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Time-Resolved Reflectance Spectroscopy Applied to the Nondestructive Monitoring of the Internal Optical Properties in Apples

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In this article, the authors used the temporal dispersion of a short laser pulse injected into the probed medium to measure the mean values of the absorption and reduced scattering coefficients of the medium.
Abstract
Time-resolved reflectance has been used for the nondestructive measurement of optical properties in apples. The technique is based on the detection of the temporal dispersion of a short laser pulse injected into the probed medium. The time distribution of re-emitted photons interpreted with a solution of the diffusion equation yields the mean values of the absorption and reduced scattering coefficients of the medium. The proposed technique proved useful for the measurement of the absorption and scattering spectra of different varieties of apples, revealing the spectral shape of chlorophyll. No major variations were observed in the experimental data when the fruit was peeled, showing that the optical properties measured were those of the pulp. With this technique the change in chlorophyll absorption during storage and ripening could be followed. Finally, a compact prototype working at few selected wavelengths was designed and constructed, demonstrating potentialities of the technique for industrial applications.

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Time-Resolved Reflectance Spectroscopy Applied to the
Nondestructive Monitoring of the Internal Optical
Properties in Apples
RINALDO CUBEDDU, COSIMO D'ANDREA, ANTONIO PIFFERI,
PAOLA TARONI, ALESSANDRO TORRICELLI, GIANLUCA VALENTINI,
MARGARITA RUIZ-ALTISENT, CONSTANTINO VALERO, CORAL ORTIZ,
COLÍN DOVER, and DAVID JOHNSON
INFM-Dipartimento di Física, and CEQSE-CNR, Politécnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milán, Italy (R.C.,
C.D., A.P., P.T., A,T., G.V.); Rural Engineering Department,
E.T.S.I.
Agrónomos, Polytechnic University of
Madrid,
Av.
Complutense, 28040
Madrid,
Spain (M.R.-A., C.V., C.O.); and Horticulture Research International (HRI), East Mailing, West
Mailing, Kent, ME19 6BJ, UK (C.D., D.J.)
Time-resolved reflectance has been used for the nondestructive
measurement of optical properties in apples. The technique is based
on the detection of the temporal dispersión of a short láser pulse
injected into the probed médium. The time distribution of re-emit-
ted photons interpreted with a solution of the diffusion equation
yields the mean valúes of the absorption and reduced scattering
coefficients of the médium. The proposed technique proved useful
for the measurement of the absorption and scattering spectra of
different varieties of apples, revealing the spectral shape of chlo-
rophyll. No major variations were observed in the experimental
data when the fruit was peeled, showing that the optical properties
measured were those of the pulp. With this technique the change
in chlorophyll absorption during storage and ripening could be fol-
lowed. Finally, a compact prototype working at few selected wave-
lengths was designed and constructed, demonstrating potentialities
of the technique for industrial applications.
Index Headings: Chlorophyll; Absorption; Scattering; Photon mi-
gration; Fruit.
INTRODUCTION
The assessment of the internal quality of fruits is of
increasing importance in an ever more competitive mar-
ket. Further, there is an increasing demand for nonde-
structive and noninvasive tests to determine the optimum
time for harvesting, to follow changes during storage, and
to determine the internal quality of individual fruit.
Different nondestructive techniques have been pro-
posed to probé a variety of quality-related factors in
fruits.
1
For example, anthocyanins in strawberries have
been detected by photoacoustic techniques.
2
The artificial
nose,
with the potential to detect small quantities of re-
leased chemicals, may prove useful for those aspects of
quality related to aroma production,
3
even though few
data on such applications are currently available. Ultra-
sounds cannot penétrate deeply into the pulp of most
fruits due to the porous nature of the tissue, yet some
promising results were obtained by using low-frequency
ultrasounds.
4
Nuclear magnetic resonance appears prom-
ising in terms of specificity and spatial resolution,
5
but is
not suitable for in-the-field or mass applications.
Other techniques using visible or near-infrared light
have been devised on the basis of the measurement of
the total diffusely reflected light at different wavelengths.
For instance, in the visible región of the spectrum, col-
orimetry has been used to determine the color of the skin
of peaches
6
and, in the near-infrared región, the spectrum
of re-emitted light has been studied mainly to estimate
the total sugar content.
7
A key limitation of these optical techniques is that the
intensity of the diffusely re-emitted light is strongly de-
pendent on the color of the skin, thus masking informa-
tion from the pulp. Moreover, the total reflected intensity
is determined by both the absorption and the scattering
properties, in such a way that it is not feasible to sepárate
the effects of these properties. Absorption and scattering
contain distinct information on the médium. Absorption
is determined by the pigments and constituents of the
pulp that produce characteristic spectral features in the
visible and near-infrared región of the spectrum. Con-
versely, scattering is due to the local variation of the di-
electric constant inside the médium. Microscopic changes
in refractive index caused by membranes, air vacuoles,
or organelles deviate the photon paths and are ultimately
responsible for light diffusion. Macroscopically, this phe-
nomenon can be described by using the scattering
coef-
ficient (|x
s
) that corresponds to the mean distance between
interaction sites and the angular probability distribution
of scattered photons. A further simplification assumes a
single parameter, the transport or reduced scattering co-
efficient |x
s
' = |x
s
-(l
g), where g is the mean cosine of
the scattering angle for a single scattering event. This
parameter corresponds to the effective scattering coeffi-
cient, assuming isotropic scattering, and is adequate to
describe light distribution for highly scattering media
(e.g., apples).
8
An interesting challenge for the noninvasive simulta-
neous measurement of the scattering and the absorption
properties of turbid media is offered by time-resolved re-
flectance spectroscopy (TRS). This technique is based on
the measurement of the temporal delay and broadening
experienced by a short láser pulse while traveling through
a turbid médium.
9
Usually, the láser light is injected into
and collected from the médium by using two optical fi-
bers placed in contact with the surface at a fixed relative
distance. If an appropriate theoretical model is used for
the analysis of the experimental data, it is possible to
accurately measure both the absorption coefficient (|x
a
)

