fiber-based lidar for atmospheric water-vapor measurements

he

Fiber-based lidar for atmospheric water-vapormeasurements

Liesl M. Little and George C. Papen

The design and evaluation of a prototype fiber-based lidar system for autonomous measurement ofatmospheric water vapor are presented. The system components are described, along with currentlimitations and options for improvement. Atmospheric measurements show good agreement withmodeled signal returns from 400 to 1000 m but are limited below 400 m as a result of errors in signalprocessing caused by violation of the assumptions used in the derivation of the differential absorptionlidar equation. © 2001 Optical Society of America

OCIS codes: 010.3640, 280.1910, 010.7340, 060.2320.

6

e

1. Introduction

Water vapor plays a crucial role in global climatechange caused by anthropogenic greenhouse gasesowing to its ability to provide a positive feedbackmechanism.1 Thus an accurate description of thedistribution and transport of water vapor is an es-sential component of climate modeling and weatherprediction. Global climate models require 1-km ver-tical resolution and 6-h temporal resolution.2Weather forecasting models also require 1-km verti-cal resolution.3 Other aspects of weather research,

owever, such as the study of storm initiation andvolution4 and the study of cloud formation,5 require

higher vertical and temporal resolution.Current water-vapor measurement techniques

have a variety of limitations that prevent them fromproviding the desired resolution. Radiosondes pro-vide high accuracy and vertical resolution, but globalcoverage is limited because of the expense and im-practicality of regular launching over oceans. Cur-rent satellite systems do not provide sufficientvertical resolution, although near-future systemsthat use radio occultation in conjunction with theglobal positioning system could increase vertical res-

When this research was performed, the authors were with theDepartment of Electrical and Computer Engineering, University ofIllinois at Urbana–Champaign, 1308 West Main Street, Urbana,Illinois 61801-2307. L. M. Little [email protected]! is now withthe Lawrence Livermore National Laboratory, L-183, P.O. Box808, Livermore, California 94551-0808.

Received 9 March 2000; revised manuscript received 31 January2001.

0003-6935y01y213417-11$15.00y0© 2001 Optical Society of America

olution to 1 km. Global coverage with satellite sys-tems is excellent, but temporal resolution remainslimited. Large bulk-optics lidar systems providehigh resolution and accuracy, but their operationalcomplexity and expense have prevented implementa-tion of a global measurement system. Recently im-plemented lidar systems based on semiconductorlasers have significantly decreased costs and simpli-fied system operation but are limited in range owingto their inability to produce pulses with large peakpowers. This peak-power limitation is fundamentalbecause of the inability of semiconductors to storeenergy owing to their short upper-state lifetime,which is of the order of nanoseconds. A more-detailed overview of current and near-future systemcapabilities has been given by Little.7

In this paper we describe a fiber-based lidar systemwith which to measure water vapor. This systemprovides the potential for bridging the gap betweenthe large-scale high-peak-power lidar systems basedon dye, solid-state, or gas lasers and the miniaturelidar systems based on semiconductor diodes. Thesystem uses a semiconductor diode laser as a masteroscillator and provides pulse amplification of the sig-nal by using a rare-earth-doped fiber amplifier.This design provides two major advantages comparedwith a system based solely on semiconductor lasers.The first advantage is the increased measurementrange of this design owing to its higher peak powers.Silica fibers have significantly higher damage thresh-olds ~;10 GWycm2! than semiconductors; they allowhigher peak pulses to be guided through the fiber.8Rare-earth elements also have long upper-state life-times ~of the order of 300 ms for Nd!, which permitsnergy storage and therefore provides higher peak-

20 July 2001 y Vol. 40, No. 21 y APPLIED OPTICS 3417

r

otvwt

oiun

3

power pulses than that for cw amplification. Thisdesign improvement provides the potential forhigher-peak-power pulses than are possible withsemiconductor-only systems.

The second advantage of the fiber-based system isthe improvement in operational simplicity that is dueto the elimination of most bulk optics. This designelement implies that little or no realignment is re-quired after the initial alignment, which makes thesystem robust. Because of the strength of the cho-sen absorption line for this system, significant andvariable intracavity losses would cause problems inan open-cavity, bulk-optics-based system. However,because there is no open cavity, variable loss withinthe system owing to water-vapor absorption is elim-inated. It is easy to reconfigure the system by use ofconnectorized fiber and simple to reposition it. Inaddition, the single-mode fiber has no pointing jitter,so telescope alignment is simplified, and it becomespossible to use small fields of view ~FOVs! for theeceiving telescope.

2. System Description

The fiber-based system was designed to be operatedwith the differential absorbing lidar ~DIAL! tech-nique. The optimal absorption line to use for theDIAL technique is one that produces a one-way opti-cal depth9,10 of ;1.1 and has little temperature vari-ation.11 Previous water-vapor DIAL systems suchas the Max-Planck-Institute system12 and the LidarAtmospheric Sensing Experiment13,14 ~LASE! usedvertone absorption bands near 720 or 820 nm, buthese absorption bands are not strong enough to pro-ide optimal absorption measurements in regionshere the atmosphere is dry, such as in the upper

roposphere ~where the LASE is operated! and overAntarctica. Optimal measurements over Antarctica

Fig. 1. Schematic diagram of the transmitter and the receiverfree-space propagation of light. AOM, acousto-optic modulator; WDbus; VCCSs, voltage-controlled current sources; APD, avalanche p

418 APPLIED OPTICS y Vol. 40, No. 21 y 20 July 2001

require cross sections of 2 3 10222 cm2 for summerand 2 3 10220 cm2 during the winter. The peakabsorption line in the 935-nm band is ;2 3 10221 cm2

at ground level. ~The peak absorption line in the720- and 820-nm bands is an order of magnitudelower.! These peak-absorption values would allowptimal measurements to be made in Antarctica dur-ng much of the year. Optimal measurements in thepper troposphere ~15 km! require cross sectionsear 6 3 10219 cm2. The 935-nm absorption band

peak is ;2 3 10220 cm2 at this altitude. Whereasthese values do not permit optimal measurement,they do permit more-efficient measurements thanthose that are possible with the LASE system to bemade.

