Scholarly article on topic 'Non-destructive firmness assessment of apples using a non-contact laser excitation system based on a laser-induced plasma shock wave'

Non-destructive firmness assessment of apples using a non-contact laser excitation system based on a laser-induced plasma shock wave Academic research paper on "Materials engineering"

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Abstract of research paper on Materials engineering, author of scientific article — Naoki Hosoya, Michiru Mishima, Itsuro Kajiwara, Shingo Maeda

Abstract Various indexes have been used to assess the ripeness of fruit, including peel color and firmness because added value is given to fruit when grade selection is determined objectively. In this paper, we realize a non-destructive firmness assessment for apples by means of a non-contact vibration test method. We investigate their natural frequencies and vibration mode shapes because these factors influence the 0S2 mode, which is related to firmness. A laser-induced plasma shock wave generated with a high-output Nd:YAG pulsed laser is applied to apples as an excitation force. Firmness is assessed with this non-contact and non-destructive method using the apple’s vibration response spectra measured with a laser Doppler vibrometer. The effectiveness of this method is experimentally demonstrated through assessments of apples’ firmness, identification of the vibration mode shapes, and a follow-up survey on the flesh firmness of apples during storage.

Academic research paper on topic "Non-destructive firmness assessment of apples using a non-contact laser excitation system based on a laser-induced plasma shock wave"

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Postharvest Biology and Technology

journal homepage www.elsevier.com/locate/postharvbio

Non-destructive firmness assessment of apples using a non-contact laser excitation system based on a laser-induced plasma shock wave

Naoki Hosoyaa,*1 Michiru Mishimab, Itsuro Kajiwarac, Shingo Maedaa

a Department of Engineering Science and Mechanics, Shibaura Institute of Technology, 3-7-5 Toyosu, Koto-ku, Tokyo 135-8548, Japan b Division of Mechanical Engineering, Shibaura Institute of Technology 3-7-5 Toyosu, Koto-ku, Tokyo 135-8548, Japan c Division of Human Mechanical Systems and Design, Hokkaido University N13, W8, Kita-ku, Sapporo 060-8628, Japan

ARTICLE INFO

ABSTRACT

Article history:

Received 20 June 2016

Received in revised form 23 January 2017

Accepted 26 January 2017

Available online xxx

Keywords:

Firmness

Non-destructive tests Laser-induced plasma shock wave Non-contact vibration tests

Various indexes have been used to assess the ripeness of fruit, including peel color and firmness because added value is given to fruit when grade selection is determined objectively. In this paper, we realize a non-destructive firmness assessment for apples by means of a non-contact vibration test method. We investigate their natural frequencies and vibration mode shapes because these factors influence the 0S2 mode, which is related to firmness. A laser-induced plasma shock wave generated with a high-output Nd: YAG pulsed laser is applied to apples as an excitation force. Firmness is assessed with this non-contact and non-destructive method using the apple's vibration response spectra measured with a laser Doppler vibrometer. The effectiveness of this method is experimentally demonstrated through assessments of apples' firmness, identification of the vibration mode shapes, and a follow-up survey on the flesh firmness of apples during storage.

© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND

license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Various indexes show the ripeness of fruit, including peel color, taste, aroma, and firmness. By objectively assessing these indexes and carrying out grade selection, it should be possible to add value to fruit. To date, many ripeness assessment methods have been proposed based on the characteristics of the concerned fruit (Abbott, 1999). Simple methods used in fruit sorting facilities include firmness and sugar content measurements, which consist of pushing a plunger into the flesh and measuring the soluble solids contained in the juice, respectively. Although these methods allow the quality of the fruit in question to be directly measured, they are destructive. In addition, in fruit with greater individual differences, the decrease in sorting accuracy is a concern. Ideally, total quality assessments should adopt non-destructive tests.

