Sensitivity Analysis and Quality Assessment of Laboratory ... · Sensitivity Analysis and Quality Assessment of Laboratory BRDF Data St. Sandmeier,* Ch. Mu¨ller,* B. Hosgood,†

Sensitivity Analysis and Quality Assessmentof Laboratory BRDF Data

St. Sandmeier,* Ch. Muller,* B. Hosgood,† and G. Andreoli†

A detailed quality and sensitivity analysis of hyper- field applications. Laboratory specific constraints such asthe nonparallelism and heterogeneity of the lamp are as-spectral BRDF data, acquired under controlled labora-

tory conditions at the European Goniometric Facility sessed and corrected where necessary and feasible. The re-producibility of the BRDF data obtained lies within 1–9%(EGO) of the Joint Research Center, Ispra/Italy, has

been performed. In regard to bidirectional reflectance rmse, depending on target type, wavelength range, andmeasurement duration. Elsevier Science Inc., 1998measurements in the field with the FIGOS goniometer,

the impact of angular data sampling, the movement ofthe Sun, and the Lambertian assumption of a Spectralonpanel have been analyzed. An erectophile grass lawn can- INTRODUCTIONopy and a planophile watercress surface were chosen as

Since the late 1970s goniometric measurements havemain targets. A GER-3700 spectroradiometer providingbeen carried out on natural and man-made targets tohyperspectral resolution allowed for analyzing the wave-derive bidirectional reflectance distribution functionslength dependency of the effects. The results of the sensi-(BRDFs). Most of the data are obtained either in thetivity analysis show that in a first step a moderate resolu-field from ground measurements (Colwell, 1974; Coul-tion of 158 and 308 in zenith and azimuth, respectively,son and Reynolds, 1971; Kimes, 1983; Deering, 1989;is adequate to capture the bidirectional reflectance distri-Deering et al., 1992) or in controlled laboratory experi-bution function (BRDF) of vegetated targets. Only in thements (Coulson et al., 1965; Breece and Holmes, 1971;

hot spot area a higher resolution is desirable. The move- Walter-Shea et al., 1989; Brakke et al., 1989), but com-ment of the light source during data acquisition is found bined laboratory and field campaigns were hardly everto be critical, and should be kept within 618 source ze- performed. Most of the BRDF data sets available todaynith angle in order to obtain homologous BRDF data lack, furthermore, a high spectral resolution.sets. Due to the wavelength dependence of BRDF effects, In 1994/95, the Remote Sensing Laboratories of thethe impact of the light source may vary significantly be- University of Zurich constructed a transportable field go-tween different wavelength ranges. A normalization of niometer (FIGOS) for the acquisition of bidirectional re-the irradiance with the help of frequent reference mea- flectance factor (BRF) data under natural illuminationsurements is recommended, and should be carried out us- conditions (Sandmeier et al., 1995). FIGOS uses a highing a panel with known BRDF characteristics. The Spec- resolution spectroradiometer and is designed to providetralon panel examined showed deviations from a Lamber- basic understanding of the wavelength dependence intian panel of up to 5% and more, but obeyed Helmholtz’s the BRDF phenomenon, to support the validation andreciprocity law. Corresponding calibration coefficients development of BRDF models, and to improve the inter-are given for correcting the non-Lambertian behavior in pretation of satellite imageries by overcoming the Lam-

bertian assumption in radiometric correction models(Sandmeier and Itten, 1997).*RSL, Department of Geography, University of Zurich, Swit-

Concurrently to the construction of FIGOS, the Jointzerland†Space Applications Institute, Joint Research Centre, Ispra, Italy Research Center of the European Commission establishedAddress correspondence to St. Sandmeier, NASA Goddard Space the European Goniometric Facility (EGO) (Koechler et

Flight Center, Biospheric Sciences Branch, Code 923, Greenbelt, MD al., 1994), a laboratory goniometer presenting almost the20771. E-mail: [email protected] 23 September 1997; revised 15 December 1997. same dimensions and design as FIGOS. EGO offers a

REMOTE SENS. ENVIRON. 64:176–191 (1998)Elsevier Science Inc., 1998 0034-4257/98/$19.00655 Avenue of the Americas, New York, NY 10010 PII S0034-4257(97)00178-8

Quality Assessment of BRDF Data 177

sampling rate, however, are not specifically addressed.Thus, they are analyzed in this study in order to find anoptimal compromise between high angular sampling res-olution and short measurement time in FIGOS fieldcampaigns. In addition, a Spectralon reference panel,used to estimate total irradiance in the field, is examinedfor its often anticipated Lambertian behavior and reci-procity characteristics. Subsequently, calibration coeffi-cients for the Spectralon’s bidirectional reflectance char-acteristics are derived. Laboratory specific constraintssuch as the nonparallelism of irradiance are analyzed andcorrected if necessary and feasible. The bidirectional re-flectance data obtained in this study are further analyzedin a companion article (Sandmeier et al., 1998).

EXPERIMENT SETUPFigure 1. Overview and dimensions of the European Go-niometric Facility (EGO). The European Goniometric Facility (EGO) mainly con-

sists of an azimuth rail with 4 m diameter and two zenitharcs for the sensor and lamp positioning (Fig. 1). Both

higher geometrical positioning accuracy than FIGOS but arcs are motor-driven with a positioning accuracy foris bound to indoor measurements. In both systems, the lamp and sensor of 60.18 (Koechler et al., 1994). Asensor always points to the center of a 2 m radius hemi- driver software installed on a PC provides full control ofsphere where the target sample is located (Fig. 1). This all movements in the goniometer. The acquired data,unique conformity between FIGOS and EGO allows us however, had to be handled manually, since no sensorto compare and combine BRDF field and laboratory mea- driver software was available in our case.surements. As recommended by Jackson et al. (1987), the labo-

