nondestructive measurement of chlorophyll pigment content in plant leaves from three-color...

Nondestructive measurement of chlorophyll pigment contentin plant leaves from three-color reflectanceand transmittance

Norihide Yamada and Sadao Fujimura

We propose a nondestructive or optical method of measuring the chlorophyll content in a leaf after construct-

ing a mathematical model of reflectance and transmittance of plant leaves as a function of their chlorophyll

pigment content. The model is based on the Kubelka-Munk theory and involves the modeling of themultiple reflection of light in a leaf that is assumed to be composed of a stack of four layers. It also includes

the assumption that the scattering coefficient and the absorption coefficient of the Kubelka-Munk theory canbe expressed as a linear function of the pigment content of a plant leaf. In the proposed method, thechlorophyll content is calculated from reflectances and transmittances at three bands whose center wave-lengths are 880,720, and 700 nm. Experiments were performed to confirm the applicability of the model and

the method. Reflectance and transmittance calculated with the model showed good agreement with mea-sured values. Furthermore, several unmeasurable constants necessary in the calculation were determined by

a least-squares fit. We also confirmed that these results were consistent with several well-known facts in the

botanical field. The method proposed here showed a small estimation error of 6.6 Ag/cm2 over the 0-80 ,ug/

cm2 chlorophyll content range for all kinds of plant tested.

1. Introduction

Recently some nondestructive methods of determin-ing the chlorophyll pigment content of a plant leaffrom its spectral properties were intensively stud-ied.'- 4

Several techniques that use the radiance ratio be-tween two bands have determined chlorophyll pig-ment content accurately. Aoki et al.1 have proposed amethod that uses a reflectance ratio between two nar-row bands at 550 and 800 nm. Minolta Camera Com-pany, Ltd. has developed a hand-held instrument,SPAD-501,2 that uses the transmittance ratio betweena 600-700 nm band and an infrared band. Tucker etal. 3 and Pearson et al. 4 have reported a technique forestimating above-ground biomass by using a reflec-tance ratio between a 650-700-nm band and a 775-

When this paper was written the authors were with the Depart-ment of Mathematical and Information Physics, Faculty of Engi-neering, University of Tokyo, Bunkyo-ku, Tokyo 113, Japan. Nori-hide Yamada is now with the Hewlett Packard Laboratories, 3500Deer Creek Road, P.O. Box 10350, Palo Alto, California 94303.

Received 13 December 1989.0003-6935/91/273964-10$05.00/0.( 1991 Optical Society of America.

825-nm band and have also developed a hand-heldinstrument. Some spectral ratio and spectral curva-ture algorithms have also been reported to estimatechlorophyll concentration in the ocean by remote sens-ing. 5 - 7

The problem remains, however, that these methodsseem applicable to too few kinds of plant, since they arebased only on experimental or phenomenological mod-els and do not take into account the effects of scatter-ing and absorption by other pigments, both of whichvary from leaf to leaf and can cause estimation errors.Their algorithmslA might possibly eliminate the ef-fects to some extent, but the mechanism is not ex-plained.

This problem is caused by the difficulty of modelinglight within a plant leaf that has a complex multilay-ered structure, with layers consisting of scattering andabsorbing material.

Willstatter and Stoll8 (W-S) have explained the re-flectance and transmittance of a plant leaf on the basisof critical reflection of light at the cell-wall-air inter-face of spongy mesophyll tissue (W-S theory). Manyauthors have reported the ray tracing of light through aplant leaf, according to the W-S theory.9- 2

Another approach to explaining the optical proper-ties of leaves is to treat the leaf as a scattering andabsorbing turbid medium. There are several populartheories'3 1 6 to describe the optical properties of such

3964 APPLIED OPTICS / Vol. 30, No. 27 / 20 September 1991

intensely scattering materials, but the Kubelka-Munktheory (KMT)17 is most frequently used. Many ex-tensions of the KMT1'2 2 have been reported.

Seyfried and Fukshansky2 3 have suggested a methodfor calculating the light gradient in a scattering andabsorbing medium such as a plant tissue based on theKMT. This model involves the modeling of light in amultilayered object. Allen and Richardson 2 4 and My-ers and Allen25 have described the reflectance andtransmittance of stacked plant leaves and field plantcanopies by means of the KMT.

The purpose of this paper is to develop a nonde-structive method for the measurement of chlorophyllcontent in a leaf applicable to many kinds of plant. Toestablish such a method, we also constructed a mathe-matical model of reflectance and transmittance ofplant leaves as a function of chlorophyll content.2 6

This model assumes a leaf to be a multilayered object,with layers being composed of macrohomogeneouslyscattering and absorbing turbid medium. It adaptsKMT in modeling for the turbid medium and intro-duces a matrix in modeling for the multilayered object.

