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Feasibility study of NIR diffuse optical tomography on agricultural produce
Available online at www.sciencedirect.com
Postharvest Biology and Technology 48 (2008) 223–230
Feasibility study of NIR diffuse optical tomography on agricultural produce E. Kate Kemsley a , Henri S. Tapp a,∗ , Richard Binns b , Robert O. Mackin b , Anthony J. Peyton c a
Institute of Food Research, Norwich Research Park, Colney, Norwich NR4 7UA, UK b Lancaster University, Engineering Department, LA1 4YR, UK c University of Manchester, School of Electrical & Electronic Engineering, Manchester M60 1QD, UK Received 14 June 2007; accepted 16 October 2007
Abstract It is desirable to monitor the quality of fresh fruit and vegetables since it benefits both producers, by offering a competitive advantage, and consumers, by improving consistency and hence encouraging a more healthy and varied diet. Near-infrared (NIR) spectroscopy is a candidate technology for monitoring agricultural produce quality. Here there has been a recent trend toward transmission-based geometries which interrogates deeper into the sample. NIR tomography is the natural progression of this, offering the possibility of detecting internal defects. The aim of this study was to evaluate a NIR tomograph built from relatively low-cost components. This comprised a stabilised VIS/NIR broadband source; a diodearray NIR spectrometer and a sample turntable. The angular positions of the detector and turntable could be moved independently of each other using two stepper motors under computer control. An experimental approach was adopted to generate a linear ‘difference image’ reconstruction matrix using 47 mm diameter potato cores, with a nominal length of 65 mm, and a 10 mm diameter black rod acting as an internal absorbing perturbation. The reconstruction matrix was generated for a single wavelength (689 nm) using multiple linear regression and evaluated for the case of two perturbing rods. The reconstructed image was of comparable quality to that typically obtained from other so-called ‘soft-field’ tomographic techniques. Although conducted under highly simplified conditions, the results suggest NIR tomography has potential for monitoring internal defects in agricultural produce. © 2007 Elsevier B.V. All rights reserved. Keywords: Quality control; Near-infrared; Food; Optical tomography; Difference imaging
1. Introduction Near-infrared (NIR) diffuse optical tomography is an emerging method for imaging the interior composition and structure of biological tissues, comprehensively reviewed by Arridge (1999), based on an understanding of the scattering properties of tissue (Wilson and Jacques, 1990). NIR radiation is well suited to the examination of such materials, since it is non-destructive and non-ionizing. NIR technologies already provide low-cost sensing solutions (including hyper-spectral imaging) for a wide range of applications, and so the move to tomographic (slice-) imaging is, in a sense, the next logical step to take, as it is the precursor to true 3D imaging (Hebden et al., 2002). NIR diffuse
∗
Corresponding author. Tel.: +44 1603 255145; fax: +44 1603 507723. E-mail address: [email protected] (H.S. Tapp).
0925-5214/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.postharvbio.2007.10.014
optical tomography is already generating interest in the medical field, but there are only limited precedents for its use in the non-medical life sciences. The focus in this proof-of-concept investigation has been on plant tissues and the aim was to establish whether the approach has the potential to be a useful tool for internal imaging of whole fruit and vegetables. The ability to detect localized variation in structure and/or composition would have an impact not only as a research tool, but also in the agricultural sector, where a rapid, cost-effective and, crucially, non-destructive approach to internal quality determination may be of interest. There is considerable research activity into the investigation of NIR-based sensors for determining various quality factors in a range of fruit and vegetables. A wide range of sensor modalities has been explored. These include reflectance and interactance probes (Greensill and Walsh, 2000; McGlone et al., 2002), through to transmission systems such as used by McGlone and