Advantages and disadvantages of laboratory and field ratory campaign was carried out with the same equip-experiments are nearly complementary. Field measurement as used in the field, except for the EGO goniome-ments suffer from an instable irradiance due to changing ter itself which is equivalent to FIGOS. A GER-3700atmospheric conditions and Sun positions. But they allow spectroradiometer with nominally 704 channels rangingmeasure of targets in situ and in vivo under natural light from 300 nm to 2500 nm was used as sensor, providingconditions, and are therefore in general better suited for a 38 field-of-view (FOV), hyperspectral resolution of 1.5 nmremote sensing applications than indoor measurements. in the visible and near-infrared part up to 1050 nm, aIn a laboratory, targets are either man-made or separated short acquisition time of >50 ms per measurement, andfrom their natural habitat, suffering from water and tem- a data depth of 16 bits. The gain factor of the instrumentperature stress introduced by the intense laboratory irra- was adapted to the energy available in the laboratory. Todiance. Still, the light intensity is usually lower than in improve the signal-to-noise ratio, all measurements werethe field leading to lower signal-to-noise ratios than in averaged over five individual samples during data acqui-the field. Compared to sunlight, laboratory irradiance is sition. The version of GER-3700 sensor available at thehighly heterogeneous and nonparallel, and may suffer time of this campaign did not provide reliable data abovefrom unstable voltage, too. Furthermore, the spectral 1000 nm wavelength due to temperature instabilities ofcharacteristics of laboratory illumination sources differ the instrument. Under 450 nm wavelength the measure-significantly from the solar spectrum. Major advantages ments are too noisy and had to be excluded from analy-of laboratory measurements, however, are the control sis, too. In a few bands between 450 nm and 1000 nmover the light source position, the nearly complete lack the sensor occasionally exposed outliers. These sectionsof diffuse irradiance, the excellent geometrical accuracy, have been mapped out and occur as gaps in the plots.and the ability to produce BRDF data sets in very high Finally, a total of 356 channels was analyzed rangingangular resolutions. Thus, calibration procedures and from 450 nm to 1000 nm, with a spectral resolution be-sensitivity analysis are generally easier to perform in a tween 1.5 nm and 1.6 nm.laboratory. In this study, we make use of these advan- Due to the radiometer’s small field-of-view, mea-tages in order to develop and validate a measurement set surements of up to 758 zenith angle could be carried outup for FIGOS field experiments. with moderately large target sample sizes (Table 1). On

Milton (1987) published detailed guidelines for im- the other hand, rather smooth and homogeneous targetsproving the consistency and accuracy of bidirectional had to be selected in order to obtain representative

BRDF measurements. A freshly grown watercress (Lepi-field data. The impacts of the moving sun and of the data

178 Sandmeier et al.

dium sativum) and a living grass lawn surface (Loliumperenne) were chosen as the main targets. The grass rep-resents an erectophile canopy, whereas the watercressexhibits a planophile canopy characteristic. A concreteslab was added as an invariant target mostly for analyzingthe stability of irradiance and the reproducibility of mea-surements. All targets are either the same as or corre-sponding to performed or planned FIGOS measure-ments and allow for comparing bidirectional field andlaboratory reflectance data. A Spectralon panel (SRT-99-100) with a 99% albedo, calibrated by Labsphere atNorth Sutton, New Hampshire, USA in November 1994,served as a reference surface. The same panel is used inFIGOS field-campaigns.

A 1 kW tungsten halogen collimated lamp with a fo-cusable beam aperture served as light source. All experi-ments were performed with the maximum apertureopening which is 398. For the majority of the experi-ments the lamp was set at 358 zenith angle, correspond-ing to an expected Sun position in the field campaigns.For this lamp position the nonparallelism of the irradi-ance was corrected as described in the section after next.

A resolution of 158 and 58 in azimuth and zenith di-rection, respectively, was chosen for the radiometer posi-tions as a high resolution mode. A low resolution modewas set to 308 and 158 in azimuth and zenith, respec-tively, equivalent to the angular sampling rate used infield applications with FIGOS.

Table 1 gives an overview on the targets, setup, andexperiments performed. Figure 2 shows an example ofthe measurement configuration.

DATA PREPROCESSING

As no driver software at the EGO facility was availablefor the GER-3700 sensor, the measurements were chro-nologically numbered during data acquisition. In a sec-ond step, a file name system was established, identifyingthe positions of the sensor. The algorithm setting up theposition-based nomenclature handles different angularsampling resolutions, measurement starting points, andsensor moving directions as well as gaps in the data se-ries. Within the preprocessing, data are transformedfrom a proprietary binary into a standard ASCII format,and can be imported in any adequate database structure.A polar coordinate system is used for identifying, analyz-ing, and plotting the data (Fig. 3).

COMPUTATIONAL METHODS

Hemispherical IrradianceHemispherical irradiance Ei denotes the total irradianceof a light source striking a target from any directionwithin the surrounding 2p steradian solid angle (i.e.,T

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Figure 3. Polar coordinate system used to identify and plotbidirectional reflectance factor data.

that is, Lambertian behavior, only within a small solidangle dhr, dur of 58 and 158, respectively, in our case (ex-periment P, Table 1). Furthermore, the hemisphericalreflectance of the surface used should be either lossless,or precisely known. Both are not quite true for Spec-tralon. But q of the panel is close to 1, and sufficientlywell characterized by the panel’s calibration protocol ofLabsphere. Strictly speaking, the calibration data for qare only approximated since they are taken from nadirmeasurements and an illumination zenith angle of 88, in-stead of from hemispherical averages. This inadequacymay introduce a slight error in estimating Ei.Figure 2. Overview of laboratory measurement configuration.

If only directional, collimated irradiance is present,Ei can be derived for any light source position fromEi(08), simply by applying the cosine law:single directional reference panel measurement, based

Ei(k,hi)5Ei(k,08)·cos(hi). (2)on the Lambertian assumption. Even in a laboratory en-vironment, an absolute calibration of the light source, the Although one can assume direct irradiance in a labo-sensor, and the reference panel is often not given. Also ratory, the nonparallelism and heterogeneity of the lightin our case, Ei (W·m22·nm21) had to be derived indirectly source have to be taken into account. In order to reduceby integrating the reflected radiance L (W·m22·sr21·nm21) these impacts as much as possible, Ei has been obtainedfrom a Spectralon panel over the hemisphere: first with the lamp at nadir position (experiment P, Table

1). Due to the relatively small size of the SpectralonEi(k,hi)5

1q#

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L(k,hr,ur)·cos(hr)·sin(hr) dhr dur, panel, measurements above 558 zenith angle had to beextrapolated. Also the hot spot region was interpolated

(1) since, for practical reasons, no measurements could betaken near the lamp. Both inter- and extrapolation of thewherepanel data were based on a second-order polynomial

q5hemispherical reflectance of panel, function (Sandmeier et al., 1997). The corresponding rel-L5sensor radiance, ative root mean square errors between measured and in-k5wavelength, terpolated data are depicted in Table 2 for various wave-

hr,ur5view zenith and azimuth angles, lengths.hi5source zenith angle. After deriving Ei(k, 08) based on Eq. (1), Ei(k, hi) for

any source zenith angle can be determined by Eq. (2).Spectralon is well suited for deducing hemisphericalirradiance since Eq. (1) assumes constant reflectance, However, the cosine relationship in Eq. (2) is only valid


Table 2. Second-Order Polynomial Coefficients for Calculating SpectralBidirectional Reflectance Factors Rref for the Spectralon Panel, UsedTo Correct the Nonideal Reflectance Characteristics [Eq. (5)]a

k (nm) Coeff. a0 Coeff. a1 Coeff. a2 rmse

450 1.0601804 22.2319185E208 22.9108199E205 2.22500 1.0628547 24.1248418E208 22.9801351E205 1.93550 1.0645435 24.2594781E208 23.0501190E205 1.83600 1.0649389 9.3524197E209 23.0666023E205 1.79650 1.0675981 21.2742371E208 23.1359529E205 1.65700 1.0644996 5.4960491E208 23.0899628E205 1.53750 1.0696763 1.3463638E208 23.2631848E205 1.55800 1.0723401 5.3013072E208 23.3321766E205 1.44850 1.0743615 21.2542019E208 23.4155847E205 1.45900 1.0745791 4.8421010E208 23.5075040E205 1.51950 1.0780474 6.7558611E209 23.6098470E205 1.58

