Classification of the reflectancespectra of pine, spruce, and birch

T. Jaaskelainen, R. Silvennoinen, J. Hiltunen, and J. P. S. Parkkinen

Statistical pattern-recognition methods are applied to the classification of the reflectance spectra ofgrowing trees (Scots pine, Norway spruce, and birch). We show by using large training sets that it ispossible to develop classification filters that are able to discriminate the tree types with a very highprobability. Our approach may offer a reference coordinate system for multispectral remote sensing ofdifferent levels of forest damage.

Introduction

The increased awareness of widespread pollution-related damage to forests in various parts of industri-alized countries has emphasized the need for researchrelated to the development of remote-sensing meth-ods for damage detection. It is well known that thespectral shape and reflectance of green vegetation issensitive to damage.1 4 However, the sensitivity topollution varies widely among different plants. Inthe northern regions of the earth conifer forestsrepresent an important part of the green vegetation,and conifers are often used as long-term pollutionindicators. Spruce and pine have slightly differentreflectance spectra,1' 5 and the variation from tree totree is large and depends on various factors. Thusspruce and pine are difficult to distinguish from eachother without any a priori information. Hence onefirst should have methods that discriminate automati-cally among the tree types. When the characteristicfeatures of the reflectance spectra of a tree type areknown, well-defined class boundaries can be deter-mined, and later this information may be used todetect damages in the same area or in another targetautomatically.

The aim of this work was to investigate the statisti-cal properties of the reflectance spectra of Scotch pine(Pinus sylvestris), Norway spruce (Picea abies), and

J. P. S. Parkkinen is with the Department of InformationTechnology, Lappeenranta University of Technology, SF-55851Lappeenranta, Finland; the other authors are with the VisalaLaboratory, Department of Physics, University of Joensuu, SF-80101, Joensuu, Finland.

Received 21 April 1993; revised manuscript received 5 October1993.

0003-6935/94/122356.07$06.00/0.i 1994 Optical Society of America.

birch (Betula pubensces) with the aid of statisticalpattern-recognition methods. Instead of absolutereflectance data we have used the normalized spectraof the trees and thus have tried to classify the dataaccording to the spectral-shape information only.This is a powerful technique because a small changein reflectance in a wavelength region effectivelychanges the shape of the normalized spectrum. Theanalyzed data consists of 1056 reflectance spectrameasured from single tree crowns in the wavelengthrange of 390-850 nm at 5-nm intervals. Because ofthe large number of wavelength bands, very smallmodifications in the spectral shape may be detected.We briefly describe two classification methods: thesubspace method6 with two variants, and the unifiedpseudoinverse algorithm. These methods are ap-plied to the data. First we study the statisticalproperties of the sample set, and then we show that itis possible to find a few spectral features from eachtree type that allow accurate recognition and classifi-cation of an unknown sample.

Methods

Measurements

Our data consists of the reflectance spectra of theneedles of young (less than 40 years old) individualScots pine and Norway spruce and the leaves of abirch. The data were collected in Finland and Swe-den. Spectroradiometric measurements were madein clear weather during the growing season in June1992. Each measurement represents the averagespectrum of thousands of leaves of a growing treebecause the measuring area was approximately 0.6m2 (all measurements were done on the ground froma distance of approximately 50 m). The measuredcrowns were very thick, which minimizes the effects

2356 APPLIED OPTICS / Vol. 33, No. 12 / 20 April 1994

of branch color and background illumination. Thetotal numbers of pine, spruce, and birch samples were370, 349, 337, respectively.

The measurements were made with a PR 713/702AM spectroradiometer operating in the wavelengthrange of 390-1070 nm, with a sampling interval of 4nm. Repetition accuracy of the device is 3.5%.Before each measurement the base line was deter-mined with the aid of a BaSO4 reference surface.8

The reference spectrum was recorded first, then thesample reflected from a tree was recorded. Thespecific reflectance of the crown is defined as a ratio ofthe corrected spectra reflected from the single treeand from the BaSO4 surface. Note that variations inillumination conditions have been eliminated by thebase-line measurements. Finally each spectrum wastransformed by linear interpolation to the wave-length range of 390-850 nm at 5-nm sampling inter-vals. The upper limit of the wavelength was set at850 nm because there are no significant differences inthe spectra in the wavelength band of 850-1070 nm.The smoothness of the spectra guarantees that the5-nm sampling interval is accurate enough. Thusthe entire data set consists of 1056 spectra, each ofwhich contains 93 reflectance values.