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Martinsen (2004) and McGlone et al. (2005). Fraser et al. (2003) used an invasive probe to measure the light variation within Satsuma mandarins. Lammertyn et al. (2000) used an alternative approach to study light penetration within ‘Jonagold’ apples. Recent trends include the adoption of multi-spectral (Kleynen et al., 2005) and hyper-spectral imaging systems (Lu, 2004; Xing et al., 2005; Lefcout et al., 2006; Nicola¨ı et al., 2006; Peng and Lu, 2006; Liu et al., 2007) as well as time resolved measurements which aim to decouple signal attenuation from scattering and absorption (Cubeddu et al., 2001; Tsuchikawa et al., 2002; Tsuchikawa and Hamada, 2004; Valero et al., 2004; Chauchard et al., 2005). The objective of the work was to build a relatively low-cost optical tomography system from a combination of commercial and custom-made components. This paper will detail how test objects, or phantoms, were use to appraise the response of the system in terms of the basic signal response and also ability to reconstruct images. 2. Materials and methods The tomograph comprised the following main components: (1) A stabilized VIS/NIR broadband source (150 W Stocker & Yale Mille Luce M1000 with an EKE-ER lamp and 630 nm long-pass filter), coupled via a ‘goose neck’ optical fibre bundle to the specimen chamber. (2) A second fibre optic coupling to an EPP2000 NIR spectrometer (StellarNet Inc., Florida, USA). (3) Two computer-driven stepper motors: one for rotating a turntable on which the phantoms are placed, and another to control the angular position of the detector. (4) A software user interface written in LabVIEW. This controlled the stepper motors, the spectrometer settings, and the logging of the subsequent data. A photograph of the system, with the housing removed, is shown in Fig. 1. The spectrometer has a nominal spectral range of 486–1325 nm. The effective range was however limited by the 630 nm long-pass filter, which allowed the source intensity to be increased without saturating the detector elements at the lower wavelengths, and the intensity profile of the combined source and transmission properties of the goose neck optical bundle. The design of the tomograph reflects our three main con-
siderations of cost, simplicity and flexibility. For example, the polychromatic source and spectrometer allowed us to appraise a range of candidate wavelengths, although the results will be presented for a single wavelength. Using a single source and detector with mechanical scanning gave flexibility, although this had the disadvantage of increasing the acquisition time. Keeping the source stationary and moving the spectrometer with the collection optics permitted the light path along the source and detector fibre optics to be unaltered. A number of considerations have led to the selection of potatoes as model specimens, or phantoms, with which to develop the image reconstruction approach. The scattering and absorbance characteristics of potatoes have been previously studied (Birth, 1978; Birth and Hecht, 1987); they have a relatively uniform internal matrix, come in a variety of sizes and can be cut into cores and have cores removed. Furthermore, the issue of internal quality is important in potatoes, where there is a need to detect the physiological problems of hollow heart and brown centre. The use of cylindrical phantoms aids in the assessment of the characterisation of the system as the general 3D geometry is reduced to one with a uniform cross-section. This simplifies the mapping of the spatial sensitivity of the system, although like other soft-field tomographic techniques, the true interaction with the sample is not confined to a single cross-sectional plane (Tapp and Wilson, 1997; Tapp et al., 2003). Using this simplified model system also allows the generation of a linear reconstruction matrix based on direct measurements. This experimental approach has previously been adopted by the authors for image reconstruction in electrical capacitance (Tapp et al., 1998) and magnetic induction (Binns et al., 2001) tomography. The potato phantoms comprised 47 mm diameter cylindrical ‘cores’, cut to length of ∼65 mm (Fig. 2a) and wrapped in plastic film to reduce dehydration during data acquisition. The sensitivity to a local spatial perturbation was investigated by inserting a 10 mm diameter black rod into cores cut out at various radial positions (Fig. 2b). The rod was assumed to have an absorbance much greater than the potato tissue throughout the spectral range investigated (i.e., a high-contrast broadband absorber). The data collection protocol, shown schematically in Fig. 3a, involved rotation of the phantom through 20 different angles, for each of 11 positions of the detector, with data collected at each different specimen-source-detector configuration. Thus, 220 spectra were collected for each phantom. Each spectrum was collected using an integration time of 50 ms and 128 coadded scans. Typical practice in infrared spectroscopy is to collect a background reading from an empty sample cell, or in a dual-beam instrument, from a second optical path that does not traverse the sample. The absorbance spectrum AS is then obtained from the ratio of the single-beam sample spectrum I to the single-beam background I0 , given in Eq. (1): As = −ln
Fig. 1. Photograph of the prototype VIS/NIR diffuse tomography system with external housing removed.
I I0
(1)
An analogue in the present work was to collect background data from internally homogeneous reference specimens (Fig. 3b). Tomographically, this approach is termed difference imaging.
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Fig. 2. Potato phantom. (a) Plastic wrapped cylinder used in collecting reference spectra (b) slice view of cylinder used in the calibration stage, showing position of inserted rod.