1000 1.0802562 22.4651279E208 23.7017440E205 1.74

a Rref of a panel nadir measurement taken in the field under an arbitrary source zenith angleh can be calculated by Rref5a01a1·h1a2·h2. The differences between measured data acquired inexp. P (Table 1) and calculated values are referenced as relative root mean square errors (rmse).

for the center point of the lamp beam, since all other Bidirectional Reflectance Factorareas are affected by the nonparallelism of the lamp. As The bidirectional reflectance factor (BRF) R is defined asa consequence, the “footprint” of the lamp’s irradiance the ratio of radiance reflected from a surface into a spe-was acquired for a source zenith angle of 358, which is cific direction to the radiance reflected from a lossless,given for most of the experiments performed. With the Lambertian reference panel measured under identicalGER-3700 spectroradiometer mounted vertically above viewing and illumination geometry. The term bidirectionalthe Spectralon panel in a distance of 47 cm, the panel implies that directional measurements in infinitesimallywas moved over the lamp spot taking measurements ev- small solid angles would be required. Therefore, actuallyery 5 cm in x and y directions (experiment M, Table 1). measured reflectance factors are sometimes referred toBased on these data, the irradiance in the sensor’s field- as biconical reflectance factors. Since the field-of-view ofof-view at each measurement position on the goniometer the GER-3700 is sufficiently small and the radiation inwas compared to the EGO center point, and subse- the laboratory is predominantly directional (Robinsonquently taken into account in the determination of hemi- and Biehl, 1979), the expression bidirectional reflectancespherical irradiance Ei(k, 358) (Muller, 1997). The extent factors is used in this study. For the same reason, we useof the lamp’s non-parallelism at a source zenith angle of the expression BRDF measurement for the results of Eq.358 is illustrated in Figures 6 and 7 (next main section). (3), knowing that the values obtained are averaged over

the sensor’s field-of-view.Bidirectional Reflectance Distribution Function If the BRDF of a surface is known, R can simplyThe bidirectional reflectance distribution function (BRDF) be deduced by multiplying fr with p, assuming isotropicfr (sr21) as defined by Nicodemus (1970) is the ratio of irradiance conditions within the full solid angle of inci-the radiance L (W·m22·sr21·nm21) reflected in one direc- dence and isotropic BRDF within the solid angles of in-tion hr, ur to the incident irradiance Ei (W·m22·nm21) cidence and viewing:from direction hi, ui. It is thus a function of two direc-

R(hi,ui; hr,ur; k)5fr(hi,ui; hr,ur; k)·p. (4)tions and of wavelength, and is an intrinsic property ofIn a laboratory, irradiance Ei can be assumed to bethe reflecting surface.

rather stable as long as the lamp is not moved. Thus, RBRDF can only be approximated by measurementscan be derived based on Eq. (3) and (4). In the field,since an infinitesimally small sensor field-of-view wouldhowever, hemispherical irradiance Ei is constantly chang-be required. In practice, BRDF values are derived bying, and R is usually derived based on a reference mea-dividing measured radiances L from small aperture solidsurement Lref taken quasi-simultaneously from a panelangles by the hemispherical irradiance Ei:with known reflectance characteristics Rref (Milton, 1987;

fr(hi,ui; hr,ur; k)≈L(hi,ui; hr,ur; k)Ei(hi,k)

. (3) Ranson et al., 1991):

R(hi,ui; hr,ur; k)5L(hi,ui; hr,ur; k)

Lref(hi,ui; hr,ur; k)Rref(hi,ui; hr,ur; k).In our case, L has been measured with a field-of-view

of about 38, and Ei was derived from Eq. (1) and (2), tak-(5)ing the nonparallelism and spatial heterogeneity of the

laboratory lamp into account. The bidirectional reflectance factor of the panel Rref


even at extreme view zenith angles and in the hot spotarea, where no measurements could be obtained due tosystem constraints. Figure 4 compares the interpolatedand the measured data in the principal and orthogonalplanes of the grass lawn surface as an example. Only inthe nadir range some outliers are revealed due to theinterpolation technique. But these inadequacies have lit-tle effect on the derived hemispherical reflectance, be-cause the sine function in Eq. (6) is zero at nadir.

QUALITY ASSESSMENT

Quality assessment was performed on raw sensor digitalnumbers (DN) for the sections on irradiance and sensorstability. The assessment of target measurement repro-ducibility is based on bidirectional reflectance factor

Figure 4. Measured versus interpolated reflectance data of which are corrected for the nonparallelism of the labora-the grass lawn in the principal and orthogonal planes. The tory lamp. Errors are specified as relative root meaninterpolation is based on a spherical Delaunay triangulation square errors (rmse), calculated asapproach. Interpolated values are derived for every 28 in zenithand azimuth over the complete hemisphere.

rmse5100·!1n o

n

i511xi2xi

xi2

2, (7)

corrects for the loss and the non-Lambertian reflection wherebehavior of the panel. Rref is preferable determined un- xi5measured data,der controlled laboratory conditions using the same radio- xi5reference data,meter as in subsequent field measurements (see the n5number of comparisons.main section after next). Another approach to derive Rref

Depending on the data set analyzed, xi and xi haveusing the Sun as the irradiance source is described indifferent meanings. When comparing measured withJackson et al. (1987).modeled BRF values (Table 2), the xi are measured andthe xi are interpolated data. The resulting rmse value forHemispherical Reflectanceeach wavelength is then the deviation between measuredHemispherical reflectance q is widely used in the com-and modeled BRF values averaged over the angularpanion article (Sandmeier et al., 1998). It is a key radio-measurement positions. Analyzing the variability of a setmetric quantity for radiation budget studies and generalof nadir measurements (Figs. 8, 10, and 13), xi are thecirculation models. q is defined as the ratio of the totalactually measured values and xi is the average of all nadirradiance reflected by a surface in any direction withinmeasurements in a specific wavelength. In a comparisonthe surrounding hemisphere to the total incoming radi-of two different measurement series taken in the princi-ance. Sometimes hemispherical reflectance is loosely re-pal plane at the beginning and end of a hemisphericalferred to as albedo, although the latter usually describesdata set (Fig. 12), xi and xi are the corresponding mea-an integration of q over the solar wavelength range.surements taken in the first and the second run. Examin-While BRF and BRDF can take on any value between

zero and infinity, hemispherical reflectances may only ing the impact of a moving light source (Figs. 19 andhave values between 0 and 1, due to the conservation of 20), xi are the measured data for an arbitrary light sourceenergy. q is computed in the same way as the hemi- position compared to the value of a reference source ze-spherical irradiance Ei, by integrating the bidirectional nith angle xi (e.g., 358).reflectance factors R of a surface over the hemisphere:

