Postharvest Biology and Technology 18 (2000) 121 – 132
www.elsevier.com/locate/postharvbio
Light penetration properties of NIR radiation in fruit with
respect to non-destructive quality assessment
Jeroen Lammertyn a,*, Ann Peirs a, Josse De Baerdemaeker b, Bart Nicolaı̈ a
b
a
Katholieke Uni6ersiteit Leu6en, Flanders Centre for Posthar6est Technology, Willem de Croylaan 42, 3001 He6erlee, Belgium
Katholieke Uni6ersiteit Leu6en, Department of Agrotechnique and -Economics, Kardinaal Mercierlaan 92, 3001 He6erelee, Belgium
Received 21 January 1999; accepted 11 October 1999
Abstract
Some issues related to the non-destructive measurement of apple quality attributes by means of NIR reflectance
spectroscopy are addressed. A comparison was made between two optical configurations, which can be used to
perform NIR-spectroscopic measurements: the bifurcated and the 0°/45° optical configuration. A relationship was
established between the reflectance spectra (880–1650 nm) and the soluble solids content by means of the partial least
squares technique. Depending on the data pre-processing method, correlation coefficients between 79 and 91% were
obtained. The results obtained with the bifurcated fibre were only marginally better than those obtained with the
0°/45° configuration. The apple skin reflectance and skin transmission properties with regard to NIR radiation were
also investigated. The intensity of the light source was high enough to penetrate through the apple skin and gather
information about the apple parenchyma tissue. A method was developed to calculate the light penetration depth for
each wavelength in the range from 500 to 1900 nm. This method was applied to measure the light penetration depth
in ‘Jonagold’ apple fruit tissue. The penetration depth is wavelength dependent: up to 4 mm in the 700 – 900 nm range
and between 2 and 3 mm in the 900–1900 nm range. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Quality; PLS; Light penetration; Sugar; Optical configuration; Apple
1. Introduction
In recent years research has been focused on the
development of non-destructive techniques for
* Corresponding author. Tel.: +32-16-322376; fax: + 3216-322955.
E-mail address: [email protected] (J.
Lammertyn)
measuring quality attributes of apples such as pH,
sugar content and firmness. The advantages of
these techniques include fast execution, limited
sample pre-processing and easy use in process
control and grading systems. NIR-spectroscopy is
one such technique, and NIR methods have already been used to detect bruises on apples (e.g.
Pen et al., 1985; Upchurch et al., 1994). Kawano
et al. (1992) studied the sugar content in peaches
0925-5214/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 5 - 5 2 1 4 ( 9 9 ) 0 0 0 7 1 - X
122
J. Lammertyn et al. / Posthar6est Biology and Technology 18 (2000) 121–132
with an optical fibre in interactance mode.
Slaughter (1995) determined that visible and NIRspectroscopy could be used to measure non-destructively the internal quality of peaches and
nectarines as characterised by their soluble solid
(SSC), sugar, sorbitol and chlorophyll contents.
Bellon-Maurel (1992) used the wavelength region
between 800–1050 nm to built a model for sugar
measurement. Recently, Moons et al. (1997) and
Lammertyn et al. (1998) established a relationship
between NIR spectra and apple fruit quality
parameters such as acidity, pH, sugar content and
texture parameters.
For internal quality measurements, it is important that the NIR radiation penetrates the apple
tissue sufficiently, an issue not often discussed in
the literature. Chen and Nattuvetty (1980) investigated the effect of the distance between the light
incident and detection points on the transmittance
and on the depth through which the detected light
penetrated into the fruit. Hother et al. (1995)
followed the changes in reflectance properties of
unpeeled apple disks of varying thickness. They
found that, depending on the variety and the
wavelength, the penetration depth varied between
0 and 7 mm. For ‘Jonagold’ apples, the maximum
depth was 5.5 mm. However, the authors only
considered a wavelength range between 480 and
800 nm. It should also be noted that, even if the
radiation sufficiently penetrates the apple tissue,
reflected radiation due to internal scattering needs
to be separated from that due to specular reflection. Several optical configurations have been
used in the literature, including bifurcated light
guides and 0°/45° configurations. It is not clear
how the configuration affects the quality of the
calibration models.
The objectives of this paper were (i) to compare
two optical configurations for measuring internal
apple quality attributes by means of NIR reflectance measurements, (ii) to obtain fruit skin
parameters which describe the interaction of the
skin and the incident radiation, and (iii) to determine the penetration depth values of NIR radiation in apple tissue for the wavelengths between
500 and 1900 nm.