Non-destructive tests that evaluate the ripeness of fruit can be roughly divided into three categories: methods employing biochemical, optical, or vibration properties. Among the approaches using biochemical properties, one method uses an electronic nose or gas chromatography to detect the flavor

* Corresponding author. E-mail addresses: hosoya@sic.shibaura-it.ac.jp (N. Hosoya), md15076@shibaura-it.ac.jp (M. Mishima), ikajiwara@eng.hokudai.ac.jp (I. Kajiwara), maeshin@shibaura-it.ac.jp (S. Maeda).

components extracted from the peel (Beaulieu and Lea, 2003; Saevels et al., 2004; Lebrun et al., 2008; Benedetti et al., 2008; Li et al., 2009; Torri et al., 2010; Oms-Oliu et al., 2011; Janzantti and Monteiro, 2014). This method, which only covers a small variety of fruit that emit a strong odor, is still under development. Among the methods based on the optical properties, one assesses the color of the peel by irradiating visible light onto the fruit, while another estimates the sugar content by irradiating near-infrared light (Kawano et al., 1992; Lancaster et al., 1997; Schmilovitch et al., 2000; Noh and Lu, 2007; Peng and Lu, 2007; Qin and Lu, 2008; Bureau et al., 2009; Pérez-Marín et al., 2009; Intaravanne et al., 2012). Although these methods have practical applications, they are difficult to apply to fruit whose surfaces do not show color changes or do not transmit light. Exciting fruit by an exciter or a hammer is one method to assess firmness using the vibration properties (Cooke, 1972; Yamamoto et al., 1981; Armstrong et al., 1990; Huarng et al., 1993; Muramatsu et al., 1996; Duprat et al., 1997; Schotte et al., 1999; Hung et al., 1999; De Belie et al., 2000; Flitsanov et al., 2000; Terasaki et al., 2001; Shmulevich et al., 2003; Motomura et al., 2004; Molina-Delgado et al., 2009; Taniwaki et al., 2009, 2010; Grimi et al., 2010; Iwatani et al., 2011; Abbaszadeh et al., 2013; Foerster et al., 2013; Macrelli et al., 2013; Zhang et al., 2014), but this contact method can only be applied to fruit with thick peels or those whose peels do not change color.

http://dx.doi.org/10.1016/j.postharvbio.2017.01.014

0925-5214/© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

The firmness of a fruit is considered a more important index to assess ripeness than the sugar or acid content because firmness is significantly related to ripeness. However, the use of contact devices such as exciters and hammers requires fruit to be examined individually, which is unrealistic as a post-harvest ripeness assessment (ripening management) of all fruit. In addition, this method cannot be applied to small, light, or soft fruit as it may induce damage. Although an approach that uses a non-contact device (Muramatsu et al., 1996) with an embedded speaker is under study, it has numerous limitations, including those related to the exciting position, difficulty generating impulse sound sources that allow the dynamic characteristics to be evaluated over a broadband in a short time, and the necessity of devices (speakers and cables) to generate sound sources.

In this paper, we perform a non-destructive assessment of the firmness of apples by measuring their natural frequencies through non-contact vibration tests in which the shock wave generated by a laser-induced plasma (LIP) (hereafter referred to as the "LIP shock wave") is turned into an impulse excitation. Although we can realize an ideal point excitation using another laser excitation method based on laser ablation (LA) (Kajiwara and Hosoya, 2011; Hosoya et al., 2012, 2014, 2016a,c,d, 2017; Huda et al., 2013), the LA-generated excitation induces sub-millimeter-sized damage onto the laser-irradiated surface of a fruit. Because an apple's firmness influences the 0S2 mode of the natural frequencies and the vibration mode shapes (Cooke, 1972; Huarng et al., 1993; Terasaki et al., 2001), we investigate these characteristics.

