The apparent brightness of a vegetation canopy var-ies strongly with view direction. For example, Figs.1 and 2 show images of homogeneous vegetation can-opies, taken through a wide-angle lens, in which thebrightness increases with off-nadir view angle. Thisbrightness variation is characterized by the direc-tional reflectance distribution, which is reflectance asa function of view direction at a fixed Sun position.Reflectance varies not only with view angle, but alsowith Sun position; hence the term bidirectional re-flectance.
Many researchers have modeled bidirectional re-flectance of terrestrial surfaces ~see Ranson et al.1and Roujean et al.2 for references!. The reasons forthe research fall into three categories. First, formonitoring vegetation condition over time, remotelysensed images need to be corrected for differingillumination and viewing geometries. Second, forquantitative assessment involving large-field-anglesensors, images need to be corrected for the differentviewing geometries occurring within a single image.Third, bidirectional reflectance data may help distin-
The authors are with Manaaki Whenua-Landcare Research, Pri-vate Bag 11052, Palmerston North, New Zealand.
Received 25 April 1996; revised manuscript received 27 Septem-ber 1996.
4314 APPLIED OPTICS y Vol. 36, No. 18 y 20 June 1997
guish among vegetation types or allow biophysicalproperties, such as average leaf inclination3 or leafarea index4, to be derived.
To acquire bidirectional reflectance data, the direc-tional reflectance distribution must be measured at arange of Sun positions. Researchers generally usenonimaging radiometers to view reflecting surfacesfrom many different directions to measure a direc-tional reflectance distribution.1,5–13 With thismethod it is difficult to sample a directional reflec-tance distribution fully before the Sun’s positionchanges. Organizing data acquisition from the dif-ferent view directions also poses significant logisticaldifficulties. In this paper we describe how a direc-tional reflectance distribution can be simply mea-sured by a calibrated digital camera fitted with awide-angle lens. By imaging a large homogeneousarea, one image captures multiple views simulta-neously, giving a fully sampled directional reflec-tance distribution that is free of variations in Sunelevation and azimuth.
2. Camera System
Digital cameras provide quantitative and repeatablemeasurements and, once calibrated, may be used asimaging radiometers. We constructed an imagingradiometer around an inexpensive color digital cam-era: the Electrim EDC-1000C. The sensor is aCCD array of 751 3 244 elements with dimensions of8.67 mm 3 6.59 mm. Successive triplets of columnsin the array record 8-bit bands of red, green, and blue
visible light. An interface card that slots into thebackplane of a PC controls the camera. It displaysimagery on the computer screen at a rate of ;1 frameper second. A wide-angle lens of 3.8-mm focallength, attached to the camera with a C-mount, givesoff-nadir viewing angles of over 70°. From the key-board, the operator controls the exposure time ~1ms–10 s! and stores selected images on disk as TIFFfiles.
We mounted the camera inside a metal cylinderthat protrudes through a helicopter hatch. Foamrubber supports the cylinder to reduce vibration.For each image acquisition, we pointed the camera tonadir by centering a bubble level. For convertingradiance to reflectance, we measured irradiance witha solarimeter mounted on the front body of the heli-copter. The irradiance was corrected for being par-tially obscured by the rotating helicopter blade. Thesystem requires two people to operate it: One topoint the camera mount to nadir, and the other tooperate the camera from the PC and record the sola-rimeter reading.
Fig. 1. Image of a homogeneous grass field acquired with theElectrim EDC-1000C digital camera. The wide-angle lens givesoff-nadir views of over 70°. The long object obscuring part of theview is the helicopter skid. The helicopter shadow is in the mid-dle of the bright backscatter area.
Fig. 2. Image of a homogeneous Pinus radiata forest acquiredwith the Electrim EDC-1000C digital camera. The wide-anglelens gives off-nadir views of over 70°. The long object obscuringpart of the view is the helicopter skid. The helicopter shadow is inthe middle of the bright backscatter area.