3. Results and discussion Fig. 4 shows the variation in the intensity with detector position, for the single-beam reference signal at 689 nm. It can be seen that, as expected, the overall signal intensity is related to the source-detector position, with the response greatest for position 1 (adjacent) and then steadily reducing to position 11 (opposite) as defined in Fig. 3a. The smoothly varying relationship between signal and detector position, suggests that it may be possible to simulate the background data, which may become important in systems where there is no obvious object to be used as a background specimen. For example, Fig. 4 also shows that the variation in the reciprocal of the chord length between source and detector position is similar to the measured variation in signal intensity, although this is for a highly simplified phantom geometry. Having found a plausible variation in the background intensity with detector position for a homogeneous phantom, the next set of experimental tests involved measurements on phantoms in which a single perturbing rod is placed at five different ini-
tial positions. This allowed the variation in absorbance for each detector position to be monitored as each phantom is rotated through one complete revolution. The results for one such test are shown in Fig. 5, with the initial position of the rod shown in the bottom right hand corner. It should be noted that the response at different source-detector configurations varies greatly, and in fact, the pattern of absorbances obtained as the sample rotates appears as may be intuitively expected. For example, compare responses from the ‘adjacent’ source-detector configuration 1 with those from the ‘straight-through’ configuration 11—in the latter, the absorbance maxima are clearly seen at ∼90◦ and ∼270◦ positions. It was found that this intuitive consistency was obtained for all of these simple phantoms. Note also the absorbance magnitudes shown in Fig. 5, where the smallest absorbances (i.e., signal changes) were found for detector position 1 (adjacent). This is consistent with greater proportions of the specimen being interrogated as the detector moved towards the position 11 (opposite). This general behaviour with the largest absolute signal for the adjacent position; and the largest change in signal
Fig. 3. Measurement of the system response. (a) Experimental protocol for investigating the spatial sensitivity (b) side-on view showing the relative separation between the source- and detector-optics and the phantom.
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Fig. 4. Measurement of the system response: background signal vs. detector position.
Fig. 5. Measured absorbance data at each detector position during a complete rotation (0–360◦ ) of a phantom shown bottom right.
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for the opposite position is common to other soft-field tomographic modalities, which is an encouraging result in terms of the potential viability of generating images. The next stage was to map out the spatial sensitivity within the potato cylinder. For each rod position a binary ‘actual’ image vector was generated. This comprised 768 values which represent the central circular region within a 32 × 32 pixel array. All the pixels occupied by the rod were then assigned as 1, with the remaining pixels assigned as 0. For a 10 mm rod, this corresponds to approximately 32 occupied pixels (see Fig. 5). Similarly, a reconstructed (i.e., predicted) image can be considered as a (1 × 768) vector of greyscale values. A representation of the spatial sensitivity for a given detector position was calculated, pixel by pixel, as the mean of the absorbance values associated with a particular pixel being occupied by the rod, described in Eq. (2): x- Ti yj Sij = yj -
(2)
Where Sij is an element in a matrix S giving the sensitivity value for the ith detector and jth pixel; x- Ti the transpose of a column vector of absorbances for the ith detector position, yi a column vector for the jth pixel, comprising ones and zeros. These were calculated for all the pixels that have been occupied by the rod at least once. The sensitivity maps for each detector position are shown in Fig. 6, with a pseudo-colour map representing the level of sensitivity. The sequence of the maps is from the left hand side of the top row to the right hand side of the bottom row. The adjacent source and detector position correspond to the map at the top left hand side with the source uppermost. The opposite source-detector position corresponds to the last map on the right hand side of the bottom row, with the source at the top and the detector at the bottom. The sequence steps through as the detec-
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tor is moved around the circumference of the object space. The maps clearly show how the regions of highest sensitivity follow the position of the detector as expected. The bright central spot is an artefact, which arises from the comparatively large number of measurements in which the central pixels are occupied compared to those closer to the perimeter. From the previous analysis we have found that there is a large variation in the background (no rod present) intensities with detector position. Also the region of sensitivity for a given detector position is not confined to a well-defined zone, with the level of sensitivity varying with position within the sample. These finding are typical of ‘soft-field’ tomographic modalities. Having shown that the response of the system is similar to other soft-field tomographic modalities, a second set of experiments was performed, with the aim of producing an image reconstruction matrix. The second set of experiments was performed on 8 single rod phantoms and 1 dual rod phantom. In each single rod experiment the rod was positioned at a different initial position. The data from the single rod experiment will be used, for ‘calibration’, to build an image reconstruction matrix. This is then ‘tested’ using the data from the dual rod experiment to produce an image. For each single rod phantom, measurements were collected at each detector location for 20 angular positions of the phantom. Prior to inserting the rod, a background set of measurement was collected to use for converting to absorbance units. Each single rod experiment therefore produces a 20 × 11 matrix of absorbances. As before, ‘ideal’ binary images were generated corresponding to each position of the rod. Each binary image, y, was converted to a 1 × 1024 image vector. Here we have used the full 1024 pixels from the 32 × 32 image array as this simplifies the rotation step described below. Each single rod experiment is associated with a 20 × 1024 matrix of pixel values. Combining the results from all 8 single rod experiments allowed the con-
Fig. 6. Example of sensitivity maps within a 47 mm diameter potato core for 11 different source-detector combinations.