A schematic diagram of the fiber-based system isshown in Fig. 1. The system prototype utilized fiberfor all system components, with the exception of thebulk coupling used between the diode laser masteroscillator and the fiber amplifier. One can eliminatethis bulk coupling by pigtailing the diode.

The master oscillator was a ridge-waveguide, dis-tributed Bragg reflector ~DBR! laser. The laserstructure and the growth methods are described indetail elsewhere.15–17 The DBR is etched withsecond-order gratings, which provide strong couplingand make the laser spectrum extremely narrow.The devices have two current connections, one thatpasses current through the gain region and providespower for the laser and one that passes currentthrough the Bragg grating. The gain region is oper-ated at a current of 60 mA with an input power of 36mW. The DBR current is 30 mW or less, with aninput power of 9 mW. The DBR’s current path pro-vides tuning for the laser wavelength with minimalchanges in laser output power. It also provides anorder-of-magnitude increase in the tuning range.

in curves, fiber; thick curves, electrical wiring; dashed curves,avelength-division multiplexers; GPIB, general-purpose interface

diode.

. ThMs, whoto

e

spwm2oteu

k

pfiuwefis;ptaT1pos

dgwErt

lwwlptAttT

aa

The tuning range with DBR current tuning was mea-sured to be 5 nm over 30 mA; a 30-mA change in thegain current provided a 0.5-nm change in wave-length. The DBR current tuning mechanism isdominated by the thermal effects of resistive heating;this implies that the minimum tuning time betweenwavelengths ~;40 ms! is limited by the thermal prop-rties of the packaging.18 This tuning is ;2 orders

of magnitude faster than pure thermal tuning with athermoelectric cooler.

The amplifiers used in this system were Nd-dopedsilica fibers, which operate on the 4F3y23

4I9y2 tran-ition at ;935 nm.19 The amplifiers are opticallyumped by fiber-coupled diode lasers operating at aavelength of 810 nm and an output power of 150W, which requires an input power of 215 mW ~at

30 mA!. This transition’s lower energy level is partf the ground-state manifold, so its thermal popula-ion causes some ground-state absorption. How-ver, a carefully optimized fiber design providesseful gain levels.20 The pulse’s duration and repe-

tition frequency are variable. The output power var-ies with the average input power, which isproportional to the product of the pulse duration andthe repetition frequency, as long as the pulse period isless than the upper-state lifetime of the Nd ~ f . 2.5

Hz!.The initial proof-of-concept system used three am-

lifier stages. The first two stages were cw, and thenal stage was pulsed by use of an acousto-optic mod-lator between stages 2 and 3. This amplifier setupas designed to minimize amplified spontaneous

mission while permitting pulse amplification in thenal stage. Amplified spontaneous emission can beignificant until the amplifier reaches saturation, at5 mW for these amplifiers. Because the third am-lifier stage becomes saturated, it is possible to placehe modulator before the final stage and still achieven extinction ratio greater than 30 dB at the output.he resultant output pulse is square, with less than% ringing. A low-power output on the second am-lifier stage provided a small amount of signal as partf the feedback loop that was used to control theignal wavelength.The receiver chain was based on a 10-in.- ~25.4-cm!-

iameter, fy1.1 refracting telescope and a siliconeiger-mode avalanche photodiode. The photodiodeas the basis of a photon-counting module fromG&G. The system control was fully automated,

unning completely unattended for all time periodsested ~as long as 6 h!.

In DIAL analysis it is generally assumed that theinewidth of the signal is a delta function comparedith the width of the absorption line used. Theater-vapor lines in the 935-nm band had an average

inewidth ~FWHM! of 6 GHz at ground level. Toroduce a cross-section error of less than 0.1%, theransmitter linewidth must be less than 100 MHz.t 15 km the water-absorption line is narrower, and

he transmitter linewidth must be less than 30 MHzo produce a cross-section error of less than 0.1%.he linewidth of the system was measured by use of

self-heterodyne technique as described by Okoshi etl.21 The measured linewidth was less than the

minimum resolution of the measurement experi-ment, which was 70 kHz.22 As the linewidth of thelaser was affected by the amount of backreflectedlight from the amplifier, careful control of reflectionswas required.7,23 The measured side-mode suppres-sion was greater than 25 dB.

The output wavelength was actively stabilized.The wavelength was measured with a Hewlett-Packard wavemeter with an accuracy of 0.1 pm.The control system read the wavelength and thenchanged the DBR current to adjust the laser wave-length appropriately. The wavelength stability wasmeasured over a 5-min period at 934.933 nm. Thestandard deviation of the wavelength was 0.24 pm.These properties provide a cross-sectional error ofless than 0.25% for altitudes less than 3 km, whichwas the system design range.

Because of the prototype nature of the system, sev-eral of the system components were not optimized.This result led to limitations in the output powercaused by losses in the amplifiers, gain limits, andnonoptimal coupling of signal. The fiber losses weredominated by ground-state absorption. Total ampli-fier loss was ;4.1 dB per stage, of which 2.8 dB wasdue to ground-state absorption, which is alwayspresent at these pump powers but decreases forhigher pump powers. The gain was limited by non-optimized fiber geometry.24 Another factor thatlimited the gain was a fiber coating upon the fiber-pigtailed pump diodes that was incompatible withour fusion splice techniques and therefore decreasedthe light coupled into the amplifiers from the pumpsto ;70% of the light into the fiber pigtail, or ;50% ofthe pump diode’s output power. Nonoptimal signalcoupling was due to the use of bulk optics for couplingbetween the diode and the 5.0-mm-core fiber. Themaximum coupling captured ;40% of the signal; afiber pigtail could increase this to ;70%. In addi-tion, thermal expansion of the supports for the bulkcoupling optics caused the amount of coupling to varyfrom 25% to 40%. The net result of all the nonopti-mized losses was that the initial system achieved apeak power of only 7.5 mW, which produced an av-erage power of 0.15 mW. This value corresponds toan electrical-to-optical efficiency of 0.02%. Optimiz-ing the system ~as discussed in Section 5 below!should dramatically increase both output power andefficiency.