3. Camera Calibration
A. Calibration of Radiometric Response at the FocalPoint
The radiometric response of a CCD element, as mea-sured by its digital number ~DN! value, is directlyrelated to the amount of radiant energy falling on theelement during the exposure time. To determinethis response, we set up a diffuse target in the labo-ratory and recorded the response of a small block ofpixels ~6 3 6! centered on the focal point at varyingexposure times and aperture settings. We mea-sured the radiance of the constant target with a Phys-ics Engineering Laboratory radiometer14 andcalculated the exposure E ~in joules per square meter!falling on the CCD elements from15 Eq. ~1!:
E 5 pLTy~4N2! (1)
where L is target radiance, T is the exposure time,and N is the f-stop defined as focal length divided byaperture. Figure 3 shows the radiometric responsefor each band. The intercepts of the response curvesvary with temperature and therefore must be deter-mined for each image from a corner of the CCD arrayunexposed to light ~see Fig. 1!. To calculate the ra-diance of any DN value, we calculate the exposurefrom Fig. 3 and substitute it into Eq. ~1!.
B. Lens Falloff
Objects imaged near the focal point appear brighterthan those closer to the extremities of the focal plane.To quantify this lens falloff, we imaged a target ofconstant radiance ~a 3 cm 3 3 cm square of fine mattepaper illuminated by a constant light source! at dif-ferent radial distances from the image center ~along ahorizontal line passing through the image center! andconverted the DN values to exposure relative to theimage center. Figure 4 shows the lens falloff for thered band. We also used this method to confirm that
Fig. 3. Radiometric response of the EDC-1000C CCD elements atthe default camera settings. The intercepts are independent ofexposure time, indicating no significant effects from variation indark current over the exposure range 40–120 ms.
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there was no low-frequency variation in responseacross the CCD array, other than radial effects, bychecking for radial symmetry about the focal pointalong horizontal and vertical lines.
C. Individual CCD Element Response
Each CCD element may respond differently to radi-ation16. Theoretically it is possible to calibrate theentire CCD array by imaging a target with constantradiance, after allowing for lens falloff; but construct-ing constant-radiance targets at the pixel scale isdifficult17. However, having established that thereis no systematic low-frequency variation in the re-sponse of the CCD elements, other than radially sym-metric lens falloff, we can complete calibration of theentire array by simply characterizing any remaininghigh-frequency variation in the response of the CCDelements. The method we adopted to do this usesclear blue sky as a readily available target that isexpected to show only low-frequency variations inradiance with little high-frequency variation. Weascribed the average high-frequency variation in skyimages to the systematic differential response of theCCD elements, as follows. We took 13 images ofclear blue sky through a lens with a small field angle~5°!, displacing each image by a few degrees in viewdirection to randomize any residual high-frequencyvariation. For each sky image, we formed a differ-ence image by calculating the difference between theresponse of each element and the average response ofits 24 nearest neighbors. We then took the medianof the 13 difference values at each CCD element toform an image of systematic differential response.Across the full range of DN values, over 99% of theCCD elements had a response to within 62 DN val-ues of their neighbors. For our purpose, this was asmall variation and did not require explicit correc-tion.
D. Geometric Lens Distortion
We used the method of Nomura et al.18 to correctspatial distortions in the imagery caused by the wide-
Fig. 4. Lens falloff for the wide-angle lens.
4316 APPLIED OPTICS y Vol. 36, No. 18 y 20 June 1997
angle lens. The method assumes that the image dis-tortion center and therefore the focal point occur atthe intersection of the only two straight orthogonallines appearing in the image of a rectangular grid.This was at 4.33 6 0.04 mm horizontally and 3.55 60.04 mm vertically from the top left-hand corner ofthe CCD array.
We measured the focal-plane distance from the fo-cal point d for 15 points on the grid that ranged fromthe focal point to the edge of the CCD array. Wethen calculated the corrected focal-plane distance d9of those points from the equation
d9 5 fDyR, (2)
where f is the effective focal length, D is the distanceon the grid from the grid center, and R is the distanceof the grid from the lens. Figure 5 shows the radiallens distortion with d9 plotted versus d. The tan-gential distortion is small compared with the radiallens distortion15 and can be neglected.