One advantage of our system is that traditional exciting devices (e.g., exciters or hammers) are replaced by a non-contact and nondestructive LIP shock wave. LIP is a kind of plasma generated by condensing a high-output pulse laser, and if factors such as the surrounding environment (temperature and humidity), the irradiated medium, and the laser fluence are identical, the LIP shock wave shows a high reproducibility. Previous studies (Oksanen and Hietanen, 1994; Georgiev et al., 2011; Hosoya et al., 2013, 2016b; Huda et al., 2014; Bahr et al., 2015; Eskelinen et al., 2015; Zhang et al., 2015) have reported using a LIP shock wave in an acoustic test as a point sound source or a vibration test as a point excitation force. However, this method has yet to be applied to assess firmness of fruit. Similar to the previous studies (Terasaki et al., 2001; Motomura et al., 2004; Taniwaki et al., 2009, 2010; Iwatani et al., 2011; Foersteret al., 2013; Abbaszadeh et al., 2013; Zhang et al., 2014), we use a laser Doppler vibrometer (LDV) for the response measurements. In our system both the input and output measurements are performed with a non-contact method by adopting a non-contact excitation as an input with a LIP shock wave, which has been considered difficult to date.

In this experiment, the firmness of apples is assessed. First, the natural frequencies of apples are measured with our system to determine the appropriate conditions (the position of the LIP shock wave generation and the magnitude of the laser pulse energy necessary for LIP shock wave generation). Second, the relationship between the measured natural frequency and the vibration mode shape is examined. Third, the changes in flesh firmness and the natural frequencies of stored apples are studied to demonstrate the validity of our method.

2. Firmness assessment system of apples using a LIP shock wave

Fig. 1 shows our firmness assessment system of apples using a LIP shock wave. The laser beam from a high-output Nd:YAG pulsed laser (Surelite III-10, Continuum Inc., wavelength: 1064 nm, laser beam radius: 4.75 mm, pulse width: 5 ns, maximum output: 1 J, and radial divergence angle: 0.25 mrad) installed on the optical bench was condensed with a plano-convex lens (focal length: 100 mm) to generate a LIP shock wave near the desired excitation

Fig. 1. Non-contact and non-destructive firmness assessment system of apples using a LIP shock wave as the input.

point on the apple. A LIP shock wave is generated when the LIP expands into the periphery at a high speed. The laser fluence I [W/m2] necessary to form LIP in air can be described by Eq. (1) (Georgiev et al., 2011; Hosoya et al., 2013) as

/ = — ST

where E is the laser pulse energy [J], T is the pulse width of the laser [s], and S is the area irradiated by the laser [m2]. Because the threshold of LIP in air is I > 1015 W/m2, we adjusted the E and S values so that they reach this threshold. To generate LIP in air, we used a plano-convex lens to focus the laser beam radius from 4.75 mm to 25 mm. The laser fluence at the focal plane rose from 2.65 x 1012 W/m2 to 9.57 x 1016 W/m2, exceeding the LIP threshold. If we generate LIP above the desired excitation point of the apple, the lens position or the focal length of lens against the apple should be properly adjusted at the focal plane (Fig. 1). The responses of the apples measured in a non-contact manner with LDV (NLV-2500-5, Polytec GmbH) were recorded with a spectrum analyzer (A/D: NI PXI-4462, National Instruments Co., Software: CAT-System, CATEC Inc.).

3. Non-destructive firmness assessment of apples

3.1. Test pieces

To consider individual differences, we used eleven apples of the cultivar "Sun Fuji" (Yamagata Prefecture, Japan) as test pieces to assess the firmness under various experimental conditions (Table 1). Fig. 2 shows the excitation points and measurement points on the apples (see Fig. 1). Apples A and B were used to clarify the relationships between an apple's vibration response, the magnitude of the LIP shock wave, and the distance between the LIP generation point to the excitation point on the apple (hereafter, the "standoff distance"). Apple C was used to identify an apple's spheroidal (elliptical) vibration mode shapes, which are associated with firmness (Huarng et al., 1993; Terasaki et al., 2001). Apples D-K were used to investigate the change in the firmness during

Table 1

Natural frequencies of the 0S2 mode of "Fuji apples".