The receiver chain was also unoptimized. Thetelescope was a legacy from another system, and itslenses were antireflection coated for operation at 550nm. This coating decreased the telescope transmis-sion to ;50%. Also, the interference filter had abroad bandwidth of ;15 nm. This filter was chosenfor initial system tests to accommodate the full tun-ing range of the system and could be narrowed sig-nificantly for a field version of the system. Doing sowould decrease the background light and thereforeincrease the signal-to-noise ratio at higher altitudes.


s

A

fohat

wsiv

vacpsf

Table 1. Comparison of Cross-section Measurement Results and

3

3. Model Verification

To model system performance initially, we use thestandard lidar scattering equation to calculate ex-pected signal return:

Ne,r~l, R! 5 Np,thb~R!DRj~R!~ AyR2!

3 expF22 *0

R

@Nw~ z!sw~l, z! 1 a~ z!#dzG ,

(1)

where Ne,r is the number of photoelectrons from thedetector per pulse, Np,t is the number of photonstransmitted per pulse, DR 5 ctDy2 is the range bin ataltitude R, tD is the integration time, b is the atmo-pheric backscatter coefficient @km21ysr21#, a is the

atmospheric extinction @km21#, Nw is the water-vapordensity @cm23#, sw is the water-vapor absorptioncross section @cm2#, h is the receiver system’s effi-ciency ~including detector quantum efficiency!, and

yR2 is the solid angle subtended by the telescope.Equation ~1! has been multiplied by an overlap

unction j~R! that accounts for the bistatic operationf the lidar. If one assumes that the output signalas a Gaussian field shape, which is an excellentpproximation for the output of a single-mode fiber,he overlap function is given by25

j~R! 51

wÎp *2r

r

erfF 1w

Îr2 2 x2GexpF2~ x 2 d!2

w2 Gdx.

(2)

here erf is the error function, w is the signal spotize, d is the separation of the telescope and laserllumination axes, and r is the radius of the telescopeiewing area. The variables d, w, and r are func-

tions of range R.The model’s water-vapor density, temperature, and

pressure profiles were interpolated or extrapolatedfrom the summer and winter U.S. mid-latitude mod-els.26 These interpolations or extrapolations weremade to force the model values at ground level tomatch the measured relative humidity, temperature,and pressure at ground level. The backscatter val-ues were based on measurements made with a back-scattersonde in Laramie, Wyo., at 940 nm.27,28

Extinction measurements near this wavelength forcontinental aerosols were not available; however,extinction-to-backscatter ratio measurements at 690nm were also made by Rosen and Kjome in Laramie.Because the variation of the backscatter-to-extinctionratio is only a slow function of wavelength,29 thesealues were used for calculation of extinction valuest 940 nm based on the backscatter profiles. Be-ause of the high variability of b and a with time, tworofiles of b and a were used in modeling an expectedignal range. The minimum profile was calculatedrom Rayleigh scatter in the absence of aerosols.30–32

The maximum profile was a 95% maximum, based on6 years of measurements at Laramie.

In most DIAL systems, high and low absorption


values are chosen to be absorption peaks that aresignificantly higher than the background absorptionbut that differ in absorption value by 2 or more ordersof magnitude. Such an approach avoids the largeerrors that can occur in calculating absorptions in thewings of an absorption line. However, because thefiber lidar was designed for low-humidity environ-ments but was tested in a high-humidity environ-ment, the only way to optimize absorption for ameasurement was to use a low-absorption peak online and to use background absorption off line. If theoff-line absorption value is small compared with theon-line absorption value, it can be neglected in thecalculation of water-vapor density, and no measure-ment is necessary. However, the calculated off-linecross section was almost 10% of the on-line value, anda large error in this value could significantly affectthe calculated water-vapor densities. Thus it wasnecessary to measure the absorptions to obtain rea-sonably accurate values of the off-line absorption.Measuring the on-line absorption value permittedvalidation of the absorption measurement throughcomparison with previously measured values fromthe HITRAN database.33

Both the on-line and the off-line absorption crosssections were measured and compared with Voightprofile cross-sectional calculations based onabsorption-line information from the HITRAN data-base. The HITRAN value for the peak absorption atthe on-line wavelength was based on previously mea-sured values of line strength and pressure-broadening coefficients.34–36 The off-line value wasbased on contributions from the wings of 500 HIT-RAN absorption lines centered about the off-linewavelength. The cross sections were measured witha multipass White cell with a path length of 100 m.The air in the cell was heated to 75 °C to increase thewater-vapor saturation such that the absorption onthe off-line wavelength was high enough for reason-able measurement accuracy over the length of thecell. The cell pressure was 1 atm. We determinedthe water-vapor density in the cell by measuring therelative humidity. We measured the absorptioncross section by taking the ratio of the transmissionthrough the cell at two different humidity levels. InTable 1 these measured cross-sectional values arecompared with the HITRAN values. The measuredon-line absorption cross section is within 13.3% of theHITRAN value, but the off-line absorption cross sec-tion differs by more than 200%. The large error is aconsequence of assuming a Lorentzian line shapebased on impact theory37 in the wings of the absorp-

Values Calculated from HITRAN Assuming a Lorentzian Line Shape inthe Absorption Wings

Wavelength~nm!

HITRAN s~cm2!

Measured s~cm2!

Difference~%!

934.933 3.08 3 10223 3.49 3 10223 13.3935.211 2.89 3 10224 9.71 3 10224 236.0

me

tmst

fe

babiuwpg4

dmbes

tion feature. As has been discussed by many au-thors, this is not a valid approximation for the off-linecross section in the far wings of the absorptionfeature.38–40 The pressure and temperature scalingof the off line is also a problem because of this issue.For the purposes of modeling the system, the off-linecross section was assumed to be temperature inde-pendent and the pressure scaling was taken to besimply ~PyP0!, where P0 5 101 kPa is the pressure atground level.