Statistical Methods

The observed reflectance data are recorded as a set ofn wavelengths X, X2, . . , m. Thus a measured spec-trum 7(X) is represented as a n-dimensional patternvector

'T = [1), TA2), ...... On )]T, (1)

where T denotes the vector transpose. In our case aspectrum for calculation is sampled at 5-nm intervalsfrom 390 to 850 nm, corresponding to a 93-dimen-sional vector. Now we have three classes of samples:Let us denote these classes as P, S, and B, denotingpine, spruce, and birch, respectively. The total num-ber of class members is Np = 370, Ns = 349, and NB =

337, half of which are used for training and the restfor testing. Let the correlation matrix of a class be

1 NrM = - z rT7 T, (2)

Nr i=l

for Nr normalized vectors T. We expect that thesevectors can be represented as linear combinations ofk < n linearly independent basis vectors, say, {vi,V2.... , vk},wherevi = [vi(Xi), .. , vi(X )]f. The firstk eigenvectors of the matrix M form such a basis.A vector set {uV, v2, . . , Vk} spans a k-dimensionalsubspace L to the original n-dimensional featurespace. Then any vector T has a projection

k

T'= (T TVi)Vi (3)i=l

to the subspace L. It has been shown in severalinvestigations that spectral distributions of day-

light,9-10 surface reflectances, or colored objectsl-' 6

can be represented by the use of only few basisvectors. This means that the dimension k of asubspace L remains low but guarantees good recon-structions for the entire data set.

The basis vectors can be used for classification asfollows: Let the number of classes be J. We haveNj training samples in class j. The eigenvectors ofeach class are computed from the correspondingcorrelation matrix, and the eigenvectors correspond-ing to the k largest eigenvalues are chosen as the basisfor the subspace representing a class j. Note thatthe basis vectors are orthonormal, but that the basesof two subspaces are not mutually orthogonal. Nowan unknown sample is classified by measuring thelength of the projection vector from Eq. (3) in eachsubspace. The longest projection vector (or the short-est distance) defines the class for the sample. Thismethod is known as the (CLAFIC) is the simplest ofthe subspace methods of classification.6

When the subspaces for each class have beendetermined and the training data is classified errorsmay remain. In the simple CLAFIC method thereare no means to handle these misclassifications. Inthe learning subspace method described by Koho-nen,6 the initial subspaces are improved as follows:If a training vector T belonging to the subspace L(i) ismisclassified into a subspace L(i), the subspace L(i) isrotated toward T and L(i) is rotated to depart from T.The procedure is continued until the number ofmisclassifications is minimized. In the average learn-ing subspace method (ASLM) instead of rotation ofthe subspaces, the correlation matrices are improvedafter each misclassification as follows:

Qrn = Qm-i(i) + z a(ij)Sm(i'j) - I b(ij, Sm('i)ji kei

(4)

where Qm_1i( is the correlation matrix of a class i atiteration (m - 1), a and b are small numbers definingthe weighting for misclassification, and Qm(i j) is theautocorrelation matrix formed by the pattern vectorsthat belong to class i but that have been classified atiteration m to classj. Learning continues until theresults become correct or stable. The number ofiteration cycles depends on the structure of the dataset and on the weighting parameters.

Another type of classification method, used in thispaper, is the unified pseudo-inverse algorithm (UPA),7

which to our knowledge is the most general linear-mapping algorithm. For instance, the synthetic dis-criminant function is a special case of the UPA.Now if we have J classes with NJ training vectors oflength n in each class, the training data is collected tothe n x N matrix:

W= [T11 ..... TN(), T1 (2), TN2(2),

T1(.). . , TNJJ], (5)

where N = N, + N2 + * + NJ. For the overdeter-mined problem (N > n) the UPA leads to linear

20 April 1994 / Vol. 33, No. 12 / APPLIED OPTICS 2357

mapping, which is same as the least-squares linear-mapping technique (LSLMT)7:

A = UWT(IWWT)1,

[1N1 0

0 [1]N2

(6)

0

0

0

0 0 ... [1]NJ_1

*-- 0

*-- 0

*-- 0

*-- 0

* ... * * *... ... [1N]N

and []N is a row vector consisting of Ni unityelements. A is a J x n matrix and contains one filterof length n for each of the J class. An unknownvector x is classified with these filters by calculation ofthe inner products between the row vectors of thematrix A and the column vector x. Decision is basedon the longest projection, as in the subspace methods.