Laser pulse energy [mJ]

Standoff distance [mm]

Excitation (upper) and measurement (lower) Examination item points

Frequency of the 0S2 mode [Hz]

C D E F G H I

510 or 940 940

5 or 20

E1 and E2 M1 and M2 15° intervals E1 M1

Laser pulse energy and standoff distance

Elastic wave propagation

Mode shape During storage

643.8 737.5

631.3 668.8

596.9 600.0 687.5

d = 5, 20 or l\

25 mm y El!"^

d = 5 mm LIP2

Equator

LIP1 ! E1

Stem end

LIP positions: LIP1 and LIP2 Excitation points: E1 and E2 Measurement points: Ml and M2 Standoff distance: d = 5, 20 or 25 mm

Fig. 2. Excitation and measurement points on an apple.

storage. Apples were placed sideways on a cushion to ensure free support. The excitation points (El and E2) and the measurement points (Ml and M2) were set on the equatorial circumference of the apple (Fig. 2). By generating a LIP shock wave just above the excitation point, the excitation force was applied to the test piece, and the velocity response on the normal direction in contact with the tangent plane of the apple was measured with the LDV. The recorded spectra were analyzed with a spectrum analyzer. In

addition, we affixed a reflection seal (2 mm x 2 mm) on the measurement point.

3.2. Natural frequency measurements

First, we validated that our system can measure an apple's natural frequencies in various conditions. To measure the detailed time histories of the velocity responses of the apples, we set the sampling frequency, the number of sampling points, and the number of trials to 204.8 kHz, 32768 points, and 5, respectively.

Fig. 3 shows the time history response and the corresponding Fourier spectrum measured when apple A is excited by a LIP shock wave. For this experiment, we set the pulse energy to 940 mJ and the standoff distance d to 5 mm (hereafter "case 1"). In addition, by using the "pretrigger mode" of the spectrum analyzer, the measurement start time t = 0 was set to 0.01 s before the time when the targeted apple actually responded.

Fig. 3(a) shows an enlargement of the area where the excitation force is applied. The responses obtained through five measurements are superimposed to confirm the reproducibility. Fig. 3(b) shows the displacements obtained by the integration of the measured velocities of Fig. 3(a). We measured the velocity responses at Point M1 during the LIP excitations at Point E1 against apple A. The time responses of the apple attenuate in a very short time. The five nearly overlapping velocity responses confirm the high reproducibility of our system. Moreover, the displacements on the apple's surface are less than 10 mm, as shown in Fig. 3(b). Fig. 3(c) shows the average value of the Fourier spectrum corresponding to Fig. 3(a); we found several natural frequencies using our system.

Next, we studied the relationships between an apple's vibration response, the magnitude of the LIP shock wave, and the standoff distance. The magnitude of the pressure generated by a LIP shock wave is given by (Georgiev et al., 2011; Hosoya et al., 2016b)

'<"- (5

2-2z5Ud-3

5 g + 1

where Z0 is a constant (Z0 = 0.93), g is the specific heat ratio (g = 1.41), E is the momentarily released energy, and d is the standoff distance. The magnitude of the LIP shock wave's pressure, which is related to the excitation force toward the apple, changes as a function of the laser pulse energy and the standoff distance. Because the LIP shock wave expands as a spherical wave from the origin of the LIP position, the excitation surface on an apple increases as the standoff distance increases.

To compare to case 1 (laser pulse energy: 940 mJ, d = 5 mm), we used two other cases; one with a lower laser pulse energy (case 2; laser pulse energy; 510 mJ, d = 5mm) and one with a

> -0.5

Time [ms]

(a) Time responses of the measured velocity.

10.1 Time [ms]

(b) Time responses of the displacement obtained by the integration of the data shown in Fig. 3 (a).

o ^ ■2 1

0.8 0.6 0.4 0.2

0 500 1000 1500

Frequency [Hz]

(c) Average Fourier spectrum corresponding to (a).

Fig. 3. Measured responses of apple A using a LIP shock wave as the input (case 1: laser pulse energy, 940 mJ; d = 5mm). (a) Time responses of the measured velocity, (b) time responses of the displacement obtained by the integration of the data shown in Fig. 3(a), and (c) average Fourier spectrum corresponding to (a).

J "S 0> -0.5 -

10.0 10.1

Time [ms]

(a) Case 2 (laser pulse energy, 510 mJ; d = 5 mm).

0.5 0.25

£^-0.25 -0.5

......v

10.1 Time [ms]

(b) Case 3 (laser pulse energy, 940 mJ; d = 20 mm).