Figure 2 shows the raw data from both on- andoff-line measurements made in Champaign, Ill., from0315 to 0830 UTC on 15 July 1999 ~10:00 p.m. on 14July to 3:30 a.m. on 15 July 1999 Central DaylightTime!. Visibility was excellent, and the moon wasbelow the horizon throughout the measurement,which minimized background light. System param-eters are listed in Table 2. The receiver bandwidthis much larger than the laser linewidth or the dis-tance between the on- and off-line wavelengths.This filter was chosen to accommodate the full tuning

Fig. 2. Raw signal returns for ~solid curves! on-line and ~pluses!off-line signals.

Table 2. System Parameters for Water-Vapor Profile Measurement

On wavelength 934.933 nmOff wavelength 935.211 nmOn seff 3.49 3 10223 cm2

Off seff 9.71 3 10224 cm2

Pout ~average! 0.15 mWPulse repetition frequency 20 kHzPulse length 1 msTelescope area 0.05 m2

Interference filter bandwidth 15 mmPinhole diameter 500 mmReceiver FOV 0.86 mradScaler bin width 200 nsReceiver efficiency 5.5%

range of the system for initial system tests. The20-kHz pulse-repetition frequency implies a maxi-mum measurement distance of 7 km to prevent alias-ing.

The data shown in Fig. 2 were averaged over 2 h ateach wavelength by interleaving of 2-min integra-tions at the two wavelengths. Switching betweenthe two wavelengths took an average of 30 s, yieldinga total measurement time of 5.25 h. The switchingtime was significantly longer than the minimum timeof 40 ms because of the long settling times of thefeedback method used ~largely a result of the mini-mum 1-s delay between wavemeter readings!. Toachieve the minimum tuning time one should lock thelaser wavelength by using an absorption cell ratherthan a wavemeter, and a direct electronic feedbackcircuit is required ~unlike in the computer-controlled

ethod used here!. The photon counts were lownough that dead-time correction was unnecessary.Figure 3 compares the on- and off-line data with

he model results used to predict system perfor-ance. The comparison shows that the measured

ignals fall within the expected range at low alti-udes.

Figure 4 shows the water-vapor profile determinedrom measured data by use of the standard DIALquation:

nw 51

2DR~son 2 soff!lnSN1,1N2,2

N1,2N2,1D . (3)

Ni, j is Ne,r~lj, Ri!, where j 5 1 is the on-line wave-length. Because the scaler bin size was 200 ns~which corresponds to 30 m in range! the data pointsare separated by 30 m. Each value is calculated byuse of bins separated by 150 m ~which is equal to fivebins; for example, if N1,1 is from bin 10, N2,1 is fromin 15!. The value calculated for these two bins isssigned to the height midway between them. Thein separation ensures that the calculation does notnclude correlated data from within the 150-m-rangencertainty ~which is a result of the 1-ms pulseidth!. The straight line in the figure is a modelrofile used for calculation of the expected signal; theround-level value in the model was measured to be.8746 3 1017 cm23 ~14.6 3 1026 gycm3!. The model

value is shown for comparison with the measureddensities and was not used in calculating the mea-sured densities. The plot also shows data from aballoon launch in Lincoln, Ill., ;50 miles west ofChampaign. The balloon measurements showedlower humidity at ground level than that measuredat the lidar site. ~At 0000 UTC the measurementwas 4.296 3 1017 cm23 or 12.9 3 1026 gycm3; at 1200UTC the measurement was 3.899 3 1017 cm23, or11.7 3 1026 gycm3.! Both balloon data and model

ata showed consistently lower densities than thoseeasured with the lidar, although above 500 m the

alloon and the model data fall within the range ofrror for the system. The data below 400 m areuspect and are discussed in more detail in Section 4.


bs

db

t

3

4. Error Analysis

A number of excellent analyses of DIAL instrumentshave been presented.10,12,41,42 Our analysis is simi-lar, but particular attention is paid to details that areunique to this system because of either its novel in-strumentation or its operating wavelength. Twotypes of error are discussed: random errors and sys-tematic errors.

The dominant random error in this system is shotnoise, which is given as41

dnw

nw5

12DRDsnw

S(i51

2

(j51

2 H@~Ni, j 1 B! F 1 D#

Ni, j2 JD1y2

,

(4)

where B is the number of photocounts that are due toackground light, which is determined from mea-urements. The contribution of dark counts, D, is

Fig. 3. Comparison of modeled and measured signals.


ue to the surface dark current, which is measured toe D # 250 countsys. The excess-noise factor, F, is

the factor by which the detector noise exceeds thenoise that is due to the quantum nature of the light.F can be calculated from detector physics.43 For thisanalysis, F was assumed to be 2.5.44 The photoncount from each range i and wavelength j ~where j 51 is the on-line wavelength! is Ni, j. Table 3 listsshot-noise contributions that are due to the signal,background, and dark current separately.

Systematic errors are due to errors in the crosssection that is used to calculate the water-vapor den-sity. One determines the contribution of a cross-sectional error by taking the derivative of the DIALequation @Eq. ~3!#:

Sdnw

nwD

total

5dsoff 2 dson

son 2 soff. (5)

Estimates of the systematic errors given in Table 3include inaccuracy in the cross-sectional measure-ment, center wavelength instability, angle into theinterference filter, and lack of knowledge of the tem-perature and pressure profiles.

Errors in the cross section from the cross-sectionalmeasurement are due to the inaccuracy of the humid-ity meter used in determining water-vapor density inthe cell. The calculated cross section is inverselyproportional to the difference in water-vapor densi-ties ~N1 2 N2! for the two absorption measurements

Fig. 4. Water-vapor profile calculated from measured data.Solid curve, model based on the U.S. 1976 Standard Atmosphere,with ground-level density tied to measured humidity. Measure-ments from Lincoln, Ill., at ~filled circles! 0000 UDT and ~filledriangles! 1200 UDT are included. Error bars show total error.

ttc

cintult

Table 3. Summary of Sources of System Errora

as described above. The cross-sectional error isgiven by

ds

s5

DN1 2 DN2

N1 2 N2. (6)

The maximum error occurs for DN1 5 0.02N1 andDN2 5 20.02N2 and gives a fractional cross-sectionalerror of 3.3%.

