Food Control 12 (2001) 37±45
www.elsevier.com/locate/foodcont
Ultrasound detection and identi®cation of foreign bodies in food products Edward Hñggstr om *, Mauri Luukkala Department of Physics, University of Helsinki, P.O. Box 9, FIN-00014, Helsinki, Finland Received 13 December 1999; received in revised form 2 February 2000; accepted 4 February 2000
Abstract This paper introduces a concept based on an ultrasound re¯ection measurement with an echo classi®er which has shown ability to detect and classify foreign bodies (FBs) in commercial food samples. The probed products were dierent kinds of cheese and marmalade. The FBs ranged from bone to steel and their size were 1 to 14 mm in diameter. The frequency was 5 MHz and the probing depths were 25, 50 and 75 mm. The research showed that all of the FBs investigated could be detected and identi®ed in one of the tested food products. The best detection temperature interval was 1±5°C. Discrimination of FBs was more dicult in the inhomogenous samples than in the homogeneous samples investigated. Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Food; Ultrasound; NDT; Foreign body detection
1. Introduction Identi®cation of foreign bodies (FBs) in food comestibles plays an important role in quality assurance of food products. Customer complaints are expensive both in terms of money and in terms of good will. Particularly organic materials constitute a problem in the modern food industry because otherwise ecient test methods based on X-rays and metal detectors are not able to detect organic residues from raw materials or packages. When food products are manufactured or packaged small foreign objects might end up in the product. Bones of animals are found in meat products, fragments of glass maybe found in food canned in glass jars and metal swarf can result from failures in production equipment (Chivers et al., 1995; Ahvenainen et al., 1989). It is naturally desirable for the food industry that all FBs are found and removed before they reach the customer. This would result in fewer dissatis®ed customers and fewer prosecutions to add to operating cost in a competitive industry. The need for a non-destructive, highly sensitive method which is resistant to harsh industrial surroundings and which allows high production rates pose severe
*
Corresponding author. Tel.: +358-9-191-8343; fax: +358-9-1918344. E-mail address: edward.haeggstrom@helsinki.® (E. HñggstroÈm).
restrictions on a potential measurement method. The required ability to deal with natural internal variability between food samples increases the demands placed on a measurement method. Ultrasound-based methods are well suited for food-industrial measurements since they do not spoil food items physically or hygienically. Ultrasound has shown its ability both to detect FBs within food items and to measure structure of food items. Rheologic measurements are especially important in quality monitoring of food products (Lee et al., 1992; Gestrelius et al., 1991; Hñggstr om, 1997). Ultrasound-based measurement methods bene®t from their large applicability. Most materials can be detected and most locations tolerated. The equipment is furthermore low-cost and performs truly nondestructive tests. Ultrasonic measurements are either transmission measurements or pulse-echo measurements which enables the use of a single transducer. Pulse-echo (PE) measurements usually have low signal-to-noise (S/N) ratios due to complex internal re¯ecting structures in food samples. PE measurements commonly suer from two dead zones: one is in the vicinity of the food package wall near the transmitter, called the shadow zone (Krautkramer & Krautkramer, 1983), and one is in the far region of the acoustic beam where attenuation eradicates echoes. At least two patents exist concerning applications which detect FBs in food (Edwards, 1980; Black et al., 1983), but to our knowledge none for identifying the FBs detected.
0956-7135/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 6 - 7 1 3 5 ( 0 0 ) 0 0 0 0 7 - 4
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E. Hñggstr om, M. Luukkala / Food Control 12 (2001) 37±45
Non-homogeneities in products such as airpockets or shrimp shells give rise to echoes which can be mistaken for FBs. One reason for investing eort in echo classi®cation is to be able to distinguish echoes from FBs from echoes from other sources.