Fig. 4. Measured velocity of apple A as a function of time. (a) Case 2 (laser pulse energy, 510 mJ; d = 5mm) and (b) case 3 (laser pulse energy, 940 mJ; d = 20mm).

greater standoff distance (case 3; laser pulse energy; 940 mJ, d = 20 mm). Fig. 4 shows the time history waveforms measured according to the above conditions, and Fig. 5 indicates the

Fig. 5. Average Fourier spectrum for each experimental condition corresponding to Figs. 3 (a) and 4 (a) and (b) (apple A).

Fourier spectrum corresponding to Fig. 4. To demonstrate the reproducibility, the responses obtained through the five measurements are superimposed in Fig. 4. In addition, the Fourier spectrum obtained in case 1 is superimposed for comparison in Fig. 5. The attenuating vibration waveforms shown in Fig. 4(a) and (b) are similar to the one in Fig. 3, indicating a high reproducibility. However, the response amplitude shown in Fig. 4(b) is smaller than the one in Fig. 4(a), which is attributed to the reduced pressure by the LIP shock wave because the pressure by a LIP shock wave is inversely proportional to the cube of the distance (the propagation distance of a LIP shock wave is 20 mm in case 3). In all cases, several natural frequencies are excited, but in view of the signal-to-noise ratio in the measurement, it is desirable that the position of the LIP shock wave generation is closer to the apple's surface and that the laser pulse energy for the LIP shock wave generation is larger. However, for fruit with extremely soft surfaces, such as peaches, both the position of and the laser pulse energy for the LIP shock wave generation must be set appropriately. Due to the variations in the apples' shapes, determining the desired point of excitation is difficult. This point will be further examined in the future.

To observe the elastic waves propagation on an apple's surface, we measured the velocity responses at Points M1 and M2 during the LIP excitations at Points E1 and E2 against apple B (see Fig. 2). Fig. 6(a-c) shows the measured velocities at Point M1 during the LIP excitation at Point E1, at Point M1 during the LIP excitation at Point E2, and at Point M2 during the LIP excitation at Point E2, respectively. Fig. 6(a) indicates that the amplitude of the measured velocity is roughly the same as the case in Fig. 3(a). The amplitudes of the measured velocities shown in Fig. 6(b) and (c) are less than one-tenth of the amplitude in Fig. 6(a). As the propagation distance of waves increases, the amplitude of the elastic waves propagating along an apple's surface attenuates.

During the LIP excitation at Point E2, the mean velocity of the elastic waves in the length of the arc of apple B from Points M1 to M2 (7.1 cm) was 338 m/s. From this, the LIP shock wave propagates along an apple's surface from the LIP excitation point to the opposite side. Immediately after the time response measurement in Fig. 6, we could observe a shock wave followed by elastic waves.

3.3. Vibration mode shapes of apples

To identify an apple's vibration mode shapes corresponding to the natural frequencies, we established a measurement system to obtain the vibration mode shapes (Fig. 7). Huarng et al. (1993) and Terasaki et al. (2001) reported that the 0S2 mode is strongly related to an apple's firmness, which corresponds to the natural frequency of interest. As a test piece, we used apple C (Table 1). We attached reflection seals (2 mm x 2 mm) on the equator of the apple's

1 0.6 £ 0.3

£ -0.3

> -0.6

10.1 Time [ms]

(a) Time responses of the measured velocity at Point Ml during the LIP excitation Point El.

in 0.03

Jd 0.015

"<3 -0.015

12.0 Time [ms]

(b) Time responses of the measured velocity at Point Ml during the LIP excitation Point E2.

0.03 0.015 0

-0.015

-°.°13)L

12.0 Time [ms]

(c) Time responses of the measured velocity at Point M2 during the LIP excitation Point E2.

