Sensitivity Analysis and Quality Assessment of Laboratory BRDF Data

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

A

detailed quality and sensitivity analysis of hyperspectral BRDF data, acquired under controlled laboratory conditions at the European Goniometric Facility (EGO) of the Joint Research Center, Ispra/Italy, has been performed. In regard to bidirectional reflectance measurements in the field with the FIGOS goniometer, the impact of angular data sampling, the movement of the Sun, and the Lambertian assumption of a Spectralon panel have been analyzed. An erectophile grass lawn canopy and a planophile watercress surface were chosen as main targets. A GER-3700 spectroradiometer providing hyperspectral resolution allowed for analyzing the wavelength dependency of the effects. The results of the sensitivity analysis show that in a first step a moderate resolution of 158 and 308 in zenith and azimuth, respectively, is adequate to capture the bidirectional reflectance distribution function (BRDF) of vegetated targets. Only in the hot spot area a higher resolution is desirable. The movement of the light source during data acquisition is found to be critical, and should be kept within 618 source zenith angle in order to obtain homologous BRDF data sets. Due to the wavelength dependence of BRDF effects, the impact of the light source may vary significantly between different wavelength ranges. A normalization of the irradiance with the help of frequent reference measurements is recommended, and should be carried out using a panel with known BRDF characteristics. The Spectralon panel examined showed deviations from a Lambertian panel of up to 5% and more, but obeyed Helmholtz’s reciprocity law. Corresponding calibration coefficients are given for correcting the non-Lambertian behavior in

* RSL, Department of Geography, University of Zurich, Switzerland † Space Applications Institute, Joint Research Centre, Ispra, Italy Address correspondence to St. Sandmeier, NASA Goddard Space Flight Center, Biospheric Sciences Branch, Code 923, Greenbelt, MD 20771. E-mail: [email protected] Received 23 September 1997; revised 15 December 1997. REMOTE SENS. ENVIRON. 64:176–191 (1998) Elsevier Science Inc., 1998 655 Avenue of the Americas, New York, NY 10010

field applications. Laboratory specific constraints such as the nonparallelism and heterogeneity of the lamp are assessed and corrected where necessary and feasible. The reproducibility of the BRDF data obtained lies within 1–9% rmse, depending on target type, wavelength range, and measurement duration. Elsevier Science Inc., 1998

INTRODUCTION Since the late 1970s goniometric measurements have been carried out on natural and man-made targets to derive bidirectional reflectance distribution functions (BRDFs). Most of the data are obtained either in the field from ground measurements (Colwell, 1974; Coulson and Reynolds, 1971; Kimes, 1983; Deering, 1989; Deering et al., 1992) or in controlled laboratory experiments (Coulson et al., 1965; Breece and Holmes, 1971; Walter-Shea et al., 1989; Brakke et al., 1989), but combined laboratory and field campaigns were hardly ever performed. Most of the BRDF data sets available today lack, furthermore, a high spectral resolution. In 1994/95, the Remote Sensing Laboratories of the University of Zurich constructed a transportable field goniometer (FIGOS) for the acquisition of bidirectional reflectance factor (BRF) data under natural illumination conditions (Sandmeier et al., 1995). FIGOS uses a high resolution spectroradiometer and is designed to provide basic understanding of the wavelength dependence in the BRDF phenomenon, to support the validation and development of BRDF models, and to improve the interpretation of satellite imageries by overcoming the Lambertian assumption in radiometric correction models (Sandmeier and Itten, 1997). Concurrently to the construction of FIGOS, the Joint Research Center of the European Commission established the European Goniometric Facility (EGO) (Koechler et al., 1994), a laboratory goniometer presenting almost the same dimensions and design as FIGOS. EGO offers a 0034-4257/98/$19.00 PII S0034-4257(97)00178-8

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sampling rate, however, are not specifically addressed. Thus, they are analyzed in this study in order to find an optimal compromise between high angular sampling resolution and short measurement time in FIGOS field campaigns. In addition, a Spectralon reference panel, used to estimate total irradiance in the field, is examined for its often anticipated Lambertian behavior and reciprocity characteristics. Subsequently, calibration coefficients for the Spectralon’s bidirectional reflectance characteristics are derived. Laboratory specific constraints such as the nonparallelism of irradiance are analyzed and corrected if necessary and feasible. The bidirectional reflectance data obtained in this study are further analyzed in a companion article (Sandmeier et al., 1998).

Figure 1. Overview and dimensions of the European Goniometric Facility (EGO).

higher geometrical positioning accuracy than FIGOS but is bound to indoor measurements. In both systems, the sensor always points to the center of a 2 m radius hemisphere where the target sample is located (Fig. 1). This unique conformity between FIGOS and EGO allows us to compare and combine BRDF field and laboratory measurements. Advantages and disadvantages of laboratory and field experiments are nearly complementary. Field measurements suffer from an instable irradiance due to changing atmospheric conditions and Sun positions. But they allow measure of targets in situ and in vivo under natural light conditions, and are therefore in general better suited for remote sensing applications than indoor measurements. In a laboratory, targets are either man-made or separated from their natural habitat, suffering from water and temperature stress introduced by the intense laboratory irradiance. Still, the light intensity is usually lower than in the field leading to lower signal-to-noise ratios than in the field. Compared to sunlight, laboratory irradiance is highly heterogeneous and nonparallel, and may suffer from unstable voltage, too. Furthermore, the spectral characteristics of laboratory illumination sources differ significantly from the solar spectrum. Major advantages of laboratory measurements, however, are the control over the light source position, the nearly complete lack of diffuse irradiance, the excellent geometrical accuracy, and the ability to produce BRDF data sets in very high angular resolutions. Thus, calibration procedures and sensitivity analysis are generally easier to perform in a laboratory. In this study, we make use of these advantages in order to develop and validate a measurement set up for FIGOS field experiments. Milton (1987) published detailed guidelines for improving the consistency and accuracy of bidirectional field data. The impacts of the moving sun and of the data