Error that is due to center wavelength instability iscaused by drifting of the laser emission away from theabsorption peak. Only the on-line wavelength con-tributes to this error, because the off-line wavelengthis at a broad minimum. We determined the cross-sectional error by recording the wavelength each sec-ond over a period of 5 min. For each recordedwavelength, the cross section was calculated for sev-eral altitudes from pressures and temperatures fromthe U.S. 1976 Standard Atmosphere model. We de-termined the effective cross section seff by averagingthe 300 calculated cross sections at each altitude.The cross-sectional error was then ds 5 seff 2 speak.

Both line strength and linewidth depend on tem-perature. The line strength temperature depen-dence S~T! is41

S~T! 5 S0S TT0D1.5

expFE0hck S 1

T02

1TDG , (7)

where E0 is the lower energy level of the transition, his Planck’s constant, c is the speed of light, k is Bolt-zmann’s constant, and S0 is the line strength at T0.The linewidth varies with both temperature andpressure for Lorentzian line broadening ~which is thedominant broadening mechanism in the lower atmo-sphere!:

gL 5 gL,O~PyP0!~T0yT!m, (8)

where 0.5 # m # 0.85, with an average of m 5 0.62.45

The exponential parameter m for a particular absorp-ion can be found in the HITRAN database. We de-ermined the cross-sectional error by calculating theross section at T 1 DT, where for this study DT was

Altitude ~km!

Random Error ~%!b

Shot Noise

TotalS B D Tempera

0.105 53.1 176.6 46.6 24.9 0.80.165 6.2 2.0 0.5 0.1 0.80.225 3.2 0.8 0.2 0.1 0.90.405 3.2 3.1 0.8 0.1 0.90.555 7.3 13.6 3.6 0.8 1.00.705 14.5 46.7 12.3 6.7 1.00.855 23.5 116.9 30.9 38.4 1.1

aError is dominated by shot noise, where the highest systematicFor shot-noise error, S is shot noise from the signal, B is shot noisecurrent. The shot noise is dominated by background light, a resu

bThe soff measurement is 0.1 in all cases.cThe soff measurement is 3.3 and the pressure is 0.2 in all case

assumed to be 10K.41 The error in cross section isds 5 s~T 1 DT! 2 s~T!, where T is the value from theU.S. 1976 Standard Atmosphere.

The pressure sensitivity of the cross section is dueto the linewidth sensitivity for Lorentzian broaden-ing, as given in Eq. ~8!. For a Lorentzian peak, thecross section is inversely proportional to the line-width and therefore inversely proportional to thepressure. In the wings of a Lorentzian, the crosssection is directly proportional to the linewidth andtherefore directly proportional to the pressure. Be-cause this system used an on-line absorption at apeak and an off-line absorption in the wings, thepotential existed for producing a fractional cross-sectional error larger than the fractional pressurechange. However, because the peak used for thesemeasurements was in the wings of an adjacentstrong-absorption line, the cross-sectional error as afunction of pressure was somewhat mitigated. Thefractional pressure change was assumed to be 2%,based on the pressure changes at ground level mea-sured in Champaign, Ill., over the month of July.7The cross-sectional error is ds 5 s~P 1 DP! 2 s~P!.

Calculation of the error as a function of interfer-ence angle was based on information from Wulfmeyerand Bosenberg.12 The interference filter angle wasbased on tolerances for the receiver system supportsand was assumed to be 5 mrad. Further details re-garding the error calculations are given by Little.7

A further systematic error at low altitudes arisesfrom problems with the signal processing. In gen-eral, use of data from the region of incomplete overlapbetween telescope and transmitter is avoided becauseof the large errors that are possible from even smalldifferences in pointing direction.12 However, be-ause the output path of the fiber-based transmitters constrained by the fiber, pointing jitter is elimi-ated for this system, and we believe that data fromhis region could be used for this test. The ability tose these data was particularly desirable because the

ow output power for the initial system test limitedhe possible measurement range. However, multi-

Systematic Error ~%!c CombinedTotalErrorl Instability Interference Filter Total

0.1 0.6 5.0 195.20.1 0.1 4.5 11.00.1 0.0 4.5 7.80.1 0.0 4.5 9.20.2 0.0 4.7 20.60.2 0.0 4.7 55.10.2 0.0 4.8 128.1

ribution is due to errors in the off-line cross-section measurement.t is due to sky background, and D is shot noise that is due to darkthe large bandwidth of the receiver filter.

ture

contthalt of

s.


3

ple measurements over a period of several daysshowed a dramatic minimum in water-vapor densityprofile consistently centered at an altitude of 175 m.As such atmospheric behavior seemed unlikely, thedata at low altitudes were considered suspect. How-ever, a reexamination of the system model providedno plausible explanation for this error, so we studiedthe data analysis technique to determine whether thedensity minimum could result from the analysis.The conclusion was that such is indeed the case; theerror at low altitude was a direct result of using thestandard DIAL equation @Eq. ~3!# in an area wherethe assumptions made in deriving the equation areviolated. When the transmission model described inSection 3 was modified such that in the calculation ofexpected signal it did not make these assumptions, ifthe standard DIAL equation ~with its inherent as-sumptions! was used to calculate the water-vaporprofile from predicted signals this modeled profileshowed the same dramatic minimum seen in themeasured data. A water-vapor profile calculatedwith a simulated processing error is shown in Fig. 5.The measured water-vapor profile is shown for com-parison. Although there are differences, the trendsare similar, with the profile minimum and the loca-tion where the profile levels out occurring at approx-imately the same altitudes for the two profiles. Thisresult shows that the error was due to signal process-ing and not to a problem with the system. The sig-nal processing and DIAL assumptions are describedin more detail in Appendix A, including an explana-tion of why the signal-processing errors were not cor-rected.

The total error, including the sum of the absolutevalues of the total random error and the net system-

Fig. 5. Comparison of measured profile shape and modeled profilewithout the slow-variation assumption.


atic error as listed in Table 3, is shown as error barsin Fig. 4.

