paper will give an overview of 2-
micron solid-state laser technology development and discuss results from recent ground-based field measurements.
KEYWORDS: Data acquisition, Digital signal processing, LIDAR, Control systems, Doppler effect, Electronics, Laser optics, Scanners, Laser systems engineering, Laser processing
A general overview of the development of a data acquisition and processing system is presented for a pulsed, 2-micron
coherent Doppler Lidar system located in NASA Langley Research Center in Hampton, Virginia, USA. It is a
comprehensive system that performs high-speed data acquisition, analysis, and data display both in real time and offline.
The first flight missions are scheduled for the summer of 2010 as part of the NASA Genesis and Rapid Intensification
Processes (GRIP) campaign for the study of hurricanes. The system as well as the control software is reviewed and its
requirements and unique features are discussed.
A pulsed, 2-μm coherent Differential Absorption Lidar (DIAL) / Integrated Path Differential Absorption (IPDA)
transceiver, developed under the Laser Risk Reduction Program (LRRP) at NASA, is integrated into a fully functional
lidar instrument. This instrument measures atmospheric CO2 profiles (by DIAL) from a ground platform. It allows the
investigators to pursue subsequent in science-driven deployments, and provides a unique tool for Active Sensing of CO2
Emissions over Night, Days, and Seasons (ASCENDS) validation that was strongly advocated in the recent ASCENDS
Workshop.
The accurate measurement of energy in the application of lidar system for CO2 measurement is critical. Different
techniques of energy estimation in the online and offline pulses are investigated for post processing of lidar returns. The
cornerstone of the technique is the accurate estimation of the spectrum of lidar signal and background noise. Since the
background noise is not the ideal white Gaussian noise, simple average level estimation of noise level is not well fit in
the energy estimation of lidar signal and noise. A brief review of the methods is presented in this paper.
The design of the software for a 2-micron coherent high-speed Doppler lidar system for CO2 measurement at NASA
Langley Research Center is discussed in this paper. The specific strategy and design topology to meet the requirements
of the system are reviewed. In order to attain the high-speed digitization of the different types of signals to be sampled
on multiple channels, a carefully planned design of the control software is imperative. Samples of digitized data from
each channel and their roles in data analysis post processing are also presented. Several challenges of extremely-fast,
high volume data acquisition are discussed. The software must check the validity of each lidar return as well as other
monitoring channel data in real-time. For such high-speed data acquisition systems, the software is a key component that
enables the entire scope of CO2 measurement studies using commercially available system components.
A 2-µm wavelength coherent Doppler lidar for wind measurement has been developed of an unprecedented laser pulse energy of 250-mJ in a rugged package. This high pulse energy is produced by a Ho:Tm:LuLiF laser with an optical amplifier. While the lidar is meant for use as an airborne instrument, ground-based tests were carried out to characterize performance of the lidar. Atmospheric measurements are presented, showing the lidar's capability for wind measurement in the atmospheric boundary layer and free troposphere. Lidar wind measurements are compared to a balloon sonde, showing good agreement between the two sensors.
KEYWORDS: Doppler effect, Signal to noise ratio, LIDAR, Data processing, Statistical analysis, Data analysis, Data acquisition, Digital signal processing, Algorithm development, Profiling
The new development of a one-sided nonlinear adaptive shift estimation technique (NADSET) is introduced. The
background of the algorithm and a brief overview of NADSET are presented. The new technique is applied to the wind
parameter estimates from a 2-μm wavelength coherent Doppler lidar system called VALIDAR located in NASA Langley
Research Center in Virginia. The new technique enhances wind parameters such as Doppler shift and power estimates in
low Signal-To-Noise-Ratio (SNR) regimes using the estimates in high SNR regimes as the algorithm scans the range
bins from low to high altitude. The original NADSET utilizes the statistics in both the lower and the higher range bins to
refine the wind parameter estimates in between. The results of the two different approaches of NADSET are compared.
