lated for each thickness. For each wavelength and thickness the standard deviation was calculated
based on the ten replications.
3. Results and discussion
3
.
1
. Comparison of the optical configuration In Table 1, a series of regression models is given
for the prediction of the soluble solid content of ‘Elstar’ apples for both the bifurcated and the
0°45° configurations. Choosing the best model is difficult, since it depends on a number of parame-
ters: the root mean squared error of prediction and calibration RMSEP and RMSEC, the dif-
ference in explained y-variance between the cali- bration and the validation set, the difference
between RMSEP and RMSEC, the correlation coefficient between the predicted and the mea-
sured values, the number of latent variables, etc. Lammertyn et al., 1998. Full cross validation is
used to validate the models. RMSEP and RM- SEC are defined as follows:
RMSEP = 1
I
p
− 1
I
p
i = 1
yˆ
i
− y
i
− bias
2
7 RMSEC =
1 I
c
− 1
I
c
i = 1
yˆ
i
− y
i 2
8 with yˆ
i
= predicted value of the i-th observation;
y
i
= measured value of the i-th observation; I
c
= number of observations in the calibration set;
I
p
= number of observations in the validation set
and bias =
1 I
p I
p
i = 1
yˆ
i
− y
i
. Amongst the different models based on spectra
taken with the bifurcated optical fibre Table 1, the model with MSC treatment has a low RMSEP
value 0.55 and a small difference between RM- SEC and RMSEP. A large difference indicates
that the calibration set does not represent the validation set. The correlation coefficient between
measured and predicted values equals 0.91 Fig. 2. Models based on data with other pre-treat-
ments require one or two extra variables to reach the same prediction properties.
With regard to the models calculated for the 0°45° configuration, two points should be noted.
First, model 6 with MSC-treatment gives a good RMSEP, a low number of latent variables and a
small difference in explained y-variance between
Fig. 2. The predicted versus the measured SSC values of the validation set, for model 1, measured with the bifurcated optical fibre.
Fig. 3. Reflectance spectra of the different backgrounds.
calibration and validation set. However, models based on the second derivative of the spectra
have, in general, low RMSEP and RMSEC values and a high correlation coefficient. The second
point concerns the scree plot of the residual y- variance as a function of the model complexity.
For the 0°45° configuration, this plot is charac- terised by a sharp peak as the minimum, which
makes it easy to choose the optimal number of latent variables. For the bifurcated fibre this plot
has an exponential curvature. The choice of the number of variables is not so easy.
A calibration set of 60 apples is rather small, but since only 5 – 7 latent variables were used to
construct the models, there are still ten times more samples than variables. This is in agreement
with a statistical rule of thumb, which says that the ratio of the number of samples to the number
of variables should be equal to or larger than 10. However, the purpose of this experiment was not
to construct a general calibration model, but rather a comparison of two optical configurations.
Despite the small number of calibration samples the results are comparable with those found in
literature for the non-destructive measurement of the sugar content in apples. Bellon-Maurel 1992
constructed a SSC-model with five latent variables and a correlation coefficient between predicted
and measured SSC values of 0.84. Lammertyn et al. 1998 obtained correlation coefficients for
SSC predictions between 0.8 and 0.9 depending on the data pre-treatment and the number of
latent variables.
A comparison of the data in Table 1 reveals that the models based on measurements with the
bifurcated cable are only marginally better than those based on measurements with the 0°45°
device.
3
.
2
. Skin reflectance and transmission properties These results were calculated based on the sim-
plified equation for reflectance of a thin layer. Filling in the results obtained with the simplified
equation in the extended equation, gives a mea- sure of the error made by simplifying the model.
Depending on the wavelength and the back- ground, this simplification results in an error of
1 – 11, which is acceptable.
Fig. 3 shows the spectra of the different back- grounds. The black background is not perfectly
absorbing and the white background is not com-
pletely reflecting the incident radiation. The green background has a low reflection at 692 nm, which
is the typical absorption wavelength for chloro- phyll. The white and the green background also
shows water absorption bands at 1495 nm. The wood has in addition a high absorption at 1180
nm, another typical water absorption band.
Fig. 4 shows the inherent skin reflectance, r
skin
, of a green and a red piece of apple skin as a
function of the wavelength. For different combi- nations of two backgrounds e.g. black and white,
black and green, green and wood the Eqs. 5 and 6 were solved to obtain the skin parameters,
r
skin
and t. The r
skin
values obtained from different measurements fall close to each other for one
colour of the skin. On average, the red skin gives higher inherent skin reflectance values than the
green one in the NIR, but not in the visible spectrum. Also the chlorophyll absorption 692
nm is higher for the green skin, since the red side of the apple has experienced more sunlight and
has lower chlorophyll contents.
The transmission, t, is plotted as a function of the wavelength for green and red apple skin Fig.
5. The thin curves indicate the calculated values for t. The two thick curves are the mean transmis-
sion curves. For the green apple skin, the mean transmission curve is strongly influenced in the
colour range 400 – 700 nm. The mean t values for the two skin colours are almost equal. At first
sight, the two means seem to be quite different, but taking only the NIR-range 800 – 2000 nm
into account, t for the green skin is only a vertical translation compared to the red skin, which indi-
cates that there is no large difference in transmis- sion properties of the red and the green skin. This
additive effect is caused by light scattering Williams and Norris, 1987 and can be corrected
by MSC-correction techniques or by calculating a second derivative spectrum.