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Fig. 7. Example of a reconstructed image (right) comprising two 10 mm diameter rods inside a 47 mm diameter potato core.
struction of an image matrix Y of dimensions 160 × 1024 and a measurement matrix X of dimensions 160 × 11. Assuming a simple first order representation of the system, a linear relationship between the measurement X and Y, the next task is to solve for Q in Eq. (3): Y = XQ
(3)
ˆ = (XT X)−1 XT Y Q
(4)
ˆ yˆ = xQ
(5)
Here Q is the image reconstruction matrix, superscripts ‘T’ and ‘−1’ refer to transpose and inverse matrix operation, respectively, and hat symbol, ‘ˆ’, used to represent the quantities as estimates. We used the least-squares ‘method of normal equations’ approach shown in Eq. (4) to solve Q, although numerically superior approaches exist (Golub and Van Loan, 1996). Further details on this method of calculating the image reconstruction matrix can be found in Tapp et al. (1998). Eq. (5) represents how a measurement vector can be used to estimate the corresponding image vector yˆ . Fig. 7 shows the image of the dual rod test example. Here measurements were collected as the phantom was rotated through 20 positions. The image from each new position was then rotated back to the start position and then the set of 20 images co-added. The reconstructed image was then normalised to aid comparison with the actual image. As this ‘test’ dataset was not used in generating the reconstruction model, the quality of the reconstructed image demonstrates the ability of the model to generalise. Note the encouraging degree of agreement between the reconstructed and ideal image, particularly in terms of the general size and position of the rods. Also note that the reconstructed image has been displayed using a pseudo-colour map rather than converting to a binary image by using an arbitrary threshold value. For example, Fig. 7 shows the height of the peak corresponding to the reconstructed left hand rod is larger than that corresponding to the right. Also present in Fig. 7 is a central halo artefact arising from a hot-spot being smeared out during the image rotation step.
4. Conclusion This paper has presented experimental results using diffuse NIR tomography, which show that it is possible to produce images of sectioned potatoes. In the tests, the images were of a comparable quality to other soft-field tomographic techniques. Although conducted under highly simplified conditions, the results suggest NIR tomography has potential for monitoring internal defects in agricultural produce. The system used in this study used a halogen bulb source and VIS/NIR spectrometer. Since the presented work was restricted to a single wavelength, in principle this could have been achieved using a monochromatic source and silicon photodetector. However the flexibility provided by this approach gave clear benefits with regard to the likelihood of success, critical for such a short-term study. The overall cost of construction was still comparatively low compared to other diffuse optical tomographs. This approach also hints toward the potential of conducting multi-spectral tomography, and by combining with well-established chemometric techniques, the possibility of mapping the concentration of specific chemical components. The optical tomography setup described was intended for laboratory use as a research tool. In the short-term, we think this is its most likely application. The approach of mixing commercial and custom components was successful in that it allowed a simple low-cost evaluation system to be constructed quickly, although the final design was far from optimal. In hindsight the performance could be improved through a more judicial choice of optical components and the mechanical scanning arrangement could have been better designed. Similarly, the image quality could have been improved by not restricting the detector positions to half the available space. We were interested in seeing how the signals changed with angular distance from the detector, and although in principle measurements from opposite positions could be synthesised, in practice it would be easier to have measured over a greater angular range. However we hope that this report will provide a simple guide to those interested in evaluating this technique. One likely research application is for comparing the sensitivity of various source-detector configurations to detect internal features. For simplified sample geometries, comparing measurements taken before and after the introduction of an internal target