11. Theory

In this section we propose a model of the structure ofleaves that is based on actual dicotyledonous leavesand describe two multiple-reflection models, one ofwhich expresses the reflectance and transmittance of amacrohomogeneous layer, where the KMT is adapted,and the other of which represents the multiple reflec-tion and absorption among such multilayers. By com-bining the models we construct a mathematical modelof reflectance and transmittance of a leaf as a functionof chlorophyll content.

A. Structure of Leaves

Leaves are generally composed of several layers. Forexample, as shown in Fig. 1, a dicotyledonous leaf canbe sliced into approximately six layers: upper andlower cuticular layers, upper and lower epidermal lay-ers, a palisade tissue layer, and a spongy mesophylllayer.

Here let us assume that a leaf is composed of fourparallel layers: the upper and lower cuticular layerswith the same optical properties, the palisade tissuelayer, and the spongy mesophyll layer. Multiple re-flection and absorption of light occurs in and amongthese layers. The epidermal layers are thin and areincluded in the palisade tissue layer or the spongymesophyll layer, making the model simpler than if alllayers were considered.

The cuticular layers are made of cutin and do notcontain any pigment; hence there is no absorption.That is, the sum of reflectance and transmittance ofthe cuticular layer is equal to unity. Later, in Subsec-tion III.A, we will assume these values to be constant.

The palisade tissue layer and the spongy mesophylllayer are macrohomogeneous with different opticalproperties as expressed by scattering and absorptioncoefficients. That is, the absorbing and scatteringmaterials such as chlorophyll, other pigments, and

CUTIC L E

CUTICLE /

Fig. 1. Actual structure of a dicotyledonous leaf.

cells are uniformly distributed in them. In SubsectionIII.A we assume that the scattering in the palisadetissue layer is negligible because its tissues are sodensely packed.

Throughout our equations we use the subscripts 0, 1,2, and 3 for quantities that belong to the upper cuticu-lar layer, the palisade tissue layer, the spongy meso-phyll layer, and the lower cuticular layer, respectively.B. Reflectance and Transmittance of aMacrohomogeneous Layer

In this subsection we describe a model of optical prop-erties of macrohomogeneous layers such as the pali-sade tissue layer and the spongy mesophyll layer inwhich radiation is absorbed and scattered.

For any macrohomogeneous layer, the KMT givesthe following differential equations to express the in-ternal radiant energy flowing (denoted by I downwardand Jupward) at point x along the spatial axis (see Fig.2):

- dI(x) = -VI(x) - uI(x) + uJ(x),dx

dxJ(x) (2.1)

where u and v are the scattering coefficient and theabsorption coefficient, respectively, and are assumedto be proportional tovolume:

x=D-X

x=O -

x+dx IX

chlorophyll content m per unit

(X)

I tI J (x)

I +dl tJ+dJ

Fig. 2. Simplified sketch of the radiant energy reflected and ab-sorbed in a macrohomogenous layer.

20 September 1991 / Vol. 30, No. 27 / APPLIED OPTICS 3965

I I t -J

u = ma, v = ma; kz.z)

a and a are proportional constants inherent to thechlorophyll pigment. The solution of Eqs. (2.1) isderived by the KMT and we easily get reflectance r andtransmittance t of the layer from it:

r = U/(A + B cothB),

t = BI(A sinhB + B coshB), if V # 0, (2.3a)

r =UI(1+ U),

t = 1/(1 + U) if V= 0,

where

U = uD, V = vD, A=U+V, B= A2 -L 2 ,

(2.3b)

-U = (u2 -1 = f[(1-)2- t2 1[(1 + r)2 _ t2]11/2 def

-U kU2 2r =''~~)

(2.10)

Here we define the functions A(r,t), tIv(r,t), and'B(r,t): Substituting Eqs. (2.8) and (2.10) into Eqs.(2.7) gives

B = n r'A(r,t) + rB(rt) 2.11)t

The parameter Ucan be obtained from Eq. (2.10) andV from Eq. (2.9) as

U = ln~'B(r,t)(2.4)

1 - r'A(r,t) + r'B(r,t)t

and D denotes the thickness of the layer. Equations(23.b) apply to the optical properties of the spongymesophyll layer at wavelengths with no absorption.When U = 0, Eqs. (2.3a) reduce to

r = 0,

t =exp-V if U = 0. (2.3c)

Equations (2.3c) apply to the nonscattering palisadetissue layer.