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1. Layout of the compact prototype hased on a semiconductor pulsed láser, fiher optics for signal injection and collection, a metal channel
compact size photomultiplier (PMT), and a computer hoard for time-correlated single photon counting (TCSPC).
and the reduced scattering coefficient of the probed-
dium.
1011
This technique has been successfully used for the de-
tection of optical properties in biological media for bio-
medical applications.
12
Recently, we have demonstrated
13
its applicability for the nondestructive measurement of
absorption and scattering spectra in different fruits and
vegetables (apple, kiwifruit, peach, tomato). In this paper
we explore the key features of this novel approach, in
particular in view of possible applications on agriculture
produce, using the apple as a test model. Relevant issues
such as influence of the skin properties or extensión of
the región involved in the measurement will be analyzed,
together with tests on sensitivity of the technique to phys-
iological changes in the fruit. Finally, a first implemen-
tation of the technique with a compact instrument will be
presented.
MATERIALS AND METHODS
Instrumentation: Laboratory Setup. Spectral mea-
surements were obtained with the use of a laboratory sys-
tem for time-resolved reflectance spectroscopy. A syn-
chronously pumped mode-locked dye láser was used as
the illuminating source. The dye (DCM) was pumped by
an actively mode-locked argón láser (CR-18, Coherent,
CA).
The repetition rate of the pulses was reduced to
about 9 MHz by means of a cavity dumper. The dye láser
is tunable between 610 and 700 nm, with an average
power of about 10 mW and a pulse width of <20 ps.
The láser light was injected into and collected from the
sample by means of
1-mm-core
1-m-long
plastic-glass
fibers set on the fruit surface at a relative distance of 1.5
cm. A fiber holder kept the fibers in parallel and in con-
tad with the sample and prevented direct collection of
specular reflected light. The distal end of the collecting
fiber was placed at the entrance slit of a scanning mono-
chromator (HR-250, Jobin Yvon, France), coupled to a
double microchannel píate photomultiplier (R1564U, Ha-
mamatsu, Japan). The signal was processed by an elec-
tronic chain for time-correlated single-photon counting.
The triggering signal was provided by coupling part of
the láser light to a fast photodiode. A small fraction of
the incident beam was coupled to another fiber and di-
rectly fed to the entrance slit of the monochromator to
compénsate for any temporal drift of the electronic chain.
The temporal width of the instrumental response function
(IRF) was <120 ps (full width at half-maximum), mea-
sured by direct contact between the injection and collec-
tion fibers. The system was controlled by a PC that fa-
cilitated the automatic acquisition of a set of time-re-
solved reflectance curves over a given wavelength range.
Typically, the overall time required to acquire a set of
time-resolved reflectance measurements from 610 to 700
nm every 5 nm with 100 000 counts per curve was about
1 min.
Instrumentation: Compact Prototype. A compact
prototype for TRS measurement suitable for application
on fruits was developed at Politécnico di Milano. The
scheme of the instrument is shown in Fig. 1. Light is
provided by a pulsed láser diode (PDL 800, Picoquant,
Germany) running at 80 MHz with an average power of
1 mW and a typical pulse width of 100 ps. Different láser
heads can be interchanged, permitting selection of the
illuminating wavelength. Results presented in this study
were obtained by using a diode emitting at 672 nm. Light
was coupled into a fused fiber splitter (FUSEDIRVIS
5/95, OZ Optics, Canadá) that conveyed most of the pow-
er (95%) to the fruit and a small fraction (5%) to the
detector for continuous monitoring of the IRF Re-emitted
photons were collected at a distance of 2 cm from the
injection point by a 1 mm-core plástic fiber and redi-
rected to a compact metal channel diode photomultiplier
(R5600U-L16, Hamamatsu, Japan). The signal was then
processed by an integrated PC board for time-correlated
single-photon counting (TimeHarp, Picoquant, Germa-
ny).
The typical acquisition time was 4 s per measure-
ment point. All the equipment can be easily hosted in a
small box and operated by a standard PC.
Analysis. The temporal profile of the TRS curve pro-
vided by either of the two instruments was analyzed by
using a solution of the radiative transport equation under
the diffusion approximation for a semi-infinite homoge-
neous médium.
10
The extrapolated boundary condition
was used
14
to take into account the refractive index mis-
match at the surface. The reflectance R(r, t)—i.e., the
photon probability of being re-emitted from the tissue at
a time t and a distance r from the injection—can be ex-
pressed as in Eq. 1:
R(r, t) = AD-
3/2
r
5/2
exp(-|x
a
vf)exp
\ ADvt
z
0
exp
ADvt
z
p
exp
ADvt
(1)