EXPERIMENT SETUP The European Goniometric Facility (EGO) mainly consists of an azimuth rail with 4 m diameter and two zenith arcs for the sensor and lamp positioning (Fig. 1). Both arcs are motor-driven with a positioning accuracy for lamp and sensor of 60.18 (Koechler et al., 1994). A driver software installed on a PC provides full control of all movements in the goniometer. The acquired data, however, had to be handled manually, since no sensor driver software was available in our case. As recommended by Jackson et al. (1987), the laboratory campaign was carried out with the same equipment as used in the field, except for the EGO goniometer itself which is equivalent to FIGOS. A GER-3700 spectroradiometer with nominally 704 channels ranging from 300 nm to 2500 nm was used as sensor, providing a 38 field-of-view (FOV), hyperspectral resolution of 1.5 nm in the visible and near-infrared part up to 1050 nm, a short acquisition time of >50 ms per measurement, and a data depth of 16 bits. The gain factor of the instrument was adapted to the energy available in the laboratory. To improve the signal-to-noise ratio, all measurements were averaged over five individual samples during data acquisition. The version of GER-3700 sensor available at the time of this campaign did not provide reliable data above 1000 nm wavelength due to temperature instabilities of the instrument. Under 450 nm wavelength the measurements are too noisy and had to be excluded from analysis, too. In a few bands between 450 nm and 1000 nm the sensor occasionally exposed outliers. These sections have been mapped out and occur as gaps in the plots. Finally, a total of 356 channels was analyzed ranging from 450 nm to 1000 nm, with a spectral resolution between 1.5 nm and 1.6 nm. Due to the radiometer’s small field-of-view, measurements of up to 758 zenith angle could be carried out with moderately large target sample sizes (Table 1). On the other hand, rather smooth and homogeneous targets had to be selected in order to obtain representative BRDF measurements. A freshly grown watercress (Lepi-

158; 58 (high) 398 2 h 58 min 23 Apr 96 308; 158 (low) 75 1 h 02 min 19 Apr 96 308; 158 (low) 75 58 min 22 Apr 96 308; 158 (low) 78 1 h 20 min 18 Apr 96 14 12 min 23 Apr 96

The time duration indicates the total measurement time excluding an optional second run in the principal plane.

158; 58 (high) 394 6 h 09 min 17 Apr 96 N/A

Grid cells of 535 cm2 195 3 h 51 min 24 Apr 96 308; 158 (low) 87 2 h 38 min 22 Apr 96 Angle Res. (u; h) No. of meas. Time dur. Acq. date

158; 58 (high) 335 6 h 02 min 16 Apr 96

1808; 358 Source (u; h)

a

1808; 358

308; 158 (low) 80 4 h 00 min 18 Apr 96

1808; 358

H Walkway concrete 50350 cm2 N/A Check for target stability

I Lepidium sativum 95395 cm2 9.5 cm Check sensitivity to target altering 1808; 358 G Lepidium sativum 95395 cm2 8 cm Check sensitivity to moving source 1808; 308 (!) F Lepidium sativum 95395 cm2 8 cm Check for target stability; compare resol.

E Lepidium sativum 95395 cm2 8 cm Check sensitivity to moving source Moving in principal plane Sensor const. at 08 30 16 min 18 Apr 96 C Lepidium sativum 95395 cm2 7.5 cm Check sensitivity to angular resolution 1808; 358 L Various albedos 5 cm diam. N/A Check for linearity of the GER Sensor N/A J 0.99 albedo 25325 cm2 N/A Check for reciprocity with sensor at 08; 08 Moving Exp. ID Target specification Size Height Purpose of experiment

P 0.99 albedo 25325 cm2 N/A Check for Lambertian reflectance charact. 08; 08 (nadir)

M 0.99 albedo 25325 cm2 N/A Characterization of Lamp’s ‘‘footprint’’

Concrete Slab Watercress Watercress Watercress Watercress Watercress Set of Panels Spectralon Panel Spectralon Panel Spectralon Panel Target

Table 1. Overview of Experiments Performeda

K Lolium perenne 60360 cm2 |7 cm Check sensitivity to angular resolution 1808; 358

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dium sativum) and a living grass lawn surface (Lolium perenne) were chosen as the main targets. The grass represents an erectophile canopy, whereas the watercress exhibits a planophile canopy characteristic. A concrete slab was added as an invariant target mostly for analyzing the stability of irradiance and the reproducibility of measurements. All targets are either the same as or corresponding to performed or planned FIGOS measurements and allow for comparing bidirectional field and laboratory reflectance data. A Spectralon panel (SRT99-100) with a 99% albedo, calibrated by Labsphere at North Sutton, New Hampshire, USA in November 1994, served as a reference surface. The same panel is used in FIGOS field-campaigns. A 1 kW tungsten halogen collimated lamp with a focusable beam aperture served as light source. All experiments were performed with the maximum aperture opening which is 398. For the majority of the experiments the lamp was set at 358 zenith angle, corresponding to an expected Sun position in the field campaigns. For this lamp position the nonparallelism of the irradiance was corrected as described in the section after next. A resolution of 158 and 58 in azimuth and zenith direction, respectively, was chosen for the radiometer positions as a high resolution mode. A low resolution mode was set to 308 and 158 in azimuth and zenith, respectively, equivalent to the angular sampling rate used in field applications with FIGOS. Table 1 gives an overview on the targets, setup, and experiments performed. Figure 2 shows an example of the measurement configuration. DATA PREPROCESSING As no driver software at the EGO facility was available for the GER-3700 sensor, the measurements were chronologically numbered during data acquisition. In a second step, a file name system was established, identifying the positions of the sensor. The algorithm setting up the position-based nomenclature handles different angular sampling resolutions, measurement starting points, and sensor moving directions as well as gaps in the data series. Within the preprocessing, data are transformed from 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, analyzing, and plotting the data (Fig. 3). COMPUTATIONAL METHODS Hemispherical Irradiance Hemispherical irradiance Ei denotes the total irradiance of a light source striking a target from any direction within the surrounding 2p steradian solid angle (i.e., hemisphere). In the field, Ei is often estimated from a

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

Figure 2. Overview of laboratory measurement configuration.

single directional reference panel measurement, based on the Lambertian assumption. Even in a laboratory environment, an absolute calibration of the light source, the sensor, and the reference panel is often not given. Also in our case, Ei (W·m22·nm21) had to be derived indirectly by integrating the reflected radiance L (W·m22·sr21·nm21) from a Spectralon panel over the hemisphere: Ei(k,hi)5

1 q

p ur52p hr5 2

# # ur50

hr50

L(k,hr,ur)·cos(hr)·sin(hr) dhr dur, (1)

where q5hemispherical reflectance of panel, L5sensor radiance, k5wavelength, hr,ur5view zenith and azimuth angles, hi5source zenith angle. Spectralon is well suited for deducing hemispherical irradiance since Eq. (1) assumes constant reflectance,

that is, Lambertian behavior, only within a small solid angle dhr, dur of 58 and 158, respectively, in our case (experiment P, Table 1). Furthermore, the hemispherical reflectance of the surface used should be either lossless, or precisely known. Both are not quite true for Spectralon. But q of the panel is close to 1, and sufficiently well characterized by the panel’s calibration protocol of Labsphere. Strictly speaking, the calibration data for q are only approximated since they are taken from nadir measurements and an illumination zenith angle of 88, instead of from hemispherical averages. This inadequacy may introduce a slight error in estimating Ei. If only directional, collimated irradiance is present, Ei can be derived for any light source position from Ei(08), simply by applying the cosine law: Ei(k,hi)5Ei(k,08)·cos(hi).