4. Examples of Directional Reflectance DistributionsMeasured with the Digital Camera
We evaluated our measuring method on two commonvegetation types in New Zealand, grass ~Lolium spp!and production pine forest ~Pinus radiata!, for redvisible light ~the procedure for blue and green visiblelight is the same!. The grass had a uniform swardheight of 5 cm and the forest a uniform stocking rateof 200 stems per hectare. The forest consisted ofmature ~.20-yr! trees of 30-m height. At zenith theaverage probability of gap through the forest canopywas 0.3.
We acquired imagery of the grass from a height ofapproximately 20 m. Before each image acquisition,we aligned the main axis of the helicopter in theprincipal plane of the Sun and pointed the camera tonadir. The helicopter shadow appeared in each im-age, providing a convenient reference point to deter-mine the principal plane accurately. For grass, wewere able to produce a satisfactory directional reflec-
Fig. 5. Radial lens distortion of the wide-angle lens.
tance distribution ~see Fig. 6! from just one image byfirst applying a 7 3 7 low-pass filter and then fittinga local regression surface19 with local quadratic func-tions of span 0.15. The low-pass filter reduces localvariations caused by small shadows and random in-homogeneity, and the local regression surface re-moves any remaining high-frequency variation.
We acquired imagery of the pine forest at a heightof approximately 40 m from the top of the canopy ~seeFig. 2!. The presence of large shadows required thateight images be averaged ~before applying the low-pass filter and fitting a local regression surface! sothat a smoothly varying reflectance distributioncould be obtained ~see Fig. 7!. Because their contri-bution to canopy radiance is as important as sunlitareas, it is necessary to average out shadows ratherthan remove them. The eight images were acquiredevery 80 m along a flight line.
The directional reflectance distribution of the grass~Fig. 6! has a bowl shape with a minimum reflectanceof 0.032 near nadir. ~An error analysis in AppendixA shows the precision of the biangular pattern to be67%.! The reflectance increases with off-nadir viewangle to approximately 0.070 at 60° off nadir. Thereis also a significant backscatter effect in which reflec-tance increases with decreasing phase angle: Thisproduces a maximum of 0.106 at the antisolar point.A valley of low reflectance extends from 15° off nadir
Fig. 6. Polar plot showing directional reflectance distribution ~inpercent! in the red visible band of grass ~Lolium spp! as a functionof azimuth, relative to the Sun, and off-nadir viewing angle. Theantisolar position is identified by a Sun sign. Reflectances fromthe hemisphere partly obscured by the helicopter skid are notplotted.
at azimuth 180° up to 45° off nadir at azimuth 65°.The high sampling density of our method, with over3000 points, makes it easy to detect such details.The directional reflectance distribution of the pineforest ~Fig. 7! also exhibits a bowl and backscattereffect but is more asymmetrical with stronger back-scatter in the antisolar direction than the grass re-flectance distribution. The minimum reflectance of0.01 occurs at 15° off nadir in the forward-scatterdirection, and the maximum of 0.05 occurs at theantisolar point. The bowl and backscatter effects re-ported here are consistent with those reported byKimes20 for a grass lawn and by Kimes et al.21 for aVirginia pine forest.
5. Discussion
For a target with shadows that are similar in size to~or smaller than! individual pixels, the total data-acquisition time with our camera system is approxi-mately 5 s, as a single image is sufficient to producea directional reflectance distribution that is smoothlyvarying. Even when the shadows are much largerthan individual pixels and image averaging is re-quired for producing a smooth variation, the totaldata-acquisition time is still under 5 min. Thesedata-acquisition times are considerably shorter thanthose usually required for constructing a directionalreflectance distribution by use of radiometers.
