airborne measurements of laser backscatter from the ocean surface

Airborne measurements of laser backscatter from theocean surface

Jack L. Bufton, Frank E. Hoge, and Robert N. Swift

Laser backscatter data for the ocean surface near nadir have been acquired from an airborne lidar platform.The unique capability of this lidar instrument to scan both transmitted laser beam and receiver field of viewup to 15° off nadir have made these data sets possible. Backscatter data were collected on eight separatemissions using laser wavelengths at 337 and 532 nm and 9.5 gm. Statistics of the mean, standard deviation,and probability density function of backscatter were computed and analyzed in terms of prior analyticalwork that relates backscatter to wind speed and mean-square wave-slope statistics. We found the full widthat half-maximum of the Gaussian-shaped mean backscatter pattern to range from 11 to 240 and the normal-ized standard deviation at a nadir-viewing angle to range from 0.1 to 0.6. We calibrated mean backscatterat nadir for the ocean surface in terms of an effective Lambertian reflectance by comparison of beach sandand ocean backscatter. Results were 16 and 24% reflectance on two missions where calibration was possible.Our data are compared with prior laser backscatter measurements and the general literature on optical scat-tering from the ocean surface.

1. Introduction

There are a variety of remote-sensing applications inwhich a knowledge of ocean surface reflection of laserradiation in the backscatter direction is important; yetthere have been few reported experimental investiga-tions.1-3 There is a large literature reporting variousanalytical treatments and laboratory or field studies ofthe general case of optical scattering from water sur-faces.4-24 Most reports have followed from the fun-damental photographic studies of sun glitter by Cox andMunk.4 While much of this literature is relevant to thelaser backscatter problem, there is a need for morebackscatter data and analysis.

We report laser backscatter data acquired from anairborne platform. In this study attempts were madeto accurately characterize mean backscatter vs angle offnadir, calibrate ocean backscatter at nadir, and presentnormalized standard deviations and probability densityfunctions for the backscatter. Our data were taken withthree different pulsed laser sources, one each in the ul-

Jack Bufton is with NASA Goddard Space Flight Center, Green-belt, Maryland 20771; Frank Hoge is with NASA Wallops Flight Fa-cility, Wallops Island, Virginia 23337; and Robert Swift is with EG&GWashington Analytical Services Center, Inc., Pocomoke City,Maryland 21851.

Received 11 January 1983.

traviolet (337.1 nm), visible (532.1 nm), and infrared (9.5gim). Although attempts were made to acquire dataunder a variety of different ocean surface conditions,our data sets were limited to a few specific flight dateswhere opportunities presented themselves. While ourdata are not comprehensive, they are intended as asupplement to existing data sets and a guide to oceansurface backscatter for laser remote-sensing instru-ments.

The primary instrument used in these experimentswas the NASA Wallops Flight Facility (WFF) airborneoceanographic lidar (AOL) system flown onboard theWFF P-3A aircraft. The AOL system is an experi-mental lidar system designed for fluorosensing,bathymetry, and altimetry applications. It can ac-commodate various laser transmitters and is capable ofscanning both transmitter and receiver optics up to 150off nadir. This feature was essential to our measure-ments. The AOL instrumentation and a number of itsapplications have been described in recent publica-tions.25-27 The data we acquired for this program arerepresentative of the actual operational environmentof the AOL in that large and highly variable laserbackscatter from the ocean surface makes water columnmeasurements more difficult to accomplish. In otherlidar applications the ocean surface reflection is veryuseful for determining the range (altitude of the sensor)or serving as a remote target for atmospheric columnmeasurements. In either case a thorough under-standing of the ocean surface backscatter and its effecton laser sensor parameters is essential for precise in-terpretation of lidar results. The major motivation of

1 September 1983 / Vol. 22, No. 17 / APPLIED OPTICS 2603

Z-h .. c

WIND -VEL CIT

OCEAN WAVE STRUCTURE

Fig. 1. Lidar backscatter measurement geometry.

the present work is to add to the laser backscatter database and relate it to current analytical work to specifythe ocean surface target signature and predict sensorperformance.

In Sec. II there is a brief discussion of fundamentalconcepts in ocean surface reflectance. This is followedby a review of analytical work required to describe op-tical backscatter statistics and make the connectionamong wind speed, ocean surface slope statistics, andthe observed optical effects. Previous analyses of themean backscatter pattern are reviewed to specify theangular backscatter pattern. Analysis of backscattervariance is extended to our application. We then reportresults of airborne measurements of laser backscatterat several wavelengths and discuss the statistics in termsof the analytical work, previous measurements, andmeasured error sources.

II. Laser Backscatter from the Ocean

In altimetry, bathymetry, or other lidar remote-sensing applications a laser beam is incident on theocean surface from the atmosphere. The reflectedportion of this incoming laser beam is an importantquantity that enables a measurement to be performedor alternatively interferes with a measurement in thewater column. The general specification of oceansurface reflectance would require bidirectional reflec-tance as a function of angle of incidence. In this anal-ysis and in the measurements reported here we consideronly the case of reflection at 180° to the incident di-rection (i.e., backscatter). The concept geometry isshown in Fig. 1. The angle 0 is the angle of incidencerelative to the normal to the mean ocean surface as wellas the angle off nadir for the laser transmitter system.Backscatter reflectance is the essential quantity forairborne lidar systems since they are monostatic; i.e.,both the transmitter and receiver are located in oneinstrument on an aircraft platform situated at a con-siderable distance above the target. The azimuth angle0 is important to the extent that the ocean surface isnonisotropic as might be expected when waves areproduced by wind blowing in one direction. In general0 is unknown when remote-sensing laser data are taken.

It was not measured in data reported here and can beconsidered second order in importance to the primarydependence of laser backscatter on angle 0.

In the experiments reported here pulsed lasers wereused, thus the measured quantity was backscatteredpulse energy ER as sampled by the receiver telescope.Backscattered average power is the important param-eter for cw lidar systems. The analysis and reportedstatistics apply to this quantity as well. It is assumedthat the receiver field of view is larger in extent than thelaser footprint on the ocean surface. In this case all thetransmitted energy ET can contribute to the return, andER can be written

ER =ET Z2LOL(1-) (1)

where z = h sec6, where h is the aircraft altitude,LO = optical system losses,

A = two-way atmospheric transmission, andAR = receiver area.

The backscatter properties of the ocean surface aremodeled by the target term (p/Q). The factor p is sur-face reflectance (0 < p < 1), and Q is a solid angle thatmodels the pattern of reflected radiation for backscat-ter. Both p and Q are functions of 0, the angle offnadir.

Optical radiation incident from the atmosphere ispartially reflected from the ocean surface because of therefractive-index discontinuity at the air-water interface.The plane-wave reflectance coefficients pII and pa forparallel () and perpendicular (I) polarizations aregiven by Rayner et al.19 from calculations using Fres-nel's equations and Snell's law,

n2- (2 r- 1 2J0l = n2+rand p = r (2)

whereI =2 - sin2ol\1- sin2 0 I

0 is the angle of incidence, and n is the real componentof refractive index. Reflectance has its lowest valuesat normal incidence, is nearly constant up to 450 offnormal, and then rises rapidly beyond 700 off normalto unity at grazing incidence. Within 200 of normalincidence, pII and P± are close in value to each other andto the normal incidence unpolarized reflectance

[n(X) - 1]2 + k2 (X)

[n(X) + 1]2 + k2(X)(3)

where we have now included k, the imaginary compo-nent of refractive index, and indicated the dependenceof refractive index on wavelength (X). Values for n (X)and k (X) in pure water at various wavelengths have beentabulated by Hale and Querry.2 8 Refractive index inthe near ultraviolet (UV), visible (VIS), and near in-frared (IR) is essentially all real with values of n near1.33. At 9.5 gim, the refractive index exhibits a smallimaginary component.