Sensor Response Characteristicsq(hi,ui; k)5

1p#

ur52p

ur50#

hr5p2

hr50R(hi,ui; hr,ur; k)·cos(hr)· Figure 5 shows the highly linear response characteristics

of the GER sensor tested with a set of calibrated Spec-sin(hr) dhr dur. (6) tralon panels of different nominal albedos. Because we

did not have a calibrated light source, the 99% panel wasTo improve the accuracy of integration, the bidirec-used as a reference for all other panel measurements.tional reflectance data used in Eq. (6) were first resam-The deviation from the nominal albedos are correctedpled to a resolution of 28 in zenith and azimuth, basedfor all panels using the corresponding Spectralon calibra-on spherical Delaunay triangulation. This step also al-

lowed us to provide data for the complete hemisphere, tion protocols. For reasons of clarity, the data are dis-


Figure 5. Linearity test of GER-3700 sensor using a set ofSpectralon panels with nominal albedos of 1.0, 0.8, 0.6, 0.4,0.2, 0.05, and 0.02 (experiment L, Table 1). The data were firstcorrected for the deviation from nominal albedo according tothe calibration protocols. Then they were normalized to the Figure 6. “Footprint” of the laboratory lamp at 600 nm1.0 albedo panel data, and multiplied with the corresponding showing irradiances relative to the EGO center point (ex-nominal albedo. periment M, Table 1). For an improved visualization,

the data has been resampled from a 535 cm2 to a131 cm2 grid.

played multiplied with the nominal panel albedo. Gapsin the data series indicate sensor dropouts or outliers.

we observed a left-right asymmetry in the lamp’s irradi-Irradiance Characteristics ance characteristics which is most probably caused by aA major problem of bidirectional reflectance measure- misalignment of the lamp’s optical axis relative to thements taken in a laboratory is the nonparallelism and EGO geometry. Throughout our experiments the lamp’snonhomogeneity of the lamp. Although using a collima- focus was slightly shifted out of the center towards thetor, the illumination source still remains highly nonparal- forward-left of the goniometer system. This inadequacylel. This effect is stronger on the data acquired at higher was corrected together with the nonparallelism of thesource zenith angles. In order to correct this inadequacy, lamp by normalizing the irradiance intensities to thethe “footprint” of the lamp, that is, the illuminated area EGO center point.at ground, was measured for the lamp at ui51808 andhi5358, which is the actual lamp position for the majorityof the experiments performed (Table 1). A special setupallowed for moving the GER sensor over the illuminated Figure 7. Contour plot corresponding to Figure 6, show-

ing the laboratory lamp’s “footprint” characteristics atarea of the lamp spot with the Spectralon panel mounted600 nm.underneath the sensor, taking measurements in a resolu-

tion of 5 cm in x and y directions (see the first subsec-tion in the previous section).

Figure 6 shows the “footprint” at 600 nm wavelengthas a percentage reflectance from the EGO center value.The first peak in the principal plane closer to the EGOcenter point is caused by high irradiance due to high in-tensity values near the spot center; the second peak,closer to the lamp, results from the short irradiance dis-tance. On the “frontside” of the lamp spot rapid drop isseen revealing a decrease of the lamp irradiance of upto 50% and more, relative to the irradiance at the centerof the spot. A wavelength dependence of the “footprint”could not be detected.

A contour plot (Fig. 7) corresponding to Figure 6reveals the detail structure of the lamp’s irradiance. Thedata again is normalized and referenced to the EGOcenter point. In agreement with Solheim et al. (1996),


Figure 8. Digital numbers and relative root mean square Figure 9. Nadir measurements of concrete slab taken duringerrors of five panel measurements acquired consecutively the acquisition of a hemispherical data set (experiment H,within 5 min from nadir view direction (without change in Table 1). The actual measurement time is indicated above theazimuth) with an illumination zenith angle of 358. graph. Note the very fine resolution of y-axis values. The

corresponding rmse data are depicted in Figure 10.

Reproducibility of Measurementsthe sensor can be assumed invariant within the measure-If one assumes that the sensor is fully reliable and stable,ment period of 59 min, the variation is most likely intro-the reproducibility of target measurements would onlyduced by the nonparallelism of irradiance and a noncir-depend on the geometric accuracy of the goniometer,cular sensor field-of-view. According to a preliminarythe stability of irradiance, and the invariability of the tar-mapping of the sensor’s FOV, the version of GER-3700get. In this study, these three effects are investigated inused in this study exposed a slightly elliptical FOV withcombination by examining the reproducibility of nadirthe major axis perpendicular to the sensor case. Turningmeasurements and of principal plane data. Further analy-the sensor in azimuth direction, therefore, results insis of the EGO characteristics can be found in Solheimviewing different areas of the target which are, in addi-et al. (1996).tion, differently illuminated. In agreement with the

Reproducibility of Nadir Measurements lamp’s “footprint” (Fig. 7), the smallest irradiance andFigure 8 shows a series of five nadir measurements of thus the lowest reflectance values are obtained when thethe Spectralon panel acquired within 5 min when the il- major axis of the elliptical FOV is aligned to the principallumination source was set at 358 zenith angle and 1808 plane, that is, when the sensor is positioned at 908 azi-azimuth angle. The graph illustrates the basic spectral muth angle. The highest values are acquired at 308 duecharacteristics of the laboratory lamp with peaks in the to the asymmetry of the lamp’s “footprint.” Figure 9 alsogreen, red, and near-infrared, and drops in the blue and confirms the precise vertical orientation of the sensorfarther near-infrared range. A very low irradiance varia- and the quite high stability of the lamp’s irradiance dur-tion of under 0.6% rmse is observed over the whole ing the measurement period of 59 min. The reflectance

factors acquired at 08 and at 1808 view azimuth anglesspectral range depicted, showing a high reproducibilityfor short-term measurements with identical view-illumi- only differ by 0.5% rmse averaged over the spectral

range of 450–1000 nm, showing that the elliptical field-nation geometry.In Figure 9 the nadir measurements of the concrete of-view covers almost the same target areas when the in-

strument is positioned at 08 and 1808 azimuth angles.slab are depicted for selected wavelengths, taken withthe spectroradiometer rotated from 08 to 1808 azimuth In Figure 10 the root mean square errors for con-

crete are depicted for all six nadir measurements as aangle during the acquisition of a hemispherical data set(experiment H, Table 1). Although one would expect function of wavelength. For comparison, the thirteen na-

dir measurements of watercress and grass derived fromidentical reflectances for all measurements, a systematicchange over the azimuth angles is observable for all experiments C and K (Table 1) are included. Whereas

the concrete nadir measurements again prove to bewavelengths selected. All of the curves show sinusoidalcharacteristics, with the highest reflectance values at 308 highly repetitive with an rmse of about 1% over the

whole spectral range, the watercress and particularly theand the lowest at 908. The amplitude of variation is about60.005 reflectance values. Since the concrete target and grass lawn show rather large wavelength-dependent varia-


Figure 11. Bidirectional reflectance factors of selected wave-lengths for watercress and grass lawn acquired in two seriesin the principal plane. The nadir measurements of the tworuns differ by 6 h 19 min for the watercress (experiment C),and by 2 h 55 min for the grass lawn (experiment K).