Results

The eigenvalues and eigenvectors of the correlationmatrices that contained the whole sample set weredetermined for pine, spruce, and birch. The firsttwo eigenvectors for pine and spruce are quite simi-lar, but there are higher differences in the third andfourth vectors. On the other hand birch, as ex-pected, shows significant differences to the others asearly as the second eigenvector. Figure 1 shows thefirst four eigenvectors of pine and birch plotted in thewavelength range of 400-800 nm, which is where themain differences occur. The first eigenvectors repre-sent the average spectra of the data sets. Hence thecorresponding eigenvalues are dominant. In thepresent case the first eigenvalues for pine, spruce, andbirch are 99.11, 99.01, and 99.79% of the sum of alleigenvalues, respectively. On the other hand thesums of the first four eigenvalues of the pine, spruce,and birch are 99.98, 99.96, and 99.99%, respectively.The first eigenvalues indicate that there are highervariations in the data sets of pine and spruce than inthe set of birch. This is shown in Fig. 2, whichrepresents the average spectra with minimum andmaximum differences at each wavelength for spruceand birch. The curves for pine are almost equal tothose of spruce. Large differences between indi-vidual spectra of spruce and pine arise mainly fromdifferences in samples because the measuring deviceis accurate and background-illumination variationshave been eliminated.

The bases constructed from the extracted eigenvec-tors effectively represent or reproduce the spectra.Consider the reconstructions with 1-8 basis vectorsaccording to Eq. (3) where the weighting factors inlinear combinations are determined by inner prod-ucts between a spectrum and the basis vectors.Error in a reconstruction was determined by calculat-ing the absolute values of differences between theoriginal and the reconstructed spectra for each wave-

(7)

Va)

_0

E0z

0.30

0.15

0.00

-0.15

-0.3041

0.30

Cl)a)

-o

_0

E0z

0.15

0.00

-0.15

-0.3041

Pine

l ......~~~~~~~~~.........

450 500 550 600 650Wavelength(nm)

(a)

Birch

Jo 450 500 550 600 650Wavelength(nm)

700 750 800

700 750 800

(b)Fig. 1. The first four eigenvectors for the reflectance spectra (a) ofpine and (b) of birch. The data consists of 370 and 337 spectralreflectances, respectively.

length. Because the differences were essentially in-dependent of the wavelength, we calculated the aver-age values of the differences across the wavelengthband. Table 1 shows the percentage maximum,percentage minimum, and average errors for the1056 spectra. One can conclude that good recon-structions are obtained in the 4-8 dimensional cases.If we plot an eight-dimensional reconstruction withthe original spectrum it is difficult to distinguish thespectra from each other.

Consider next classification of the samples. Firstwe need to point out that usually we consider normal-ized data. Thus we investigate the differences inspectral shape only, and not the differences in bright-ness of the samples. On the other hand birch oftencould be recognized from spruce and pine on the basisof only the higher absolute reflectance level, whereasthe reflectances of pine and spruce look alike. Thisis seen in Fig. 3, which shows examples of theabsolute reflectance spectra of pine, spruce, andbirch. However, as pointed out above the in-classvariation is so large that sometimes even the data forbirch and conifers are mixed. We consider the classi-fication of the reflectance data by three methods:CLAFIC, ALSM, and UPA. The original data wasdivided into the training data and the test data. Setsof 185, 175, and 169 arbitrarily chosen spectra of

2358 APPLIED OPTICS / Vol. 33, No. 12 / 20 April 1994

.. ......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . ... .. . . . . . . . . . . . . . .. .. . . . . . .

300

15

0.10

0.05

0.20

15F

10I

0.05

Spruce

.............