Changes in temperature as well as in the concentra-tions of dissolved and particulate matter all affect theform of n() and k(X) applicable to ocean water. The

2604 APPLIED OPTICS / Vol. 22, No. 17 / 1 September 1983

Table I. Reflectance vs Wavelength for Clean Ocean Water

Fresnel Vol. Vol.Laser reflectance absorp. backscatter Volumetric

wavelength Refractive index coeff. a bb reflectanceX n(X) k(X) p (m-1) (m-) R(O-)

337 nm 1.345 8.6(-9) 0.022 0.32 0.017 8.8(-3)532 nm 1.334 1.5(-9) 0.020 0.035 2.2(-3) 0.01

9.5 Am 1.255 0.046 0.013 5.8(4) -0 -0

refractive index increases with increasing salinity andturbidity but decreases with increasing temperature.Values of refractive index for realistic ocean waters atwavelengths between the UV and IR can be found in theliterature. 2 9 3 0 Values of p were calculated for thewavelengths used in our experiments and are listed inTable I. These calculations apply to clean ocean waterat 20'C temperature and normal incidence. Reflec-tance for clean ocean water is only a few percent atnormal incidence for all the wavelengths we used.

Solid angle Q is determined by detailed wave struc-ture within the laser footprint. If the ocean surfacecould be characterized as a diffuse reflector, the Lam-bertian model of = r/cosO together with the p fromTable I would specify ocean backscatter in Eq. (1).While Lambertian reflectance is often the case for ter-rain targets where multiple scattering is an importantprocess, the ocean is more like a distorted mirror surfacethat gives rise to specular reflections or glints from wavefacets that are aligned for backscattering to the laserreceiver. The angular spread in the reflected laser ra-diation is determined by the distribution of wave slopes(mirror angles) within the laser footprint. Typicalbackscatter patterns are tens of degrees wide and arepresumably a function of sea state, wind speed, and laserfootprint size. In the limit of a perfectly calm sea Qwould be determined by the laser-beam divergenceangle. As a result Q would be quite small, of the orderof 10-6 sr, for a 1-mrad divergence laser beam. A mirrorreflection is unlikely since even a calm sea is not flat tooptical tolerances. It is the purpose of this analysis andthe measurements reported here to specify the oceansurface target factor (p/Q) that realistically falls be-tween the two extremes of Lambertian (diffuse) re-flection and mirror (pure specular) reflection. Most ofour data can only be reported as mean received energy(ER) normalized by the value of this quantity at normalincidence ( = 0). This gives information only on the0 dependence of p/Q. To report absolute (calibrated)values of pQ for the ocean surface, we also used theairborne lidar instrument to acquire some samples ofdata over beach areas. The well-known reflectance ofsand, which was verified in our laboratory, and its as-sumed Lambertian backscatter pattern are then usedto calibrate the nadir ocean reflectance.

Backscattered laser radiation from the water volumemust be considered in addition to surface backscatterfor predicting pulse energy reaching the lidar receiver.Volume backscatter is an important effect at 532.1- and337.1-nm laser wavelengths but is negligible at 9.5 gimbecause of essentially no surface penetration at this X.

Gordon 3 l gives a concise method for treating volumebackscatter by defining the parameter R(0-), the sub-surface irradiance reflectance for zero depth. Thispermits the entire water column to be handled as aLambertian reflector of value R(0-) located just be-neath the surface. Whitlock et al.

3 2 quote work byMorel and Prieur3 3 that approximates R(0-) as fol-lows:

R(0-) 0.33 b (4)

where b = the volume backscatter coefficient, and a= the volume absorption coefficient. The quantityR(0-) is an inherent optical property of water. Itsvariation with wavelength yields the ocean color ob-served from high altitude under solar illumination. Inour experiments the natural solar background wasnegligible compared to laser backscatter, and we needonly consider R(0-) evaluated at our respective laserwavelengths. Values of R(0-) are calculated from a andbb values34 for pure water and are included in Table Ifor comparison with Fresnel reflectance coefficients. Atthe two laser wavelengths, 337 and 532 nm, R(0-) is-1%. It is negligible at 9.5 ,im, where absorption isstrong.

In ocean water containing dissolved and particulatematter both backscatter and absorption increase. Datapresented by Whitlock et al. 32 and Morel and Prieur3 3

show a suppression of UV volumetric reflectance asocean turbidity increases. Apparently, as turbidityincreases, absorption increases faster than backscatterat UV wavelengths. Thus turbid water takes on a greenhue rather than the blue appearance of pure water orclean ocean water. When organic materials like phy-toplankton are present chlorophyll and other pigmentsplay a major role in increasing absorption more or lessequally with backscatter at visible wavelengths.33 Asa result, R (0-) increases slowly with increasing organicparticulate load. Morel and Prieur33 report R (0-)values at 532 nm from 0.008 to 0.02 for a variety of oceanwater samples. When organic particulate materialdominates, the visible wavelength backscatter increasesmore rapidly than absorption, and R (0-) increases.The R(0-) values given by Morel and Prieur33 rangefrom 0.01 to 0.1 at 532 nm for ocean water samples ofthis type. Whitlock et al.32 report R(0-) values from0.06 to 0.1 for even more sediment-ladened waters at 532nm.

Values of R (0-) cos/7r must be added to the targetterm (p/Q) in Eq. (3) to predict laser backscatter energy.


The largest R (0-) effect in our experiment would be at532 nm, where most data were collected. This addi-tional factor should contribute at most only a few per-cent reflectance or less for the open ocean and coastalwater types applicable to our data.

Ill. Analysis of the Backscatter Pattern

The principal uncertainty in the analysis of oceansurface backscatter is the angular extent and form of thereflectance pattern. We have chosen to model thispattern by an effective solid angle Q. In this model allreflectance is uniformly distributed over the solid angle;while in reality reflectance depends on both angle ofincidence and angle of observation. Thus the readeris cautioned against using the analysis and data reportedhere for geometries other than backscatter. The oceanreflectance pattern is determined by the distributionof surface (wave) slopes and their alignment. Waveslopes aligned perpendicular to the incident beam andincluded within the incident laser footprint on the oceanappear to the lidar receiver as specular points or glints.Surface slopes are dependent primarily on the wind asa disturbing force and the action of gravity and surfacetension as restoring forces. The larger wave structures,ones with dimensions larger than -2 cm, are gravitywaves. Waves of smaller dimensions are called capil-lary waves, and surface tension is the restoring force.Capillary waves are the smallest facets on the oceansurface and are bounded on the small scale end by vis-cous dissipation near 1 mm.

A number of published reports 1 1"12 35-37 address as-pects of radar reflection (centimeter or longer wave-length) from the ocean surface. These include discus-sions of the role of gravity and capillary waves in pro-ducing backscatter signals. Since the radar wavelengthis larger than capillary waves, diffraction effects becomeimportant. All optical wavelengths are much smallerthan the smallest capillary wave, diffraction effects arenot important, and laser backscatter can be satisfacto-rily explained by a geometrical optics analysis of scat-tering from the ocean surface.

Modern work in the analysis of optical angularbackscatter began with the mean-square slope statisticsof Cox and Munk.4 Their work was based on theanalysis of sun glitter patterns in aerial photographsobtained over the open ocean under various wind andwave conditions. They reported a near-Gaussian dis-tribution of wave slopes and proposed a relationship forthe 2-D mean-square slope:

(S 2 ) = (S2) + (S2),

(S2) = 0.003 + 5.12 X 10- U 12 .4 , (5)

where (S2) and (S2) are, respectively, upwind andcrosswind mean-square slopes, and U12.4 is wind speedat 12.4 m above the ocean surface. Cox and Munkproposed a Gram-Charlier distribution to account fordifferences in the upwind and crosswind componentsof (S2) that result in the departure from a Gaussiandistribution. This is a second-order effect and is

especially weak for the low wind speed regime mostprevalent in clear weather and most applicable to ourdata sets.

The Cox and Munk4 data have been reanalyzed byWU, 5 who was able to show that the mean square slopevaries logarithmically with wind velocity. He furthergrouped the data and proposed that slopes for windsbelow 7 m/sec were characteristic of gravity wave action,while slopes for winds above 7 n/sec were primarilydetermined by capillary wave slopes. The Wu 5 ex-pressions for the two regimes are

S2) = (lnUjo + 1.2)10-2, U10 < 7 m/sec (6)

1(0.85 lnU10 - 1.45)10-1, U1 0 > 7 m/sec.