Figure 10. Relative root mean square errors (rmse) of nadirmeasurements of watercress, grass, and concrete. All datawere taken during the acquisition of hemispherical data know the shape and dimension of the field-of-view bestsets; that is, the radiometer has been rotated in azimuth

possible.direction. The first and the last nadir measurements differby 59 min for the concrete slab (experiment H, Table 1), by Reproducibility of Principal Plane Data2 h 55 min for the grass lawn (experiment K, Table 1), and

In order to analyze the maximum error in hemispheri-by 6 h 19 min for watercress (experiment C, Table 1).cally acquired reflectance data, a second measurementseries was obtained in the principal plane immediatelyafter completing the full hemisphere. Figure 11 shows

bilities with an rmse of up to 9%. Surprisingly, the water- examples of comparisons between the first and the sec-cress data, which are acquired over a very long measure- ond run in the principal plane for the grass lawn and thement time of about 5 h due to a break in themeasurement series, appear more stable than the grasslawn. This is even more of a surprise since the water-

Figure 12. Relative root mean square errors versus wavelengthcress exposed some heliotrophic behavior during data ac-for two runs in the principal plane. The data correspond toquisition whereas the grass remained more stable fromFigure 11. The nadir measurements of the first and the secondthis point of view. The main difference between the wa- run differ by 6 h 19 min for the watercress (experiment C),

tercress and the grass data is evident in the red, and to by 2 h 55 min for the grass lawn (experiment K), and by 59some extent in the blue chlorophyll absorbtion bands. min for concrete (experiment H).According to the results in the companion article (Sand-meier et al., 1998), this can be explained by the canopystructure and the multiple scattering effect. The erecto-phile grass lawn appears rather heterogeneous comparedto the planophile watercress canopy. This is mainly dueto unevenly distributed gaps in the grass canopy, whichare particularly dominant in the nadir view direction be-cause of the erectophile structure of grass. Turning thesensor’s slightly elliptical field-of-view at nadir in azimuthdirection yields to a change in reflectance values becausea different number of gaps in the grass lawn canopy isobserved. In the green and near-infrared, multiple scat-tering inside the grass lawn canopy is high and leads toa smoothing of the gap effect. But, in the highly ab-sorbing blue and red wavelength ranges, where multiplescattering is much lower, the canopy heterogeneity isdominant. It is therefore crucial to check the target’sheterogeneity against the sensor’s field-of-view, and to


watercress canopies. In Figure 12 the rmse for the twoseries in the principal plane are displayed as a functionof wavelength. In addition to the lamp’s intensity fluctua-tions, the analysis of the two principal plane series showsthe impact of sensor repositioning, and changes in thetarget’s BRDF introduced between the beginning andthe end of a hemispherical data set. Since the goniome-ter positioning accuracy of nominally 60.18 is excellent,the deviations between the first and the second run inthe principal plane must be mainly due to irradiance in-stabilities and to target altering such as leave dehydrationand wilting caused by the strong irradiance of the labora-tory lamp. Particularly those parts of the leaves facingtowards the light source indicate water stress, resultingin generally larger differences between the two principalplane series in the backscatter directions than in the na-dir and the forward scattering measurements (Fig. 11). Figure 13. Relative root mean square errors of the halogenThe effects of the lamp’s intensity fluctuations are dem- lamp’s intensity variations derived from a Gore-texe experi-

ment performed by Solheim et al. (1996). The four series de-onstrated in the concrete and watercress data of Figurepict different time sections of the nadir measurements which12. In both data sets the peaks of rmse in the visiblewere taken periodically every 158 s over 6.5 h.range coincide with the lamp’s irradiance characteristics

given in Figure 8. In the grass lawn data, however, theimpact of the lamp’s fluctuations seems to be smaller

experiment the rmse remained rather stable in the sec-since the peaks can no longer be observed.ond measurement hour, but increased after 2.5 h withinThe concrete slab data, which are acquired during a45 min by about 0.5% rmse from 0.9% to 1.4% rmse attime period of 59 min, exhibit an average rmse of about600 nm. Afterwards, the intensity variations remained2.7% over the wavelength range examined. The water-again stable at about 1.4% rmse. One can therefore as-cress data of the first and the second run in the principalsume that the impact of the lamp’s intensity fluctuationsplane differ by 6 h 19 min, resulting in an rmse of 6.8%,on long-term measurement series of over 3 h is up toand the grass lawn data, acquired within 2 h 55 min,2% rmse between 450 nm and 1000 nm wavelength. Inshow an rmse of 7.8% averaged over the wavelengthshort-term measurements of up to 1 h, one can expectrange analyzed. Since only measurements of the begin-variations smaller than 1% rmse. To further improve thening and the end of a hemispherical data set are takendata quality the lamp’s irradiance should be monitored,into account in Figure 12, the rmse values are muchparticularly in long-term experiments, and the targets cho-higher than for the continuously acquired nadir measure-sen should be as resistant as possible against heat and wa-ments in Figure 10. Furthermore, a long acquisition timeter stress. (Note: The problem of irradiance instability atwas given for the watercress series due to a break in thethe EGO facility has been solved later on by the use of ameasurement series (Table 1).DC power supply. However, the spectral limitation of theThe high rmse values of the two vegetation canopieshalogen bulb remains a difficulty in laboratory experi-can be explained by target altering caused by the lamp’sments. Below 450 nm and above 1000 nm wavelength theheat as discussed above. Concrete, however, is assumedlow radiation not only leads to unfavorable signal-to-noiseto be a stable and homogeneous target. Thus, the varia-ratios, but also to unstable irradiance conditions.)tions within the data must be mostly due to the lamp’s

intensity fluctuations. This is in good agreement with themeasurements acquired by Solheim et al. (1996) with a SENSITIVITY ANALYSISSE590 spectroradiometer over a Gore-texe reference

Spectralon Reference Panelpanel which show an intensity drift of the 1000 W colli-In field campaigns, hemispherical irradiance Ei is oftenmated lamp of up to 5.5% during a 6-h period. In theirdeduced from a single nadir measurement of a referenceexperiment at the EGO laboratory, nadir measurementspanel. However, a perfectly Lambertian panel cannot bewere acquired every 158 s for 6.5 h without a change inachieved in practice. Kimes and Kirchner (1982) re-the experiment setup. Figure 13 shows the correspond-ported errors of 6%, 13%, and 27% in total irradianceing rmse values of the lamp versus wavelength for fourestimates for solar zenith angles of 458, 608, and 758, re-different time periods of 1 h, 2 h, 4 h, and 6.5 h. Evenspectively, due to the assumption of Lambertian behaviorfor a relatively small measurement time of 1 h, thefor a spray-painted barium sulfate panel measured fromlamp’s intensity varies with an rmse of 0.8% at 600 nm,

most probably due to voltage fluctuations. In this specific nadir under clear-sky conditions at 0.68 lm.