2. Theory Ultrasound probing relies on the damping, re¯ection, scattering and harmonics generation of sound as it propagates through a sample. The attenuation of the probing sound stems partly from energy transfer from the acoustic beam to vibrating molecules of the medium and partly from apparent absorption of acoustic energy due to scattering and re¯ection of the sound beam (Bhatia, 1967). The attenuation is proportional to the square of the probing frequency which means that good resolution, inversely proportional to the frequency, requires a very high probing frequency (Kinsler, Frey, Coppens, & Sanders, 1982). The acoustic power attenuation for a plane wave is P P0 eÿ2ax ;
1
where P0 is the power of the source, and x is the propagation distance which is twice the probing depth. The attenuation coecient, a, is classically (Morse & Ingard, 1986) a
gx2 ; 2c3 q
2
where g is the dynamic viscosity of the product, w the angular frequency of the probing sound, c the phase velocity of the sound in the product and q is the eective density of the product. The acoustic power re¯ection coecient is C
Z2 cos h ÿ Z1 ; Z2 cos h Z1
Z qc;
3
where Z1 is the acoustic impedance in the incident medium, Z2 the acoustic impedance in the transmission region and h is the angle of incidence (Morse & Ingard, 1986). The power transmission coecient is de®ned as T 1 ÿ jCj:
4
When sound impinges on an FB it is scattered particularly if the acoustic impedance of the FB diers from its surroundings. If the diameter of the FB is large and its surface roughness (the standard deviation of the sample thickness per area (Rakels, 1988)) is small compared to the wavelength of the probing sound, then the sound is
re¯ected evenly into the surrounding space. The intensity of the sound transmitted from a specular re¯ector is 2 Ca I
a; r Iin ;
5 2r where a is the diameter of the FB, r the distance from the FB, Iin the intensity of the incident wave and G is the acoustic re¯ection coecient of the FB. For specular re¯ectors C 1. The surface ®nish is important for the scattering properties of the FB. The surfaces of the FBs in this investigation were considered nonreactive and rough (Morse & Ingard, 1986). Increased surface roughness of the sample reduces the re¯ected amplitude and widens the cone of re¯ection (Krautkramer & Krautkramer, 1983). A re¯ector, whose diameter is small compared to the wavelength of the probing sound, scatters every wave individually and the re¯ections show a random pattern. A cluster of such small re¯ectors tends to act like a diuse re¯ector where the scattered intensity is inversely proportional to the fourth power of the incident intensity (Kino, 1987). The non-homogenous products showed this tendency. The acoustic cross-section of spherical FBs is smaller than their geometric cross-section since much of the sound incident on the sphere is not re¯ected back to the transducer. The acoustic cross-section of the FB can be estimated by assuming that the FB lies on the acoustic axis of the transducer. With a 25 mm-diameter transducer and an equally large FB the diameter of the observed scattering patch is approximately 1.15 mm when the object is at 50 mm distance from the transducer. Misalignment of the transducer reduces considerably the apparent acoustic cross-section due to the curvature of the sphere. The detection ability of a measurement system can be evaluated by comparing required echo signals from dierent FBs. In order to assess and compare relative detectabilities of particular FBs in dierent food products the measured signals have to be normalized. Normalization takes into account size and impedance of the FB, impedance of the food product and probing depth. This can be done with the following formula Urel 20 log
ÿ ÿG Umax 10U Gmax 20 ; U0 eÿ2ax T12 T22
6
where Urel is the corrected signal, Umax the maximum excitation voltage available, U0 the pulse excitation voltage, Gmax the maximum gain available, G the receiver gain, U the measured echo amplitude, T1 the transmission coecient between water and product package, T2 the transmission coecient between product package and food stu, a the attenuation coecient of water and x is the probing depth.