Not only chlorophyll pigment but also other kinds ofscattering and absorbing material are contained in aleaf. Therefore we have to add the contribution termsUo and Vo from such material to Eqs. (2.2):

U=Ma+ U0 , V=Ma + V, (2.5)

where M is the chlorophyll content per unit area.Note that any parameter included in these equa-

tions is not a quantity per unit volume but a quantityper unit area.

In the above discussion, we did not consider thediffuseness of light. The effective optical length de-pends on the diffuseness; hence the proportional coef-ficients o- and a are also dependent on it.13-15,19 Thesecoefficients become larger as the light becomes morediffuse. The coefficients for uniformly diffuse lightare twice as large as those for collimated light.'5"19 Wefix the values of of and a by the coefficients for thediffuse light as the KMT did and introduce a parame-ter 7 into Eqs. (2.5) that represents this effect:

U = nMa + UO, V = Ma + VO. (2.6)

In this case, iq = 1 for perfectly diffuse light and n = 1/2for collimated light.

In preparation for constructing the method, we cal-culate the parameters U and V from r and t.

From Eqs. (2.3a) the following are derived:expB = (U- rA + rB)/Ut,

exp-B = (U-rA-rB)/Ut.

Using Eqs. (2.7) and A2 = B2 + U2, we obtainA = (1-t2 + r') elU 2r = *~~)

and immediately we get

VA (1r) 2 t2 defU U 2r =''~~)

(2.7).

(2.8)

(2.9)

'V(rst) 1 - rA(r,t) + rIB(r,t)*,(rt) t

(2.12a)

here r $6 0 and r + t 0 1 are assumed.If r+ t =lorr=(i.e., V=Oor U=), Uand Vhave

to be calculated from Eqs. (2.3b) or (2.3c), respectively,since the denominators of several equations above be-come zero:

U=rlt, V=O if r+t=1,

U=O, V=-lnt if r=0.

(2.12b)

(2.12c)

In the method described in Section III, Eqs. (2.12a)and (2.12b) will apply to the spongy mesophyll layer atwavelengths with and without absorption, respective-ly, and Eqs. (2.12c) to the nonscattering palisade tissuelayer.

C. Multiple Reflection and Absorption in a MultilayeredObjectWe now have relationships between optical propertiesand chlorophyll content for the palisade tissue layerand the spongy mesophyll layer. Furthermore, cutic-ular layers have been assumed to have simple opticalproperties, that is, ro = r3 = 1 - to = 1 - t3 independentof the chlorophyll content. In this subsection we con-sider the multiple reflection of light among these lay-ers, because each layer has a different optical property.

As is shown in Fig. 3, it is assumed that radiantenergy Io and J 4 are originally incident upon the first(uppermost) layer and the last (lowermost) layer andthat Jo and I4 flow out of the first and the last layers.The light irradiating the kth layer from above is denot-ed Ik, and that irradiating the (k - 1)th layer frombelow is denoted Jk. The reflectance and the trans-mittance of the kth layer are denoted by rk and tk,respectively. The recursion formula among them isexpressed by

- lo 4 tJ6oI0 - , ro to0 J _

1 1 r1 ti 1 -

-i- V I _ __ _ti -_2 r t2

ig 1. Rr t3

Fig. 3. Radiant-energy flow in a four-layered leaf.


Jk rkIk + tkJk+l, Ik+1 = tkIk + rkJk+l-

By introducing 2 X 2 matrices Gk defined as

d 1 [tk -rk2 rk]

we get

[ 'k+11 [ 1= Gk I~J

and the relationshipsimple form

I= [ J*

Here,def

G = G3 G2 G 1Go.

(2.13)

(2.14)

(2.15)

between (U4,J4) and (IoJo) as a

(2.16)

Fig. 4. Model for the structure of a dicotyledonous leaf.

flectance and the transmittance of the inside are ob-tained from the elements (gIij) = GI as

rIa =-g921/9221

(2.17) rIb = 9I12/9221

The reflectance and the transmittance from above(ra = Jo/Io and t = I4/1o, respectively) are calculatedby assuming that J4 = 0. And the reflectance andtransmittance from below (rb = I4/J4 and tb = JJ 4 )are calculated by assuming that Io = 0. These aregiven by

r. =-g 2 1 /g22 , rb = g12 /g2 2, t = t = tb = 1/g2 2. (2.18)

Here gij is the ith element of the matrix G. In ourmodel, generally ra rb because G3G2G1G0 dG0G1G2G3. Transmittances from both sides are equal;that is, t = t = tb, since

91922- 12g 21 = 1 (2.19)

whenever Gk is defined by Eq. (2.14). [See Eq. (2.21)described below.]