In order to correct the deviation from a losslessLambertian reflector, the panel’s reflectance characteris-tics have to be known for the specific illumination-view-ing geometries and spectral ranges the reference mea-surements are taken. Based on experiment P (Table 1),the bidirectional reflectance factor values R of the Spec-tralon panel can be determined using Eq. (3) and (4).Hemispherical irradiance Ei for nadir illumination is de-rived from Eq. (1) using the same data set. The panel’shemispherical reflectance q used in Eq. (1) is taken fromthe Spectralon calibration protocol.

The acquisition of a complete BRDF data set forany source zenith angle is not feasible even in a labora-tory. For simplification, we assumed and verified later onthat the Spectralon panel obeys Helmholtz’s reciprocitylaw, allowing the exchange of the source and the viewingdirections without changing the resulting bidirectional Figure 14. Bidirectional reflectance factors of thereflectance factor: Spectralon reference panel at 600 nm derived

from experiment P (hi508). The contour line indi-Rref(hi,ui; hr,ur; k)5Rref(hr,ur; hi,ui; k). (8) cates value 1.0, where the bidirectional reflectancefactor equals hemispherical reflectance. OutliersIt can be anticipated that panel measurements in theare corrected.field are always taken from a near-nadir position. In case

of FIGOS, vertical measurement position is affirmed bya special panel support consisting of two parallel rods panel’s diagonals, which are coincident with the diagonalsplaced onto the goniometer’s azimuth rail when taking of the illustration. This small effect is most probablyreference measurements (Sandmeier et al., 1995). Apply- caused by a combination of the elliptical field-of-view anding reciprocity, one can therefore derive the panel’s re- the impact of adjacent surfaces on measurements. Theflectance characteristics Rref for an arbitrary source zenith randomly distributed irregularities are even smaller, and itangle from experiment P (Table 1), where the panel is is hard to predict if they are intrinsic to the panel’s charac-measured with the lamp at nadir. In that way the impact teristics or caused by variations in the intensity of theof the laboratory lamp’s nonparallelism and nonheteroge- lamp. In regard to field applications where the panel isneity can be largely reduced. According to Eq. (3) and certainly assumed to be rotation symmetrical, the panel(4), the panel’s bidirectional reflectance factors Rref, used measurements are averaged over the view azimuth anglesin Eq. (5), are therefore determined by to derive Rref. Therefore, Lref of each azimuth slice ac-

quired between 2558 to 1558 zenith angle, is first inter-Rref(hi,ui; 08; k)5

Lref(08; hr,ur; k)·pEi(08; k)

, (9) polated with a second-order polynomial function as de-scribed in the section before last. By this means, valid

where Lref is the radiance reflected from the panel and Ei estimates of Lref at nadir and at high view zenith anglesthe hemispherical irradiance for the lamp at nadir, both could be obtained. Then the interpolated values for eachmeasured in experiment P. azimuth slice were averaged, and the corresponding

Figure 14 shows Rref derived from experiment P at polynomial coefficients derived (Table 2).600 nm wavelength. The contour line indicates value 1.0 In Figure 15 the interpolated data at 600 nm de-where the panel’s bidirectional reflectance factors Rref rived from experiment P, acquired with the lamp at na-and hemispherical reflectance q are identical. At nadir dir, are shown as a solid black line. The correspondingno measurements could be acquired due to the position- data of experiment J (Table 1) obtained with the sensoring of the lamp. The values depicted instead are interpo- at nadir are depicted as a dotted line. Changes in thelated using the same spherical triangulation technique as irradiance intensity due to varying source zenith anglesillustrated in Figure 4. The data indicate a faint hot spot. in experiment J have been corrected by applying the co-Measurements with view zenith angles larger than 558 are sine law [Eq. (2)]. For comparison reasons the mean andaffected by the dark background, because the panel size standard deviations of a group of eleven Spectralon pan-was too small to completely fill the sensor’s field-of-view els calibrated by Jackson et al. (1992), as well as mea-at these extreme view angles (Table 1). In general, the surements of a 50% albedo Spectralon panel performedreflectance characteristics of the Spectralon panel is rota- by Meister (1996) are added. The latter have been di-tion symmetrical to nadir, although some irregularities can vided by the nominal albedo of 0.5 to allow a direct com-be seen. As a curiosity the quadratic shape of the panel parison. Except for the very extreme zenith angles, all of

the data are within 1 standard deviation of the measure-is imaged in the data as smooth breaking lines along the


Figure 16. Bidirectional reflectance factors of the Spectralonreference panel acquired with the lamp at nadir (experimentP) for various view zenith angles versus wavelength.

2) are applied in Eq. (5) to correct the nonideal reflec-tance characteristics of the panel in field applications.

Unlike the results of Jackson et al. (1992) the coeffi-Figure 15. Bidirectional reflectance factors of Spectralon for cients in Table 2 vary rather strongly for different wave-four different settings: 1) RSL Spectralon panel with hi508 at

lengths. It may be that the band width of the MMR in-600 nm (experiment P); 2) RSL Spectralon panel with hr508at 600 nm (experiment J); 3) average of 11 Spectralon panels strument used in the study of Jackson et al. (1992) areat 655 nm measured by Jackson et al. (1992) with hr508; 4) too broad to adequately trace this effect. Figure 1650% albedo Spectralon panel at 600 nm measured by Meister shows the data of experiment P (Table 1) versus wave-(1996) with hr508. The data of the 50% albedo panel have length in a range of 450–1000 nm. As a matter of fact,been divided by 0.5 for comparison reasons. The bars indicate

the panels bidirectional reflectance factors are a function1 standard deviation of the 11 Spectralon panels measuredby Jackson et al. (1992). of wavelength, exposing a stronger non-Lambertian be-

havior at higher wavelengths. According to the Spec-tralon calibration protocol, the panel’s hemispherical re-

ments of Jackson et al. (1992). They exhibit a rather flectance only varies by 0.002 reflectance values in thestrong non-Lambertian behavior for all experiments de- wavelength range depicted. The wavelength dependencepicted. Only near 458 zenith angle bidirectional reflec- shown in Figure 16 and captured in the polynomial coef-tance factor data equal hemispherical reflectance. At all ficients of Table 2 seems therefore to be intrinsic to theother zenith angles errors of up to 5% and more are ob- panel’s reflectance characteristics.tained in hemispherical irradiance estimates, if they arebased on a single nadir measurement.