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3. Measurement system
4. Methods
The measurements were performed in an asymmetric basin made of polystyrene that minimizes in¯uence of echoes re¯ected from the walls of the basin. The bottom of the basin was coated with 10 mm Dow Corning silicon. The basin was ®lled with degassed water which had been kept in room temperature for 24 h. The product to be tested was lowered into the basin in a specially designed sample box whose front face was 100 lm thick and made of polyethylene terephtalate (PET). The acoustic impedance of the PET wall was measured to be 1:75 0:1 MRayl. The other three walls of the sample box were made of polystyrene with an impedance of 2.55 MRayl (Morse & Ingard, 1986). A customized sample box was used in order to avoid airpockets commonly present near the walls of a commercial package. The measurement system is depicted in Fig. 1. The temperature dependence of the acoustic parameters in the test products was determined experimentally in the temperature range 0.5±22°C. During the temperature dependence tests, an isolated ice reservoir was used to control the temperature of the product by adjusting the temperature of the water in the basin. This reservoir was placed in the measurement basin so that it would not disturb the measurements. It was possible to maintain the temperature of the product within 0:5°C of the target temperature during the measurements. The ultrasound transducer was a 25 mm-diameter ¯at-focussed 5 MHz Harrisonic transducer. The frequency range of the water-matched transducer was 3.45±5.4 MHz. It was possible to automatically move the transducer. The distance from the transducer to the sample box was 20 mm. The ultrasonic source was a UTEX 320 pulser-receiver. The amplitude of the excitation signal was 350 V. The received signal was preampli®ed, 69 dB with two Panametrics 5052 ampli®ers and digitized at 150 MHz with a LeCroy 9410 oscilloscope. The digitized signal was averaged 200 times.
4.1. Foreign bodies
Fig. 1. The measurement apparatus.
39
The food products were stored in the laboratory refrigerator at 3°C. The packages were taken out of the cold store the day before the tests for insertion of FBs. The food product to be tested was placed in a sample box and the FB to be identi®ed was implanted into the food product. Implanting was done in the following way: (1) a vertical canal was drilled using a drill with a diameter 1 mm less than the diameter of the FB to be implanted, (2) the FB was gently put into position after which the canal was carefully ®lled and sealed. The absolute positioning errors of the FBs were estimated to be less than 2 mm horizontally and 3 mm vertically. These maximum ratings would induce an error in relative amplitude of approximately 3% estimated by raytracing without interference considerations. After the implanting procedure, the sample was stored in the refrigerator over night. The following day the tests were commenced. One sample at a time was taken out of the refrigerator and measured immediately to minimize the aeration of the sample. Five parallel samples were used for each FBproduct combination. The echo sequence was transferred over the GPIB bus to the computer for o-line analysis. The amplitude of the echo and the travel time to the echo were also recorded manually. The manual readings were compared with the data-analytic estimates. Eight dierent FBs in eight products were tested at probing depths 25, 50 and 75 mm. The food products are tabulated in Table 1 and the FBs tested are shown in Table 2. 4.2. Temperature dependence of the acoustic parameters of the products An optimal detection temperature for each product was determined from temperature dependence measurements of sound attenuation, phase velocity and density. The sound attenuation coecient of each product was minimized while the impedance ratio between the FB and the test product was maximized. The density of the products was determined classically. The sample box was weighed both ®lled with foodstu and with water. The density was determined from volume and weight measurements. The relative error of weighting was 0.02% and of volume 1%. Prior to the temperature dependence measurements, samples were cooled down to 0.5°C. The phase velocity of sound in each product was determined by ®lling the sample box ®rst with water and then with the test product: the ¯ight times were compared. The timeof-¯ight of the acoustic signal in the product was recorded as a function of temperature. The measured time-