5. Conclusions

In this paper we have presented the first atmosphericDIAL water-vapor measurements made with a fiber-based lidar system. The measured signal for on-and off-line wavelengths showed good agreementwith model predictions and fell within the expectedvariability caused by changing aerosol loading andvariations in water-vapor density. The measuredwater-vapor profile showed reasonable agreementwith a modified mid-latitude summer model that wastied to a measured water-vapor density at groundlevel and to balloon measurements made at a station50 miles from the lidar site. This experiment vali-dated the system design and permitted the evalua-tion of component performance for optimization infuture system implementations. A collocated bal-loon measurement will be required for direct compar-ison of measured water-vapor profiles for evaluationof system measurement performance for an opti-mized system.

An error analysis of the system showed that erroris dominated over much of the range by shot-noiseerror. The largest contribution to the shot noise isthe background light that results from the largebandwidth of the receiver filter. This shot-noisecontribution could be reduced by a factor of 4 byreduction of the bandwidth of the filter to 1 nm. Thelow signal also caused significant degradation of thesignal-to-noise ratio as a result of shot noise. Therange was limited at low altitudes by errors that weredue to violations of DIAL assumptions.

The output power of this prototype system was lowbecause of the presence of nonoptimized system com-ponents. Fiber pigtailing the signal diode, usingcompatible fiber for the pump diodes, and optimizingthe fiber core size and numerical aperture could in-crease the output power by an order of magnitudewithout increasing the required electrical power.Using the proper antireflection coatings would im-prove the signal-to-noise ratio by a factor of 2. Nar-rowing the filter bandwidth would decrease the errorby another factor of 2 in regions where the back-ground is larger than the signal for the current sys-tem. Further improvements in the transmitter,requiring an increase in electrical power needed,could also increase output power. These improve-ments include using multiple-quantum-well devicesfor the master oscillator rather than the single-quantum-well devices used here. The second andthird stages of the amplifier could have optical pumpsin both forward and backward directions to increasethe gain in these stages. Also, 200-mW single-modepump diodes are now available. These improve-ments should permit an average output power of theorder of 100 mW, which would allow measurement to3 km with an error of 10% or less with a 5-h averageand a 1-nm interference filter. ~All other parame-ters are the same as those for the current system.!

This system is robust, stable, and easy to use.

cvted

dscFswtfrct

i

Pump diodes and all receiver components are com-mercially available. The master oscillator and thefiber amplifier that we used were research devices,but no impediments to commercial production havebeen noted. With the suggested improvements, thissystem shows considerable potential for use in themeasurement of water vapor in dry climates.

6. Appendix A

The derivation of the standard DIAL equation as-sumes that all parameters vary slowly with alti-tude.25 Because of the bistatic transmitter–receiveronfiguration and the high concentration of waterapor, this assumption is not valid at low ranges forhe fiber lidar. To determine the magnitude of thisffect we use the general form of the equation foretected power:

Pr~t! 5 *R1

R2

Pt~R!j~R!b~R!V~r!Twv2~R!Tatm

2~R!dR,

(A1)

where Pt~R! is the transmitted power as a function ofR, j~R! is the overlap fraction as given by Eq. ~2!, andb~R! is the backscatter coefficient. V~R! is the solidangle subtended by the telescope, which is ~A0yR2!for large R but is limited at low ranges to the solidangle of the telescope’s FOV. A0 is the area of thetelescope aperture, Twv~R! is the transmission func-tion that is due to water-vapor absorption, andTatm~R! is the transmission function that is due toextinction by all other particles.

It is often assumed that Pt~R! is uniform over theextent of the pulse, which is a valid assumption forthe square pulse used for this system. In this case Ptcan be pulled out of the integral. The integrationlimits are R2 5 cty2 and R1 5 c~t 2 tL!y2, where tL isthe pulse length. It is also generally assumed thatall other variables change slowly over the range R1–R2. This assumption is usually reasonable when R.. ~R2–R1!. The assumption of slow variation al-lows all terms to be pulled out of the integral in Eq.~A1!, resulting in a common form for the lidar scat-tering equation in terms of power:

Pr~t! 5 Ptj~R!b~R! A0SR2 2 R1

R2 D3 expH22 *

0

R

@Nwv~ z!s~ z! 1 a~ z!#dzJ . (A2)

Equation ~3!, which is the standard DIAL equation,is based on Eq. ~A2!. To investigate the effect ofusing the standard DIAL equation in a region wherethe overlap function, the solid angle, and the trans-mission that are due to water-vapor absorption do notchange slowly, we retained several of the parameterswithin the integral in Eq. ~A1!, which is used in thecalculation of the expected signal for the model de-scribed in Section 3. To compare the expected withthe measured signals, which are given in terms of

photoelectron counts from the detector, Ne,r, we inte-grate Eq. ~A1! over the detector integration time tD.For regions where the solid angle is limited by thetelescope’s FOV, the equation for the backscatteredsignal is

Ne,r 5 hSPttD

hn Db~R!VFOVTatm2~R!Twv

2~R1!

3 *R1

R2

j~R!exp@22Nwv~R!s~R!~R 2 R1!#dR,

(A3)

whereas for all other regions the scattering equationhas the form

Ne,r 5 hSPttD

hn Db~R! A0 Tatm2~R!Twv

2~R1!

3 *R1

R2

j~R!S 1R2Dexp@22Nwv~R!s~R!

3 ~R 2 R1!#dR. (A4)

We used Eqs. ~A3! and ~A4! to calculate an expectedsignal return at the on- and off-line wavelengths,based on the atmospheric water-vapor model shownin Fig. 4. We then used the signals expected withoutthe assumption of slow variation in Eq. ~3!, the stan-

ard DIAL equation, to determine an expected mea-ured water-vapor profile, which is shown as a solidurve in Fig. 6. For comparison, the dashed curve inig. 6 shows the model water-vapor profile. If thelow-variation assumption were valid, the two curvesould be identical. For reference, a normalized plot of

he expected photocounts and the Gaussian overlapunction are plotted in the same figure to show theelationship between the profile discrepancy and thehanges in overlap and signal. At higher altitudes,he two water-vapor profiles are quite similar.