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can provide convincing evidence of the ability to detect internal aberrations. For single source-detector geometries this change may be small, since the signal will be sensitive to varying degrees throughout a relative large spatial region. Tomographic modelling methods potentially provide an analytical framework for combining data collected from multiple locations to pull out these subtle changes. Essentially, this can be considered as taking a set of measurements and then transforming them to a new domain to provide better discrimination. Using simple phantoms is of course far removed from the various difficulties that will need to be overcome in real life situations. These problems include: irregular shape and sizes, and their associated 3D effects; skin and dirt on the surface; smaller contrasts between the optical properties of healthy and diseased tissue; variations in detection limits with position from the surface; and constraints on the time available for data acquisition and processing. To address these now would be highly speculative and so we will restrict ourselves to some general comments. These problems are common to all NIR sensors, and so it may be possible to adopt some of the current methods of overcoming them. For example, adopting the approach described by Krivoshiev et al. (2000) for accommodating peel in potatoes. Methods developed by Dahm and Dahm (1999) could be used to model the interactions within the tissue. These are known to involve both absorption and scattering, which may be separated using approaches described in a pair of papers by Leonardi and Burns (1999a,b). Where there is little dispersion the scattering properties, which depend on differences in the refractive index, will not vary significantly with wavelength. In such instances scatter corrections based at a single wavelength can be applied across a spectrum, using an approach described in Leonardi and Burns (1999b). Here time resolved measurement were used to characterise the scattering properties, although steady-state methods, such as those described by Birth (1978), and updated by Lu (Lu, 2004; Peng and Lu, 2006) may be used instead. Finally, although optical tomography systems have been built that operate at high-acquisition rates, these were for studying certain processes confined to a fixed geometry, such as gas flow in bubble columns. For agricultural produce, additional size and shape information would be required. This could be acquired by projecting light patterns onto the object, which are then viewed by cameras—a technique called structured light. Combining this information during the image reconstruction is a potential time bottle neck, and so this technique may well first be restricted to supermarket applications rather than the, say 10 fruit/s, requirements of a conveyer line. Acknowledgment The authors thank the EPSRC, grant reference GR/ S71323/01, for funding this work, and the referees for their helpful comments. References Arridge, S., 1999. Optical tomography in medical imaging. Inverse Probl., R41–R93.
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Feasibility study of NIR diffuse optical tomography on agricultural produce E. Kate Kemsley a , Henri S. Tapp a,∗ , Richard Binns b , Robert O. Mackin b , Anthony J. Peyton c a
Institute of Food Research, Norwich Research Park, Colney, Norwich NR4 7UA, UK b Lancaster University, Engineering Department, LA1 4YR, UK c University of Manchester, School of Electrical & Electronic Engineering, Manchester M60 1QD, UK Received 14 June 2007; accepted 16 October 2007
Abstract It is desirable to monitor the quality of fresh fruit and vegetables since it benefits both producers, by offering a competitive advantage, and consumers, by improving consistency and hence encouraging a more healthy and varied diet. Near-infrared (NIR) spectroscopy is a candidate technology for monitoring agricultural produce quality. Here there has been a recent trend toward transmission-based geometries which interrogates deeper into the sample. NIR tomography is the natural progression of this, offering the possibility of detecting internal defects. The aim of this study was to evaluate a NIR tomograph built from relatively low-cost components. This comprised a stabilised VIS/NIR broadband source; a diodearray NIR spectrometer and a sample turntable. The angular positions of the detector and turntable could be moved independently of each other using two stepper motors under computer control. An experimental approach was adopted to generate a linear ‘difference image’ reconstruction matrix using 47 mm diameter potato cores, with a nominal length of 65 mm, and a 10 mm diameter black rod acting as an internal absorbing perturbation. The reconstruction matrix was generated for a single wavelength (689 nm) using multiple linear regression and evaluated for the case of two perturbing rods. The reconstructed image was of comparable quality to that typically obtained from other so-called ‘soft-field’ tomographic techniques. Although conducted under highly simplified conditions, the results suggest NIR tomography has potential for monitoring internal defects in agricultural produce. © 2007 Elsevier B.V. All rights reserved. Keywords: Quality control; Near-infrared; Food; Optical tomography; Difference imaging
1. Introduction Near-infrared (NIR) diffuse optical tomography is an emerging method for imaging the interior composition and structure of biological tissues, comprehensively reviewed by Arridge (1999), based on an understanding of the scattering properties of tissue (Wilson and Jacques, 1990). NIR radiation is well suited to the examination of such materials, since it is non-destructive and non-ionizing. NIR technologies already provide low-cost sensing solutions (including hyper-spectral imaging) for a wide range of applications, and so the move to tomographic (slice-) imaging is, in a sense, the next logical step to take, as it is the precursor to true 3D imaging (Hebden et al., 2002). NIR diffuse
∗
Corresponding author. Tel.: +44 1603 255145; fax: +44 1603 507723. E-mail address: [email protected] (H.S. Tapp).