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Table 1 The tested products Product class
Product
Producer
Margarine (80% fat content)
BreGott extra salty (2%) BreGott normal salty (1%) Naturelle 17% fat content Greve 13% fat content J amtg ard cheese 28% fat content Unprocessed Processed R akost
Swedish Butter, Sweden
Processed cheese Chunk cheese Cherry marmalade Shrimp cheese
NNP, Sweden Norrost, Sweden Danone, France NNP, Sweden
Table 2 The data of the foreign bodies tested Foreign body
Size
Impedance
Bone sphere Wood sphere Wood cube Plastic sphere Steel sphere Stone Piece of glass Piece of plastic
Diameter 10 mm Diameter 10 mm Side length 10 mm Diameter 10 mm Diameter 14 mm 20 10 5 mm 2 5 7 mm 10 10 1 mm
8 MRayl (CRC Handbook of Chemistry & Physics, 1986; Linser, 1979) 1.6 MRayl (Kinsler, Frey, Coppens, & Sanders, 1982) 1.6 MRayl (Kinsler, Frey, Coppens, & Sanders, 1982) 3 MRayl (Kinsler, Frey, Coppens, & Sanders, 1982) 11 MRayl (Kinsler, Frey, Coppens, & Sanders, 1982) 10 MRayl (CRC Handbook of Chemistry & Physics, 1986) 12 MRayl (Kinsler, Frey, Coppens, & Sanders, 1982) 3 MRayl (Kinsler, Frey, Coppens, & Sanders, 1982)
of-¯ight values were then linearly correlated with temperature. The attenuation coecient of each product was classically determined by linearly ®tting echo-amplitudes from a plane steel re¯ector placed at ®ve depths in the sample. The procedure was repeated at dierent temperatures. The values of the attenuation coecient were plotted as a function of sample temperature. 4.3. O-line data analysis 4.3.1. Detection of foreign bodies Classic A-mode analysis was used to determine whether it was possible to detect particular FBs in the dierent products. Five parallel samples were analysed and the average results were recorded. The analysis consisted of three steps: 1. Forming a dierence signal between the measurements on a sample with a FB and the measurements on a sample without FB, Fig. 2 block 1. 2. Filtering the dierence signal with a 1 MHz±6 MHz software bandpass ®lter and windowing the ®ltered signal using 5% window width, thus segmenting the signal into 20 time windows, Fig. 2 block 2. 3. Testing the echo signal in the sample window against the noise ¯oor in the other windows. A particular FB in a product was labelled detectable if its echo S/N ratio was above 1.5. This corresponded to an echo amplitude of approximately 5 mV.
Comments Semi-rough surface Polished surface Polyhedron Rough surface Rhombic
4.3.2. Identi®cation of foreign bodies In the explorative data analysis eort such properties of the received ultrasonic signal were looked for that distinguished particular FBs in dierent products. The strategy was to mathematically transform the signal vector in order to reveal acoustic characteristics of the FB. A CV represents a feature of a transform, e.g., the most energetic frequency in the Fourier transform. Five parallel samples were analysed and the average results were recorded. The analysis was performed in six steps. The ®rst two steps were identical with those in Section 4.3.1. The following four steps were: 1. Performing 18 transformations of the echo sequence in each window and extracting the 200 characteristic values (CV) of the dierent transforms into a characteristic value pro®le (CVP), Fig. 2 block 3. 2. Subtracting a reference window pro®le obtained from the #2 window from the CVPs of the other windows, Fig. 2 block 4. 3. Testing the sample window pro®le against the CVPs of the other windows, Fig. 2 block 5. 4. Testing the successful CVs of the sample window pro®le against the corresponding CVs of the other windows, Fig. 2 block 6. The identi®cation of the FBs was done in block 5 and 6. Essentially CVs that were larger than the noise ¯oor of all windows were labelled successful, block 5. They were considered useful only after having proved not to
E. Hñggstr om, M. Luukkala / Food Control 12 (2001) 37±45
41
Fig. 2. The o-line data analysis depicted schematically.
be larger than the noise ¯oor in any other window than in the FB window, block 6.