Fig. 6. Elastic waves propagation on the surface of apple B (laser pulse energy, 940 mJ; d = 5 mm). (a) Time responses of the measured velocity at Point Ml during the LIP excitation Point El, (b) time responses of the measured velocity at Point Ml during the LIP excitation Point E2, and (c) time responses of the measured velocity at Point M2 during the LIP excitation Point E2.

surface in l5° intervals. Applying an excitation force to point l on the apple with a LIP shock wave, we measured the velocity response in the normal direction in contact with the tangent plane of the apple on points 2 to 24 using a sequentially moved LDV. To improve the frequency resolution around the 0S2,0S3, and 0S4 mode frequencies as well as the signal-to-noise ratio in the measurement, we set the sampling frequency, the number of sampling points, and the number of trials to l02.4 kHz, 32768 points, and 30 times, respectively.

The equation of motion of an isotropic elastic sphere is given by (Huarng et al., l993)

mV u + (i + m)V[V • u] = ru

where l and m, u, p, V2, and V are the Lamé coefficients, displacement vector, density, Laplacian operator, and gradient operator, respectively. Solving Eq. (3), Huarng et al. (l993) described the deformation of the sphere expressed using the Legendre polynomial. Table 2 shows the Legendre polynomials used as the theoretical vibration mode shapes on the equatorofthe apple by Huarng et al. (l993). The theoretical and experimental vibration mode shapes are both described as the ratio of an arbitrary point to a reference point. That is, the amplitude of the

Fig. 7. Experimental system using a LIP shock wave to estimate the vibration mode shapes of apples.

Table 2

Vibration mode shapes (Legendre polynomials).

Mode Legendre polynomial

0S2 P2(cos U) = (1/4)(3cos2U + 1)

0S3 P3(cos U) = (1/8)(5cos3U + 3cos U)

0S4 P4(cos U) = (1/64)(35cos4U + 20cos4U + 9)

vibration mode shapes in Fig. 7 is the ratio. We can visualize the theoretical vibration mode shapes through the polar coordinates displayed by adding the value of the Legendre polynomial at each degree to the radius (e.g., the 0S2 mode of the sphere radius R yields R + P2(cos0)).

Fig. 8 shows the 0S2 (lowest second), 0S3 (lowest third), and 0S4 (lowest forth) vibration mode shapes for apple C measured with our method. The theoretically obtained vibration mode shapes are displayed for comparison. The 0S2 and 0S3 modes in Fig. 8 show that the values obtained in our method and the theoretical values agree well, but the values for the 0S4 mode differ (Fig. 8). We confirmed that the lowest first frequency of about l0 Hz measured by our

0 15 0 18' 30 21

0 '0 30

0S2 mode (617 Hz) — — ■ Base circle

0S3 mode (944 Hz) 0S4 mode (1213 Hz) — Theoretical — Experimental Fig. 8. Vibration mode shapes for apple C.

Table 3

Relationship between an apple's firmness and natural frequency during storage.

Apple Frequency of the 0S2 mode [Hz]

Day 0 Day 21 Day 42 Day 63 Day 84

D 631.3 587.5 553.1 512.5 456.3

E 668.8 640.6 581.3 506.3

F 596.9 531.3 462.5

G 643.8 571.9 450.0

H 596.9 531.3

I 600.0 546.9

J 687.5

K 609.4

system is a rigid body mode similar to the longitudinal mode (Terasaki et al., 2001 ).

According to previous studies (Yamamoto et al., 1981; Armstrong et al., 1990; Huarng et al., 1993; De Belie et al., 2000; Shmulevich et al., 2003; Motomura et al., 2004), apples have a primary natural frequency of 60-100 Hz in the longitudinal mode, and secondary and tertiary natural frequencies of 760-970 Hz and 1100-1450 Hz, respectively, in the spheroidal mode. Huarng et al. (1993) and Terasaki et al. (2001) reported that a fruit's firmness is related to its 0S2 mode.

Table 1 shows the measured natural frequencies of apples in various conditions. The average natural frequency and the standard deviation are 639.4 Hz and 42.1 Hz, respectively. In the vibration tests for apple C, we validated that the natural frequency of 617 Hz is the 0S2 mode, indicating that the natural frequencies of the eleven apples in the frequency band of 596.9-737.5 Hz correspond to the 0S2 mode. Therefore, we can assess the firmness of apples using the LIP shock wave excitation method in a non-contact and non-destructive manner.