Cox and Munk data 4 for U10 < 7 m/sec also show afactor of 2 reduction in (S 2 ) in the presence of a capil-lary wave-suppressing oil slick on the ocean surface.This suggests that, for U10 7 m/sec, capillary andgravity waves are about equally important in producingthe mean-square slopes observed at optical frequencies.Most authors agree that the observed slopes for U10 >7 m/sec are produced primarily by the presence ofcapillary waves. Recent measurements of capillarywave slopes in the ocean by Schau'8 and in wave tanksby Bobb et al.

2 2 generally support the conclusions ofCox and Munk 4 and Wu5

,17 38; but unresolved questions

remain on the exact form of the probability distributionfor wave slopes and the practical applicability of wavetank data in predicting optical angular backscatterstatistics in the open ocean.

Those who want calculations based on a more de-tailed model of the ocean surface and the effect of windvelocity are referred to the work of Krishnan and Pep-pers.' 5 They used the comprehensive ocean wavemodeling work of Pierson and Stacy3 9 that produced sixfunctions for the surface height power spectrum S(k)to span the spatial frequency (k) range from the low-frequency cutoff (k _ 10-2 m-1) determined by thelargest gravity waves to the high-frequency cutoff (k -103 m-) determined by viscous dissipation of capillarywaves. The Pierson and Stacy spectrum is based onwave tank and open ocean data sets and is a function ofwind-driven frictional velocity u. The quantity u* isdependent on wind speed and atmospheric stability,which in turn depend on air/sea temperature differ-ences. The equations

u* = 0.4U./ln(Z/Z 0 ),

0.684Z =- + 4.28 X 10-5 u*2 - 0.0443

u*(7)

can be used to compute u* given wind speed U, atheight Z, and the assumption of atmospheric stability(neutral stratification), e.g., u* = 12 cm/sec follows fromU10 = 3.3 m/sec. Krishnan and Peppers1 5 have per-formed numerical calculations of spectral moments ofthe form mnm which apply to upwind (n) and crosswind(m) components:

mnm = f S(k)k2 +lkcm+ldkudk,. (8)


Table II. Relationship of Ocean Surface Slope Statistics to Wind Speed

Wind speed Krishnan & Peppers15U10 U* Wu5 Cox & Munk 4

nm22 i 40 M0 4 NA(m/sec) (cm/sec) (S 2 ) TS) (Sr;) Mn20 Mn02 (Mn2) (rn 2 ) (M-2) (rn-2 )

2.0 8 0.0189 0.0063 0.00683.3 12 0.0239 0.0104 0.0049 0.0245 0.0182 0.0376 0.136 0.0927 1.2(4)5.0 17 0.0281 0.0158 0.0126 0.032a 0.0233a 0.065a 0.24a 0.15a 1.7(4)7.0 24 0.0315 0.0221 0.0164 0.0413 0.0293 0.0977 0.358 0.228 2.2(4)

10 40 0.0507 0.0316 0.0222

a Interpolated.

The results for several low wind speeds are listed inTable II. In this notation mean-square slopes (S2) and(S2) are represented by M2 0 and M0 2 . They are abouta factor of 2 greater than the Cox and Munk4 and WU 5

results.In a recent paper on open ocean optical radiance ob-

servations obtained from just beneath the surface,Stotts and Karp2 4 report a surface slope variance of 4.4X 10-2 rad2 for a wind speed of 9.3 m/sec (20 mph)measured at 9 m above the water surface. Despite theirclaim to the contrary this result is close to the valuesobtained from Eqs. (5) and (6). This is because sub-surface radiance just like backscatter depends on the2-D mean-square slope (S2), which is the sum of (S2)and (S2). Stotts and Karp2 4 also suggest, as originallypointed out by Bobb et al.,22 that adjacent waves mayobscure steeper wave slopes (a shadowing effect) whenthe observations are obtained from above the surface,while subsurface radiance measurements are not alteredby this effect. This could explain the discrepancy be-tween slopes calculated with the Pierson and Stacyspectrum and the data of Cox and Munk. They suggestthat the sun glitter data and by implication the laserbackscatter data as reported here fail to measure con-tributions from the highest slopes (40°), thus statis-tical analyses of the data sets yield smaller variances.The result is at most a factor of 2 uncertainty in thepresent understanding of mean-square wave slope asa function of wind speed. Similar factor of 2 increasesin variance above the Cox and Munk 4 values have beenreported based on wave tank data. Wu17 attributes thisto suppression of capillary wave growth by gravity wavesin open ocean conditions. We will use the mean-squares slope of Eq. (6) throughout our analysis of meanbackscatter because of its basis in optical data acquiredunder realistic ocean conditions.

The next step in analysis of laser backscatter requiresthe connection between mean-square slope statisticsand the mean backscatter measured in a series of laserpulses collected by the receiver telescope. Kodis'0showed mean backscatter to be proportional to the av-erage number of specular points on the ocean surfacemultiplied by the average curvature of these points.Barrick" used this result and derived expressions forboth quantities under the assumption of a Gaussiandistribution for ocean surface height and a Gaussianshape for the height correlation of surface points. Hisresult for number NA of specular points or glints in anocean area A specialized to the case of backscatter is

7.255 -tan 2 OlNA =2 exp (32))NA=212 eX (S2) )'

2) =4(h 2 )(3) 1 2

(9)

1 is the height correlation length, and (h2) is themean-square surface roughness height. His corre-sponding result for mean surface curvature is

r1r21) = .13787r 2) sec 4 , (10)

where r1 and r2 are the two principal radii of curvatureat a specular point.

Barrick's" radar cross section o.0 specialized to thecase of backscatter and expressed in our notation is

a = 7rpNA ( Ir,r2) I (11)

This is the total scattering cross section of the oceansurface. Normalization by 47r sr yields the scatteringcross section per steradian that is equivalent to ourfactor p/Q in Eq. (1):

Or0 p pNA (I rr21)4r 0 4

p p sec4O | tan 20

Q 4 r(S2) expV (S2))'

or

(12)

P_= P Se4OP5 (tanO).4

The factor P, (tanO) is a normalized Gaussian distri-bution for surface slope (tanO) whose width is deter-mined by mean-square slope (S2). The ocean back-scatter factor p/IQ is plotted in Fig. 2 for a family of

5.01 1 I I I

0.0E

0.06 -

0.04

0.02 -

" I l I 1I 1 I I ( I I I I 0 5 10 15 20 25

0 (degee)

Fig. 2. Teoretical mean backscatter factor p/O of Eq. (12) vs off-nadir angle 0.


low-to-moderate wind speeds. For this plot the (S2)of Eq. (6) is used.

The solid angle Q that we use to model the back-scatter pattern is

Q = 4/[sec 4 0P,(tan0)], (13)

and Q = 47r(S2 ) at 0 = 00, while the expression in Eq.(1) for mean backscattered energy becomes

(ER) = LOLA P seC20P (tan0). (14)

The decrease in (ER) from its maximum valueETARLOL2p/47rh 2 (S 2 ) at 0 = 00 is controlled by thefactor sec20 exp(-tan 2 0/(S2 )). The full width athalf-maximum (FWHM) of this pattern is approxi-mately

FWHM (degrees) 2 arctan[0.83(S 2 )1/2 ]. (15)

For a wind speed of 5 m/sec the (S2 ) of Eq. (6) is 0.0281(see Table II). This predicts a FWHM of ,16°. Byway of contrast the Lambertian pattern has a solid angleQL = r/cosO and yields a FWHM of 1200.

The factor QL/ gives the enhanced reflectance of theocean surface and can be used to define an effectiveLambertian reflectance

QL p7rsec50Peff = P 0= Ps(tan0). (16)

Q 4

At nadir ( = 00) the effective Lambertian reflectanceis p/4(S 2 ) or 0.18 for our example used above of (S 2 )= 0.0281 for U10 = 5 m/sec. This is an enhancement ofa factor of 9 over the Fresnel reflectance of 0.02. Incalculating sensor performance as in Eq. (1) the valuefor Peff from Eq. (16) or Fig. 2 would be divided by7r/cosO (the Lambertian solid angle) to yield the modelfor ocean surface backscatter.