When we introduced the recursion formula ex-pressed by Eqs. (2.13), each side of the layer was as-sumed to have the same reflectance and transmittance.For a multilayered object such as a whole leaf, thisassumption is not valid, so the recursion formula andthe matrices G must be written as

JO= r.I0+ tbJ4, I4 = tIo + rbJ4, (2.20)

Gtb (-ra 1)(.1

By using Eq. (2.21), we show the way to obtain theoptical properties of the inside (i.e., the combination ofthe palisade tissue layer and the spongy mesophylllayer) without cuticular layers from those of a wholeleaf. The matrix GI = G2G, for the inside is obtainedby

G = G3 -'GGo-1, (2.22)

where Go and G3 are the matrices for the upper andlower cuticular layers:

G3 =G =[ ro l (2.23)

and Gk-I denote the inverse matrices of Gk. The re-

t4a = (9-1l9I22 glI29I21)/9221

tlb = 1/g922. (2.24)

D. Combined Model

When the chlorophyll content per unit area M of aplant leaf and the parameters (,,flroe,a,Uo,U 2,Vo,V02,P) are given, we can calculate the reflectance fromboth sides and transmittance by the following proce-dures:

(1) First we obtain the absorption coefficient andthe scattering coefficient for each tissue layer from M:

U1 = %1 PMa + U01, U2 = f72(l - P)Ma + U02,

V1 = ' 1PMc+ V01, V2 = fl2(l -P)Ma + V02, (2.25)

where P is the probability of finding chlorophyll pig-ment in palisade tissue and the values of is mentionedin Subsection III.A.1 below.

(2) We calculate rk,tk (k = 1,2) by Eqs. (2.3) fromUk,Vk obtained above.

(3) We create the matrices Gk (k = 0,1,2,3) definedby Eq. (2.14) for each layer and calculate their product,expressed as Eq. (2.17). Note that r3 = r and t3 = t =1- r.

(4) Finally, we obtain r,rb,t by Eqs. (2.18) from theelements of G.

These procedures are sketched in Fig. 4.

111. Method for the Nondestructive Measurement ofChlorophyll Content

In this section we propose a nondestructive opticalmethod to measure chlorophyll content in a leaf, whichis based on the model presented in Section II. Itemploys three narrow bands (<1 nm) at wavelengths of880 nm (e), 720 nm (XI), and 700 nm ( 2). The longestwavelength, Xo, is employed to determine the scatter-ing coefficient. The others are located at the slope ofthe peak of chlorophyll absorption at 679 nm. Thedifferentiation of absorption coefficients betweenthese bands eliminates the contribution from otherpigments.


A. Assumptions for the Method

At this stage, the unknowns are (M;71i,n2,roa,a,Uo0,U02 V01YV02,P). With exceptions of M and P, theseunknowns usually have wavelength dependences. Onthe other hand, we can obtain information about re-flectance and transmittance from both sides. It isimpossible to determine the chlorophyll content withsuch a small number of observation equations becauseclearly there are more unknowns than knowns.

The following assumptions are made for the parame-ters at the wavelengths Xo, X1, and 2 in accordancewith physical and botanical considerations. Theymake it possible to calculate the chlorophyll content.

1. r = 0. 05The cuticular layers have no absorption. Their reflec-tances are caused by discontinuity of refractive indicesat interfaces between the cuticular layer and the airoutside and between the cuticular layer and the insideof the leaf. So their spectral dependence is negligiblecompared with that of pigments.

Also, we can learn from Section II that the reflec-tance of leaves approaches ro when the absorption ofthe pigment inside becomes large. In our preparatoryexperiments, the reflectance was 0.05 + 0.01. We canalso calculate it from the values of the refractive indi-ces. The calculated results are 0.065 and 0.035 whenthe inside of the leaf is filled with air and with leaf sap,respectively. [The refractive index of leaf sap is 1.36,27and that of cuticle is 1.45.28] Both of these resultspermit us to assume that the reflectance of the cuticu-lar layer is constant and is equal to 0.05. This assump-tion is discussed again in Subsection V.B.

2. U1 = andi-r = 1/2Compared with the spongy mesophyll, which includesmany air pockets among nonarranged tissues, the pali-sade tissue is much more densely packed. Thereforethe scattering coefficient of the palisade tissue layer isassumed to be negligible. The W-S theory also impliesthe negligible scattering in the palisade tissue. Thisassumption leads to another assumption: that thelight flowing in the palisade tissue layer is collimated;that is, that '1l = 1/2.

3. U2 ' = U2 /ij2 = Constant

The wavelength dependence of the scattering coeffi-cient can be neglected if the effect of n has been elimi-nated, since scattering is attributed mainly to refrac-tion and reflection at the cell-wall-air interfaces.Hereafter, U' and V' denote U/7 and V/1, respectively.

