Table 1. Parameters, and RMSE (root mean square error) for the best fits between the measured C c IC a 
ratios and the several indices tested. Both power (5) and exponential ( 6 ) functions were computed. 
Indices 
Model 
^2 
a 
b 
Ö 
RMSE 
R 2 
SRPI 
Power 
420 
670 
0.305 
0.003 
5.854 
0.148 
0.977 
690 
705 
0.271 
4.847 
9.127 
0.128 
0.983 
Exponent 
430 
665 
0.306 
267.7 
13.97 
0.199 
0.958 
690 
705 
0.245 
2.3 10 ' 4 
-9.973 
0.127 
0.983 
NDPI 
Power 
420 
670 
0.321 
713.2 
8.625 
0.160 
0.973 
590 
650 
559.6 
560.5 
0.0014 
0.280 
0.917 
Exponent 
420 
670 
0.313 
0.0006 
16.17 
0.153 
0.976 
590 
650 
0.305 
4.087 
34.60 
0.171 
0.969 
690 
705 
0.268 
4.853 
18.30 
0.127 
0.983 
SIPI 
Power 
450 
680 
0.0055 
-0.0053 
0.0006 
0.157 
0.974 
510 
590 
0.0065 
-0.0063 
-0.0003 
0.207 
0.955 
Exponent 
445 
680 
4.44 
-6.7691 
-0.4807 
0.112 
0.987 
505 
690 
4.469 
-5.5665 
-0.2631 
0.139 
0.980 
However, there is still a great symmetry between the power and the exponential models. Three main spectral 
domains showing the greatest interest to estimate the C ( JC a ratio are observed: First, the blue-red domain [450 
nm<li<500 nm, 650 nm <l2<690 nm]. Then, the green-red domain [500 nm<lj<620 nm, 650 nm<l2<690 
am]. Finally the red edge domain [600 nm<lj<700 nm, 700 nm<l2<800 nm]. Because there is no carotenoid 
absorption in the red edge domain, the goodness of the fit is explained here by the strong link observed between 
chlorophyll a and carotenoid concentration as illustrated by figure lb: Carotenoids are roughly linearly linked 
with chlorophyll a concentrations. However, a large scatter appears for low values of pigment concentration. It 
explains most of the variability of C c IC a ratio. It appears that the highest values of the ratio are observed for 
low pigment concentrations. Very poor performances are observed when both reflectances used to compute the 
Pis are in the blue-green spectral domain [400 nm<lj<600 nm, 400 nm<l2<600 nm] where both chlorophyll 
and carotenoid are absorbing concurrently strongly. In the near infrared domains [750 nm<lj<800 nm, 750 
mn<l 2<800 nm] where there is no absorption by the pigments, the fit is of course very poor. 
The semi-empirically derived SIPl pigment index uses a near infrared waveband to minimize the 
structural confounding effects. This band was set to 800 nm. To avoid possible divide by zero problems when 
computing SIPI, we restricted the spectral domain of search for the wavebands set [1 j_, I 2 ] to Pj <750 nm, 
l2<750 nm]. This SIPI pigment index provides the best results as expected. Both power and exponential models 
have very similar performances. However, the highest degree of explanation of the C c IC a ratio variability 
corresponds to the exponential model ( 6 ) in the blue/green and red spectral regions [400 nm<lj<530 nm, 600 
nm<l2<700 nm]. It is in good agreement with our former theoretical considerations: the combination of a 
blue/green band where both carotenoid and chlorophyll absorb simultaneously with the red domain where only 
chlorophyll pigments absorb appeared to be optimal. Further, the greatest variability of C c IC a ratio is observed 
for low pigment concentrations (Fig. lb). It is then expected to be more sensitive and thus more accurate in 
strong absorption spectral regions such as in the blue or in the red. This was confirmed by our experimental 
results for which the best set of wavebands [lj, I 2 ] was [445 nm, 680 nm] both corresponding to in vivo 
maximum absorption of chlorophyll and carotenoid pigments: 
C ( JC a = 4.44-6.77 exp(-0.48 (R 800 -R 445 )I(R 800 -R 680 )) (7) 
Figure 3 shows the relationship between C c !C a and SIPI. It is strongly non linear, with an asymptotic limit 
approached for C c IC a values higher than 10. For low C c !C a values, mostly corresponding to medium to high 
concentrations of pigment, the SIPI expresses lower sensitivity. 
5. CONCLUSION 
This paper shows that the C ( JC a ratio can be estimated accurately from the leaf reflectances measured in the blue, 
red and near infrared spectral domains. Classical indices such as SRPI and NDPI show very good performances. 
Slight improvement is brought here through the SIPI index developed here. It aimed to minimize the surface and 
leaf internal mesophyll structure effects that could be confounded with variations in the pigment concentration. 
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