(2)

Although one can assume direct irradiance in a laboratory, the nonparallelism and heterogeneity of the light source have to be taken into account. In order to reduce these impacts as much as possible, Ei has been obtained first with the lamp at nadir position (experiment P, Table 1). Due to the relatively small size of the Spectralon panel, measurements above 558 zenith angle had to be extrapolated. Also the hot spot region was interpolated since, for practical reasons, no measurements could be taken near the lamp. Both inter- and extrapolation of the panel data were based on a second-order polynomial function (Sandmeier et al., 1997). The corresponding relative root mean square errors between measured and interpolated data are depicted in Table 2 for various wavelengths. After deriving Ei(k, 08) based on Eq. (1), Ei(k, hi) for any source zenith angle can be determined by Eq. (2). However, the cosine relationship in Eq. (2) is only valid

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Table 2. Second-Order Polynomial Coefficients for Calculating Spectral Bidirectional Reflectance Factors Rref for the Spectralon Panel, Used To Correct the Nonideal Reflectance Characteristics [Eq. (5)]a k (nm)

Coeff. a0

Coeff. a1

Coeff. a2

rmse

450 500 550 600 650 700 750 800 850 900 950 1000

1.0601804 1.0628547 1.0645435 1.0649389 1.0675981 1.0644996 1.0696763 1.0723401 1.0743615 1.0745791 1.0780474 1.0802562

22.2319185E208 24.1248418E208 24.2594781E208 9.3524197E209 21.2742371E208 5.4960491E208 1.3463638E208 5.3013072E208 21.2542019E208 4.8421010E208 6.7558611E209 22.4651279E208

22.9108199E205 22.9801351E205 23.0501190E205 23.0666023E205 23.1359529E205 23.0899628E205 23.2631848E205 23.3321766E205 23.4155847E205 23.5075040E205 23.6098470E205 23.7017440E205

2.22 1.93 1.83 1.79 1.65 1.53 1.55 1.44 1.45 1.51 1.58 1.74

a Rref of a panel nadir measurement taken in the field under an arbitrary source zenith angle h can be calculated by Rref5a01a1·h1a2·h 2. The differences between measured data acquired in exp. 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 areas are affected by the nonparallelism of the lamp. As a consequence, the “footprint” of the lamp’s irradiance was acquired for a source zenith angle of 358, which is given for most of the experiments performed. With the GER-3700 spectroradiometer mounted vertically above the Spectralon panel in a distance of 47 cm, the panel was moved over the lamp spot taking measurements every 5 cm in x and y directions (experiment M, Table 1). Based on these data, the irradiance in the sensor’s fieldof-view at each measurement position on the goniometer was compared to the EGO center point, and subsequently taken into account in the determination of hemispherical irradiance Ei(k, 358) (Mu¨ller, 1997). The extent of the lamp’s non-parallelism at a source zenith angle of 358 is illustrated in Figures 6 and 7 (next main section). Bidirectional Reflectance Distribution Function The bidirectional reflectance distribution function (BRDF) fr (sr21) as defined by Nicodemus (1970) is the ratio of the radiance L (W·m22·sr21·nm21) reflected in one direction hr, ur to the incident irradiance Ei (W·m22·nm21) from direction hi, ui. It is thus a function of two directions and of wavelength, and is an intrinsic property of the reflecting surface. BRDF can only be approximated by measurements since an infinitesimally small sensor field-of-view would be required. In practice, BRDF values are derived by dividing measured radiances L from small aperture solid angles by the hemispherical irradiance Ei: fr(hi,ui; hr,ur; k)≈

L(hi,ui; hr,ur; k) . Ei(hi,k)

(3)

In our case, L has been measured with a field-of-view of about 38, and Ei was derived from Eq. (1) and (2), taking the nonparallelism and spatial heterogeneity of the laboratory lamp into account.

Bidirectional Reflectance Factor The bidirectional reflectance factor (BRF) R is defined as the ratio of radiance reflected from a surface into a specific direction to the radiance reflected from a lossless, Lambertian reference panel measured under identical viewing and illumination geometry. The term bidirectional implies that directional measurements in infinitesimally small solid angles would be required. Therefore, actually measured reflectance factors are sometimes referred to as biconical reflectance factors. Since the field-of-view of the GER-3700 is sufficiently small and the radiation in the laboratory is predominantly directional (Robinson and Biehl, 1979), the expression bidirectional reflectance factors is used in this study. For the same reason, we use the expression BRDF measurement for the results of Eq. (3), knowing that the values obtained are averaged over the sensor’s field-of-view. If the BRDF of a surface is known, R can simply be deduced by multiplying fr with p, assuming isotropic irradiance conditions within the full solid angle of incidence and isotropic BRDF within the solid angles of incidence and viewing: R(hi,ui; hr,ur; k)5fr(hi,ui; hr,ur; k)·p.

(4)

In a laboratory, irradiance Ei can be assumed to be rather stable as long as the lamp is not moved. Thus, R can be derived based on Eq. (3) and (4). In the field, however, hemispherical irradiance Ei is constantly changing, and R is usually derived based on a reference measurement Lref taken quasi-simultaneously from a panel with known reflectance characteristics Rref (Milton, 1987; Ranson et al., 1991): R(hi,ui; hr,ur; k)5

L(hi,ui; hr,ur; k) Rref(hi,ui; hr,ur; k). Lref(hi,ui; hr,ur; k) (5)

The bidirectional reflectance factor of the panel Rref

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even at extreme view zenith angles and in the hot spot area, where no measurements could be obtained due to system constraints. Figure 4 compares the interpolated and the measured data in the principal and orthogonal planes of the grass lawn surface as an example. Only in the nadir range some outliers are revealed due to the interpolation technique. But these inadequacies have little effect on the derived hemispherical reflectance, because the sine function in Eq. (6) is zero at nadir. QUALITY ASSESSMENT