Angular Sampling ResolutionAn exchange of the source and viewing directions,Changes in atmospheric conditions and the moving ofhowever, has little effect on the resulting bidirectionalthe Sun force one to keep the measurement time in fieldreflectance factor. The averaged, interpolated data of ex-campaigns as short as possible. The angular resolution ofperiment P and J at 600 nm, as depicted in Figure 15,bidirectional reflectance measurements, on the otherdiffer only by 0.6% rmse. The measured nonfitted datahand, has to be adequate to the dynamics of the BRDFbetween 6558 zenith angle differed by 2.8% rmse at 600effects. In order to visualize the impact of angular sam-nm. Both rmse measurements are representative for thepling rate on BRDF representations, the grass lawn datawavelength range between 450 nm and 1000 nm. The(experiment K, Table 1) are depicted in Figure 17 in twodifferences might also be introduced by the nonparallel-different resolutions. In Figures 17b and 17d the originalism of the light, which is not corrected for the data ofresolution of 58 and 158 in zenith and azimuth, respec-experiment J, and the intensity fluctuations of the lamp,tively, is shown; in Figures 17a and 17c the sampling raterather than by the panel’s reflectance characteristics. Weis reduced to 158 and 308 in zenith and azimuth, respec-therefore conclude that the Spectralon panel under in-tively. In all four illustrations the hot spot area is interpo-vestigation obeys Helmholtz’s reciprocity law. As a con-lated from the surrounding measurements based on asequence, the fitted, averaged data of experiment P,spherical Delaunay triangulation (compare Fig. 4). Thetaken with the lamp at nadir, are used for Lref in Eq. (9).

The corresponding polynomial coefficients for Rref (Table two wavelengths of 600 nm and 675 nm are chosen be-


Figure 17. BRDF of grass at 600 (a, b) and 675 nm (c, d), interpolated from two different an-gular resolutions. b) and d) are based on the original data set which is acquired with a resolutionof 58 and 158 in zenith and azimuth, respectively (experiment K, Table 1). In a) and d) theoriginal resolution has been reduced to 158 and 308 in zenith and azimuth, respectively, priorto the interpolation.

cause of the high BRDF dynamics (Sandmeier et al., smooths this highly dynamic range and may lead to mis-interpretations of the BRDF shape.1998). In both bands the effect of the two different an-

In order to keep the data acquisition time in FIGOS-gular sampling rates are rather small, and both resolu-like field campaigns reasonably low, we therefore recom-tions preserve the general shape of the grass lawn’smend for vegetated targets choosing a resolution of 158BRDF. The lower resolution tends to smooth localand 308 in zenith and azimuth for the main part of theanomalies and distinctive features like the two ridgeshemisphere and a sampling rate of at least 58 in zenithleading from the hot spot to the forward scattering direc-angle in the hot spot region. If time constraints allow, twotion along both sides of the principal plane. Only the hotadditional data series at, for example, 6158 azimuth anglesspot area exhibits major differences and appears muchnext to the principal plane would be desirable to improvesharper and more realistic in the higher angular resolu-the characterization of the hot spot area.tion. This is confirmed in Figure 18 showing the interpo-

lated principal plane data in detail, compared to the ac-Moving Light Sourcetual measurements. Except for the hot spot region the

two resolutions result in little differences, in spite of the The movement of the sun affects BRDF data acquiredrather high BRDF dynamics. However, a probably even in the field in three different ways: 1) the reflectancehigher resolution than the 58 and 158 in zenith and azi- measured under identical viewing positions changes ac-muth, respectively, would be required to fully character- cording to the target’s BRDF; 2) the Sun’s irradiance in-

tensity varies with the Sun zenith angle; 3) the principalize the hot spot area. The lower resolution clearly


data to movements of the source position is highly wave-length-dependent, and can exhibit rather high rmse val-ues even when the irradiance intensity is normalized.Figure 20a shows the result from a 128 change in sourcezenith angle from 358 to 378. In Figure 20b the corre-sponding data for a change by 228 from 358 to 338 aredepicted. In the cosine-corrected data the impact of var-ying irradiance intensities due to different source zenithangles are eliminated using the cosine law. These dataare comparable to field measurements which are takenunder clear sky conditions and are corrected for irradi-ance instabilities using multiple reference panel mea-surements or a second intercalibrated radiometer moni-toring irradiance conditions during data acquisition.

In general, the irradiance normalized data showlower rmse values than the uncorrected data. But whilein Figure 20a the irradiance normalization clearly re-duces the impact of the moving source for the wholewavelength range, in Figure 20b this is only true for the

Figure 18. Principal plane data of grass at 600 nm and 675 nm near-infrared range. In the visible part of the spectrum,in two different angular resolutions as depicted in Figure 17. however, changes in the irradiance intensity and BRDFThe data also correspond to Figure 4.

effects are obviously compensating each other and leadto smaller differences in the reflectance signature in theuncorrected data. Similar effects can be seen for differ-plane moves with the Sun’s azimuth angle and affects theent source zenith angle variations and other referenceintegrity of the measurement coordinate system. Besidespositions.variations in atmospheric conditions, the change of the

Interactions between BRDF effects and irradianceSun’s zenith angle is the major concern in BRDF fieldchanges are target specific and hard to predict. It is there-campaigns since it has a direct impact on the intensity

of irradiance. In order to examine this impact, the water-cress target was measured from nadir under various lamppositions (experiment E, Table 1). Keeping the source Figure 19. Relative root mean square errors for five referenceazimuth angle constant at 1808, the lamp was moved in angles at 258, 308, 358, 408, and 458, testing the impact of

source zenith angle changes on the reflectance signature ofsteps of 18 from 258 to 458 zenith angle. Figure 19 showswatercress at 550 nm. In order to reduce singularities, the datathe resulting bidirectional reflectance factors at 550 nm,are averaged over seven bands ranging from 446 nm to

and the corresponding root mean square errors for five 555 nm. Changes in irradiance intensities due to differentreference positions at 258, 308, 358, 408, and 458 source source zenith angles are not corrected. The corresponding

bidirectional reflectances are depicted as a solid line. For com-zenith angle. In order to reduce the singularity of oneparison the BRF data corrected with the cosine of the sourcewavelength, the data are averaged over seven bandszenith angle are added as a gray line.ranging from 446 nm to 555 nm. All five rmse series

show similar results: Even for a source zenith anglechange of 618, reflectances deviate from the referencevalue by about 2% rmse. This disturbance is primarilyintroduced by the changing irradiance intensity which isnot accounted for in the rmse series of Figure 19. Nor-malizing irradiance intensity to nadir source positionbased on the cosine law leads to much smaller differ-ences in the bidirectional reflectance factors over therange of source zenith angles as seen in the gray line ofFigure 19. It has to be kept in mind, however, that atarget with a more dynamic BRDF characteristic thanthe planophile watercress would expose higher BRF vari-ations due to the BRDF effect.