_:::::::. . . . ... . . . . . ... . . . .

~~~~~~~~~..... ,......, ,S..

400 450 500 550 600 650 700 750 800 850 900Wavelength(nm)

(a)

Birch

u.uu350 400 450 500 550 600 650 700 750 800 850 9

Wavelength(nm)100

(b)

Fig. 2. The average spectra (a) of spruce and (b) of birch.Maximum positive and negative differences from the average ateach wavelength are shown by the dotted curves.

pine, spruce, and birch, respectively, formed thetraining data, and the remaining 185, 174, and 168spectra were used for testing of the derived classifica-tion filters. Let us start with the two-class problem:distinguishing conifers from birch. Results for thetraining and test data with the CLAFIC algorithm areshown in Tables 2 and 3, respectively. One can notethat the dimension of the subspaces needs to besurprisingly high in order to achieve a probability ofmore than 90% for correct results. In the conifer

aD

C0.,

aua)

0.4

0.3

0.2

0.1

0.03! 400 450 500 550 600 650 700 750 800 850 900

Wavelength(nm)

Fig. 3. Absolute reflectance spectra of pine (solid curve), spruce(dot-dot-dashed curve), and birch (dotted curve).

class the results improve rapidly as the dimension ofthe subspace increases to approximately 12, then thenumber of errors stabilizes. This indicates that thehigher order eigenvectors represent noise in the data.On the other hand the best results for the leafy treeclass were obtained with subspaces of 2 and 3 dimen-sions. These results stem from the low variance inthe birch reflectance data. The reason for the largevariance in the conifer data is that these trees containcrowns from the past four years that are a slightlydifferent color from the current year's crown, and thecolor of the trees depends on environment in whichthe trees grow up. One can note from Table 2 thatthe CLAFIC can classify correctly nearly 90% of allsamples. It is important to note that if the dimen-sion of the subspace representing the birch class iskept low but the dimension of the conifer subspace ishigher, the number of errors increases. Thus thedimension of each subspace was kept equal.

The ALSM offers the means to classify the trainingset correctly. We start from the subspaces deter-mined for unnormalized data, as described above.Iteration according to Eq. (4) leads to correct classifi-cation of the training set, as shown in Table 4. Inthis example the dimension of the subspaces was 11,which gave the best results for our data. The classi-fication results for the test data are shown in Table 5,which summarizes the classification results for the

Table 1. Maximum, Minimum, and Average Percent Errora of Reconstructions for 1056 Spectral Reflectances

Minimum Error (%) Maximum Error (%) Average Error (%)Number of

Eigenvectors Pine Spruce Birch Pine Spruce Birch Pine Spruce Birch

1 1.13 1.70 0.70 51.86 44.75 25.71 7.37 8.36 4.68

2 0.79 0.63 0.49 12.12 15.68 11.18 2.75 3.42 1.88

3 0.58 0.56 0.37 7.02 7.24 5.65 1.75 2.32 1.19

4 0.38 0.51 0.36 4.34 6.34 3.72 1.28 1.62 0.97

5 0.32 0.38 0.29 3.84 6.34 3.31 1.08 1.25 0.79

6 0.25 0.27 0.25 2.45 4.01 2.24 0.91 1.07 0.68

7 0.22 0.26 0.23 1.80 2.52 2.69 0.81 0.93 0.64

8 0.21 0.24 0.20 1.63 2.21 1.49 0.75 0.79 0.59

aThe errors are defined as the absolute values of the difference between the original and the reconstructed spectral reflectances averagedover the wavelength band.

20 April 1994 / Vol. 33, No. 12 / APPLIED OPTICS 2359

0.25

0.20

0.

U,a)

a)

Nl

0z

. . . . . . ..| .| g @ . .PINE:

-:SPRUCE : : : : .

.................... ............ .... .........................

......... .... . ... ....... ... .. . .. .... ....... . ... . . . . .. . .. ..... ......... .

. '. : ' :.. ... ... .: .. '1 '

n An

0.25

na)

0

a)N

0E

0.

0.

. . . . . . ... . . . . . . . . . . . . . . . . ..

...................................

. . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . ..

50

350

Table 2. Classification of the Training Data in the Two-Class Problemwith the CLAFIC Algorithm

Number of Samples