NASA Langley Research Center has been developing 2-micron lidar technologies over a decade for wind measurements,
utilizing coherent Doppler wind lidar technique and carbon dioxide measurements, utilizing Differential Absorption
Lidar (DIAL) technique. Significant advancements have been made towards developing state-of-the-art technologies
towards laser transmitters, detectors, and receiver systems. These efforts have led to the development of solid-state lasers
with high pulse energy, tunablility, wavelength-stability, and double-pulsed operation. This paper will present a review
of these technological developments along with examples of high resolution wind and high precision CO2 measurements
in the atmosphere. Plans for the development of compact high power lasers for applications in airborne and future space
platforms for wind and regional to global scale measurement of atmospheric CO2 will also be discussed.
This paper presents the comparison study of the theoretical and the empirical Cramer-Rao lower bounds (CRLBs) of
wind parameter estimates from a 2-μm wavelength coherent Doppler lidar system called VALIDAR located in NASA
Langley Research Center in Virginia. The statistical behavior of Doppler shift (DS) estimates in particular is of interest.
The estimates are commonly modeled as single-modal Gaussian random variables and this study is based on such
convention. The empirical statistics of DS estimates are estimated from a large amount of sample data in order to obtain
meaningful statistical moments. The impact of the new nonlinear adaptive Doppler-shift estimation technique known as
NADSET is also briefly presented in terms of the statistics of wind parameter estimates.
A coherent Doppler lidar at 2 µm wavelength has been built with higher output energy (100 mJ) than previously available. The laser transmitter is based on diode-pumped Ho:Tm:LuLiF, a recently developed laser material that allows more efficient energy extraction. Single-frequency operation is achieved by a ramp-and-fire injection seeding technique. An advanced photodetector architecture is used incorporating photodiodes in a dual-balanced configuration. A digital signal processing system has been built, allowing real-time display of wind and aerosol backscatter data products. The high pulse energy and receiver efficiency provides for measurement of wind fields to ranges not seen before with 2 µm lidars, and example wind measurements were made to show this capability.
Early concepts to globally measure vertical profiles of vector horizontal wind from space planned on an orbit height of
525 km, a single pulsed coherent Doppler lidar system to cover the full troposphere, and a continuously rotating
telescope/scanner that mandated a vertical line of sight wind profile from each laser shot. Under these conditions system
studies found that laser pulse energies of approximately 20 J at 10 Hz pulse repetition rate with a rotating telescope
diameter of approximately 1.5 m was required. Further requirements to use solid state laser technology and an eyesafe
wavelength led to the relatively new 2-micron solid state laser. With demonstrated pulse energies near 20 mJ at 5 Hz,
and no demonstration of a rotating telescope maintaining diffraction limited performance in space, the technology gap
between requirements and demonstration was formidable. Fortunately the involved scientists and engineers set out to
reduce the gap, and through a combination of clever ideas and technology advances over the last 15 years, they have
succeeded. This paper will detail the gap reducing factors and will present the current status.
Different methods of energy estimation for a differential absorption lidar (DIAL) system at NASA Langley Research
Center in Virginia are investigated in this paper. The system is a 2- &mgr;m wavelength coherent Doppler lidar called
VALIDAR that has been traditionally used for measuring wind. Recent advances in laser wavelength control have
allowed the new use of this lidar for measuring atmospheric CO2 concentration by a DIAL technique. In order to realize
accurate DIAL measurements, optimal signal processing techniques are required to represent the energy of the
heterodyned backscatter signals. The noise energy was estimated by minimizing the mean square error in its estimate
and was used to normalize its adverse influence on accurate estimation of the concentration of CO2 in the atmosphere.
The impact of different methods on the statistics of CO2 concentration measurements is compared.
KEYWORDS: Doppler effect, LIDAR, Signal to noise ratio, Wind measurement, Nonlinear optics, Data acquisition, Digital signal processing, Optical engineering, Statistical analysis, Signal processing
The signal-processing aspect of a 2-µm wavelength-coherent Doppler lidar system under development at NASA Langley Research Center in Virginia is investigated in this paper. The system is named VALIDAR (validation lidar), and its signal-processing program estimates and displays various wind parameters in real time as data acquisition occurs. The goal is to improve the quality of the current estimates of power, Doppler shift, wind speed, and wind direction, especially in the low signal-to-noise-ratio (SNR) regime. A novel nonlinear adaptive Doppler-shift estimation technique (NADSET) is developed for this purpose, and its performance is analyzed using the wind data acquired over a long period of time by VALIDAR. The quality of Doppler-shift and power estimations by conventional Fourier-transform-based spectrum estimation methods deteriorates rapidly as the SNR decreases. NADSET compensates this deterioration by adaptively utilizing the statistics of Doppler-shift estimates in a strong SNR range and identifying sporadic range bins where good Doppler-shift estimates are found. The authenticity of NADSET is established by comparing the trend of wind parameters with and without NADSET applied to the long-period lidar return data.