2. Materials and methods
2.1. Fruit
Apples (Malus domestica Borkh. cv. Elstar)
used for the first experiment were purchased at a
local auction and stored for 2 days at 20°C and
70% relative humidity to equilibrate. For the calibration models, 60 apples were used. From each
apple, four spectra (880–1650 nm) with the bifurcated and with the 0°/45°-configuration (see further) were taken at exactly the same position. The
soluble solids content, which is strongly correlated
with the sugar content, was measured at the same
positions with a digital refractometer (PR-101
Palette Series, ATAGO CO., Ltd., Japan).
‘Jonagold’ apples, used for the light penetration
experiments, were also purchased at a local auction and measured after 2 days of equilibration at
20°C and 70% relative humidity.
2.2. Reflectance measurements
For each apple, four reflection spectra (880–
1650 nm, wavelength increment 0.5 nm) were
taken at four equidistant positions around the
equator, with a spectrophotometer (Optical Spectrum Analyser (OSA) 6602, Rees Instruments
Ltd., Godalming, UK). The light source consisted
of a 12 V/100 W tungsten halogen lamp (Philips
7724.M/28) that could be used both in the visible
and near infrared region. Two different optical
configurations were used. With the bifurcated optical configuration (type MIO-6134) the light is
guided to the sample by source fibres, and from
the sample with the detector fibres. In the head of
the bifurcated cable, the source and detector fibres
are situated randomly (Fig. 1(A)). The fibre has
an active surface of 4 mm2 and was held directly
on the skin of the fruit. This has the advantage of
a higher light intensity than a non-contact source.
It can only be used in the wavelength range from
380 to 1650 nm. The 0°/45° optical configuration
(Fig. 1(B)) consists of a black box (type 6151) in
which the source and the detector fibres are positioned at an angle of 45°. The incident beam falls
perpendicularly onto the sample and is detected
under an angle of 45°, to avoid specular reflec-
J. Lammertyn et al. / Posthar6est Biology and Technology 18 (2000) 121–132
tion. Since the illuminated surface is larger, the
intensity will be lower than with the bifurcated
cable for a given light intensity. In both cases the
reflected light is divided into individual wavelengths by the diffracting gratings of the
monochromator. Grating A is used for the wavelength range from 300 to 1080 nm and grating B
for the range 1080– 2000 nm. A silicon detector
was used for the visible and the beginning of the
near infrared range (300 – 1100 nm) and a PbS
detector was used in the NIR range (1000 – 2000
nm). To compare both optical configurations the
0°/45° device was only used in the 880 – 1650 nm
range. The signals were processed with software,
model 6857 v1.30. The configuration was calibrated with a He/Ne laser and a spectrum from a
BaSO4-disc served as reference.
2.3. Measurement of internal apple quality
An average spectrum was calculated for each
apple. The average spectra were pre-processed by
reducing the number of points of measurement
and taking the second derivative using the method
of Savitzky–Golay (Savitzky and Golay, 1964).
The second derivative or multiplicative scatter
correction (MSC) was used to correct for additive
and multiplicative effects in the spectra (Martens
and Naes, 1989). The technique used for the
calibration was partial least squares (PLS) (Haaland and Thomas, 1988). The calculations were
carried out using ‘The Unscrambler’ (CAMO, AS,
Trondheim, Norway), a statistical software package for multivariate calibration.
123
2.4. Skin reflectance and transmission properties
To obtain information about the light penetration properties, an experiment based on earlier
work of Lillesaeter (1982) was performed. Lillesaeter (1982) divided the information in a reflectance spectrum of a leaf into two components:
information coming from the leaf and information coming from the background. In the present
study the leaf surface was replaced by the skin of
the apple and the background corresponded to
the tissue under the skin.
The total reflected radiation (Rtot) consists of
two components: the skin component, Rskin,
which is the radiation reflected by the skin with a
perfectly black background, and a background
component, being the radiation reflected by a
non-black background, changed by transmission
through the skin. With the intensity of the incident light beam and t, the transmission of the
skin, the following formula can be derived:
Rtot = Rskin + Rback = rskinI+ rbackt 2I
(1)
with rskin and rback the reflectance of the skin and
the background, respectively. The transmission
parameter t is squared because the incident light
crosses the skin twice before it is detected. Eq. (1)
is a simplification of the formula for total reflection from a thin layer (Kortüm, 1969). The denominator of the second term (1 − rskinrback) is
omitted here. This can be done when rskinrback 1.
Fig. 1. The bifurcated optical configuration (A) and the 0°/45° optical configuration (B).
J. Lammertyn et al. / Posthar6est Biology and Technology 18 (2000) 121–132
124
Table 1
Survey of the prediction performance of the different calibration SSC models for the bifurcated and the 0°/45° optical
configurationsa
Model
Pre-treatment
Bifurcated optical configuration
1
*10
2
*10
3
*10
4
*10
5
*10
c5
c10
c15
c20
0 °/45 ° optical configuration
6
*10
7
*10
8
*10
9
*10
10
*10
c5
c10
c15
c20
Lat. Var.