Figure 4. Measured versus interpolated reflectance data of the grass lawn in the principal and orthogonal planes. The interpolation is based on a spherical Delaunay triangulation approach. Interpolated values are derived for every 28 in zenith and azimuth over the complete hemisphere.

corrects for the loss and the non-Lambertian reflection behavior of the panel. Rref is preferable determined under controlled laboratory conditions using the same radiometer as in subsequent field measurements (see the main section after next). Another approach to derive Rref using the Sun as the irradiance source is described in Jackson et al. (1987). Hemispherical Reflectance Hemispherical reflectance q is widely used in the companion article (Sandmeier et al., 1998). It is a key radiometric quantity for radiation budget studies and general circulation models. q is defined as the ratio of the total radiance reflected by a surface in any direction within the surrounding hemisphere to the total incoming radiance. Sometimes hemispherical reflectance is loosely referred to as albedo, although the latter usually describes an integration of q over the solar wavelength range. While BRF and BRDF can take on any value between zero and infinity, hemispherical reflectances may only have values between 0 and 1, due to the conservation of energy. q is computed in the same way as the hemispherical irradiance Ei, by integrating the bidirectional reflectance factors R of a surface over the hemisphere: p ur52p hr5 2

# #

1 q(hi,ui; k)5 p

ur50

h r 50

R(hi,ui; hr,ur; k)·cos(hr)·

sin(hr) dhr dur.

(6)

To improve the accuracy of integration, the bidirectional reflectance data used in Eq. (6) were first resampled to a resolution of 28 in zenith and azimuth, based on spherical Delaunay triangulation. This step also allowed us to provide data for the complete hemisphere,

Quality assessment was performed on raw sensor digital numbers (DN) for the sections on irradiance and sensor stability. The assessment of target measurement reproducibility is based on bidirectional reflectance factor which are corrected for the nonparallelism of the laboratory lamp. Errors are specified as relative root mean square errors (rmse), calculated as

! 1 2

2 n rmse5100· 1 o xi2xˆi , n i51 xˆi

(7)

where xi5measured data, xˆi5reference data, n5number of comparisons. Depending on the data set analyzed, xi and xˆi have different meanings. When comparing measured with modeled BRF values (Table 2), the xi are measured and the xˆi are interpolated data. The resulting rmse value for each wavelength is then the deviation between measured and modeled BRF values averaged over the angular measurement positions. Analyzing the variability of a set of nadir measurements (Figs. 8, 10, and 13), xi are the actually measured values and xˆi is the average of all nadir measurements in a specific wavelength. In a comparison of two different measurement series taken in the principal plane at the beginning and end of a hemispherical data set (Fig. 12), xi and xˆi are the corresponding measurements taken in the first and the second run. Examining the impact of a moving light source (Figs. 19 and 20), xi are the measured data for an arbitrary light source position compared to the value of a reference source zenith angle xˆi (e.g., 358). Sensor Response Characteristics Figure 5 shows the highly linear response characteristics of the GER sensor tested with a set of calibrated Spectralon panels of different nominal albedos. Because we did not have a calibrated light source, the 99% panel was used as a reference for all other panel measurements. The deviation from the nominal albedos are corrected for all panels using the corresponding Spectralon calibration protocols. For reasons of clarity, the data are dis-

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Figure 5. Linearity test of GER-3700 sensor using a set of Spectralon 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 first corrected for the deviation from nominal albedo according to the calibration protocols. Then they were normalized to the 1.0 albedo panel data, and multiplied with the corresponding nominal albedo.

Figure 6. “Footprint” of the laboratory lamp at 600 nm showing irradiances relative to the EGO center point (experiment M, Table 1). For an improved visualization, the data has been resampled from a 535 cm2 to a 131 cm2 grid.

played multiplied with the nominal panel albedo. Gaps in the data series indicate sensor dropouts or outliers. Irradiance Characteristics A major problem of bidirectional reflectance measurements taken in a laboratory is the nonparallelism and nonhomogeneity of the lamp. Although using a collimator, the illumination source still remains highly nonparallel. This effect is stronger on the data acquired at higher source zenith angles. In order to correct this inadequacy, the “footprint” of the lamp, that is, the illuminated area at ground, was measured for the lamp at ui51808 and hi5358, which is the actual lamp position for the majority of the experiments performed (Table 1). A special setup allowed for moving the GER sensor over the illuminated area of the lamp spot with the Spectralon panel mounted underneath the sensor, taking measurements in a resolution of 5 cm in x and y directions (see the first subsection in the previous section). Figure 6 shows the “footprint” at 600 nm wavelength as a percentage reflectance from the EGO center value. The first peak in the principal plane closer to the EGO center point is caused by high irradiance due to high intensity values near the spot center; the second peak, closer to the lamp, results from the short irradiance distance. On the “frontside” of the lamp spot rapid drop is seen revealing a decrease of the lamp irradiance of up to 50% and more, relative to the irradiance at the center of the spot. A wavelength dependence of the “footprint” could not be detected. A contour plot (Fig. 7) corresponding to Figure 6 reveals the detail structure of the lamp’s irradiance. The data again is normalized and referenced to the EGO center point. In agreement with Solheim et al. (1996),

we observed a left-right asymmetry in the lamp’s irradiance characteristics which is most probably caused by a misalignment of the lamp’s optical axis relative to the EGO geometry. Throughout our experiments the lamp’s focus was slightly shifted out of the center towards the forward-left of the goniometer system. This inadequacy was corrected together with the nonparallelism of the lamp by normalizing the irradiance intensities to the EGO center point.

Figure 7. Contour plot corresponding to Figure 6, showing the laboratory lamp’s “footprint” characteristics at 600 nm.

Quality Assessment of BRDF Data

Figure 8. Digital numbers and relative root mean square errors of five panel measurements acquired consecutively within 5 min from nadir view direction (without change in azimuth) with an illumination zenith angle of 358.