A more detailed model for Ps (tanG) in terms of theupwind (S2) and crosswind (Sc2) mean-square slopesand azimuth angle of observation 0 can account forelongation of the mean backscatter pattern in the di-rection of the wind:

eptan 2 0 (COS2 0+ sin2 okP.,(tan0) = e- v 1S7(S)J

2,(S2 )/2(S2)1z/2 (7

Barrick'2 points out the equivalence of these resultsfor mean backscatter to results of Kodis'0 and explainshow they are a simple consequence of geometrical op-tics. Krishnan and Peppers' 5 also carry through ananalysis of mean backscatter. They start with theHuygens-Fresnel formulation for scattered intensity asthe Fourier transform of spatial coherence, relate co-herence to the ocean surface height covariance, and thenexpress the result as a Taylor's expansion in spectralmoments of S(k) as in Eq. (8). They retain only thesecond-moment term, which is equivalent to making anassumption of Gaussian statistics. Their final resultfor mean backscattered field intensity [their Eq. (3.30)]when written in terms of (ER) gives the same propor-tionality to P, (tanG) as above.

All analyses to this point are based on plane-wavepropagation and plane-wave reflectance coefficients.In a recent analysis of temporal moments of laserbackscatter, Tsai and Gardner'3 and, in this issue,Gardner et al. 14 have followed an analysis similar to thatof Barrick" but included effects of laser pulse shape andlaser divergence OT. They obtain expressions similarto Eqs. (13) and (14) which include the factor tan2

0T

added to (S2). Their final expression'4 for be-comes

Q = 4r[(S2) + tan2 OT], (18)

which has the correct limiting behavior as (S2) goes tozero (a perfectly calm ocean). In this limit Q is deter-mined by the mirror reflection of OT. In our experi-ments OT is typically 10-3 rd, so that tan2OT - 10-6 isnegligible compared to even the small (S 2 ) for a 1-m/secwind. When OT is of the order of 10-1rd (several de-grees), it is necessary to account for the source diver-gence which acts to reduce mean backscatter.

While there is general agreement on the form andmagnitude of the mean backscatter, the second moment(backscatter variance) is not so well understood. Wewere unable to find a comprehensive analytical treat-ment of the subject in the literature but will presenthere several approximations that can be used for com-parison with data. The statistical quantity we will useis the normalized backscatter variance

C2 = ((ER - (ER) 2 ))(ER)2 (19)

or its square root E. The quanity E, the normalizedstandard deviation, is frequently used to describe thespace/time variability of a random process because ithas the form of a unitless modulation factor

A lower bound for E2 can be set by a calculation of the

density of glints within the laser footprint. Krishnan40

has reported a derivation of e2 in terms of the NA of Eq.(13). He expresses E2 as the sum over the normalizedmean-square variations in curvature (I r1r2 J ) and NAas

E2(Irlro)

N N(20)

and uses Longuet-Higgins69 analysis to justify E2( Irlr2l)

1 and gives Ec = 1/N, where N = AF -NA is the totalnumber of glints in laser footprint area AF. As a result,E2 2/N = 2/(AF * NA). Finally, he accounts for theincrease in AF with 0 for a fixed laser divergence by acos3 0 factor

- 2 cos30

AF NA(21)

Longuet-Higgins8 9 has shown that NA can be expressedin terms of second- and fourth-order moments of thesurface height power spectrum as

N+M22 P3NA =(Mn4 0 Mn0 4 + 22)1/2 -P0 ,(tanO),2

(22)

thus,


0 5 10 15 20 250 (deg-.s)

Fig. 3. Estimates of normalized standard deviation of backscatterfrom Eq. (23) (--- ) and from Eq. (26) and a tanO dependence (-)

for various values of wind speed and a footprint area AF = 1 In2 .

--I 3 cos03 11/2[Ae nAiM40Mo4 + 3m22)1/2Ps(tan0)j

The dependence of on is determined by cos3 0 and bytanG in the Gaussian slope distribution P, (tani). Windspeed dependence is implicit in P, (tani) and in thefourth-order moments. Values of were calculatedfrom the moments of Table II and are plotted in Fig. 3as a function of 0 for a wind speed U10 = 5 m/sec and alaser footprint area of 1 M2 . As we shall see these pre-dictions are substantially lower than the data presentedhere. Correlation between specular points reducesaveraging within the footprint and could easily explainlarger measured E values. The physical basis for spec-ular point correlation is simply the action of gravitywaves with wavelengths that are an appreciable fractionof or larger than the laser footprint. The larger wavestend to tilt the entire footprint and could account forsubstantial pulse-to-pulse backscatter variation.

Jackson3 7 has proposed a simple tilt model for pre-diction of reflectivity modulation at radar wavelengths.The central idea behind this model is that ocean wave-lengths larger than the beam footprint, while contrib-uting to mean-square slope, also act to give a uniformtilt to the footprint. Variations of this tilt with time andspace contribute to because they are the same asvariations in off-nadir angle 0. He showed that -tanOi( I A I )/(S2), where ( I A I) is the mean tilt of theentire footprint. We can repeat this calculation for ourparticular case of optical backscatter by calculating

E2 -UER ) ) (24)

which becomes with Eq. (14)

E2 [2tan0 1 -(s32))] (IA01)2, (25)

or

E= 2tan (1-HS 2 )) (IAlI).

The value of (I A1i 1) should increase with increasingwind speed (more tilt) and decreasing footprint size (less

spatial averaging of smaller tilts). This can be under-stood by noting that footprint tilt is caused by wavemotion between the input spatial frequency g/U2 de-termined by wind speed U and acceleration due togravity and a cutoff spatial frequency determined by thereciprocal of footprint size. As this spatial frequencyrange expands due to either an increase in U or decreasein AF, a larger fraction of wave energy goes into tilts ofthe whole footprint, hence (IALI) < (S2)1/2 and is afunction of U and AF-

In a separate effort, Jackson4 l computed the pro-portionality constant relating e to U and footprint areaAF for observation at nadir. He expressed the samplemean-square slope as the space-time average of thesquared-wave slope and then computed the variance ofthis quantity by use of the transform relation betweencovariance and spectrum for the wave slope assumingGaussian statistics. His results required numericalintegration for finite footprint size but have the as-ymptotic form (for large AF) that gives

0.12U 2

co = ggAF

(26)

where the subscript denotes = 0. This result wasused by Petri' (his Fig. 16) and is used here in Fig. 3 toplot Eo plus the tanG dependence of Eq. (25), AF = 1 M2 ,

and U10 = 2, 5, and 10 m/sec.Jackson4' points out that all these estimates of

backscatter variance should be considered lower boundsdue to the assumption of Gaussian statistics. Onereason for this is that ocean wave structure is oftencharacterized by the phenomena of patchiness. Thisis the sudden appearance and then disappearance ofcapillary wave motion resulting from the breaking ac-tion of longer waves and the intermittent nature of windspeed at the ocean surface. This departure fromGaussian statistics is an especially important factor forthe transitional wind speed range (2-4 m/sec), where wemade most of our backscatter measurements. Wecannot measure the contribution of patchiness to butconsider it a major factor that may account for mea-sured in excess of the estimates above.

Target-induced speckle is a separate process from thespecular (glint) nature of the ocean surface reflectanceand is known to be an important cause of backscattervariance at radar wavelengths. Speckle results fromthe coherent combination at the receiver of backscatterfrom various portions of the radiation footprint on theocean surface. The optically rough ocean surface withineach footprint results in significant optical phase dif-ferences and an interference or speckle pattern is pro-duced in the receiver plane. The largest radial sepa-rations r in the laser footprint result in the smallestspeckle structure p according to p = XZ/r, where Z isthe path length between aircraft and ocean. The squareof the ratio of receiver diameter to the speckle size pgives the number of speckle correlation elements or cellsthat are averaged in the receiver aperture for each laserpulse. Estimates for the 0.3-m diam AOL receiver andour propagation paths are 103 cells for the UV andvisible data. A similar estimate for the infrared lidar


1.2

PRO\

system and its 0.18-m diam aperture results in 150-300cells. There is further averaging in the time domainbecause of a multimode structure in all these lasers thatis averaged over the laser pulse length. On the basis ofthese averaging effects it is likely that speckle modu-lation is reduced to less than the 1% level for each laserpulse. This is not true for radar (microwave wave-lengths) due to the much larger X, the temporal coher-ence of the radiation, and the diffraction-limited re-ceiver which observes only one speckle correlation cell.Radar speckle modulation is severe, and averaging overmany Rayleigh distributed pulse returns is necessaryto arrive at good estimates of ocean backscatter crosssection even under high-detection signal-to-noise con-ditions.