RMSEC
RMSEP
Correlation
!
5
7
7
6
7
0.45
0.37
0.43
0.43
0.47
0.55
0.73
0.59
0.57
0.62
0.91
0.85
0.90
0.91
0.88
!
5
7
7
6
5
0.61
0.39
0.52
0.53
0.56
0.72
0.84
0.70
0.65
0.66
0.83
0.79
0.86
0.87
0.87
a
*x indicates the size (x) of the reduction of the original spectrum; c x denotes the half of the interval (x) used for the calculation
of the second derivative using the method of Savitzky–Golay and ‘!’ indicates that multiplicative scatter correction (MSC) has been
applied.
2.5. Penetration depth as a function of the
wa6elength
The total reflectance is defined as:
rtot =
Rtot
= rskin + rbackt 2
I
(2)
Two measurements with a different background
(back1 and back2) are sufficient to solve the equations in the skin parameters t and rskin.
rtot,back1 =rskin + rback1t 2
(3)
rtot,back2 =rskin + rback2t 2
(4)
rtot,back1 − rtot,back2
rback1 − rback2
(5)
rskin =rtot,back1 − rback1t 2
(6)
t=
'
All the measurements for this test were executed with the spectrophotometer as described
above using the 0°/45° optical configuration. For
this test a piece of the red and the green side of
the apple were used. The skin was carefully isolated from the fruit flesh with a razor blade and
used for the measurements with the different
backgrounds.
In a third experiment, the light penetration
depth in apple tissue was evaluated for each wavelength (l) in the range from 500 to 1900 nm. The
test was performed on ‘Jonagold’ apples. The
apple was cut in two and on the green skin side,
ten spectra were taken in the wavelength range
from 500 to 1900 nm with the 0°/45° optical
configuration. During the measurements, the
slices were protected from drying air movement
and external light by a black box cover. Subsequently, a thin slice of apple tissue was removed
with a professional slice cutter (Graef, Germany)
and again ten spectra were taken on the skin side
of the apple. The thickness of the slice was measured with a calliper. This procedure was repeated
several times until all the tissue was removed from
the skin. Finally, ten spectra of the skin were
taken. The different apple slice thickness values
(u) were 3.5, 2.78, 2.48, 2.2, 2.02, 1.68, 1.47, 1.25,
1.15, 1.02, 0.93, 0.82, 0.73, 0.59, 0.43, 0.3, 0.18,
0.1 and 0.04 cm. An average spectrum was calcu-
J. Lammertyn et al. / Posthar6est Biology and Technology 18 (2000) 121–132
'
125
lated for each thickness. For each wavelength and
thickness the standard deviation was calculated
based on the ten replications.
RMSEC=
3. Results and discussion
with ŷi = predicted value of the i-th observation;
yi = measured value of the i-th observation; Ic =
number of observations in the calibration set;
Ip = number of observations in the validation set
and
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 parameters: the root mean squared error of prediction
and calibration (RMSEP and RMSEC), the difference in explained y-variance between the calibration and the validation set, the difference
between RMSEP and RMSEC, the correlation
coefficient between the predicted and the measured values, the number of latent variables, etc.
(Lammertyn et al., 1998). Full cross validation is
used to validate the models. RMSEP and RMSEC are defined as follows:
RMSEP =
'
1 Ip
% (ŷ −yi −bias)2
Ip −1i = 1 i
(7)
bias=
1 Ic
% (ŷi − yi )2
Ic − 1i = 1
(8)
1 Ip
% (ŷi − yi ).
Ipi = 1
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 RMSEC 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-treatments 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.
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J. Lammertyn et al. / Posthar6est Biology and Technology 18 (2000) 121–132
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 yvariance as a function of the model complexity.
For the 0°/45° configuration, this plot is characterised 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 simplified equation for reflectance of a thin layer.
Filling in the results obtained with the simplified
equation in the extended equation, gives a measure of the error made by simplifying the model.
Depending on the wavelength and the background, this simplification results in an error of
1–11%, which is acceptable.
Fig. 3 shows the spectra of the different backgrounds. The black background is not perfectly
absorbing and the white background is not com-
J. Lammertyn et al. / Posthar6est Biology and Technology 18 (2000) 121–132
pletely reflecting the incident radiation. The green
background has a low reflection at 692 nm, which
is the typical absorption wavelength for chlorophyll. 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, rskin,
of a green and a red piece of apple skin as a
function of the wavelength. For different combinations 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,
rskin and t. The rskin 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-
127
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 indicates that there is no large difference in transmission 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 dependent 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 average inherent reflectance of the red skin and the
Fig. 4. The skin reflectance (rskin) of green and red apple skin.