4. Changes in the firmness of apples during storage

We evaluated the change in firmness of eight apples (D-K) (Table 1 ) during storage by observing the changes in the natural frequency as measured with our system (Fig. 1). The excitation and measurement points are Points E1 and M1, respectively (Fig. 2). The same measurement conditions as Section 3.3. were employed. We monitored the change in the natural frequencies of the apples on five different days (on days 0, 21, 42, 63, and 84). (The experiment lasted a total of 84 d.) The storage periods were as follows: 84 d for apple D, 63 d for apple E, 42 d for apples F and G, 21 d for apples H and I, and 0 d for apples J and K. After the storage period, we implemented a breaking test to

-x 10"

y 63,- )ay 21 J)

Frequency [Hz]

- Day 0,631 Hz

- Day 21, 588 Hz

Day 42, 553 Hz

- Day 63, 513 Hz

- Day 84, 456 Hz

Fig. 9. Changes in apple D's 0S2 mode during storage.

observe the inner state and to conduct the Magnes-Taylor firmness test. However, we omitted these results from this manuscript due to the insufficient sample size. During this experiment, the apples were stored in a refrigerator at a constant temperature of 7 °C.

Table 3 shows the relationship between firmness and natural frequency (the 0S2 mode) of apples during storage. A blank in Table 3 indicates that the natural frequency of the apple could not be measured due to implementation of a break test. Fig. 9 shows the superimposed Fourier spectra of the measured responses on each observation day. The 0S2 mode of the apple is confirmed within the frequency band of 400-700 Hz as shown in Fig. 9 and Table 3. The 0S2 mode shifts to a lower frequency band as the storage time increases. As reported in previous studies (Duprat et al., 1997; De Belie et al., 2000; Shmulevich et al., 2003; Motomura et al., 2004; Molina-Delgado et al., 2009), an apple's firmness and the 0S2 mode decrease as the storage period increases. These experimental results show the same tendency. Therefore, our system should help elucidate the softening process of apples during storage.

5. Conclusions

In this experiment, we performed a non-contact and nondestructive assessment of changes in the firmness of apples during storage ("Sun Fuji" variety produced in Yamagata Prefecture, Japan) by means of vibration tests in which a LIP shock wave generated by high-output Nd:YAG pulsed laser was turned into an impulse excitation force.

The natural frequencies of the 0S2,0S3, and 0S4 modes measured with our system fell within a frequency band of 500-1500 Hz. In addition, the vibration mode shapes on an apple's equator correspond well to the vibration mode shapes reported in previous studies (Cooke, 1972; Huarng et al., 1993; Terasaki et al., 2001) as well as those obtained through an analytical approach. Therefore, we conclude that our system enables the firmness of apples to be assessed.

We studied the change in an apple's quality during storage by examining the changes in firmness of an apple's flesh and the 0S2 mode frequency during storage. Consistent with previous studies (Duprat et al., 1997; De Belie et al., 2000; Shmulevich et al., 2003; Motomura et al., 2004; Molina-Delgado et al., 2009), the 0S2 mode frequency shifts to the lower frequency band as the storage period increases, indicating that our system can be used to understand the softening process of apples during storage.

To realize full-field firmness assessment techniques for fruit, several challenges remain, including determination of the desired excitation and measurement points, a calibration for firmness quantification, practical examples using different kind of fruit, and development of an easy-to-use and accurate LIP positioning system similar to a scanning LDV (Polytec GmbH) or a laser tracking system (Kajiwara et al., 2006). If these obstacles are overcome, a non-contact and non-destructive method can be extended to evaluate firmness of fruit on trees.

Conflict of interest

The authors certify that there is no conflict of interest with the Japan Society for the Promotion of Science.

Acknowledgements

We thank the Japan Society for the Promotion of Science for their support under Grants-in-Aid for Scientific Research programs

(Grants-in-Aid for Scientific Research (B), Project No. 16H04291, No. 16H04286, and No. 16H04306, and Grants-in-Aid for Challenging Exploratory Research, Project No. 26630080, No. 26630102, and No. 16K14201).

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