Previous field measurements of laser backscatterfrom a wind-driven water surface have been reportedby Petri.' He made measurements of the laser beamreflection at 1.06 Aim from a platform suspended be-neath the Chesapeake Bay Bridge. His data exhibitangular spreading in qualitative agreement with theanalysis of mean backscatter discussed above. An ap-proximate comparison between his data and theoreticalcalculations is possible since he recorded wind speeddata near the water surface (Z = 2.1 m). His data fora wind speed of 5 m/sec show an angular spread(FWHM) of ,14° that compares with predicted valuesof ,16° for a wind speed U10 of 5 m/sec. It should benoted that he used a smaller laser spot size (15 cm) onthe water surface. He observed strong variability inlaser backscatter, particularly at very low and at highspeeds. He reported a receiver signal dynamic rangewhich is related to E. A major finding in his data wasthe calibration of backscatter power with respect to aLambertian target. He obtained enhancement factorsequivalent to a Lambertian reflectance of 2.0-3.0 formeasurements of laser returns from the water surfaceat nadir incidence under low wind velocity conditions.Moderate wind velocities (3.4 m/sec) produced an en-hanced reflectance of 1.0. The corresponding predic-tion from Eq. (16) for Peff and the value of (S2) = 0.0239for U10 = 3.3 m/sec in Table II is Peff = 0.21 or a factorof 5 smaller.

Jellalian2 reported backscatter statistics from a lasersystem mounted on an aircraft platform. He also usedthe 1.06-,um Nd:YAG laser wavelength. His resultswere acquired with the laser pointed near nadir andwere analyzed for mean backscatter and standard de-viation for both ocean and sand as well as other terraintargets. He reported that the ratio of sand-to-oceanmean backscatter was -2:1 or less for smooth water and-3 or 4:1 for rougher water (up to 1-m waves). He alsoreported effective target cross sections of 0.24-0.15,respectively for smooth and rough ocean targets. Thesetarget cross-section values represent the calibration ofthe mean backscatter signal and are equivalent to thePeff coefficients. Note that the Jellalian values are afactor of 4-7 less than Petri's and in general agreementwith Peff of Eq. (10) for low-to-moderate wind speeds.His reported standard deviations as normalized bymean backscatter were -0.25 for sand and ranged from

0.25 to 0.5 for ocean returns. No indication of surfacewind speeds or angular width of the backscatteredpattern was reported.

IV. Instrument Description

The primary laser instrument we used to collect oceanbackscatter data was the airborne oceanographic lidar(AOL) operated by NASA/Wallops Flight Facility(WFF). This instrument and its application inbathymetry and fluorosensing are described in recentpublications. 252 7 An artist's concept of the instrumentappeared on the front cover of this Journal on 1 Oct.1981. The optical assembly of this lidar system permitsexchange of laser transmitters, filters, and adjustmentof transmitter beam divergence and receiver field ofview. The collinear arrangement of the receiver andtransmitter optical paths eliminates the need for focusor alignment corrections to compensate for changes inaircraft altitude. The AOL data system records posi-tion and aircraft attitude information from an inertialnavigation system (INS), slant range (distance) to thetarget, and the temporally resolved laser backscattersignal.

During the experiments described here the AOL wasinstalled in the WFF P-3A aircraft. The P-3A is afour-engine turboprop aircraft with sufficient room forthe AOL as well as supporting instrumentation thatincluded the NASA/WFF pulse compression radar al-timeter (PCRA) and surface contour radar (SCR). Theradar instruments, the INS, and a video camera systemprovided auxiliary data sets on sea state, aircraft alti-tude and attitude, and ocean, cloud, and terrain targetsto characterize the laser backscatter data.

A schematic of the transmitter and receiver opticalsystems is given in Fig. 4. Laser output is directedthrough a Galilean beam expander, a diplexer mirror,and a folding mirror onto a large scanning mirror.Scattered radiation in the transmitter optics is sampledby a silicon photodiode, which is used for the laserranging start pulse. The scanner mirror is used to di-rect the laser beam toward the ocean surface at anglesof up to 15° off nadir and a scanning rate of 5 Hz. Ashaft encoder is used to measure scan azimuth for eachlaser shot. Laser backscatter returns through the samepath and is directed by the diplexer mirror into a 30-cmCassegrain telescope. The receiver telescope brings thecollected laser radiation to a focus where the field ofview is controlled by two pairs of adjustable knife-edgeswith variable separations. Relay optics, bandpass filter,and photomultiplier tube (PMT) complete the receiveroptical system.

The AOL system was operated in the bathymetrymode for all the laser backscatter data collected andreported here. A block diagram of the receiver elec-tronics and data acquisition system is given in Fig. 5. Inthis mode PMT output is digitized as a function of timeusing thirty-six separate ADCs. The ADCs are chargedigitizers set for a 4-nsec integration period and areseparated by 2.5 nsec to provide overlapping coverage.The pulse generated by the PMT from ocean surfacelaser backscatter is first used to stop the time-interval


SECTION THROUGH A-A

Nd: YAG LASER FOLDING MIRROR

+-F= - COLLIMATOR

N2LASER I

SECTION THROUGH B-B30 CM DIAM. MULTI-CHANNELCASSEGRAIN / POWER SUPPLYTELESCOPE\

VARIABLE - DIPLEXERFIELD STOP e MIRROR

BEAMSPLITTER3R M

NARROWBAND GATE DELAYINTERFERENCEGFILTER FLUOROSENSINC

BATHYMETRY PMT DETECTOR ASSY/ SPECTROMETER m I

FRONT END I ISIGNAL PROCESSOR *-POWER SUPPLY

A/C FWD

Fig. 4. Optical schematic of Airborne Oceanographic Lidar system.

Fig. 5. Laser backscatter receiver electronics and waveform digitizerin Airborne Oceanographic Lidar bathymetry mode.

unit for a slant range measurement. It is then split andsent one way through a variable delay into three fan-outfilter banks for analog input to the thirty-six separate10-bit charge digitizers. They are gated on for the 4-nsec measurement interval by outputs of a second fan-out amplifier bank driven by the original pulse. Theseoutputs are first passed through fixed delay cables toprovide the 2.5-nsec channel separation. Digitizeroutput is transferred through the CAMAC dataway andis recorded on a nine-track magnetic tape under controlof the data acquisition computer program. Instrumentparameters, time, and aircraft INS data are also re-corded for each laser pulse record.

The primary laser system for this series of laserbackscatter measurements was a frequency-doubledNd:YAG with output at 532 nm. Some data reportedhere were acquired with a pulsed nitrogen laser oper-ating at 337 nm. Specifications for these two lasertransmitters and the AOL optical system parametersthat applied when each laser was in operation are listedin Table III.

Postmission computer processing was used to obtainstatistics of the laser backscatter pulses. Individualpulse records were grouped into files of duration fromtens of seconds to minutes. Each file corresponded toa pass by the aircraft for a given set of experiment pa-rameters. In most cases the file was chosen to be arepresentative subset of all data available for a givenpass. Statistics computed for the received pulses werethe average, standard deviation, probability density,and maximum and minimum signals of backscatterpulse energy. This calculation was performed bysumming counts in the digitizer channels containing thebackscatter laser signal. The digitizer counts werecorrected for individual channel gain and bias variationprior to the integration. The gain and bias correctionsfor the digitizer channels were obtained during groundcalibration tests in which a variable pulse delay was usedto step the receiver pulse from a fixed retroreflectorthrough all channels.

Aircraft roll and pitch angles and the scanner azimuthangle were used to compute the ocean surface incidenceangle for each laser pulse measurement. The data werethen grouped in 10 increments of this angle off nadir ().A record was also made of the total number of receivedpulses and missing pulses for each 0. The setting of thereceiver threshold value was variable among the flightmissions as was evident from the minimum pulse energyand number of missing shots (receiver pulse belowthreshold).