Reproducibility of Measurements If one assumes that the sensor is fully reliable and stable, the reproducibility of target measurements would only depend on the geometric accuracy of the goniometer, the stability of irradiance, and the invariability of the target. In this study, these three effects are investigated in combination by examining the reproducibility of nadir measurements and of principal plane data. Further analysis of the EGO characteristics can be found in Solheim et al. (1996). Reproducibility of Nadir Measurements Figure 8 shows a series of five nadir measurements of the Spectralon panel acquired within 5 min when the illumination source was set at 358 zenith angle and 1808 azimuth angle. The graph illustrates the basic spectral characteristics of the laboratory lamp with peaks in the green, red, and near-infrared, and drops in the blue and farther near-infrared range. A very low irradiance variation of under 0.6% rmse is observed over the whole spectral range depicted, showing a high reproducibility for short-term measurements with identical view-illumination geometry. In Figure 9 the nadir measurements of the concrete slab are depicted for selected wavelengths, taken with the spectroradiometer rotated from 08 to 1808 azimuth angle during the acquisition of a hemispherical data set (experiment H, Table 1). Although one would expect identical reflectances for all measurements, a systematic change over the azimuth angles is observable for all wavelengths selected. All of the curves show sinusoidal characteristics, with the highest reflectance values at 308 and the lowest at 908. The amplitude of variation is about 60.005 reflectance values. Since the concrete target and

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Figure 9. Nadir measurements of concrete slab taken during the acquisition of a hemispherical data set (experiment H, Table 1). The actual measurement time is indicated above the graph. Note the very fine resolution of y-axis values. The corresponding rmse data are depicted in Figure 10.

the sensor can be assumed invariant within the measurement period of 59 min, the variation is most likely introduced by the nonparallelism of irradiance and a noncircular sensor field-of-view. According to a preliminary mapping of the sensor’s FOV, the version of GER-3700 used in this study exposed a slightly elliptical FOV with the major axis perpendicular to the sensor case. Turning the sensor in azimuth direction, therefore, results in viewing different areas of the target which are, in addition, differently illuminated. In agreement with the lamp’s “footprint” (Fig. 7), the smallest irradiance and thus the lowest reflectance values are obtained when the major axis of the elliptical FOV is aligned to the principal plane, that is, when the sensor is positioned at 908 azimuth angle. The highest values are acquired at 308 due to the asymmetry of the lamp’s “footprint.” Figure 9 also confirms the precise vertical orientation of the sensor and the quite high stability of the lamp’s irradiance during the measurement period of 59 min. The reflectance factors acquired at 08 and at 1808 view azimuth angles only differ by 0.5% rmse averaged over the spectral range of 450–1000 nm, showing that the elliptical fieldof-view covers almost the same target areas when the instrument is positioned at 08 and 1808 azimuth angles. In Figure 10 the root mean square errors for concrete are depicted for all six nadir measurements as a function of wavelength. For comparison, the thirteen nadir measurements of watercress and grass derived from experiments C and K (Table 1) are included. Whereas the concrete nadir measurements again prove to be highly repetitive with an rmse of about 1% over the whole spectral range, the watercress and particularly the grass lawn show rather large wavelength-dependent varia-

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Figure 11. Bidirectional reflectance factors of selected wavelengths for watercress and grass lawn acquired in two series in the principal plane. The nadir measurements of the two runs 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 nadir measurements of watercress, grass, and concrete. All data were taken during the acquisition of hemispherical data sets; that is, the radiometer has been rotated in azimuth direction. The first and the last nadir measurements differ by 59 min for the concrete slab (experiment H, Table 1), by 2 h 55 min for the grass lawn (experiment K, Table 1), and by 6 h 19 min for watercress (experiment C, Table 1).

bilities with an rmse of up to 9%. Surprisingly, the watercress data, which are acquired over a very long measurement time of about 5 h due to a break in the measurement series, appear more stable than the grass lawn. This is even more of a surprise since the watercress exposed some heliotrophic behavior during data acquisition whereas the grass remained more stable from this point of view. The main difference between the watercress and the grass data is evident in the red, and to some extent in the blue chlorophyll absorbtion bands. According to the results in the companion article (Sandmeier et al., 1998), this can be explained by the canopy structure and the multiple scattering effect. The erectophile grass lawn appears rather heterogeneous compared to the planophile watercress canopy. This is mainly due to unevenly distributed gaps in the grass canopy, which are particularly dominant in the nadir view direction because of the erectophile structure of grass. Turning the sensor’s slightly elliptical field-of-view at nadir in azimuth direction yields to a change in reflectance values because a different number of gaps in the grass lawn canopy is observed. In the green and near-infrared, multiple scattering inside the grass lawn canopy is high and leads to a smoothing of the gap effect. But, in the highly absorbing blue and red wavelength ranges, where multiple scattering is much lower, the canopy heterogeneity is dominant. It is therefore crucial to check the target’s heterogeneity against the sensor’s field-of-view, and to

know the shape and dimension of the field-of-view best possible. Reproducibility of Principal Plane Data In order to analyze the maximum error in hemispherically acquired reflectance data, a second measurement series was obtained in the principal plane immediately after completing the full hemisphere. Figure 11 shows examples of comparisons between the first and the second run in the principal plane for the grass lawn and the

Figure 12. Relative root mean square errors versus wavelength for two runs in the principal plane. The data correspond to Figure 11. The nadir measurements of the first and the second run differ by 6 h 19 min for the watercress (experiment C), by 2 h 55 min for the grass lawn (experiment K), and by 59 min for concrete (experiment H).

Quality Assessment of BRDF Data

watercress canopies. In Figure 12 the rmse for the two series in the principal plane are displayed as a function of wavelength. In addition to the lamp’s intensity fluctuations, the analysis of the two principal plane series shows the impact of sensor repositioning, and changes in the target’s BRDF introduced between the beginning and the end of a hemispherical data set. Since the goniometer positioning accuracy of nominally 60.18 is excellent, the deviations between the first and the second run in the principal plane must be mainly due to irradiance instabilities and to target altering such as leave dehydration and wilting caused by the strong irradiance of the laboratory lamp. Particularly those parts of the leaves facing towards the light source indicate water stress, resulting in generally larger differences between the two principal plane series in the backscatter directions than in the nadir and the forward scattering measurements (Fig. 11). The effects of the lamp’s intensity fluctuations are demonstrated in the concrete and watercress data of Figure 12. In both data sets the peaks of rmse in the visible range coincide with the lamp’s irradiance characteristics given in Figure 8. In the grass lawn data, however, the impact of the lamp’s fluctuations seems to be smaller since the peaks can no longer be observed. The concrete slab data, which are acquired during a time period of 59 min, exhibit an average rmse of about 2.7% over the wavelength range examined. The watercress data of the first and the second run in the principal plane differ by 6 h 19 min, resulting in an rmse of 6.8%, and the grass lawn data, acquired within 2 h 55 min, show an rmse of 7.8% averaged over the wavelength range analyzed. Since only measurements of the beginning and the end of a hemispherical data set are taken into account in Figure 12, the rmse values are much higher than for the continuously acquired nadir measurements in Figure 10. Furthermore, a long acquisition time was given for the watercress series due to a break in the measurement series (Table 1). The high rmse values of the two vegetation canopies can be explained by target altering caused by the lamp’s heat as discussed above. Concrete, however, is assumed to be a stable and homogeneous target. Thus, the variations within the data must be mostly due to the lamp’s intensity fluctuations. This is in good agreement with the measurements acquired by Solheim et al. (1996) with a SE590 spectroradiometer over a Gore-texe reference panel which show an intensity drift of the 1000 W collimated lamp of up to 5.5% during a 6-h period. In their experiment at the EGO laboratory, nadir measurements were acquired every 158 s for 6.5 h without a change in the experiment setup. Figure 13 shows the corresponding rmse values of the lamp versus wavelength for four different time periods of 1 h, 2 h, 4 h, and 6.5 h. Even for a relatively small measurement time of 1 h, the lamp’s intensity varies with an rmse of 0.8% at 600 nm, most probably due to voltage fluctuations. In this specific