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FIG.
2. Typical fit of a time-resolved reflectance curve. Experimental
data (dots) are fitted with the convolution (continuous line) of the in-
strumental transfer function (dashed line) with a theoretical model (not
shown).
where A is a normalization constant; v = c/n is the speed
of light in the médium; and z
0
= l/|x
s
' is the scattering
mean free path; while z
p
derives from the extrapolated
boundary conditions and depends on the refractive index
of the tissue. The diffusion coefficient D =
1/(3|x
s
')
was
taken to be independent of the absorption properties of
the médium.
15
The experimental curve was fitted with a convolution
of the theoretical function with the IRF. The best fit was
reached by minimizing the x
2
» varying both |x
a
, and |x
s
'
using a Levenberg Marquard iterative procedure.
16
The
range of the fit included all the points of the experimental
curve with a number of counts higher than 10% of the
peak valué on the rising edge of the curve and 1% of the
peak valué on the falling edge. Figure 2 shows the best
fit of a typical experimental curve. The IRF is also shown
for comparison (dashed line). The scattering properties of
the médium yield the temporal shift and broadening of
the reflectance curve as compared to the transfer function,
while the absorption properties determine the slope of the
tail in a logarithmic plot. The fitting procedure can au-
tomatically analyze a full batch of experimental curves
on a standard PC at a speed of 10 curves per second.
Synchronization of the analysis PC with the measurement
one over a network permits on-line processing of the ex-
perimental data so that the absorption and scattering spec-
tra are shown on the screen in real time while the mea-
surement is in progress.
The accuracy of a TRS measurement for the detection
of |x
a
and |x
s
' in a turbid médium has been already dis-
cussed elsewhere.
1718
In general, for a given set of |x
a
and
|x
s
'
valúes, the accuracy of the measurement increases
with the interfiber distance p, provided that enough pho-
tons can be collected (about 100 000). We have shown
that, for p = 1.4 cm, |x
s
' = 10 cm
-1
, and |x
a
< 0.25 cm
-1
,
the measurement of |x
a
is accurate within 10%, while the
measurement of |x
s
' is accurate within
20%.
18
For p = 1.5
cm as used in the present study, and a |x
s
' valué around
10 cm
-1
or higher, a comparable or better accuracy can
be expected.
Fruit Samples. Apples of the Golden Delicious, Gran-
ny Smith, and Starking Delicious varieties, used for the
characterization of the technique, were taken from the
local market. Fruits involved in the picking date experi-
ment performed with the compact prototype were taken
from controlled orchards at Horticulture Research Inter-
national (UK). A total of 30 apples of the Gala variety
were harvested on three different occasions during Sep-
tember/October and then stored in refrigerated controlled
atmospheric conditions until early May when all fruits
were characterized within the same measurement session.
RESULTS
The absorption and scattering spectra obtained from
intact apples of three different varieties (Golden Deli-
cious,
Granny Smith, and Starking Delicious) are shown
in Fig. 3. For each variety, two fruits of different maturity
(green and yellow background color, respectively) were
measured and, for each fruit, two sides were probed: the
side most exposed to sunlight and the opposite side. This
was done to highlight the variation in optical properties
observed between and within fruits. The main feature of
the absorption spectra is the peak around 675 nm, which
corresponds to absorption by chlorophyll-a (CHL). Con-
siderable variation between different varieties is evident,
with the less mature fruit showing more CHL absorption,
particularly for Granny Smith. In general, there was less
CHL absorption for the side of the fruit most exposed to
sunlight; this difference was greater for the less mature
fruit of each variety, and the inter-fruit variation was low-
er than the intra-fruit variability. In apples with quite a
low CHL absorption (e.g., Golden, Triangles), the ab-
sorption spectrum was characterized by a slightly de-
creasing line shape that is probably the tail of an antho-
cyanine spectral peak. Water absorption is negligible in
this wavelength range (<0.005 cm
-1
for puré water).
Scattering spectra of the same fruits are presented in
the right pane. No particular spectral features were evi-
dent. However, a slight decrease in |x
s
' with increasing
wavelength was observed. Starking Delicious apples had
higher |x
s
' (13-22 cm
-1
) than Golden Delicious or Granny
Smith apples (12-15 cm
-1
and 8-13 cm
-1
, respectively).
Variation in scattering coefficient was found between
dif-
ferent fruits of the same variety and different positions
on the same apple. There seemed not to be any relation-
ship between CHL absorption and the scattering spectra.
Yet, the number of individual fruits analyzed is too small
to draw any conclusión.
The influence of the skin on the result of a TRS mea-
surement is shown in Fig. 4. Absorption and scattering
spectra were obtained for a Golden Delicious, a Granny
Smith, and a Starking Delicious apple. Each fruit was
measured before and after skin removal with the fibers
positioned at the same point to probé the same región.
The spectra obtained for the whole apples overlap the
spectra for the peeled apples for both absorption and scat-
tering. Thus, it is possible to infer that the TRS mea-
surement probes the optical properties of the pulp of the
fruit regardless of the skin color.
In a further experiment, the penetration depth of a TRS
measurement was determined. It is well known that the
volume probed by a TRS measurement is a "banana
shaped" región connecting the injection and collection
points.
19
It is difficult to define the measurement volume,