Conifer Classa Birch 2 Classb

Conifer Birch Conifer BirchDimension Spectra Spectra Spectra Spectra

1 228 132 26 1432 249 111 9 1603 243 117 10 1594 223 137 15 1545 229 131 20 1496 261 99 12 1577 269 91 19 1508 293 67 25 1449 302 58 22 147

10 314 46 20 14911 327 33 22 14712 336 24 19 15013 331 29 28 14114 333 27 19 15015 336 24 15 15416 337 23 15 15417 341 19 17 15218 338 22 16 15319 340 20 16 15320 341 19 14 155

aThe total number of samples in the class is 360.bThe total number of samples in the class is 169.

two-class problem. Table 4 shows that a 4.36% errorin the results for the test data remained with theALSM.

Table 3. Classification of the Test Data with the CLAFIC Algorithm

Number of Samples

Conifer Classa Birch 2 Classb

Conifer Birch Conifer BirchDimension Spectra Spectra Spectra Spectra

1 225 134 26 1422 253 106 11 1573 250 109 7 1614 219 140 13 1555 232 127 20 1486 250 109 12 1567 271 88 23 1458 309 50 37 1319 307 52 30 138

10 320 39 33 13511 319 40 30 13812 327 32 25 14313 327 32 39 12914 327 32 33 13515 331 28 30 13816 333 26 29 13917 333 26 32 13618 333 26 28 14019 333 26 27 14120 331 28 24 144

aThe total number of samples in the class is 359.bThe total number of samples in the class is 168.

Table 4. Classification of the Training Set with the ALSM DuringIteration with Eq. 4a

Number of Samples

Conifer Class Birch Class

Iteration Conifer Birch Conifer BirchCycle Spectra Spectra Spectra Spectra

1 283 77 6 1632 285 75 2 1673 294 66 2 1674 295 65 1 1685 290 70 3 1666 294 66 0 1697 304 56 0 1698 311 49 0 1699 319 41 0 169

10 328 25 0 16911 335 25 1 16812 333 27 1 16813 332 28 0 16914 339 21 1 16815 283 77 1 16816 325 35 0 16917 332 28 0 16918 343 17 1 16819 333 27 1 16820 336 24 0 16921 345 15 0 16922 348 12 0 16923 350 10 0 16924 351 9 0 16925 356 4 0 16926 357 3 2 16727 353 7 0 16928 358 2 1 16829 352 8 1 16830 336 24 0 16931 352 8 0 16932 358 2 1 16833 360 0 1 16834 355 5 0 16935 359 1 0 16936 360 0 0 169

aThe dimension of the subspaces is 11.

In the two-class problem the UPA also gives goodresults (see Table 5), as 20 conifer samples weremisclassified to the birch class, and only 5 birch

Table S. Summary of the Classification Results of the Test Data in theTwo-Class Problem

Number of Samples

Conifer Class Birch Class

Misclassified MisclassifiedConifer Birch Conifer Birch

Method Spectra Spectra Spectra Spectra % Error

CLAFIC 319 40 30 138 13.28ALSMa 343 16 7 161 4.36UPA 339 20 5 163 4.74

aDimension of the subspaces was 11.

2360 APPLIED OPTICS / Vol. 33, No. 12 / 20 April 1994

Table 6. Summary of the Classification Results of the Test Data in the Three-Class Problem

Number of Samples

Pine Class Spruce Class Birch Class

Method Pine Spruce Birch Pine Spruce Birch Pine Spruce Birch % Error

CLAFICa 157 13 15 7 154 13 10 5 153 11.95

ALSMa 172 10 3 7 162 5 10 7 161 7.97

UPA 171 4 10 8 161 5 1 5 162 6.26

aDimension of the subspaces was 11.

samples were misclassified as conifers, which yields a95.3% probability the right decision will be made in arecognition test. The UPA is also able to separatepine and spruce samples from each other. In ourtest-data set, eight samples that were known to bepine were classified to the spruce class. Similarly,there were seven misclassifications in the spruceclass. This indicates a 95.8% probability for correctclassification. Similar results were obtained withthe ALSM.

Now consider a three-class problem. We used theabove-mentioned training and test data and con-structed subspaces and classification filters with theaid of the training data. Then the test data wasassigned to one of the three classes (pine, spruce, orbirch). The results followed the trends stated above,and the results of classification are shown in Table 6.The ALSM and the UPA both gave rather goodresults, but now the UPA gave the best classification.However, it is difficult to say which results were thebest possible results of ALSM, because if iteration iscontinued many subspaces from the training set willbe classified correctly, but the test set will not beequally well classified.