Significant advancements in the 2-micron laser development have been made recently. Solid-state 2-micron
laser is a key subsystem for a coherent Doppler lidar that measures the horizontal and vertical wind
velocities with high precision and resolution. The same laser, after a few modifications, can also be used in
a Diffrencial Absorption Lidar (DIAL) system for measuring atmospheric CO2 concentration profiles. The
world record 2-micron laser energy is demonstrated with an oscillator and two amplifiers system. It
generates more than one joule per pulse energy with excellent beam quality. Based on the successful
demonstration of a fully conductive cooled oscillator by using heat pipe technology, an improved fully
conductively cooled 2-micron amplifier was designed, manufactured and integrated. It virtually eliminates
the running coolant to increase the overall system efficiency and reliability. In addition to technology
development and demonstration, a compact and engineering hardened 2-micron laser is under development.
It is capable of producing 250 mJ at 10 Hz by an oscillator and one amplifier. This compact laser is
expected to be integrated to a lidar system and take field measurements. The recent achievements push
forward the readiness of such a laser system for space lidar applications. This paper will review the
developments of the state-of-the-art solid-state 2-micron laser.
KEYWORDS: LIDAR, Statistical analysis, Statistical modeling, Data modeling, Signal to noise ratio, Solids, Doppler effect, Data processing, Profiling, Data acquisition
The wind parameter estimates from a state-of-the-art 2-μm coherent lidar system located at NASA Langley, Virginia,
named VALIDAR (validation lidar), were compared after normalizing the noise by its estimated power spectra via the
periodogram and the linear predictive coding (LPC) scheme. The power spectra and the Doppler shift estimates were the
main parameter estimates for comparison. Different types of windowing functions were implemented in VALIDAR data
processing algorithm and their impact on the wind parameter estimates was observed. Time and frequency independent
windowing functions such as Rectangular, Hanning, and Kaiser-Bessel and time and frequency dependent apodized
windowing function were compared. The briefing of current nonlinear algorithm development for Doppler shift
correction subsequently follows.
KEYWORDS: LIDAR, Signal to noise ratio, Doppler effect, Interference (communication), Data processing, Profiling, Stochastic processes, Signal processing, Backscatter, Aerosols
The current nonlinear algorithm of the coherent Doppler lidar system VALIDAR at NASA Langley Research Center
estimates wind parameters such as Doppler shift, power, wind velocity and direction by locating the maximum power
and its frequency from the periodogram of the stochastic lidar returns. Due to the nonlinear nature of the algorithm,
mathematically tractable parametric approaches to improve the quality of wind parameter estimates may pose a very
little influence on the estimates especially in low signal-to-noise-ratio (SNR) regime. This paper discusses an alternate
approach to accurately estimate the nonlinear wind parameters while preventing ambiguity in decision-making process
via the subspace decomposition of wind data. By exploring the orthogonality between noise and signal subspaces
expanded by the eigenvectors corresponding to the eigenvalues representing each subspace, a single maximum power
frequency is estimated while suppressing erroneous peaks that are always present with conventional Fourier-transformbased
frequency spectra. The subspace decomposition approach is integrated into the data processing program of
VALIDAR in order to study the impact of such an approach on wind profiling with VALIDAR.
KEYWORDS: LIDAR, Doppler effect, Signal processing, Data processing, Solids, Digital signal processing, Stochastic processes, Interference (communication), Statistical analysis, Signal to noise ratio
A 2-μm wavelength coherent Doppler lidar system under development at NASA Langley Research Center in Virginia is
discussed from the perspective of signal processing. The current data processing algorithm returns a variety of wind
parameters such as power spectra, Doppler shift, wind speed, and wind direction. This paper compares the quality of
selected wind parameter estimates by computing the power spectral density of stochastic lidar return data via the
periodogram and the maximum likelihood power estimation method. The improvement in resolution of power spectra
and Doppler shift estimates is witnessed by means of zero padding before the power spectral density was estimated in
each range bin.