V. Experiment Description

Data reported here were acquired in eight separateflight missions. These missions are summarized inTable IV. Three missions were conducted specificallyto obtain the angular backscatter data. In the firstmission (24 Mar. 1980), data were acquired over thecalm waters of Chincoteague Bay and at three positionsoffshore from Assateague Island over the AtlanticOcean. The sea state was low at all these sites, in-cluding the furthermost offshore location. Radar al-


GE

Table 111. Lidar Instrument Specifications

AOLsystem

Laser type N 2 - Nd:YAG CO2Wavelength 337 nm 532 nm 9.5 gmRepetition rate (pps) 200-400 6.25 2Pulse width (nsec) 10 15 100Divergence (mrad) 2.6 0.4-4.0 1-2Telescope diam (m) 0.3 0.18Digitizer resolution 2.5 nsec 3 gsecAngle scan Yes (0-15°) No

Table IV. Summary of Mission Parameters, Ocean Surface Parameters, and Backscatter Measurements

Ocean surface parametersData Laser RMS FWHMrun Aircraft Footprint Wave Wave- of mean

Mission time altitude X diam U1o height length backscatter eNo. Symbol Date (UT) (m) (Am) (m) (m/sec) (m) (m) (degrees) (0 = 00)

1 0 3/26/80 15:45 1777 0.532 7.1 2.8 0.4 100 16 0.102 a 4/13/80 13:25 840 0.337 2.2 4.0 1.1 230 17 0.653 + 4/20/80 12:02 205 0.337 0.53 4.5 0.25 186 20 0.204 0 11/19/80 19:35 1295 0.532 0.52 2.2 0.2 - 11 0.35 A 3/20/81 22:25 445 0.532 1.8 1.8 0.2 - 12 0.456 * 7/2/81 18:45 1000 9.5 2 3 0.25 - 18 0.317 A 8/27/81 15:30 1000 9.5 1 3 0.15 - 14 0.298 * 6/2/82 18:40 163 0.337 0.42 6.5 0.3 100 24 0.55

timeter data for this flight gave rms wave heights of 0.5m or less. Similar ocean conditions applied to the othertwo flights on 19 Nov. 1980 and 20 Mar. 1981. Theseoperations were also conducted in the coastal watersnear Wallops Flight Facility and Assateague Island. Inthese latter missions, beach-crossing data were acquiredin a nonscanning/profiling mode with the scan mirrorlocked in a fixed position near nadir. In all the abovemissions the Nd:YAG laser at 532-nm wavelength and6.25-pps repetition rate was used.

Two missions characteristic of open ocean conditionsoff the coast of Ireland were performed on 13 and 20Apr. 1980. This provided an opportunity for data col-lection under moderate sea states. Recorded rms waveheights were as high as 1.1 m on 13 Apr. 1980. Thesedata were acquired at 337-nm wavelength and at highrepetition rates of up to 400 Hz. This enabled a largernumber of pulse records to be recorded in just a fewminutes of flight time. One additional open ocean337-nm data set was acquired on 2 June 1982,45 km offthe New Jersey coast. We include these data becauseof the higher wind speed of 6.5 m/sec. In all AOL mis-sions the scanner was set to sweep out a 300 cone angleat a 5-Hz rate.

The two missions on 2 July and 27 Aug. 1981 em-ployed a carbon-dioxide (C02) laser system operatingat 9.5 gm. This system was also installed on the P-3Aaircraft but separate from the AOL system. Details ofits operation are described elsewhere.42 There was noscanner system with the CO2 lidar to rapidly vary inci-dence angle on the ocean surface. As a result, the database was limited to data records acquired by bankingthe aircraft at 5, 10, and 15° increments. Both laser

pulse length and digitizer resolution were much longer,100 nsec and 3 tm, respectively, for these infraredmeasurements.

In a number of the data missions simultaneous radardata were acquired with PCRA and SCR instruments.The PCRA operated at 13.9 GHz with a 5-nsec pulsewidth (after compression) and a repetition rate of 50 Hz.It had a 1.60 beam divergence and as a result produceda beamwidth-limited radar signature of the ocean sur-face. More details of this device are reported else-where.43 This particular instrument was the prototypefor the SEASAT satellite radar altimeter.44 Sea-statestatistics were obtained from the leading edge of radarbackscatter waveforms. The PCRA data output wasavailable in 30-sec averages of altitude and significantwave height. This later parameter is assumed to be fourtimes the rms wave height. The SCR instrument op-erated at 36 GHz and used a 2-nsec pulse width. Itsbeam was scanned t16° perpendicular to the aircraftflightline. These radar data had very high range reso-lution (a few centimeters). Further details of the in-strument and its operation are reported elsewhere.45

The nadir track of the SCR data output provided ahigh-resolution picture of wave structure. The PCRAdata depend on pulse spreading from ocean surfacewave structure and were, therefore, less reliable underlow sea-state conditions.

Important parameters from the INS data streamincluded the roll and pitch angles, true air speed, air-craft position (latitude and longitude), and altitude.The angular data were extremely important in assigningan angle off nadir to each AOL system data pulse record.The INS angular data are specified to be accurate within


0.4

E~~l~~h~t! y | X r U~~0 2m_

0

0 10 15 20 25

8 (degre.)

Fig. 6. Normalized mean backscatter (ER )/(ER )0 vs off-nadir angle 0 for missions (see synbol key in Table IV) in the Wallops Flight Facilityvicinity at 532-nm wavelength and theoretical result (- -- ) of Eq. (14) for wind speed U10 = 2 m/sec.

5 10

8 degre)

15 20 25

Fig. 7. Normalized mean backscatter (ER)/(ER)o° vs off-nadir angle 0 for open ocean missions (see symbol key in Table IV) at 337-nmwavelength and theoretical result (-- -) of Eq. (14) for wind speed Ulo = 10 m/sec.

0.2° rms. Larger errors (of the order of 10) are probablypresent due to uncertainty in calibration of azimuth andelevation angles of the scan mirror with respect to theaircraft INS platform.

In two of the missions laser backscatter data wereacquired over beach areas as a means of calibrating thelaser return from the ocean surface. In these missionsa zigzag maneuver was performed over AssateagueIsland where there are relatively wide areas of beach andsand dunes. During these passes data were acquiredalternately over ocean, beach, and Chincoteague Baytargets for as many as eight separate beach crossings.During these data runs all instrument parameters wereheld constant so that the statistics of surface reflectancecould be directly compared. Beach sand is assumed tobe a Lambertian reflector with a reflectance coefficientreported 4 6 to be -0.36 at 0.55-,um wavelength. Asample of this sand was also tested in the laboratory for

its reflectance coefficient using the same Nd:YAG laseras in the flight experiments. For these tests backscatterpulse energy at normal incidence was measured with apyroelectric detector for sand relative to a standardbarium sulfate (BaSO4) painted surface. Reflectanceof the freshly painted BaSO4 surface was assumed to be0.97. This gave a measured value of 0.38 for the sandsample, which is in good agreement with the reportedvalue.

VI. Laser Backscatter Data

Our primary objective in the flight experiments wasthe measurement of mean backscatter dependence onangle off nadir. Results from the various flights aresummarized in Figs. 6 and 7. In both figures meanbackscatter normalized by peak mean backscatter isplotted as a function of off-nadir angle. In all the ex-


.E n '~~ ' I ' ' I ' I I I ' 1-0.0-

0.06-

0.4-

0.2-

I , , , I . . . . I , . , ,~ ~ I -

0.3

0.2

0.1 LZ 0 (d,.,)

Fig. 8. Calibrated ocean backscatter in terms of effective Lambertianreflectance Peff for 532-nm wavelength laser backscatter data (seesymbol key in Table IV) in the Wallops Flight Facility vicinity vsoff-nadir angle 0 and theoretical predictions ( -- ) for this quantitybased on Eq. (14), Fresnel reflectance of 0.02, and wind speeds U1o

of 2 and 5 in/sec.

periments the peak mean backscatter occurred within1 or 20 of nadir. Each data point shown on these figuresrepresents the average of several hundred to severalthousand backscatter pulse energy measurements, andeach curve was obtained from data collected duringpasses of 30 sec to several minutes duration conductedover a relatively homogeneous stretch of ocean sur-face.