Fig. 6 shows the reflectance spectra for the red apple skin with white and black background.
Since the reflectance of a black background is very small, the reflectance of the red apple skin
has to be equal to the reflectance spectrum of the skin with the black background. This result also
shows that background information can be found in a NIR-spectrum, since the spectrum is depen-
dent of the background, and the fact that t differs from zero proves that light is penetrating through
the skin. The area between the curve of the aver- age inherent reflectance of the red skin and the
Fig. 4. The skin reflectance r
skin
of green and red apple skin.
Fig. 5. The transmission spectra t
2
of green and red apple skin.
Fig. 6. The influence of the background on the reflectance spectra of red apple skin.
reflectance spectrum of that skin with a certain background is an indicator of the amount of
information coming from the background. Thus, it can be concluded that the amount of information
from the background exceeds the amount of information from the skin. This experiment was
also performed with a piece of apple tissue as background, and led to the same conclusions.
3
.
3
. Penetration depth as function of the wa6elength Fig. 7 shows the spectra of the apple slices with
varying thickness. The spectra of the thinnest slices are situated at the bottom, indicating a low
relative reflectance. Thin slices transmit more and thus reflect less radiation than thicker ones. The
spectra on top represent the thicker slices. In the range from 500 to 1300 nm there is a clear
difference between the spectra with different thickness. However, in the 1300 – 1900 nm range,
the spectra are close. This will have its influence on the determination of the penetration depth in
this region, as discussed later. On top of the spectra a converging tendency is noticed. The
spectrum of the thickest slice is taken as a refer- ence spectrum R
ref
l to which the spectra of slices with thickness u, called Rl,u are com-
pared. For R
ref
, u equals 3.5 cm. This thickness is assumed not to transmit the incident light. This
assumption is confirmed at the end of the experi- ment. For each wavelength l, the R
ref
lRl,u ratio is calculated as function of the thickness u.
The ratio tends to 1 for increasing values of u. Fig. 8 shows the measured R
ref
lR l,u values as a function of u for the wavelength l = 900 nm.
In a next step, a non-linear model of the form gl,u = 1 + al·exp − bl,u
9 with al, bl parameters of the equation;
gl,u, the fitted value for the R
ref
lRl,u ra- tio, and u, the thickness of the apple slice, is fitted
to the measured points, using the least squares procedure in MATLAB, The MathWorks Inc.,
Natick, MA. Theoretically, the intersection point of the fitted curve with the line y = 1, corresponds
to the penetration depth, of the wavelength under investigation, into the apple tissue. However, in
practice, noise on the measurements should be taken into account. This is done by the construc-
tion of an interval around 1. The variance of gl,u = R
ref
lRl,u value is approximately equal to:
Vargl,u =
g¯l,u
2
R
ref
l
2
VarR
ref
l + g¯l,u
2
R l,u
2
VarRl,u 10
The average values are based on ten replicate measurements. In practice the defined variance is
dependent on the thickness, u, of the apple slice. However, this relationship is of minor importance
Fig. 7. Reflectance spectra of apple slices with varying thickness.
Fig. 8. Derivation of light penetration.
Fig. 9. NIR radiation penetration depth in ‘Jonagold apple’ green side.
and hence neglected for reasons of simplicity. Since the probability density function of gl, u is
unknown it is not obvious how to construct confi- dence intervals. Therefore a value of 2.5 times the
standard deviation was chosen to calculate the size of the interval around one. If gl, u had a
standard normal distribution, this value would indicate a 99 confidence interval. For each
wavelength an average variance is calculated over- all thicknesses. The maximum penetration depth
is then defined as the value for which: gl, u = 1 + 2.5
1 n
n i = 1
Vargl, u
i
11 where n is number of slices with different thick-
ness. Fig. 8 shows the upper limit for l = 900 nm thin full straight line.
The calculated penetration depths are pre- sented in Fig. 9. A maximum penetration depth
of almost 4 mm was observed in the wavelength rangebetween 700 and 900 nm. A minimum of 2
mm was located around 692 nm. The chloro- phyll absorption peak is situated at this wave-
length. Chlorophyll is a strong absorbing skin component,
explaining the
low penetration
depth at this wavelength. For higher wave- lengths the penetration depth fluctuates between
2 and 3 mm. As shown in Fig. 7, the relative reflectance
values for wavelengths between 1400 and 1500 nm are low, since this is a very strong water
absorption band in NIR-spectroscopy. Small in- evitable changes in water content due to dry-
ing of the slices during the measurements can influence the gl, u value considerably in this
wavelength region. This drying effect mainly ap- plies to relatively thin slices and not for thicker
slices, since a thick slice dries less quickly. Dur- ing the experiments a small black box cover was
used to prevent the slices from drying by air movement. Since all tests were performed over a
short time period 20 min, the temperature was considered constant. But even then the signal-to-
noise ratio in this region calculated as gl, u vargl, u was up to 40 times smaller than
in other regions. The ratio equalled 2.5 for the 1400 – 1500 nm wavelength ratio. This source of
large error led us to discard the points in wave- length region between 1400 and 1500 nm for
thin slices for the calculation of the penetration depth. These points influence the fit of the
model
and thus
the calculated
penetration depth.
The calculated
penetration depth
as shown on Fig. 9 is in fact a conservative result,
since a 99 pseudo-confidence interval was con- structed around 1 Eq. 11. A factor of 1.96
95 pseudo-interval would have given higher penetration depths of NIR radiation into fruit
tissue.
4. Conclusion