KEYWORDS: Doppler effect, LIDAR, Signal to noise ratio, Statistical analysis, Wind measurement, Data acquisition, Autoregressive models, Data processing, Control systems, Aerosols
A novel Nonlinear Adaptive Doppler Shift Estimation Technique (NADSET) is introduced in this paper. The quality of
Doppler shift and power estimations by conventional Fourier-transform-based spectrum estimation methods deteriorates
rapidly in low signal-to-noise-ratio (SNR) environment. The new NADSET algorithm compensates such deterioration in
the quality of wind parameter estimates by adaptively utilizing the statistics of Doppler shift estimate in strong SNR
ranges and identifying sporadic range bins where good Doppler shift estimates are found. NADSET is based on the
nature of continuous wind profile and significantly improves the accuracy and the quality of Doppler shift estimates in
low SNR ranges. The authenticity of NADSET is established by comparing the trend of wind parameters with and
without NADSET applied to the lidar returns acquired over a long period of time by the coherent Doppler lidar system
VALIDAR at NASA Langley Research Center in Virginia.
State of the art 2-micron lasers and other lidar components under development by NASA are being demonstrated and validated in a mobile test bed Doppler wind lidar. A lidar intercomparison facility has been developed to ensure parallel alignment of up to 4 Doppler lidar systems while measuring wind. Investigations of the new components; their operation in a complete system; systematic and random errors; the hybrid (joint coherent and direct detection) approach to global wind measurement; and atmospheric wind behavior are planned. Future uses of the VALIDAR (VALIDation LIDAR) mobile lidar may include comparison with the data from an airborne Doppler wind lidar in preparation for validation by the airborne system of an earth orbiting Doppler wind lidar sensor.
High-energy 2-micron lasers have been incorporated in a breadboard coherent Doppler lidar to test component technologies and explore applications for remote sensing of the atmosphere. Design of the lidar is presented including aspects in the laser transmitter, receiver, photodetector, and signal processing. Sample data is presented on wind profiling and CO2 concentration measurements.
Knowledge of the spatial and temporal distribution of atmospheric carbon dioxide (CO2) is important for understanding the carbon natural cycle, predicting its future levels and its impact on global warming and climate changes. Laser technology has advanced considerably during the past few years in the 2-micron region where strong optimum lines are available for measuring CO2 using the Differential Absorption Lidar (DIAL) technique. Although several types of detectors might be suitable for this particular wavelength, an ideal device would have high gain, low noise and narrow spectral response peaking around the wavelength of interest. This increases the signal-to-noise ratio and minimizes the background signal, thereby increasing the instrument sensitivity and dynamic range. In this paper the detector requirements for a long range CO2 DIAL measurement will be presented. The requirements were compared to commercially available and newly developed infrared (IR) detectors. The IR detectors considered for this study consist of the well developed InGaAs and HgCdTe p-n junction photodiodes, beside the newly developed and proposed InGaAsSb and InGaSb detectors. All of the detectors were characterized and their performances were compared with the CO2 DIAL detector requirements. The characterization experiments included spectral response, dark current and noise measurements. CO2 DIAL measurements using InGaAs detectors were attempted and indicated the need for better detector performance. While InGaAs detectors showed the closest performance to the instrument requirements, InGaSb detectors indicated a promising solution.
Wavelength modulation spectroscopy was employed to investigate water vapor absorption lines in the 1.462 micrometer wavelength region using an external-cavity diode laser. These measurements were necessary in the development of a lidar (light detection and ranging) instrument for differential absorption measurement of the concentration and movement of water vapor in the Earth's atmosphere. Differential absorption measurements require that the laser frequency remain stable throughout the duration of the measurement. To ensure this stability, the laser output wavelength is monitored and a feedback control loop set up to minimize laser line drift. Three lines were investigated in the 1.462 micrometer region. The first-harmonic spectroscopic signal of the strongest of these lines was used as an error signal for the stabilization feedback loop. The derivative-like nature of harmonic signals provides a zero crossing for odd harmonics which can be used to determine the polarity of the requisite feedback voltage and compensate the laser wavelength accordingly. The feedback control loop utilized the virtual instrument capabilities of Labview and locking to within plus or minus 5.2 MHz was achieved using this method.
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