0925-5214/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.postharvbio.2007.10.014
optical tomography is already generating interest in the medical field, but there are only limited precedents for its use in the non-medical life sciences. The focus in this proof-of-concept investigation has been on plant tissues and the aim was to establish whether the approach has the potential to be a useful tool for internal imaging of whole fruit and vegetables. The ability to detect localized variation in structure and/or composition would have an impact not only as a research tool, but also in the agricultural sector, where a rapid, cost-effective and, crucially, non-destructive approach to internal quality determination may be of interest. There is considerable research activity into the investigation of NIR-based sensors for determining various quality factors in a range of fruit and vegetables. A wide range of sensor modalities has been explored. These include reflectance and interactance probes (Greensill and Walsh, 2000; McGlone et al., 2002), through to transmission systems such as used by McGlone and
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Martinsen (2004) and McGlone et al. (2005). Fraser et al. (2003) used an invasive probe to measure the light variation within Satsuma mandarins. Lammertyn et al. (2000) used an alternative approach to study light penetration within ‘Jonagold’ apples. Recent trends include the adoption of multi-spectral (Kleynen et al., 2005) and hyper-spectral imaging systems (Lu, 2004; Xing et al., 2005; Lefcout et al., 2006; Nicola¨ı et al., 2006; Peng and Lu, 2006; Liu et al., 2007) as well as time resolved measurements which aim to decouple signal attenuation from scattering and absorption (Cubeddu et al., 2001; Tsuchikawa et al., 2002; Tsuchikawa and Hamada, 2004; Valero et al., 2004; Chauchard et al., 2005). The objective of the work was to build a relatively low-cost optical tomography system from a combination of commercial and custom-made components. This paper will detail how test objects, or phantoms, were use to appraise the response of the system in terms of the basic signal response and also ability to reconstruct images. 2. Materials and methods The tomograph comprised the following main components: (1) A stabilized VIS/NIR broadband source (150 W Stocker & Yale Mille Luce M1000 with an EKE-ER lamp and 630 nm long-pass filter), coupled via a ‘goose neck’ optical fibre bundle to the specimen chamber. (2) A second fibre optic coupling to an EPP2000 NIR spectrometer (StellarNet Inc., Florida, USA). (3) Two computer-driven stepper motors: one for rotating a turntable on which the phantoms are placed, and another to control the angular position of the detector. (4) A software user interface written in LabVIEW. This controlled the stepper motors, the spectrometer settings, and the logging of the subsequent data. A photograph of the system, with the housing removed, is shown in Fig. 1. The spectrometer has a nominal spectral range of 486–1325 nm. The effective range was however limited by the 630 nm long-pass filter, which allowed the source intensity to be increased without saturating the detector elements at the lower wavelengths, and the intensity profile of the combined source and transmission properties of the goose neck optical bundle. The design of the tomograph reflects our three main con-
siderations of cost, simplicity and flexibility. For example, the polychromatic source and spectrometer allowed us to appraise a range of candidate wavelengths, although the results will be presented for a single wavelength. Using a single source and detector with mechanical scanning gave flexibility, although this had the disadvantage of increasing the acquisition time. Keeping the source stationary and moving the spectrometer with the collection optics permitted the light path along the source and detector fibre optics to be unaltered. A number of considerations have led to the selection of potatoes as model specimens, or phantoms, with which to develop the image reconstruction approach. The scattering and absorbance characteristics of potatoes have been previously studied (Birth, 1978; Birth and Hecht, 1987); they have a relatively uniform internal matrix, come in a variety of sizes and can be cut into cores and have cores removed. Furthermore, the issue of internal quality is important in potatoes, where there is a need to detect the physiological problems of hollow heart and brown centre. The use of cylindrical phantoms aids in the assessment of the characterisation of the system as the general 3D geometry is reduced to one with a uniform cross-section. This simplifies the mapping of the spatial sensitivity of the system, although like other soft-field tomographic techniques, the true interaction with the sample is not confined to a single cross-sectional plane (Tapp and Wilson, 1997; Tapp et al., 2003). Using this simplified model system also allows the generation of a linear reconstruction matrix based on direct measurements. This experimental approach has previously been adopted by the authors for image reconstruction in electrical capacitance (Tapp et al., 1998) and magnetic induction (Binns et al., 2001) tomography. The potato phantoms comprised 47 mm diameter cylindrical ‘cores’, cut to length of ∼65 mm (Fig. 2a) and wrapped in plastic film to reduce dehydration during data acquisition. The sensitivity to a local spatial perturbation was investigated by inserting a 10 mm diameter black rod into cores cut out at various radial positions (Fig. 2b). The rod was assumed to have an absorbance much greater than the potato tissue throughout the spectral range investigated (i.e., a high-contrast broadband absorber). The data collection protocol, shown schematically in Fig. 3a, involved rotation of the phantom through 20 different angles, for each of 11 positions of the detector, with data collected at each different specimen-source-detector configuration. Thus, 220 spectra were collected for each phantom. Each spectrum was collected using an integration time of 50 ms and 128 coadded scans. Typical practice in infrared spectroscopy is to collect a background reading from an empty sample cell, or in a dual-beam instrument, from a second optical path that does not traverse the sample. The absorbance spectrum AS is then obtained from the ratio of the single-beam sample spectrum I to the single-beam background I0 , given in Eq. (1): As = −ln
Fig. 1. Photograph of the prototype VIS/NIR diffuse tomography system with external housing removed.