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FIG.
3.
Ahsorption (left pane) and scattering (right pane) spectra
of
Golden Delicious (top row), Granny Smith (middle row), and Starking Delicious
apples (hottom row). Yellow hackground color (triangles), green hackground color (diamonds). Side more exposed
to
sunlight (empty symhols),
opposite side (filled symhols).
as photon paths can
be
distributed
in
the whole médium,
although they
are
more densely packed
in the
banana
región. Thus,
an
attempt was made
to
determine the máx-
imum depth
in the
pulp
for
which there
was
some
de-
tectable contribution
to the
TRS curve.
A
series
of
mea-
surements were performed
on a
Starking Delicious apple,
with slices
of
pulp
cut
from
the
side
of
the fruit opposite
to that
in
contact with the fibers. Spectra were taken from
the whole apple
and
then from tissue with
a
total thick-
ness
of
4.1,
2.7,
2.1,
and 1.5 cm. The
fitted absorption
and scattering spectra are shown
in
Fig. 5. The absorption
coefficient was unchanged down
to a
thickness
of
2.7 cm.
At 2.1
cm,
|x
a
had increased
by
25%
at
675
nm
from
the
measurement
on the
whole apple, while
at a
thickness
of
1.5
cm the
increase
was
50%.
The
greatest differences
were observed
on the
tails
of the
spectrum, where
ab-
sorption
was
lower.
The
results
for the
scattering coeffi-
cient show similar behavior, with almost no change down
to
a
thickness
of
2.7
cm, and
increases
of
15%
and
25%
for 2.1
and 1.5 cm
thickness, respectively.
To determine
the
sensitivity
of
the technique,
we fol-
lowed the change
in
chlorophyll absorption
as a
result of
storage
at
room temperature. Two Golden Delicious
ap-
ples
at
different ripeness stages were measured
at
differ-
ent times (time
0, and
after
4
days
of
storage
at
room
temperature).
The
results
are
reported
in
Fig.
6. In
both
apples there
is a
clear decrease
in the
absorption coeffi-
cient, related
to a
decrease
in
CHL content,
of
about 30%