4. a is Independent of Plant Type

a is a parameter inherent to the pigment chlorophyll,and it generally shows little variation over differenttypes of leaf, although chlorophyll combines with dif-ferent proteins to form a chloroplast. Furthermore,even though four kinds of chlorophyll exist, the ratio ofthe probabilities of finding them in a leaf is almost

Fig. 5. Model shown in Fig. 4 simplified by the inclusion of theassumptions.

constant. This assumption is discussed again in Sub-section V.B.

5. V(Xo) = 0 [i.e., a (X0) = Vi(Xo) = 0] and 72(X0) = 1

The pigments usually contained in leaves are chloro-phyll, carotenoid, and anthocyanin. Xo was selected tobe so far beyond the absorption peaks of all the pig-ments that we can assume that V(Xo) = 0.

We also assume that the spongy mesophyll is scat-tering enough to make the light almost perfectly dif-fused if there is no absorption. This leads to anotherassumption, that 72(XO) = 1. This is not the case forthe other wavelengths that usually have absorption.The scattering makes the light more diffuse; on theother hand, absorption further collimates the light.There generally exists some absorption at both of thewavelengths XA and X2 so that the light in the spongymesophyll is not perfectly diffuse at X, or X2. There-fore it cannot be assumed that 12(X) = 1 or N2(X2) = 1.

6. Vok'(A 1) = V0ok(X 2), i e., Vo,(X )/,qk(X 1) = Vo(2)1k(X2 ), (k = 1,2)Absorption by carotenoid and anthocyanin occurs

near wavelengths of 400-550 nm, which are far shorterthan the 679 nm of the chlorophyll peak. Therefore,even if the absorption of carotenoid and anthocyanin isfinite at XA or X2, their wavelength dependence is negli-gible compared with that of chlorophyll.

B. Algorithm

We can now calculate the chlorophyll content in a leafby the following procedures, using the mathematicalpreparation in Section II and the assumptions de-scribed above. Figure 5 shows the model simplified bythe inclusion of the assumptions. The algorithm is asfollows:

(1) Measure ra, rb, and t (= ta = tb) integrated overa hemisphere at each wavelength of X0 (880 nm), XA(720 nm), and X2 (700 nm). ta(X1) = tb(Xl)(l = 0,1,2) isalways satisfied in our model. Therefore, if ta(XI) andtb(XI) are measured and found to be unequal, set t(Xl)as their average. Furthermore, our model shows ra=rb at a wavelength with no absorption. If ra(Xo) #rb(XO) in the measurement, then the following correc-tions are made for all wavelengths: The measuredvalues r,(Xi) and rb(Xl) (1 = 0,1,2) are replaced by


ra(Xo) + rb(XO) r(Xo) + rb(Xo)

2ra(Xo) a(Xi), 2rb(XO) rb( )

respectively. These corrections are made according tothe consideration that the differences between ra(Xo)and rb(XO) and between ta(Xi) and tb(Xl) are induced bythe incomplete integration by the integrating sphere.

(2) At each wavelength, calculate the matrix GIinside cuticular layers, by Eqs. (2.21)-(2.23) and r =0.05.

(3) Calculate U2'(X0 ) by Eqs. (2.12b) and (2.24)from GI(o):

U2 '(XO) = U2(XO) = r(XO)/t(XO) = gI1 2(X0 ). (3.1)

Here note that rj(Xo) = ra(Xo) = rb(AO), V(XO) = 0, and?72(XO) = 1.

(4) Calculate t, r2 and t2 from GI at k (k = 1,2throughout this section).

tl(Xk) = [-gz21(Xk)/9I12(Xd]

r2(Xk) = 9I12(Xk)/9I22(Xk)'

t2(Xk) = [-g~l2(Xk)/gI2l(Ak)1 /gI22(k)- (3.2)

Here note that

1 [t12(t 2

2- r2

2) r2] 33G = G2G = tt [ -t

2r2 1 (3-3)

since Ul = 0, that is, r = 0.(5) Calculate V1' = V,/1q by Eqs. (2.12c) and V2' =

V2/A2 by Eqs. (2.9) or (2.12a) at X, and X2:

vl'(Xk) = - t(Xk) = 2 ln t(Xk), (3.4)?71 (Xk)

U2'(XO)V2'(Xk) = V2(Xk) U v() [r2(Xk),t2(X)1 U2 (O)

[1 - r2(Xk)]2 - t(Xk)22 r2 (Xk)

Note that ql(Xk) = 1/2 and U2(Xk)/n2(Xk) = U2'(Xk) =U2'(XO).