The profile shape can be explained with the follow-ng reasoning: At very low altitudes, ~R2 2 R1! ,,

ctLy2 because only a small portion of the pulse hasleft the transmitter. In this region the assumptionthat T, V, and j are slowly varying over the integra-

Fig. 6. Comparison of ~dashed curve! model profile and ~solidcurve! profile calculated when the scattering equation does notmake a slow-variation assumption. The overlap factor ~pluses!and the normalized signal ~filled circles! are shown for comparison.


TDeft

absorption lidar for water-vapor profiling: assessment of ac-

2

2

2

3

tion range is valid because the integration range issmall and the model-based profile calculation ap-proaches the original model profile. However, as tincreases and the front edge of the pulse moves awayfrom the transmitter, the integration range also in-creases. In this region, the assumption of slow vari-ation becomes less valid and the discrepancy betweenthe two profiles increases. The error increases untilsome of the photons that are returning during theintegration time return from regions where the over-lap function slope is decreasing. Beyond this point,the error decreases.

When the overlap function is left inside the integralin Eq. ~5!, the result must be numerically integrated;there is no closed-form solution. This stricture pre-vents derivation of a simple expression such as Eq. ~3!for calculating water-vapor density without knowl-edge of the extinction coefficient @a~R! in Eq. ~A1!#.

he extinction is difficult to measure ~which is whyIAL systems are desirable!; therefore a quantitativestimate cannot be made of the error at low altitudesor the measured profile. However, it is clear thathe data below ;400 m are unreliable.

References1. A. Raval and V. Ramanathan, “Observational determination of

the greenhouse effect,” Nature ~London! 342, 758–761 ~1989!.2. D. Starr and S. H. Melfi, “The role of water vapor in climate,”

NASA Conf. Publ. 3120, ~1991!.3. H. H. Aumann and R. J. Pagano, “Atmospheric Infrared

Sounder on the Earth Observing System,” Opt. Eng. 33, 776–784 ~1994!.

4. K. Emanuel, D. Raymond, A. Betts, L. Bosart, C. Bretherton,K. Droegemeier, B. Farrell, J. M. Fritsch, R. Houze, M. LeMone, D. Lilly, R. Rotunno, M. Shapire, R. Smith, and A.Thorpe, “Report of the first prospectus development team ofthe U.S. Weather Research Program to NOAA and the NSF,”Bull. Am. Meteorol. Soc. 76, 1194–1208 ~1995!.

5. R. Cess, M. Zhang, P. Minnis, L. Corsetti, E. Dutton, B. For-gan, D. Garber, W. Gates, J. Hack, E. Harrison, X. Jing, J.Keihl, C. Long, J.-L. Morcrette, G. Potter, V. Ramanathan, B.Subasilar, C. Whitlock, D. Young, and Y. Zhou, “Absorption ofsolar radiation by clouds: observations versus models,” Sci-ence 267, 496–499 ~1995!.

6. E. R. Kursinski, G. A. Hajj, W. I. Bertiger, S. S. Leroy, T. K.Meehan, L. J. Romans, J. T. Schofield, D. J. McCleese, W. G.Melbourne, C. L. Thornton, T. P. Yunck, J. R. Eyre, and R. N.Nagatani, “Initial results of radio occultation observations ofEarth’s atmosphere using the global positioning system,” Sci-ence 271, 1107–1110 ~1996!.

7. L. M. Little, “A fiber-based lidar system for atmospheric watervapor measurement,” Ph.D. dissertation ~University of Illinois,Urbana-Champaign, Urbana, Ill., 2000!.

8. L. B. Jeunhomme, Single-Mode Fiber Optics ~Marcel Dekker,New York, 1983!.

9. H. Kildal and R. L. Byer, “Comparison of laser methods for theremote detection of atmospheric pollutants,” Proc. IEEE 59,1644–1663 ~1971!.

10. E. E. Remsberg and L. L. Gordley, “Analysis of differentialabsorption lidar from the Space Shuttle,” Appl. Opt. 17, 624–630 ~1978!.

11. E. Browell, S. Ismail, and B. Grossman, “Temperature sensi-tivity of differential absorption lidar measurements of watervapor in the 720-nm region,” Appl. Opt. 30, 1517–1524 ~1991!.

12. V. Wulfmeyer and J. Bosenberg, “Ground-based differential


curacy, resolution, and meteorological applications,” Appl.Opt. 37, 3825–3844 ~1998!.

13. S. Ismail and E. Browell, “Recent lidar technology develop-ments and their influence on measurements of troposphericwater vapor,” J. Atmos. Ocean. Technol. 11, 76–84 ~1994!.

14. V. Brackett, S. Ismail, E. Browell, S. Kooi, M. Clayton, R.Ferrare, P. Minnis, B. Getzwich, and J. Staszel, “LASE vali-dation experiment: preliminary processing of relative humid-ity from LASE derived water vapor in the middle to uppertroposphere,” in 19th International Laser Radar Conference,NASA Conf. Publ. CP-1998-207671 ~1998!, pp. 465–468.

15. G. M. Smith, J. S. Hughes, R. M. Lammert, M. L. Osowski,G. C. Papen, J. T. Verdeyen, and J. J. Coleman, “Wavelengthtunable asymmetric cladding ridge waveguide distributedBragg reflector lasers with very narrow linewidth,” IEEE J.Quantum Electron. 32, 1225–1229 ~1996!.

16. G. M. Smith, “Single frequency semiconductor lasers,” Ph.D.dissertation ~University of Illinois at Urbana-Champaign, Ur-bana, Ill., 1996!.

17. S. D. Roh, J. S. Hughes, R. M. Lammert, M. L. Osowski, K. J.Beernink, G. C. Papen, and J. J. Coleman, “Asymmetric clad-ding InGaAs–GaAs–AlGaAs ridge waveguide distributedBragg reflector lasers with operating wavelengths of 915–935nm,” IEEE Photon. Technol. Lett. 9, 285–287 ~1997!.