Fig. 7. Polar plot showing directional reflectance distribution ~inpercent! in the red visible band of pine forest ~Pinus radiata! as afunction of azimuth, relative to the Sun, and off-nadir viewingangle. The antisolar position is identified by a Sun sign. Reflec-tances from the hemisphere partly obscured by the helicopter skidare not plotted.
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Data-acquisition times of 20 min are reported for theAdvanced Solid-State Array Spectroradiometer in-strument,1 although this instrument is more radio-metrically accurate than the camera system usedhere. Data-acquisition times as short as 5 min havebeen reported previously,5 but have required that amore limited set of azimuth and view directions besampled. The detailed reflectance distributionsachieved by our camera system, combined with theshort data-acquisition times, should make it possibleto evaluate readily how management factors, such asstocking rate, plant age, and pruning regime, affectforest reflectance distributions. The directional re-flectance distributions of a wide range of crop andgrassland targets could also be easily measured withthis system.
Fully sampled reflectance distributions providedby imaging radiometers allow local regression tosmooth spatial variability caused by shadows. Withnonimaging methods of measuring the reflectancedistribution, large shadows must be avoided and thefield of view must be large enough to average out thevariability caused by smaller shadows. The avoid-ance of large shadows would bias results towardsmooth parts of forest canopies. This may explainwhy Kimes et al.’s21 reflectance distribution of a Vir-ginia pine forest has a lower relative range ~0.025–0.08! and less asymmetry than our forest reflectancedistribution.
6. Conclusion
A standard CCD digital camera can be calibrated asan imaging radiometer by use of equipment readilyavailable in most remote sensing laboratories. Im-ages of homogeneous targets may be acquiredthrough a wide-angle lens and then processed to pro-duce directional reflectance distributions. The tech-nique is quick, uses inexpensive equipment, andgives the biangular pattern of reflectance to a preci-sion of 67%. It produces directional reflectance dis-tributions consistent with those obtained by morelogistically difficult, time-consuming, nonimaging ra-diometry. Now that the technique has been shownto be effective, we plan to acquire directional reflec-tance distributions for vegetation types at a range ofSun elevations to build up an understanding of bidi-rectional reflectance distribution functions. The ra-pidity and simplicity of the method also offer theopportunity to quantify the variation in directionalreflectance distributions resulting from normal envi-ronmental variation in a given vegetation type.
Appendix A: Error Analysis
The total error of a reflectance measurement by thecamera is given by eR, where
eR 5 eT 1 eN 1 eE1 1 eE2 1 eE3 1 eH 1 eG 1 eI,
eT is the error in measuring the exposure time T~.0.01!, eN is the error in the measured f-stop ~.0.1!,eE1 is the error in the radiometric calibration curve~.0.02!, eE2 is the error in lens falloff curve ~.0.03!,
4318 APPLIED OPTICS y Vol. 36, No. 18 y 20 June 1997
eE3 is the error in differential CCD response ~.0.02!,eH is the error that is due to inhomogeneity in thetarget ~this is almost impossible to measure, but itcan be roughly estimated from the magnitude of anysharp changes in the relectance distribution, as wewould expect the contours to change smoothly for auniform target; .0.06!, eG is the geometric error thatis due to imprecision in pointing the camera to nadir~.0.03!, and eI is the error in irradiance ~.0.05!.
The assigned values of errors given in the paren-theses are maximum relative errors. If we assumethat all the maximum relative errors are indepen-dent, then the total maximum relative error of a re-flectance measurement will be approximately thesquare root of the sum of the maximum relative er-rors squared ~treating maximum errors similarly toroot-mean-square errors!. This gives a total maxi-mum relative error of approximately 0.12.
We can calculate the precision of the biangularpattern in a directional reflectance distribution bysetting to zero all the error terms that do not varyspatially ~i.e., eT, eN, eEI, and eI! to obtain a maximumrelative error of 0.07.
The Foundation for Research, Science, and Tech-nology, New Zealand, funded this research undercontract C09419. Ted Pinkney designed and con-structed the camera mount.
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