The initial base vectors shown in Fig. 1 are shiftedin the learning phase of the ALSM, but the smoothshape of the first base vectors remains. On the otherhand, the classification filters produced with the UPAhave a completely different shape, as is shown inFig. 4.

Conclusions

We have shown that by applying statistical pattern-recognition methods to multispectral reflectance dataof pine, spruce, and birch trees, one can designclassification filters that effectively classify the data.Instead of absolute reflectance information, normal-ized spectral information was used in this investiga-tion. This approach is based on the detection ofspectral shape differences, and thus can distinguishsmall spectral modifications in the data. We haveshown that pattern-recognition methods allow accu-rate discrimination between spruce and pine, whichhave very similar reflectance spectra. On the otherhand, once a large data set for a tree has beenmeasured and the spectral features of the set havebeen extracted, these features could be applied laterto detect changes in the data that possibly werecaused by damage to the trees. This has not beenexplicitly shown in this paper, but other studies have

shown that damage-caused modifications in the rededge of a spectrum of, e.g., spruce seem to be higherthan the differences we see between the spectra ofpine and spruce. Thus our approach can detect thetree type automatically and offers tools for the mea-surement of change within a class.

We have used only few statistical pattern-recogni-tion methods that have proved to be effective forspectral data in other problems. Certainly there are

8000

4000

0

-4000

8000

4000

0

-4000

8000

4000

0

-4000 1-.....

-8000'350 400 450 500 550 600 650 700 750 800

Wavelength(nm)850 900

Fig. 4. The classification filters for pine, spruce, and birchproduced with the UPA.

20 April 1994 / Vol. 33, No. 12 / APPLIED OPTICS 2361

PINE::

. . . .. . . . .

. .SPRUCE- .... . .......... ... ........ .. ........, ... . .

. .. .. . .. . . . . . . . .. . . .

. . . .. . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . ..........

: : :i: :.

.1

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: : : : : : :

.; : , ;

: : : : . : :

: : :* : : - . :

: : :

i .; .; ;. . . . . . . . . . . . ... . . .

. .. .

other methods that could be as good as the methodsused in this study. However, it is important to notethat instead of absolute spectral reflectances, ourmethod detects the spectral shape of multispectraldata at certain wavelength bands. Modifications to aspectrum caused by any reason can be seen easilyfrom such data.

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spruce and Scotch pine, measured from a helicopter," RemoteSensing Environ. 20, 253-265 (1986).

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3. E. Hoque, P. J. S. Hutzler, and H. Hiendl, "Studies onreflective features of Norway spruce and their possible applica-tions in remote sensing of forest damage," Toxicol. Environ.Chem. 27,209-215 (1990).

4. B. N. Rock, J. E. Vogelmann, D. L. Williams, A. F. Vogelmann,and T. Hoshizaki, "Remote detection of forest damage,"BioScience 36, 439-445 (1986).

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statistical pattern-recognition algorithms for hybrid processing.I: Linear-mapping algorithms," J. Opt. Soc. Am. A 5, 1655-1669 (1988).

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9. D. B. Judd, D. L. MacAdam, and G. Wyszecki, "Spectraldistribution of typical daylight as a function of correlated colortemperature," J. Opt. Soc. Am. 54, 1031-1040 (1964).

10. E. R. Dixon, "Spectral distribution of Australian daylight," J.Opt. Soc. Am. 68, 437-450 (1978).

11. T. Jaaskelainen, J. Parkkinen, and S. Toyooka, "Vector-subspace model for color representation," J. Opt. Soc. Am. A 7,725-730 (1990).

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2362 APPLIED OPTICS / Vol. 33, No. 12 / 20 April 1994