18. L. M. Little, K. J. Beernink, G. C. Papen, and J. J. Coleman,“Performance characteristics of a narrow-linewidthdistributed-Bragg-reflector laser for optical remote sensingsystems,” IEEE Photon. Technol. Lett. 8, 1302–1304 ~1996!.

19. P. D. Dragic, L. M. Little, and G. C. Papen, “Fiber amplificationin the 940-nm water vapor absorption band using the 4F3y234I9y2 transition in Nd,” IEEE Photon. Technol. Lett. 9, 1478–1480 ~1997!.

0. P. D. Dragic and G. C. Papen, “Efficient amplification using the4F3y23

4I9y2 transition in Nd-doped silica fiber,” IEEE Photon.Technol. Lett. 11, 1593–1595 ~1999!.

1. T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method forhigh resolution measurement of laser output spectrum,” Elec-tron. Lett. 16, 630–631 ~1980!.

2. D. Simeonidou, S. Hamidi, and A. Siddiqui, “Theoretical andexperimental study of a new delayed self-heterodyne tech-nique for laser spectral linewidth measurement,” Int. J. Opto-electron. 8, 727–736 ~1993!.

23. N. Schunk and K. Petermann, “Numerical analysis of the feed-back regimes for a single-mode semiconductor laser with ex-ternal feedback,” IEEE J. Quantum Electron. 24, 1242–1247~1988!.

24. M. J. F. Digonnet, K. Liu, and H. J. Shaw, “Characterizationand optimization of the gain in Nd-doped single-mode fibers,”IEEE J. Quantum Electron. 26, 1105–1110 ~1990!.

25. R. M. Measures, Laser Remote Sensing ~Wiley, New York,1984!.

26. G. S. Anderson, S. Clough, F. Kneizys, J. Chetwynd, and E.Shettle, “AFGL atmospheric constituent profiles ~0–120 km!,”Rep. AFGL-TR-86-0110 ~U.S. Air Force Geophysics Labora-tory, Hanscom Air Force Base, Mass., 1986!.

27. J. M. Rosen and N. T. Kjome, “Backscattersonde: a new in-strument for atmospheric aerosol research,” Appl. Opt. 30,1552–1561 ~1991!.

28. J. M. Rosen and N. T. Kjome, “Balloon-borne measurements ofthe aerosol extinction-to-backscatter ratio,” J. Geophys. Res. D102, 11165–11169 ~1997!.

29. T. Takamura and Y. Sasano, “Ratio of aerosol backscatter toextinction coefficients as determined from angular scatteringmeasurements for use in atmospheric lidar applications,” Opt.Quantum Electron. 19, 293–302 ~1987!.

30. A. Bucholtz, “Rayleigh-scattering calculations for the terres-trial atmosphere,” Appl. Opt. 34, 2765–2773 ~1995!.

31. A. Bucholtz, “Response to comment on Rayleigh-scattering cal-

3

3

self-broadening coefficients, and pressure shifts in air,” J.

3

3

3

culations for the terrestrial atmosphere,” Appl. Opt. 37, 430~1998!.

32. F.-M. Breon, “Comment on Rayleigh-scattering calculationsfor the terrestrial atmosphere,” Appl. Opt. 37, 428–429 ~1998!.

3. L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P.Edwards, J.-M. Flaud, Perrin, C. Camy-Peyret, V. Dana, J.-Y.Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Watt-son, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V.Nemtchinov, and P. Varanasi, “The HITRAN molecular spec-troscopic database and HAWKS ~HITRAN Atmospheric Work-station!: 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer60, 665–710 ~1998!.

34. J.-P. Chevillard, J.-Y. Mandin, J.-M. Flaud, and C. Camy-Peyret, “H2

16O: line positions and intensities between 9500and 11500 cm21. The interacting vibrational states ~041!,~220!, ~121!, ~022!, ~300!, ~201!, ~102!, and ~003!,” Can. J. Phys.67, 1065–1084 ~1989!.

5. Z. Chu, T. D. Wilkerson, and U. N. Singh, “Water-vapor ab-sorption line measurements in the 940-nm band by using aRaman-shifted dye laser,” Appl. Opt. 32, 992–998 ~1993!.

36. L. P. Giver, G. Gentry, G. Schwemmer, and T. D. Wilkerson,“Water absorption lines, 931-961 nm: selected intensities, N2

collision-broadening coefficients, self-broadening coefficients,

Quant. Spectrosc. Radiat. Transfer 27, 423–436 ~1982!.7. A. Corney, Atomic and Laser Spectroscopy ~Oxford U. Press,

New York, 1977!.8. W. S. Benedict, R. Herman, G. E. Moore, and S. Silverman,

“The strengths, widths, and shapes of infrared lines. II. TheHCl fundamental,” Can. J. Phys. 34, 850–875 ~1956!.

9. W. S. Benedict and S. Silverman, “Line shapes in the infrared,”Phys. Rev. 94, 752 ~1954!.

40. L. D. Kaplan, “A quasi-statistical approach to the calculation ofatmospheric transmission,” in Proceedings of the Toronto Me-teorological Conference 1953 ~Royal Meteorological Society,London, 1954!, p. 49.

41. S. Ismail and E. V. Browell, “Airborne and spaceborne lidarmeasurements of water vapor profiles: a sensitivity analy-sis,” Appl. Opt. 28, 3603–3614 ~1989!.

42. R. M. Schotland, “Errors in the lidar measurement of atmo-spheric gases by differential absorption,” J. Appl. Meteorol. 13,71–77 ~1974!.

43. P. P. Webb, R. J. McIntyre, and J. Conradi, “Properties ofavalanche photodiodes,” RCA Rev. 35, 234–279 ~1974!.

44. S. Melle and A. MacGregor, “How to choose avalanche photo-diodes,” Laser Focus World 31(10), 145–156 ~1995!.

45. W. S. Benedict and L. D. Kaplan, “Calculation of line widths inH2O–N2 collisions,” J. Chem. Phys. 30, 388–398 ~1959!.


fiber-based lidar for atmospheric water-vapor measurements

Documents