(6) Differentiate V'(Xk) between X, and X2:def

AVk' = Vk'(X2) - Vk'(Xl). (3.6)

This procedure eliminates the contribution from V,that is,

AV1 '= V19(X2) - Vl'(Xl) = [a(X2) - a(Xi)]PM

+ [V011(X2) - o'(1\0]

[a(X2) - a(X1)]PM, (3.7)

AV2' = V21(X2 ) - V2'(X1) = [a(X2) - a(X1)](1 - P)M

+ [V02'(X2) -V2'(Xl)]

[a(X2) - a(X)(1 -P)M. (3.8)

(7) Calculate M by eliminating P:

M = O(AV1' + AV21) (3.9)

Heredef= 1/[a(X2) -a(l)]. (3.10)

Note that the parameter ,B is independent of plant, as isa.

IV. Experiment and Results

To confirm the validity of our model, we measured thespectral reflectance from both sides and the spectraltransmittance of leaves of hydrangea and chinquapin,which are dicotyledonous, and leaves of rice and drag-on tree, which are monocotyledonous. The wave-lengths ranged from 360 to 900 nm in 20-nm incre-ments. The reflected or transmitted light must beintegrated over a hemisphere. In the reflectance mea-surement, an integrating sphere was attached to themonochromator. In the transmittance measurement,the light is integrated by locating the leaf close to thephotodetector (photomultiplier).

The chlorophyll content per unit area of each leafwas also measured by a direct destructive measure-ment29 and found to vary over a 0-80-_Ag/cm2 range,even for the same type of leaf.

Reflectance and transmittance as functions of chlo-rophyll content are shown in Figs. 6(a) (880 nm) and6(b) (720 nm). The curves are model predictions, andthe symbols are measurements made on hydrangealeaves. Good agreement between them indicates thevalidity of the model. Good agreement was seen forany type of plant at any wavelength.

Several unmeasurable constants were necessary inthe calculation, and their values were determined by anonlinear least-squares fit. We fixed the values of qequal to unity since they make products and have toohigh a correlation with other parameters for a stableleast-squares fit. This makes the estimates of scatter-ing and absorption coefficients somewhat smaller thantheir correct values. We can, however, determine thequalitative characteristics of the coefficients, whichare sufficiently useful. Figure 7(a) shows the spectralproperties of a, Fig. 7(b) shows Vol and V02, and Fig.7(c) shows Uol and U02 for hydrangea. Similar resultswere seen for all other types of plant. These resultsmean that the spectral absorption coefficient of chlo-rophyll pigment takes its maximum peaks at -440 and-680 nm, that the absorption coefficient of other pig-ments contained in a leaf is large for blue and greencolor, and that the palisade tissue has negligible smallscattering compared to the spongy mesophyll.

These are well-known facts in the botanical field.30'31Also, was determined to be negligible at any wave-length; that is, chlorophyll pigment shows little scat-tering. af is considered to be much smaller than thescattering attributed to cell-wall-air interfaces, al-though chlorophyll pigment shows a little scattering oflight since it forms a chloroplast in a leaf. We notethat the large values of Uo, at wavelengths longer than720 nm have no importance because there is no absorp-tion (i.e., V1 = V2 = 0) there. When V, = V2 = 0, theoptical properties of a leaf are functions of Uo1 + U02


0 20 40 60 80

Chlorophyll content(a)

0.0

0.2 c,

0.4.

0.6 EC',Ccc

0.8 FH

1.0

:I.

?e

0.3

0.2

0.1

0.0

(pg/cm2 )

0 20 40 60 80

Chlorophyll

0.0 5.0

C0.2 as

._

0.6 EC0

0. 8 H-

4.0

3.0

2.0

1.0

0.01.0

content (pg/cm 2 )(b)

Fig. 6. Reflectance and transmittance of hydrangea leaves at wave-lengths of (a) 880 nm and (b) 700 nm. The symbols show theexperimental data; the curves, the model predictions. Reflectancefrom above is denoted by * and the lower solid curve, reflectancefrom below by 03 and the dashed curve [in (b) only], and transmit-tance by * and the upper solid curve.

but not functions of either of them separately; there-fore it is impossible to determine Uo1 and U02 separate-ly by a least-squares fit.

The experimental results of the nondestructive mea-surement of chlorophyll by our method are shown inFig. 8. The value of a necessary for the method waspreviously determined by a linear least-squares fit (theregression model is M = I3AV + error) using the dataobtained for several sampled leaves. The root-mean-square error was 6.6 gg/cm 2, and the correlation coeffi-cient was 0.98 over a 0-80-_g/cm 2 range.