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J. Lammertyn et al. / Posthar6est Biology and Technology 18 (2000) 121–132
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.
J. Lammertyn et al. / Posthar6est Biology and Technology 18 (2000) 121–132
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 reference spectrum (Rref(l)) to which the spectra of
slices with thickness u, called R(l,u) are compared. For Rref, u equals 3.5 cm. This thickness is
assumed not to transmit the incident light. This
assumption is confirmed at the end of the experiment. For each wavelength l, the Rref(l)/R(l,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 Rref(l)/R (l,u) values
as a function of u for the wavelength l =900 nm.
129
In a next step, a non-linear model of the form
g(l,u)= 1+ a(l)·exp(− b(l),u)
(9)
with a(l), b(l) parameters of the equation;
g(l,u), the fitted value for the Rref(l)/R(l,u) ratio, 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 construction of an interval around 1. The variance of
g(l,u)=Rref(l)/R(l,u) value is approximately
equal to:
Var(g(l,u))
=
(ḡ(l,u))2
(ḡ(l,u))2
Var(Rref(l))+
Var(R(l,u))
2
(R( ref(l))
(R( (l,u))2
(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.
130
J. Lammertyn et al. / Posthar6est Biology and Technology 18 (2000) 121–132
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 g(l, u) is
unknown it is not obvious how to construct confidence intervals. Therefore a value of 2.5 times the
standard deviation was chosen to calculate the
size of the interval around one. If g(l, u) had a
standard normal distribution, this value would
indicate a 99% confidence interval. For each
wavelength an average variance is calculated overall thicknesses. The maximum penetration depth
J. Lammertyn et al. / Posthar6est Biology and Technology 18 (2000) 121–132
is then defined as the value for which:
'
g(l, u)= 1+ 2.5
1 n
% Var(g(l, ui ))
ni = 1
131
penetration depths of NIR radiation into fruit
tissue.
(11)
where n is number of slices with different thickness. Fig. 8 shows the upper limit for l =900
nm (thin full straight line).
The calculated penetration depths are presented 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 chlorophyll absorption peak is situated at this wavelength. Chlorophyll is a strong absorbing skin
component, explaining the low penetration
depth at this wavelength. For higher wavelengths 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 inevitable changes in water content (due to drying) of the slices during the measurements can
influence the g(l, u) value considerably in this
wavelength region. This drying effect mainly applies to relatively thin slices and not for thicker
slices, since a thick slice dries less quickly. During 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-tonoise ratio in this region calculated as g(l, u)/
(var(g(l, 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 wavelength 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 constructed around 1 (Eq. (11)). A factor of 1.96
(95% pseudo-interval) would have given higher
4. Conclusion
A comparison between the two optical
configurations suggested that the bifurcated optical fibre gives only slightly better results for the
prediction of sugar content than the 0°/45°
configuration: for the same number of latent
variables, the explained y-variance and the validation correlation coefficient were higher for the
bifurcated cable. However, the low cost, the
possibility to measure without contact and the
only slightly less satisfactory results compared to
the bifurcated cable, make the 0°/45° configuration the best choice for commercial applications.
A NIR-spectrum, measured with a 0°/45°
configuration, can provide information about
the state of the fruit flesh. The background influences the spectrum of the skin and the transmission coefficient differs from zero. The
proportion of the skin reflectance to the transmission coefficient is an indicator for the
amount of information coming from the background compared to that coming from the skin.
A technique was developed to measure the
penetration depth of light in the wavelength
range from 500 to 1900 nm. Depending on the
wavelength, the light penetrates the apple tissue
from 2 to 4 mm. These values correspond with
those obtained by Hother et al. (1995), who
found a light penetration depth of 5.5 mm in
the 500–800 nm wavelength range for ‘Jonagold’ apples. However, the presented model,
which was developed on apple tissue only,
should be considered as a preliminary mathematical construct to analyse the depth penetration measurements. At critical points, a very low
signal-to-noise ratio caused much uncertainty on
the calculated penetration depths. The model
needs to be further refined and the suitability of
a similar model based on the Lambert–Beer law
will be investigated. In the future, more work
will be carried out on the light penetration
properties of apple tissue in the 1300–2500 nm
range, and other apple cultivars and horticultural products will be investigated.
132
J. Lammertyn et al. / Posthar6est Biology and Technology 18 (2000) 121–132
Acknowledgements
The authors wish to thank the EU (FAIR
project CT95-0302) and the Flemish Minister of
Science and Technology for financial support.
Bart Nicolaı̈ and Jeroen Lammertyn are Research
Associate and Aspirant with the Flemish Fund of
Scientific
Research
(FWO
Vlaanderen),
respectively.
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