Data in Fig. 6 were acquired for the 532-nm wave-length over the coastal waters near Wallops Flight Fa-cility (WFF), Va., during the three missions designedspecifically for making these backscatter measurements.Table IV summarizes the instrument, ocean surface,and wind velocity parameters applicable to the differentflight dates. Even though the flight dates were sepa-rated by up to one year, the wind velocity and sea-stateconditions were similar and relatively low. It is ap-parent from Fig. 6 that the angular pattern of back-scatter is similar for all three flights. The data fromMission show a slight increase of 1 or 2 in angularhalfwidth, which correlates with Mission 's highestwind speed and sea state of the three flight missions inFig. 6. The predicted mean backscatter from Eq. (14)using the mean-square slope from Eq. (16) for a windspeed U10 of 2 in/sec is also plotted in Fig. 6 for com-parison. Wind speed measurements for these missionswere acquired from a 9-in tower located on WallopsIsland near WFF. Since these wind speed estimateswere not acquired at the same place as our backscattermeasurements and we lack accurate data on air/seatemperature differences, it is not possible to make anexact comparison with the theory based on u. Nev-ertheless there is good qualitative agreement betweentheory and data.

The data summarized in Fig. 7 were acquired duringtwo missions flown over the North Atlantic well off thecoast of Ireland and one mission flown recently, 45 kmoff the New Jersey coast. These data, which were ob-tained at an UV (337-nm) wavelength, are representa-tive of clear ocean water. These data sets have beenincluded to get data representative of additionalphysical conditions. While the wind speed measure-ments in the Irish data were only slightly greater thanthose in the data of Fig. 6, the wave heights (swell) weresubstantially larger. The wave height and length es-timates given for all these open ocean experiments wereindependently acquired by the SCR. Wind speedmeasurements for the Irish data were obtained from aparticipating surface vessel operating within the surveyarea during the experiment.

During the 13 Apr. mission wave heights were mea-sured from 4 to 7 in (1.1 in ins). The angular patterndetermined for this mission is distinctive in that themonotonic decrease with angle off nadir observed in allother data sets was replaced by a shallow minimumfrom 3 to 70 off nadir and a secondary maximum at 8 to90 off nadir. We attribute this secondary maximum tothe large-scale gravity wave pattern that produced the4-7-in wave height and 230-in wavelength. This wavefield would result in an ocean surface with a predomi-nant slope of several degrees. Laser pulses incident onthe ocean surface at the off-nadir angle equal to thewave slope would either encounter the ocean surface atnormal incidence or twice the slope dependent on slopepolarity. Pulses with the former angle would producemaximum backscatter, while those with the latter wouldproduce a lower amplitude return. The result may havebeen a resonantlike behavior, where the characteristicslope of a large amplitude gravity wave pattern pro-duced a second maximum. In low sea-state data, e.g.,that acquired at 532 nin near WFF, both amplitude andslope of the predominant wave pattern are lower, andthe resonantlike behavior is lost in the Gaussian dis-tribution of wave slopes near nadir. Not all high am-plitude sea-state data would exhibit the angular back-scatter pattern of Fig. 7. What was special about datafrom the 13 Apr. mission was the presence of high wavesin conjunction with low wind speeds. Thus the waveswere not in equilibrium with the wind, and the Gaussianwave height spectrum probably does not apply. Theangular backscatter pattern in Fig. 7 for the 20 Apr.mission exhibits a more normal backscatter pattern witha shape lower but close to that of the analytical resultsfor a 10-in/sec wind velocity. The pattern for 2 June1982 has the largest angular width, which correlates wellwith its highest wind speed (for our data) of 6.5 in/sec.On all three curves of open ocean data in Fig. 7 note thatthe falloff of mean backscatter with increasing angle offnadir levels off beyond 150 more so than for the ana-lytical result. This may be real, but it is more likely dueto a threshold effect at the low end of the receiver dy-namic range.

A summary of the FWHM angular width of thebackscatter patterns for all missions is included in TableIV. Angular width varies from 11 to 240, and there is


0

0 5 10 15 20 25

Fig. 9. Summary of normalized standard deviation of laser backscatter for all missions (see symbol key in Table IV) vs off-nadir angle with prediction (--- ) for this quantity based on Eqs. (25) and (26), a wind speed U10 = 5 m/sec, and a laser footprint area AF of 1 M2

.

reasonable correlation with wind speed, more so thanwith ocean wave length or location. Our main disap-pointment with the data is the limited range of windspeeds. Since all our data were acquired at wind speedsbelow 7 m/sec, the capillary wave patterns were prob-ably not fully developed.

The infrared data for two flights, which are includedin Table IV, are in good agreement with the WFF vi-cinity visible wavelength data. The infrared data wereacquired only at the fixed aircraft bank angles of 5, 10,and 150 off nadir. The data obtained at 15° off nadiron both missions show a decrease to <10% of the peakbackscatter measured at nadir. Since there are essen-tially no volume backscatter effects at 9.5 ,4m and lowFresnel reflectance (0.013), we believe that these datashould be quite accurate in specifying the angularbackscatter pattern.

During two of the missions conducted near WFF at532 nm it was possible to calibrate laser backscatterfrom the ocean by taking sequential data sets over beachsand targets with all instrument parameters fixed.Laboratory measurements of sand obtained from As-sateague Island, where the beach overflights occurred,yielded absolute reflectance values of -0.38. Our as-sumption of a Lambertain backscatter pattern gives ap1Q factor in Eq. (1) of 0.38/7r for sand. We then scaledthe ocean backscatter data by dividing it by relativevalues for sand backscatter and multiplying by 0.38/r.The results are presented in Fig. 8 as Peff cosO/t- (Peff/QL) as a function of angle off nadir. Note that the nadirvalues of Peff of 0.18-0.25 are approximately ten timesthe Fresnel reflectance coeffcient. This agrees with theenhancement expected when the available 0.02 Fresnelreflectance is concentrated in the angular backscatterpatterns shown in Fig. 8 instead of into 7r steradians.The data results, particularly those of 20 Mar. 1981 for

U, 0 = 1.8 m/sec, are in good agreement with the pre-dicted results of Eq. (16) for Peff when U,0 = 2 i/sec.The data of 19 Nov. 1980 seem to be more characteristicof a higher wind speed curve (U1o = 5 m/sec) but theselower values for Peff may also be due to experimentalerror in calibration using beach backscatter.

Our equivalent Lambertian reflectance values of Fig.8 are a factor of 5 less than those reported by Petri butagree closely with those reported by Jellalian.2 Someof the Petri' data were acquired above very calm water,which would result in a smaller angular pattern and alarger nadir reflectance. But even his data for a 4-m/secwind have a factor of 3-5 times greater Lambertian re-flectance than either our measurements or the resultsby Jellalian.2 Our results appear to be more consistentwith realistic ocean backscatter patterns and are moreconsistent with the redistribution of the 0.02 Fresnelreflectance into the measured cone angle.

The second backscatter statistic we considered wasthe normalized standard deviation E for the same datasets for which we computed mean backscatter. We firstderived the variance of the backscatter signal for 10increments of angle off nadir for each data file and thennormalized these results by the square of mean back-scatter from the same data file. The parameter e is thesquare root of this normalized variance. Data in Fig.9 summarize for the same data sets shown in Figs. 6and 7. An increase in E with 0 is apparent between 0 and10° off nadir for all the data sets. Between 10 and 150off nadir the function tends to level off and even de-crease on occasion beyond 15 off nadir. We attributethis to the dynamic range limitation in the receiverelectronics. Evidence for this effect is contained in thenumber of null shots, laser pulses for which the receiversignal does not exceed threshold, which increased sub-stantially for 0 beyond 15°.