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625
650 675 70
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i
i 1 i i i i 1 i i i i 1 i i i i 1
600 625 650 675 700
wavelength
(nm)
FIG.
4.
Ahsorption (left pane)
and
scattering (right pane) spectra
of a
Golden Delicious
(top row), a
Granny Smith (middle
row), and a
Starking
Delicious apple (hottom
row).
Before (filled diamonds),
and
after (empty diamonds) skin removal.
0.12
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1—I—|—I—I 1—I—|—I—I 1—I—|—I—I 1—I
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600
625 650 675
wavelength
(nm)
700
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600
625 650 675
wavelength
(nm)
700
FIG.
5.
Ahsorption (left pane)
and
scattering (right pane) spectra
for
different thicknesses
of
tissue from
a
Starking Delicious apple.

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References
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Book

Numerical Recipes in C: The Art of Scientific Computing

TL;DR: Numerical Recipes: The Art of Scientific Computing as discussed by the authors is a complete text and reference book on scientific computing with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, with many new topics presented at the same accessible level.
Book

Wave propagation and scattering in random media

TL;DR: This IEEE Classic Reissue presents a unified introduction to the fundamental theories and applications of wave propagation and scattering in random media and is expressly designed for engineers and scientists who have an interest in optical, microwave, or acoustic wave propagate and scattering.
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Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties.

TL;DR: A simple model is developed, based on the diffusion approximation to radiative transfer theory, which yields analytic expressions for the pulse shape in terms of the interaction coefficients of a homogeneous slab.
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