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Figure 13. Relative root mean square errors of the halogen lamp’s intensity variations derived from a Gore-texe experiment performed by Solheim et al. (1996). The four series depict different time sections of the nadir measurements which were taken periodically every 158 s over 6.5 h.

experiment the rmse remained rather stable in the second measurement hour, but increased after 2.5 h within 45 min by about 0.5% rmse from 0.9% to 1.4% rmse at 600 nm. Afterwards, the intensity variations remained again stable at about 1.4% rmse. One can therefore assume that the impact of the lamp’s intensity fluctuations on long-term measurement series of over 3 h is up to 2% rmse between 450 nm and 1000 nm wavelength. In short-term measurements of up to 1 h, one can expect variations smaller than 1% rmse. To further improve the data quality the lamp’s irradiance should be monitored, particularly in long-term experiments, and the targets chosen should be as resistant as possible against heat and water stress. (Note: The problem of irradiance instability at the EGO facility has been solved later on by the use of a DC power supply. However, the spectral limitation of the halogen bulb remains a difficulty in laboratory experiments. Below 450 nm and above 1000 nm wavelength the low radiation not only leads to unfavorable signal-to-noise ratios, but also to unstable irradiance conditions.) SENSITIVITY ANALYSIS Spectralon Reference Panel In field campaigns, hemispherical irradiance Ei is often deduced from a single nadir measurement of a reference panel. However, a perfectly Lambertian panel cannot be achieved in practice. Kimes and Kirchner (1982) reported errors of 6%, 13%, and 27% in total irradiance estimates for solar zenith angles of 458, 608, and 758, respectively, due to the assumption of Lambertian behavior for a spray-painted barium sulfate panel measured from nadir under clear-sky conditions at 0.68 lm.

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In order to correct the deviation from a lossless Lambertian reflector, the panel’s reflectance characteristics have to be known for the specific illumination-viewing geometries and spectral ranges the reference measurements are taken. Based on experiment P (Table 1), the bidirectional reflectance factor values R of the Spectralon panel can be determined using Eq. (3) and (4). Hemispherical irradiance Ei for nadir illumination is derived from Eq. (1) using the same data set. The panel’s hemispherical reflectance q used in Eq. (1) is taken from the Spectralon calibration protocol. The acquisition of a complete BRDF data set for any source zenith angle is not feasible even in a laboratory. For simplification, we assumed and verified later on that the Spectralon panel obeys Helmholtz’s reciprocity law, allowing the exchange of the source and the viewing directions without changing the resulting bidirectional reflectance factor: Rref(hi,ui; hr,ur; k)5Rref(hr,ur; hi,ui; k).

(8)

It can be anticipated that panel measurements in the field are always taken from a near-nadir position. In case of FIGOS, vertical measurement position is affirmed by a special panel support consisting of two parallel rods placed onto the goniometer’s azimuth rail when taking reference measurements (Sandmeier et al., 1995). Applying reciprocity, one can therefore derive the panel’s reflectance characteristics Rref for an arbitrary source zenith angle from experiment P (Table 1), where the panel is measured with the lamp at nadir. In that way the impact of the laboratory lamp’s nonparallelism and nonheterogeneity can be largely reduced. According to Eq. (3) and (4), the panel’s bidirectional reflectance factors Rref, used in Eq. (5), are therefore determined by L (08; hr,ur; k)·p Rref(hi,ui; 08; k)5 ref , Ei(08; k)

(9)

where Lref is the radiance reflected from the panel and Ei the hemispherical irradiance for the lamp at nadir, both measured in experiment P. Figure 14 shows Rref derived from experiment P at 600 nm wavelength. The contour line indicates value 1.0 where the panel’s bidirectional reflectance factors Rref and hemispherical reflectance q are identical. At nadir no measurements could be acquired due to the positioning of the lamp. The values depicted instead are interpolated using the same spherical triangulation technique as illustrated in Figure 4. The data indicate a faint hot spot. Measurements with view zenith angles larger than 558 are affected by the dark background, because the panel size was too small to completely fill the sensor’s field-of-view at these extreme view angles (Table 1). In general, the reflectance characteristics of the Spectralon panel is rotation symmetrical to nadir, although some irregularities can be seen. As a curiosity the quadratic shape of the panel is imaged in the data as smooth breaking lines along the

Figure 14. Bidirectional reflectance factors of the Spectralon reference panel at 600 nm derived from experiment P (hi508). The contour line indicates value 1.0, where the bidirectional reflectance factor equals hemispherical reflectance. Outliers are corrected.

panel’s diagonals, which are coincident with the diagonals of the illustration. This small effect is most probably caused by a combination of the elliptical field-of-view and the impact of adjacent surfaces on measurements. The randomly distributed irregularities are even smaller, and it is hard to predict if they are intrinsic to the panel’s characteristics or caused by variations in the intensity of the lamp. In regard to field applications where the panel is certainly assumed to be rotation symmetrical, the panel measurements are averaged over the view azimuth angles to derive Rref. Therefore, Lref of each azimuth slice acquired between 2558 to 1558 zenith angle, is first interpolated with a second-order polynomial function as described in the section before last. By this means, valid estimates of Lref at nadir and at high view zenith angles could be obtained. Then the interpolated values for each azimuth slice were averaged, and the corresponding polynomial coefficients derived (Table 2). In Figure 15 the interpolated data at 600 nm derived from experiment P, acquired with the lamp at nadir, are shown as a solid black line. The corresponding data of experiment J (Table 1) obtained with the sensor at nadir are depicted as a dotted line. Changes in the irradiance intensity due to varying source zenith angles in experiment J have been corrected by applying the cosine law [Eq. (2)]. For comparison reasons the mean and standard deviations of a group of eleven Spectralon panels calibrated by Jackson et al. (1992), as well as measurements of a 50% albedo Spectralon panel performed by Meister (1996) are added. The latter have been divided by the nominal albedo of 0.5 to allow a direct comparison. Except for the very extreme zenith angles, all of the data are within 1 standard deviation of the measure-

Quality Assessment of BRDF Data

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Figure 16. Bidirectional reflectance factors of the Spectralon reference panel acquired with the lamp at nadir (experiment P) for various view zenith angles versus wavelength.