V. Discussion

A. Number of Layers

We have assumed that a leaf is composed of four paral-lel layers. More complex models involving, for exam-ple, consideration of more layers, assumption of un-parallel structure, or adaptation of the extendedmodels of KMT might be closer to reality or describethe optical properties of leaves better. But their com-

2.0

S 1.0

0.0

400 500 600 700 800 900

Wavelength (nm)

(a)

400 500 600 700 800 90(

Wavelength (nm)

(b)

II I I

I -- I I

/ ~~~~~~~.

400 500 600 700 800 900

Wave I ength (nm)

(c)

Fig. 7. Spectral characteristics of (a) a, (b) Vo1 (solid curve) and V02(dashed curve), and (c) U01 (solid curve) and U02 (dashed curve)determined by a least-squares fit for hydrangea leaves.

plexity also makes it impossible to determine the chlo-rophyll content in a leaf because many additional coef-ficients become included in the models, which areusually impossible to determine or even to assume orapproximate.


p .0

i a a_ < _

I I

1.0

as 0.8

cc 0.6

a0 0.4.

9+-

r 0.2

0.0

1.0

,, 0.8

co 0.6

a' 0.4.

9+-a)G 0.2

0.0

I II I

II I

II I ~ r-- --__

l

l l l

I

25 50True Content

75(pg/cm 2

Table 1. Values of P and ra (360 nm) Determined for Each Type of Plant

A (Ag/cm2

)XA = 720 nm, A = 722 nm,

Plant A2 = 700 nm X2 = 704 nm ra (360 nm)

Hydrangea 20.1 - 0.056 + 0.3Chinquapin 22.6 53.4 0.055 + 0.2Dragon tree 18.0 56.4 0.055 + 0.6Rice 15.7 - 0.043 + 0.5

c)i

EC,1

cm

100

Fig. 8. Results of the nondestructive measurement by the methodproposed in this paper. , 0, , and 0 denote results for hydran-gea, chinquapin, rice, and dragon tree, respectively.

On the other hand, if we make the model simpler, wecannot give enough explanations for the optical prop-erties of leaves. For example, models in which fewerinside layers are considered cannot describe the differ-ence between reflectances from above and below,which is especially significant in dicotyledonousleaves. Of course, our model is applicable to a leafwith a simpler structure, for example, two indistin-guishable tissue layers. (In this case, both V, and U,equal zero in our model.)

Therefore we recognize our model as having reachedthe limits of complexity and simplicity for the purposeof determining chlorophyll content in a leaf.

B. Dependence of 3 on Plant Type

In our model, ,3 is assumed constant over plant types;however, it is actually slightly dependent on planttypes for the reason given in Subsection III.A.4.

To check the validity of this assumption, we calcu-late a by the linear least-squares fit for each plant type.The values of ,3 are shown in Table I. It can be seenthat variation of f3 is distributed +20% around 19 Mg!cm 2 .

This variation is caused not only by the variation ofthe spectral characteristics of chlorophyll itself butalso by the spurious change of , which is due to severalother factors. We will consider two other factors.

One is the error included in the direct destructivemeasurement, which is not random but is dependenton plant types. Several factors may cause such anerror, but it is definitely related to the hardness ofleaves, that is, the difficulty of extracting chlorophyllout of leaves. We got the impression from the experi-ment that rice leaves are especially hard to grind (thisresults in a small amount of chlorophyll and a smallerOl). However, we did not find a quantitative explana-tion.

The other factor is the invalidity of the assumptionfor the reflectance of the cuticular layers r0, which wasassumed to be 0.05 although it is distributed 0.01

-4-CCD

C0C-)

al

E

U')

LUJ

100

75

50

25

00 25 50

True ContentFig. 9. Simulated results for the method proposed in this paperwhen the true ro varies from 0.03 to 0.07.

around 0.05. When the reflectance of the whole leaf ismuch larger than r, this factor causes a small error.However, as the chlorophyll content increases and re-flectance of the whole leaf approaches that of cuticular,the error increases rapidly. This is shown by a simula-tion in which the error is calculated as a function of Mvarying from 0 to 80 ,ug/cm2 when the true r is 0.03-0.07, as shown in Fig. 9. Here the other parameters(772,ae^,U02,Vo,Vo2,P) are constant and equal to thoseof an average hydrangea leaf. Furthermore, it can beseen that the error increases as the true r0 becomes farfrom 0.05. The error is negative when the true r islarger than 0.05 (this gives us a larger estimate of fi);the error is positive when the true r is smaller than0.05 (this gives us a smaller estimate of A). The esti-mate of a is 11% larger and 11% smaller when the true rois 0.07 and 0.03, respectively.