5. Results 5.1. Acoustic properties of the test products Phase velocities and attenuation coecients, measured at 20°C, of the test products 1 are tabulated in Table 3. The results follow those of (Lee et al., 1992; Povey, 1989) reporting sound velocities of 1365±1645 m/s for cheese with 45±55% fat content and attenuations of 5±15 Np/m for egg. The calculated acoustic impedances of the products are given in Table 4. The temperature dependence of both attenuation and of sound velocity in the dierent products were obtained with a least squares regression technique. The amplitude and time-of-¯ight of a test signal was regressed on propagation distance. The greatest velocity dependence on temperature, 0.5%/°C, was found by Naturelle and the greatest attenuation dependence on temperature, 8.1%/°C, was found by Margarine extra salty. The corresponding values for water are 0.3%/°C and 0.5%/°C (Kinsler, Frey, Coppens, & Sanders, 1982; Frederick, 1965). Since attenuation increased as a function of temperature the optimal detection temperature was 1±5°C. Transmission coecients for the front face of the sample box were calculated from the measured impedance values of both PET and the samples. The calculated transmission coecients necessary to determine the corrected echo amplitudes are shown in Table 4. 5.2. Detected echo signals from foreign bodies A particular FB in a product was labelled detectable if its echo amplitude was larger than 5 mV. 1 Shrimp cheese was incorporated as a test product only at a later stage of the project.
Table 5 contains raw signals and normalized signals obtained with detectable FB-product combinations (see footnote 1). Normalization facilitated comparison of detectability between particular FBs in dierent products by removing the in¯uence of the sample box, the water path and the ampli®er. Only in Naturelle, Margarine extra salty, Greve and Margarine normal salty was it possible to detect FBs at 75 mm probing depth. At 25 mm probing depth the same FB-product combinations were detectable as those shown in Table 5. 5.3. Successful characteristic values for identifying foreign bodies Identi®ability of the FB in a product was determined with the two-step test outlined in Section 4.3.2. The required S/N ratio for the CVs was 3 in the ®rst test and 1.5 in the second test. The data analysis revealed 22 successful CVs which are listed in Table 6. Only 17 of these were required to achieve maximum identi®cation ability of the system. In Table 6, the 17 required CVs are made bold, whereas italics is used, where two FBs cannot be distinguished from each other in the same product. Table 6 indicates that it was possible to distinguish all FBs from each other in Naturelle only. The most successful CVs were #29; the maximum amplitude of the bicoherence function, #85; the total power in the Wigner bi-spectrum, #86; the total power in the Wigner tri-spectrum, #88; the maximum amplitude in the Wigner bi-spectrum, #89; the maximum amplitude in the Wigner tri-spectrum, #114; the maximum value of the wavelet packet coecient on level (3,3) with Daubechies ``db4'' wavelet, and #153; the temporal change of the frequency with maximum energy. Fig. 3 shows the magnitude of CV#153 measured at 8°C in dierent time windows with the stone and the piece of plastic in normal salty margarine. The reference window is window #2 and the foreign body is detected in window #13.
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E. Hñggstr om, M. Luukkala / Food Control 12 (2001) 37±45
Table 3 Acoustic parameters of the products measured at 20°C Product
Sound velocity (m/s)
Attenuation coecient (Np/m)
Water (Frederick, 1965) Processed cheese: Naturelle Margarine: extra salty Margarine: normal salty Processed cheese: Greve Chunk cheese: Jamtg ard Cherry marmalade: unprocessed Cherry marmalade: processed
1483 1311 50 1118 20 1145 130 1323 20 1842 70 1330 30 1420 30
0.62 3:72 0:34 8:93 0:46 2:36 0:44 9:05 0:37 7:97 0:22 n.d. n.d.