I I0
(1)
An analogue in the present work was to collect background data from internally homogeneous reference specimens (Fig. 3b). Tomographically, this approach is termed difference imaging.
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Fig. 2. Potato phantom. (a) Plastic wrapped cylinder used in collecting reference spectra (b) slice view of cylinder used in the calibration stage, showing position of inserted rod.
3. Results and discussion Fig. 4 shows the variation in the intensity with detector position, for the single-beam reference signal at 689 nm. It can be seen that, as expected, the overall signal intensity is related to the source-detector position, with the response greatest for position 1 (adjacent) and then steadily reducing to position 11 (opposite) as defined in Fig. 3a. The smoothly varying relationship between signal and detector position, suggests that it may be possible to simulate the background data, which may become important in systems where there is no obvious object to be used as a background specimen. For example, Fig. 4 also shows that the variation in the reciprocal of the chord length between source and detector position is similar to the measured variation in signal intensity, although this is for a highly simplified phantom geometry. Having found a plausible variation in the background intensity with detector position for a homogeneous phantom, the next set of experimental tests involved measurements on phantoms in which a single perturbing rod is placed at five different ini-
tial positions. This allowed the variation in absorbance for each detector position to be monitored as each phantom is rotated through one complete revolution. The results for one such test are shown in Fig. 5, with the initial position of the rod shown in the bottom right hand corner. It should be noted that the response at different source-detector configurations varies greatly, and in fact, the pattern of absorbances obtained as the sample rotates appears as may be intuitively expected. For example, compare responses from the ‘adjacent’ source-detector configuration 1 with those from the ‘straight-through’ configuration 11—in the latter, the absorbance maxima are clearly seen at ∼90◦ and ∼270◦ positions. It was found that this intuitive consistency was obtained for all of these simple phantoms. Note also the absorbance magnitudes shown in Fig. 5, where the smallest absorbances (i.e., signal changes) were found for detector position 1 (adjacent). This is consistent with greater proportions of the specimen being interrogated as the detector moved towards the position 11 (opposite). This general behaviour with the largest absolute signal for the adjacent position; and the largest change in signal
Fig. 3. Measurement of the system response. (a) Experimental protocol for investigating the spatial sensitivity (b) side-on view showing the relative separation between the source- and detector-optics and the phantom.
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Fig. 4. Measurement of the system response: background signal vs. detector position.
Fig. 5. Measured absorbance data at each detector position during a complete rotation (0–360◦ ) of a phantom shown bottom right.