Table I also shows r (360 nm) for each type of plant.At 360 nm, absorption inside is strong. Consequently,ra (360 nm) can give us some qualitative ideas about ro,although it is not exactly equal to r. The noticeablysmall values of rice leaves are consistent with the smallA for them.

Further investigations are necessary to eliminate thelatter factor completely. One notices, however, thatsuch errors can be reduced by using wavelengths atwhich chlorophyll absorption is smaller; that is, reflec-tance of a leaf is still much larger than r even whenchlorophyll content is large.


100"rJ

0

-0

E

LU

75

50

25

/

Cd/

0 /ag

/ U

lo O/ ad up0 /0' **/ 0

hi 0p ,OWN

g10/ -F91. 0e-0I

0 0

75(pg/cm 2 )

100

i {

I

0.6

;.T-0.44-

- 0.2ac:)

0--C _

Oh I o

20rophyl I

4-0 60 80Content M (pg/cm2 )

Fig. 10. Reflectance from above r as a function of chlorophyllcontent M at wavelengths of 740, 720, 700, and 680 nm. Curves aremodel predictions obtained in Section IV.

We made additional measurements, using wave-lengths of 722 and 704 nm at which absorption issmaller. Unfortunately, rice and hydrangea were notavailable at this time. The values of ,B obtained by theleast-squares fit for each type of chinquapin and drag-on tree are shown in Table I. It can be seen that 3 isalmost the same for two types. Note that A is larger inthis case because of small absorption coefficients (andalso because of a smaller difference between Xi and X2).

Considerating these factors, we conclude that thevariation of spectral properties of chlorophyll has nomajor effect in our method. When we eliminate mostof the other major factors, the variation of spectralproperties of chlorophyll will become a major factorand further studies focusing on this variation will benecessary. Still, this variation would possibly give thelimit of accuracy of any optical method as long as we donot destroy leaves and chloroplasts to extract chloro-phyll pigment separately.

C. Selection of the Wavelengths Employed in the Method

We discuss the selection of wavelengths with chloro-phyll absorption, X2 and X1. Here we consider only rabecause ra shows the most noticeable characteristics inra, rb, and t. Figure 10 shows ra versus M at wave-lengths of 740, 720, 700 and 680 nm. At these wave-lengths the absorption coefficients of chlorophyll arelarger when wavelengths are shorter. The lines wereobtained by the least-squares fit in Section IV. It canbe seen that

(1) At wavelengths with large absorption coeffi-cients, r first decreases rapidly, approaches r, andfinally shows only a small change;

(2) At wavelengths with small absorption, r de-creases slowly and remains much larger than rothroughout.

as M increases.A rapid change of ra is acceptable for the measure-

ment, while a slow change is not acceptable because a

small measurement error generally has a large effect onthe results in the latter case. Furthermore, the effectof error in r0 (mentioned in Subsection V.B) becomeslarger as ra approaches ro.

Therefore the selection of wavelengths is a trade-off;that is, one loses accuracy at large chlorophyll contentsand gets accuracy at small chlorophyll contents if oneselects wavelengths with large absorption coefficients,and one gets relatively low accuracy over the wholerange if one selects wavelengths with small absorptioncoefficients. The optimum wavelengths can be select-ed by further studies for a given range of chlorophyllcontent.

The bandwidths employed in this method are rela-tively narrow, less than 1 nm. Wide bands usuallyreduce errors in the reflectance and transmittancemeasurements. However, they also reduce the linear-ity between absorption coefficient and pigment con-tent ( Vversus Min the model), especially for Xi and X2-Further studies are necessary to apply this method towider bands.

VI. Conclusions

We have presented a mathematical model of reflec-tance and transmittance of a plant leaf as a function ofchlorophyll content. The leaf was assumed to be com-posed of a pile of four parallel layers, the layers beingcomposed of macrohomogeneous scattering and ab-sorbing material described by the Kubelka-Munk the-ory.

We have developed a nondestructive method to de-termine chlorophyll content from reflectance andtransmittance at three spectral bands. This method issuperior where results are little affected by the varia-tions of scattering properties and other pigments, andthe mechanism is clearly explained.

We have checked the validity of our model and ourmethod by experiments that include measurements ofspectral reflectance and transmittance of plant leavesand direct destructive measurement of chlorophyllcontent. The estimation of chlorophyll content by ourmethod resulted in a root-mean-square error of 6.6 Ag!cm2 and a correlation coefficient of 0.98 over four kindsof plants with chlorophyll content ranging from 0 to 80,Mg/cm2. These results show that our method has highaccuracy and can be applied to many kinds of plant.

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