Table 4 Impedances of test products and calculated transmission coecients between the test container and test products measured at 20°C Product
Acoustic impedance (MRayl)
PET
Polystyrene
Water Processed cheese: Naturelle Margarine: extra salty Margarine: normal salty Processed cheese: Greve Chunk cheese: Jamtg ard Cherry marmalade: unprocessed Cherry marmalade: processed
1:48 0:01 1:32 0:04 1:21 0:02 1:28 0:03 1:38 0:02 1:73 0:06 1:44 0:03 1:63 0:03
0:92 0:03 0:90 0:04 0:82 0:03 0:84 0:06 0:88 0:03 0:99 0:04 0:90 0:03 0:96 0:03
0:74 0:02 0:72 0:03 0:64 0:02 0:67 0:05 0:70 0:02 0:81 0:03 0:72 0:04 0:78 0:04
Table 5 Echo amplitudes (mV) measured at 20°C and calculated normalized echo amplitudes (dB/cm2 ) of FBs in dierent products at 50 mm depth FB/Product
Stone (5 10 20 mm)
Piece of glass (2 5 7 mm)
Woodsphere (10 mm)
Wood cube (10 mm)
Plasticsphere (10 mm)
Bone Sphere (10 mm)
Steel sphere (14 mm)
Processed cheese: Naturelle Margarine: extra salty Margarine: normal salty Processed cheese: Greve Chunk cheese: Jamtg ard Cherry marmalade: unprocessed Cherry marmalade: processed
11.9 6.0 9.0 5.5 9.2 5.9 26.8 8.0 15.5 6.9 14.3 12.6 25.0 6.4
8.5 mV 15.5 8.5 mV 16.6 12.5 mV 21.1 24.7 mV 24.1 18.5 mV 23.4 15.4 mV 39.6 21 mV 19.1
10.0 10.9 8.7 10.8 11.5 13.0 18.5 13.6 14.2 13.3 12.6 24.9 21.0 12.2
15.3 42.2 9.1 34.7 15.2 46.4 18.3 42.5 13.6 41.0 10.3 76.0 20.0 37.9
5.7 20.4 7.2 26.6 13.1 38.4 21.4 40.4 13.3 35.8 13.1 69.3 20.0 33.5
11.6 mV 29.8 8.6 mV 27.3 18.3 mV 40.9 21.3 mV 37.0 14.4 mV 34.2 23.6 mV 63.1 21 mV 31.1
9.6 21.8 7.6 20.2 11.7 26.8 22.5 30.3 12.0 24.9 12.8 50.8 22.0 25.1
mV mV mV mV mV mV mV
mV mV mV mV mV mV mV
6. Discussion The ability to identify the various FBs in each individual product was considered to be the prime task of the system. The results suggested that if the FB could be identi®ed in a certain product then its identi®cation required only one CV. This ®nding reduces the computational burden of the system. The results also showed
mV mV mV mV mV mV mV
mV mV mV mV mV mV mV
mV mV mV mV mV mV mV
that the identi®cation task is harder than the detection task since all FBs reported could be detected but not identi®ed in the test products. The results indicated that the system was most successful (7/7 FBs identi®ed) with Naturelle cheese which is characterized by its spreadability and homogeneity. Fairly good results (5/7 FBs identi®ed) were obtained with margarine and processed cheese, which are also homogeneous and spreadable.
a
#29
Processed cheese: Naturelle Margarine: extra salty Margarine: normal salty Processed cheese: Greve Chunk cheese: J amtg ard Cherry marmalade: unprocessed Shrimp cheese #114, #153
#62, #84, #86±89 #10, #29, #69, #71, #72, #75 #29
#43, #45, #54
#54, #86, #89
Piece of glass (2 5 7 mm) #41, #42, #53, #83±#85
Woodsphere (10 mm)
#17, #19, #25 #77, #99 #29, #51, #114, #153
#22, #27, #53 #62, #77, #80 #86, #87, #88, #89
#54, #84, #86, #88, #89 #86, #89
Wood cube (10 mm)
#1, #11, #64, #104±106
#29
#29
#154
#143
#85
#86, #89
Plasticsphere (10 mm)
The bold entries are the optimal CVs. Italics are used where two FBs cannot be distinguished from each other in the same product.