A compensation of irradiance variations does notnecessarily allow for long-term measurement series. Fig-ure 20 demonstrates that the sensitivity of the watercress


Figure 20. Relative root mean square errors as a function of wavelength for source zenith angles deriving by a) 128and b) 228 from 358. The “original” data correspond to rmse values in Figure 19 referenced to 358. In the “cosine-corr.” data, varying irradiance intensities due to different source zenith angles are corrected based on the cosine law.

fore certainly advisable to correct irradiance changes as of-view on nadir measurements taken under differentazimuth angles. Also the calibration of a reference panelbest as possible by periodically or simultaneously obtaining

reference measurements. This also helps to reduce the im- is ideally performed in a laboratory as long as the samepact of changing atmospheric conditions in the field. Fur- radiometer is used as in consecutive field measurements.thermore, the measurements should be performed within For the Spectralon panel analyzed a wavelength-depen-a solar zenith angle change of 618, that is, 28, which cor- dent deviation from Lambert of about 7% was found inresponds, for example, at 458N on 21 June, 2 p.m. local the hot spot configuration, and of about 5% for nadirtime to a measurement time of about 13 min and a solar measurements taken under a source zenith angle of 608.azimuth angle change of about 48. The panel, however, obeys Helmholtz’ reciprocity and

results in almost the same reflectance factor when thesensor and source positions are exchanged. Correspond-

CONCLUSIONS ing data derived from interpolation differed only by 0.6%rmse at 600 nm when averaged over all azimuth angles.Even under controlled laboratory conditions accurate bi-

directional reflectance data are not easy to obtain. Fluc- A detailed comparison of the raw measurements revealeda rmse of 2.8% at 600 nm which might also be intro-tuations of the lamp’s intensity may introduce variations

in irradiance of up to 2% rmse depending on the set up duced by the lamp’s intensity fluctuations.An analysis of the angular sampling rate showed thatand wavelength range. The nonparallelism of the light

source must be taken into account, especially for high in a first step a moderate resolution of 158 and 308 inzenith and azimuth, respectively, is adequate to capturesource zenith angles and small sensor field-of-views. An-

other constraint to deal with in a laboratory is the impact the BRDF effect even for vegetated targets with ratherhigh BRDF dynamics. In the hot spot area, which is in-of the lamp’s heat affecting particularly fragile vegetated

surfaces. The rmse of the grass lawn and the watercress terpolated based on a spherical Delaunay triangulationdue to system constraints, the higher resolution of 58 andcanopies were up to 9% at certain wavelengths when

comparing principal plane data from the very beginning 158 in zenith and azimuth angle, respectively, leads to amuch more realistic characterization. It is therefore rec-and the very end of a hemispheric data set.

Major advantages of laboratory measurements are ommended to choose at least a resolution of 58 in thehot spot area of the principal plane. Additional measure-the control over the light source position, the almost

complete absence of diffuse irradiance and the high geo- ments at, for example, 6158 of the principal plane wouldbe a further improvement.metrical precision. This compensates for many of the

drawbacks listed above and allows to trace even extreme Movement of the illumination source was found tobe crucial for the data quality. Even a source zenithsmall effects like the impact of a nonideal circular field-


rectional calibration results for 11 Spectralon and 16 BaSO4angle movement of only 618 changes the reflectance ob-reference reflectance panels. Remote Sens. Environ. 40:tained by about 2% rmse, depending on the target and231–239.wavelength range under consideration. Since BRDF ef-

Kimes, D. S. (1983), Dynamics of directional reflectance factorfects are wavelength-dependent, the impact of a movingdistributions for vegetation canopies. Appl. Opt. 22(9):light source on bidirectional data varies for different1364–1372.wavelengths. A solar zenith angle change of 618 was

Kimes, D. S., and Kirchner, J. A. (1982), Irradiance measure-concluded to be an optimal compromise between short ment errors due to the assumption of a Lambertian refer-measurement time and high angular resolution in case of ence panel. Remote Sens. Environ. 12:141–149.FIGOS measurements. Frequent acquisition of reference Koechler, C., Hosgood, B., Andreoli, G., et al. (1994), The Eu-measurements in the field with a panel of known BRDF ropean Optical Goniometric Facility: technical descriptioncharacteristics is highly recommended in order to nor- and first experiments on spectral unmixing. In Proceedingsmalize irradiance changes. of IGARSS’94, Pasadena, 8–12 August, pp. 2375–2377.

The data obtained in this experiment were further Meister, G. (1996), Messung der spektralen Reflexionsfunktion(BRDF) ausgewahlter Oberflachen bei naturlicher Beleuch-analyzed for wavelength dependency in BRDF effects intung, Master’s thesis, CENSIS Report No. 18, University ofa companion article (Sandmeier et al., 1998), and will beHamburg, Germany, 117 pp.compared to corresponding field measurements acquired

Milton, E. J. (1987), Principles of field spectroscopy. Int. J.with the FIGOS goniometer.Remote Sens. 8(12):1807–1827.

Muller, Ch. (1997), Erfassung der bidirektionalen ReflexionWe gratefully acknowledge the support of the following people: von Objekten—Grundlagen, erste Feldversuche und Labor-Dr. Alois Sieber of JRC, Ispra, Italy allowed full access to the experimente, Master’s thesis, Department of Geography,EGO facility; Professor Dr. Klaus I. Itten of RSL, Zurich, University of Zurich, Switzerland, 91 pp.Switzerland continuously supported the research; Tom Eck, and

Nicodemus, F. E. (1970), Reflectance nomenclature and direc-Dr. Don Deering of NASA/GSFC, Greenbelt, Maryland con-tional reflectance and emissivity. Appl. Opt. 9(6):1474–1475.tributed most valuable inputs and guidance; Inger Solheim of

Ranson, K. J., Irons, J. R., and Daughtry, C. S. T. (1991), Sur-NORUT-IT, Norway provided the irradiance stability data. Ste-face albedo from bidirectional reflectance. Remote Sens. En-fan Sandmeier is financed by the Swiss National Science Foun-

dation and supported by the Universities Space Research Asso- viron. 35:201–211.ciation of the United States. Robinson, B. F., and Biehl, L. L. (1979), Calibration proce-

dures for measurement of reflectance factor in remote sens-ing field research. In Proceedings of the Society of Photo-

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Sensitivity Analysis and Quality Assessment of Laboratory ... · Sensitivity Analysis and Quality Assessment of Laboratory BRDF Data St. Sandmeier,* Ch. Mu¨ller,* B. Hosgood,†