Figure 15. Bidirectional reflectance factors of Spectralon for four different settings: 1) RSL Spectralon panel with hi508 at 600 nm (experiment P); 2) RSL Spectralon panel with hr508 at 600 nm (experiment J); 3) average of 11 Spectralon panels at 655 nm measured by Jackson et al. (1992) with hr508; 4) 50% albedo Spectralon panel at 600 nm measured by Meister (1996) with hr508. The data of the 50% albedo panel have been divided by 0.5 for comparison reasons. The bars indicate 1 standard deviation of the 11 Spectralon panels measured by Jackson et al. (1992).

ments of Jackson et al. (1992). They exhibit a rather strong non-Lambertian behavior for all experiments depicted. Only near 458 zenith angle bidirectional reflectance factor data equal hemispherical reflectance. At all other zenith angles errors of up to 5% and more are obtained in hemispherical irradiance estimates, if they are based on a single nadir measurement. An exchange of the source and viewing directions, however, has little effect on the resulting bidirectional reflectance factor. The averaged, interpolated data of experiment P and J at 600 nm, as depicted in Figure 15, differ only by 0.6% rmse. The measured nonfitted data between 6558 zenith angle differed by 2.8% rmse at 600 nm. Both rmse measurements are representative for the wavelength range between 450 nm and 1000 nm. The differences might also be introduced by the nonparallelism of the light, which is not corrected for the data of experiment J, and the intensity fluctuations of the lamp, rather than by the panel’s reflectance characteristics. We therefore conclude that the Spectralon panel under investigation obeys Helmholtz’s reciprocity law. As a consequence, the fitted, averaged data of experiment P, taken with the lamp at nadir, are used for Lref in Eq. (9). The corresponding polynomial coefficients for Rref (Table

2) are applied in Eq. (5) to correct the nonideal reflectance characteristics of the panel in field applications. Unlike the results of Jackson et al. (1992) the coefficients in Table 2 vary rather strongly for different wavelengths. It may be that the band width of the MMR instrument used in the study of Jackson et al. (1992) are too broad to adequately trace this effect. Figure 16 shows the data of experiment P (Table 1) versus wavelength in a range of 450–1000 nm. As a matter of fact, the panels bidirectional reflectance factors are a function of wavelength, exposing a stronger non-Lambertian behavior at higher wavelengths. According to the Spectralon calibration protocol, the panel’s hemispherical reflectance only varies by 0.002 reflectance values in the wavelength range depicted. The wavelength dependence shown in Figure 16 and captured in the polynomial coefficients of Table 2 seems therefore to be intrinsic to the panel’s reflectance characteristics. Angular Sampling Resolution Changes in atmospheric conditions and the moving of the Sun force one to keep the measurement time in field campaigns as short as possible. The angular resolution of bidirectional reflectance measurements, on the other hand, has to be adequate to the dynamics of the BRDF effects. In order to visualize the impact of angular sampling rate on BRDF representations, the grass lawn data (experiment K, Table 1) are depicted in Figure 17 in two different resolutions. In Figures 17b and 17d the original resolution of 58 and 158 in zenith and azimuth, respectively, is shown; in Figures 17a and 17c the sampling rate is reduced to 158 and 308 in zenith and azimuth, respectively. In all four illustrations the hot spot area is interpolated from the surrounding measurements based on a spherical Delaunay triangulation (compare Fig. 4). The two wavelengths of 600 nm and 675 nm are chosen be-

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

cause of the high BRDF dynamics (Sandmeier et al., 1998). In both bands the effect of the two different angular sampling rates are rather small, and both resolutions preserve the general shape of the grass lawn’s BRDF. The lower resolution tends to smooth local anomalies and distinctive features like the two ridges leading from the hot spot to the forward scattering direction along both sides of the principal plane. Only the hot spot area exhibits major differences and appears much sharper and more realistic in the higher angular resolution. This is confirmed in Figure 18 showing the interpolated principal plane data in detail, compared to the actual measurements. Except for the hot spot region the two resolutions result in little differences, in spite of the rather high BRDF dynamics. However, a probably even higher resolution than the 58 and 158 in zenith and azimuth, respectively, would be required to fully characterize the hot spot area. The lower resolution clearly

smooths this highly dynamic range and may lead to misinterpretations of the BRDF shape. In order to keep the data acquisition time in FIGOSlike field campaigns reasonably low, we therefore recommend for vegetated targets choosing a resolution of 158 and 308 in zenith and azimuth for the main part of the hemisphere and a sampling rate of at least 58 in zenith angle in the hot spot region. If time constraints allow, two additional data series at, for example, 6158 azimuth angles next to the principal plane would be desirable to improve the characterization of the hot spot area. Moving Light Source The movement of the sun affects BRDF data acquired in the field in three different ways: 1) the reflectance measured under identical viewing positions changes according to the target’s BRDF; 2) the Sun’s irradiance intensity varies with the Sun zenith angle; 3) the principal

Quality Assessment of BRDF Data

Figure 18. Principal plane data of grass at 600 nm and 675 nm in two different angular resolutions as depicted in Figure 17. The data also correspond to Figure 4.