#85
#16, #17, #18, #25, #143
#54
Stone (5 10 20 mm)
FB/Product
Table 6 Successful CVs identifying FBs in dierent products at 50 mm deptha
#29, #51, #85, #153
#66, #152
#84, #86±89 #29
#31, #84, #86±89
#85
Bone Sphere (10 mm)
#86±89
#86, #88, #89
#86, #88, #89
Steel sphere (14 mm)
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products chosen for testing at 20±75 mm probing depth. Non-homogenous products restricted probing depth to 50 mm due to poor S/N ratios. It was also shown that all dierent FBs could be identi®ed in the Naturelle cheese. The concept could allow for preliminary automatic sorting of food containers prior to more thorough manual testing. Automatic sorting would thus enable a higher output rate with the same quality control. The optimal detection temperature interval was found to be 1±5°C. Fig. 3. The CV #153 depth pro®le for the stone and the piece of plastic in normal salty margarine.
Moreover it was noticed that the plastic bead, the piece of glass and the bone bead were easiest to identify in the dierent products (6/7 FBs identi®ed). The results obtained with shrimp cheese is to be considered promising since this product is a non-homogenous product. The measurements indicated that it was possible to detect FBs in commercial food products using ultrasound. The greatest diculties, due to spurious echoes, were encountered with products having an internal structure whose spatial dimensions are similar to the wavelength of the probing sound. This problem could partly be overcome with a multi-frequency probing concept. Low impedance FBs with small acoustic crosssection tend to show weak echoes. Some cases of alignment error of the FB, positioning it o the acoustical axis, were observed. These problems could have been remedied with a horizontal scanning facility. Horizontal scanning could also have enhanced echo classi®cation as it does in medical equipment. Some cases with contact problems were observed. The acoustic contact should be carefully designed since it greatly determines the reliability of the measurement system. A 50-mm detection depth enables inspection of standard packages with contents of approximately 400 g. A spherical transducer would enhance penetration depth and spatial resolution of the system. A proper choice of wall material of the food package reduces the shadow zone, thus improving the detection ability of the system. The detection and identi®cation capability of the concept might be improved with a scattering measurement set-up. Such a set-up might enhance the ability of the system to identify FBs since the scattering pattern is a function of target shape. Moreover echoes from implanted airpockets should be compared with the echoes from the FBs. 7. Conclusion The research indicated that it was possible to detect the inspected foreign bodies (FB) in the homogeneous
Acknowledgements This work has been supported by the Swedish Cultural Foundation in Finland. The authors wish to thank Mrs J. Korvenoja and K. Vuori for their help with the measurements. Appendix A The successful characteristic values in Table 6 were de®ned in the following way: #1: Maximum amplitude of the wavelet transform on approximation level 1. #10: Maximum amplitude of the wavelet transform on approximation level 10. #11: Maximum amplitude of the Fourier transform. #16±19, 22, 25: Temporal position of maximum amplitude of the wavelet transform on approximation level 1±4, 7, 10. #27: f2 coordinate of the maximum bicoherence. #29: Total power in the bicoherence spectrum. #31: Maximum amplitude of the cumulant. #41±43, 45: Maximum power in the wavelet transform on approximation level 1±3, 5. #51, 53, 54: Maximum power in the wavelet transform on detail level 1, 3, 4. #62: Total power in the cross-correlation spectrum. #64, 66, 69, 71, 72: Maximum amplitude of the wavelet transform on detail level 2, 4, 7, 9, 10. #75, 77, 80: Temporal position of maximum amplitude of the wavelet transform on detail level 3, 5, 8. #83: Total power in the Hilbert transform. #84±86: Total power in the Wigner mono-, bi-, trispectrum. #87±89: Maximum amplitude in the Wigner mono-, bi-, tri-spectrum. #99: Maximum amplitude of median ®ltered signal. #104±106, 114: Maximum amplitude of the wavelet packet transform on level 0, 1, 2, 3,. #143: Maximum value of the moving coecient of variance. #152: Maximum value of the half-width gradient. #153: Maximum value of the entropy gradient.
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