0.11 0.20

0.08 3/26/80 0.16r 4/13/80 -

0.06 - o0 127

P E1 -P (El -

0.04 -i 0.08-

0.02 0.041

01 00 0.5 1.0 1.5 2.0 2.5 0 1.0 2 .0 3.0 4.0 5.0

E/<E>E<E

EI<E>E<>

Fig. 10. Probability density function of laser backscatter data for various missions and off-nadir angles.

0.08

0.06'Lu

0.04

E (relative units) E (relative units) E (relative units)

0.02 Id 002 j \-.V 0 . 4 ' A l_ __0__04_

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10E (relative units) E (relative units) E (relative units)

Fig. 11. Probability density function of laser backscatter data for two open ocean missions at 337-nm wavelength for off-nadir angles 0 of4, 8, and 12'.


6/2/820=120

0.08

0.06 6/2/82 -

e u 0=80 0

0.16-

0.12 6/2/82i; 0=40

0.08 tk

a;

We have tested the e observations for a dependenceon laser footprint dimensions. This was done by se-lecting typical e values for each mission and comparingthem with the footprint diameter based on aircraft al-titude and laser divergence. Results are listed in TableIV and show no clear dependence of e on diameter.During Mission 4 we even varied laser divergence by afactor of 10 and measured identical e'values. The mostsignificant factor seemed to be changes in from oneflight date to the next. The two major variables amongmissions other than footprint diameter and X, were windspeed and long-wavelength gravity wave structure.

There are four more factors in addition to oceansurface backscatter fluctuations which could contributeto observed e. These are (1) variations in transmitterpulse energy; (2) detector and data electronics noise; (3)solar background noise; and (4) turbulence in the two-way atmospheric path. When the ocean backscatterdata were taken, we had not yet implemented thetransmitter pulse energy monitor circuitry. As a result,the receiver pulses could not be normalized by transmitenergy. We have since measured transmitter pulsestatistics and can bound their short-term amplitudestability by a normalized standard deviation of -0.10.Typical E contributions from laser pulse energy fluctu-ations are <0.05 for the nitrogen laser, -0.05 for theNd:YAG laser, and up to 0.10 for the CO2 laser. Thiseffect results in an independent and, therefore, additivenoise variance that could account for a substantialfraction of e data near nadir but would be a small factorin the higher E data near 150 off nadir.

At UV and visible wavelengths detector noise can beeasily dominated by solar background noise. Use of anarrowband interference filter and restricted field ofview in the AOL receiver kept this background levelbelow the threshold of the pulse processing electronics.Even in the infrared, where detector noise and back-ground noise are comparable and large, we were able tomaintain at least a 40-dB SNR in the flight data. Amore serious problem was the threshold level set for UVand visible wavelength data. Rather than increasinge, the threshold compressed the fluctuations in lowsignal level data. We believe this effect was importantonly at 0 values of the order of 150 or larger which areassociated with large numbers of null shots.

The strength of atmospheric turbulence and the in-tensity scintillation it produces were not measured di-rectly in our experiments, but these can be estimatedfor the vertical path between aircraft and ocean. Thelongest propagation path was 1.8 km for the 532-nmdata in the WFF vicinity data. Daytime refractive-index structure coefficient C2 in the ocean boundarylayer has been measured by others4 7 to vary from-10-17 m-2/3 to 10-15 m-2/3. This produces an opticalscintillation (intensity modulation) that correspondsto an E of 0.03-0.29 for a point detector assuming auniform distribution of turbulence over the 1.8-kmpath.47 The two-way path from aircraft to ocean andreturn contributes at most the square root of the sumof the squares of two one-way paths. The AOL receiveris far from a point detector, however, since it is 30 cm

in diameter. The aperture averaging factor (for vari-ance E2) has been reported 4 7 to be 0.01 or less at 532 niand at 337 nm for this size receiver. As a result, e worstcase is only 0.003 at 532 nm. At 337 nm the atmo-spheric propagation path was 0.8 km or less, and theworst-case estimate for e is -0.002 for the assumed CNvalues. Scintillation estimates for 9.5 um are evenlower because of the X-7/6 dependence which dominatesthe decrease in aperture averaging at this longer wave-length. Thus the largest effect of turbulence is likelyto have occurred in the 532-nm data, but it does notseem very significant.

The net result of consideration of all these factors isthat most of the observed E, especially values above 0.5,are likely the result of fluctuations in the ocean surfacebackscatter cross section. These data are at least afactor of 10 larger than predictions in Eq. (23) based onthe density of specular glints for the moments of TableII, a wind speed of 5.0 m/sec, and the applicable laserfootprint dimensions. The e data also rise more rapidlyas a function of 0 than these predictions. Our data aremore in agreement with the tilt model derivation of e inEq. (25) and the analysis by Jackson4' that results in Eq.(26) and is plotted in Fig. 3. The predicted value of Eat nadir is 0.1-0.3 for the low wind speed regime. Thetilt model predicts an angular dependence (tanO), whichis consistent with the results. These predictions for U10= 5 m/sec and AF = 1 M 2 are plotted in Fig. 9. Notealso that the largest e values are associated with thehighest sea state that occurred in Mission 2. We feelour statistics support the concept of mean footprint tilt,that is, wave motion on scales larger than the footprint,as the largest determining factor in backscatter vari-ability.

The probability density function (PDF) of back-scatter pulse energy was also computed for each datafile. Illustrative examples are plotted in Figs. 10 and11. In all these plots the PDF was derived from a his-togram of 50 subintervals spanning the dynamic rangeof the receive data, and the results were normalized bythe backscatter variance. Each curve was drawn bysimply connecting the dots between subinterval points.Several hundred to several thousand pulse energy datapoints went into each PDF calculation. It is apparentthat PDF shape varies widely from mission to missionand with angle off nadir. Low wind speed data in theWFF vicinity (Fig. 10) display a near-Gaussian behaviorthat might be expected from the near-Gaussian distri-bution of surface slopes. Most data, including thehigher wind speed observations in the vicinity of WFFand those from the open ocean experiments, exhibitsignificant asymmetries. The asymmetric PDF dis-tributions typically have a tail toward high pulse energyand resemble a Rayleigh or lognormal distribution.The electronics threshold setting of the lidar systemwould contribute to this appearance by supplying asharp drop-off in PDF at lower backscatter energylevels. This may have been an important considerationin the open ocean data (at 337 nm) at larger 0 valueswhere there were a significant number of null shots.

The Mission 3 PDF data in Fig. 11 are unusual in that


a bimodal distribution appears. At 120 off nadir thePDF has an asymmetric shape with a long, almost flattail extending toward higher energy. The data obtainednear nadir at 0 = 40 are almost a mirror image of thisshape, with a peak occurring at relatively high energy.At 8 off nadir the shape shows both peaks and atnearby angles is almost a uniform distribution.

The PDF data in Fig. 11 for Mission 8 also show evi-dence of more than one peak, particularly at 0 = 8° offnadir. The bimodal characteristic may have been theresult of large amplitude gravity waves which tilt theentire laser footprint and could give high probability toboth low- and high-amplitude backscatter pulses. Datafrom Mission 2 however, which had the highest waves,do not exhibit the same bimodal characteristic. Thesedata resemble a lognormal distribution at all values of0, and a sample is plotted at 0 = 100 in Fig. 10. Clearlymore analytical work and experimental studies withimproved dynamic range are required to understandand specify the PDF of laser backscatter.

VII. Conclusions

The data we acquired on mean laser backscatter andits variation with angle off nadir are consistent withprior analytical and some of the prior experimentalwork. The absolute calibration of this backscatter interms of an effective Lambertian reflectance was lessprecise, but our data support values near nadir of -0.20for low wind speeds. These values are 1 order of mag-nitude larger than the Fresnel reflectance for an air/water discontinuity in refractive index. The normal-ized standard deviation (modulation factor) of back-scatter is less well-understood analytically but has beendefined by our measurements to range from a few per-cent to over 50% at nadir and to increase off nadir astanO or faster. Our data are uncertain beyond 150 offnadir due to a dynamic range limitation. The PDF dataexhibit a variety of shapes, some of which undoubtedlyinclude instrument effects. We recommend furtherefforts in prediction of and PDF statistics and dataacquisition at a wider variety of wind speeds and laserfootprint characteristics.

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airborne measurements of laser backscatter from the ocean surface

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