plane moves with the Sun’s azimuth angle and affects the integrity of the measurement coordinate system. Besides variations in atmospheric conditions, the change of the Sun’s zenith angle is the major concern in BRDF field campaigns since it has a direct impact on the intensity of irradiance. In order to examine this impact, the watercress target was measured from nadir under various lamp positions (experiment E, Table 1). Keeping the source azimuth angle constant at 1808, the lamp was moved in steps of 18 from 258 to 458 zenith angle. Figure 19 shows the resulting bidirectional reflectance factors at 550 nm, and the corresponding root mean square errors for five reference positions at 258, 308, 358, 408, and 458 source zenith angle. In order to reduce the singularity of one wavelength, the data are averaged over seven bands ranging from 446 nm to 555 nm. All five rmse series show similar results: Even for a source zenith angle change of 618, reflectances deviate from the reference value by about 2% rmse. This disturbance is primarily introduced by the changing irradiance intensity which is not accounted for in the rmse series of Figure 19. Normalizing irradiance intensity to nadir source position based on the cosine law leads to much smaller differences in the bidirectional reflectance factors over the range of source zenith angles as seen in the gray line of Figure 19. It has to be kept in mind, however, that a target with a more dynamic BRDF characteristic than the planophile watercress would expose higher BRF variations due to the BRDF effect. A compensation of irradiance variations does not necessarily allow for long-term measurement series. Figure 20 demonstrates that the sensitivity of the watercress

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data to movements of the source position is highly wavelength-dependent, and can exhibit rather high rmse values even when the irradiance intensity is normalized. Figure 20a shows the result from a 128 change in source zenith angle from 358 to 378. In Figure 20b the corresponding data for a change by 228 from 358 to 338 are depicted. In the cosine-corrected data the impact of varying irradiance intensities due to different source zenith angles are eliminated using the cosine law. These data are comparable to field measurements which are taken under clear sky conditions and are corrected for irradiance instabilities using multiple reference panel measurements or a second intercalibrated radiometer monitoring irradiance conditions during data acquisition. In general, the irradiance normalized data show lower rmse values than the uncorrected data. But while in Figure 20a the irradiance normalization clearly reduces the impact of the moving source for the whole wavelength range, in Figure 20b this is only true for the near-infrared range. In the visible part of the spectrum, however, changes in the irradiance intensity and BRDF effects are obviously compensating each other and lead to smaller differences in the reflectance signature in the uncorrected data. Similar effects can be seen for different source zenith angle variations and other reference positions. Interactions between BRDF effects and irradiance changes are target specific and hard to predict. It is there-

Figure 19. Relative root mean square errors for five reference angles at 258, 308, 358, 408, and 458, testing the impact of source zenith angle changes on the reflectance signature of watercress at 550 nm. In order to reduce singularities, the data are averaged over seven bands ranging from 446 nm to 555 nm. Changes in irradiance intensities due to different source zenith angles are not corrected. The corresponding bidirectional reflectances are depicted as a solid line. For comparison the BRF data corrected with the cosine of the source zenith angle are added as a gray line.

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Figure 20. Relative root mean square errors as a function of wavelength for source zenith angles deriving by a) 128 and b) 228 from 358. The “original” data correspond to rmse values in Figure 19 referenced to 358. In the “cosinecorr.” 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 best as possible by periodically or simultaneously obtaining reference measurements. This also helps to reduce the impact of changing atmospheric conditions in the field. Furthermore, the measurements should be performed within a solar zenith angle change of 618, that is, 28, which corresponds, for example, at 458N on 21 June, 2 p.m. local time to a measurement time of about 13 min and a solar azimuth angle change of about 48. CONCLUSIONS Even under controlled laboratory conditions accurate bidirectional reflectance data are not easy to obtain. Fluctuations of the lamp’s intensity may introduce variations in irradiance of up to 2% rmse depending on the set up and wavelength range. The nonparallelism of the light source must be taken into account, especially for high source zenith angles and small sensor field-of-views. Another constraint to deal with in a laboratory is the impact of the lamp’s heat affecting particularly fragile vegetated surfaces. The rmse of the grass lawn and the watercress canopies were up to 9% at certain wavelengths when comparing principal plane data from the very beginning and the very end of a hemispheric data set. Major advantages of laboratory measurements are the control over the light source position, the almost complete absence of diffuse irradiance and the high geometrical precision. This compensates for many of the drawbacks listed above and allows to trace even extreme small effects like the impact of a nonideal circular field-

of-view on nadir measurements taken under different azimuth angles. Also the calibration of a reference panel is ideally performed in a laboratory as long as the same radiometer is used as in consecutive field measurements. For the Spectralon panel analyzed a wavelength-dependent deviation from Lambert of about 7% was found in the hot spot configuration, and of about 5% for nadir measurements taken under a source zenith angle of 608. The panel, however, obeys Helmholtz’ reciprocity and results in almost the same reflectance factor when the sensor and source positions are exchanged. Corresponding data derived from interpolation differed only by 0.6% rmse at 600 nm when averaged over all azimuth angles. A detailed comparison of the raw measurements revealed a rmse of 2.8% at 600 nm which might also be introduced by the lamp’s intensity fluctuations. An analysis of the angular sampling rate showed that in a first step a moderate resolution of 158 and 308 in zenith and azimuth, respectively, is adequate to capture the BRDF effect even for vegetated targets with rather high BRDF dynamics. In the hot spot area, which is interpolated based on a spherical Delaunay triangulation due to system constraints, the higher resolution of 58 and 158 in zenith and azimuth angle, respectively, leads to a much more realistic characterization. It is therefore recommended to choose at least a resolution of 58 in the hot spot area of the principal plane. Additional measurements at, for example, 6158 of the principal plane would be a further improvement. Movement of the illumination source was found to be crucial for the data quality. Even a source zenith

Quality Assessment of BRDF Data

angle movement of only 618 changes the reflectance obtained by about 2% rmse, depending on the target and wavelength range under consideration. Since BRDF effects are wavelength-dependent, the impact of a moving light source on bidirectional data varies for different wavelengths. A solar zenith angle change of 618 was concluded to be an optimal compromise between short measurement time and high angular resolution in case of FIGOS measurements. Frequent acquisition of reference measurements in the field with a panel of known BRDF characteristics is highly recommended in order to normalize irradiance changes. The data obtained in this experiment were further analyzed for wavelength dependency in BRDF effects in a companion article (Sandmeier et al., 1998), and will be compared to corresponding field measurements acquired with the FIGOS goniometer. We gratefully acknowledge the support of the following people: Dr. Alois Sieber of JRC, Ispra, Italy allowed full access to the EGO facility; Professor Dr. Klaus I. Itten of RSL, Zurich, Switzerland continuously supported the research; Tom Eck, and Dr. Don Deering of NASA/GSFC, Greenbelt, Maryland contributed most valuable inputs and guidance; Inger Solheim of NORUT-IT, Norway provided the irradiance stability data. Stefan Sandmeier is financed by the Swiss National Science Foundation and supported by the Universities Space Research Association of the United States.

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