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for the opposite position is common to other soft-field tomographic modalities, which is an encouraging result in terms of the potential viability of generating images. The next stage was to map out the spatial sensitivity within the potato cylinder. For each rod position a binary ‘actual’ image vector was generated. This comprised 768 values which represent the central circular region within a 32 × 32 pixel array. All the pixels occupied by the rod were then assigned as 1, with the remaining pixels assigned as 0. For a 10 mm rod, this corresponds to approximately 32 occupied pixels (see Fig. 5). Similarly, a reconstructed (i.e., predicted) image can be considered as a (1 × 768) vector of greyscale values. A representation of the spatial sensitivity for a given detector position was calculated, pixel by pixel, as the mean of the absorbance values associated with a particular pixel being occupied by the rod, described in Eq. (2): x- Ti yj Sij = yj -
(2)
Where Sij is an element in a matrix S giving the sensitivity value for the ith detector and jth pixel; x- Ti the transpose of a column vector of absorbances for the ith detector position, yi a column vector for the jth pixel, comprising ones and zeros. These were calculated for all the pixels that have been occupied by the rod at least once. The sensitivity maps for each detector position are shown in Fig. 6, with a pseudo-colour map representing the level of sensitivity. The sequence of the maps is from the left hand side of the top row to the right hand side of the bottom row. The adjacent source and detector position correspond to the map at the top left hand side with the source uppermost. The opposite source-detector position corresponds to the last map on the right hand side of the bottom row, with the source at the top and the detector at the bottom. The sequence steps through as the detec-
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tor is moved around the circumference of the object space. The maps clearly show how the regions of highest sensitivity follow the position of the detector as expected. The bright central spot is an artefact, which arises from the comparatively large number of measurements in which the central pixels are occupied compared to those closer to the perimeter. From the previous analysis we have found that there is a large variation in the background (no rod present) intensities with detector position. Also the region of sensitivity for a given detector position is not confined to a well-defined zone, with the level of sensitivity varying with position within the sample. These finding are typical of ‘soft-field’ tomographic modalities. Having shown that the response of the system is similar to other soft-field tomographic modalities, a second set of experiments was performed, with the aim of producing an image reconstruction matrix. The second set of experiments was performed on 8 single rod phantoms and 1 dual rod phantom. In each single rod experiment the rod was positioned at a different initial position. The data from the single rod experiment will be used, for ‘calibration’, to build an image reconstruction matrix. This is then ‘tested’ using the data from the dual rod experiment to produce an image. For each single rod phantom, measurements were collected at each detector location for 20 angular positions of the phantom. Prior to inserting the rod, a background set of measurement was collected to use for converting to absorbance units. Each single rod experiment therefore produces a 20 × 11 matrix of absorbances. As before, ‘ideal’ binary images were generated corresponding to each position of the rod. Each binary image, y, was converted to a 1 × 1024 image vector. Here we have used the full 1024 pixels from the 32 × 32 image array as this simplifies the rotation step described below. Each single rod experiment is associated with a 20 × 1024 matrix of pixel values. Combining the results from all 8 single rod experiments allowed the con-
Fig. 6. Example of sensitivity maps within a 47 mm diameter potato core for 11 different source-detector combinations.
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Fig. 7. Example of a reconstructed image (right) comprising two 10 mm diameter rods inside a 47 mm diameter potato core.
struction of an image matrix Y of dimensions 160 × 1024 and a measurement matrix X of dimensions 160 × 11. Assuming a simple first order representation of the system, a linear relationship between the measurement X and Y, the next task is to solve for Q in Eq. (3): Y = XQ
(3)
ˆ = (XT X)−1 XT Y Q
(4)
ˆ yˆ = xQ
(5)
Here Q is the image reconstruction matrix, superscripts ‘T’ and ‘−1’ refer to transpose and inverse matrix operation, respectively, and hat symbol, ‘ˆ’, used to represent the quantities as estimates. We used the least-squares ‘method of normal equations’ approach shown in Eq. (4) to solve Q, although numerically superior approaches exist (Golub and Van Loan, 1996). Further details on this method of calculating the image reconstruction matrix can be found in Tapp et al. (1998). Eq. (5) represents how a measurement vector can be used to estimate the corresponding image vector yˆ . Fig. 7 shows the image of the dual rod test example. Here measurements were collected as the phantom was rotated through 20 positions. The image from each new position was then rotated back to the start position and then the set of 20 images co-added. The reconstructed image was then normalised to aid comparison with the actual image. As this ‘test’ dataset was not used in generating the reconstruction model, the quality of the reconstructed image demonstrates the ability of the model to generalise. Note the encouraging degree of agreement between the reconstructed and ideal image, particularly in terms of the general size and position of the rods. Also note that the reconstructed image has been displayed using a pseudo-colour map rather than converting to a binary image by using an arbitrary threshold value. For example, Fig. 7 shows the height of the peak corresponding to the reconstructed left hand rod is larger than that corresponding to the right. Also present in Fig. 7 is a central halo artefact arising from a hot-spot being smeared out during the image rotation step.
4. Conclusion This paper has presented experimental results using diffuse NIR tomography, which show that it is possible to produce images of sectioned potatoes. In the tests, the images were of a comparable quality to other soft-field tomographic techniques. Although conducted under highly simplified conditions, the results suggest NIR tomography has potential for monitoring internal defects in agricultural produce. The system used in this study used a halogen bulb source and VIS/NIR spectrometer. Since the presented work was restricted to a single wavelength, in principle this could have been achieved using a monochromatic source and silicon photodetector. However the flexibility provided by this approach gave clear benefits with regard to the likelihood of success, critical for such a short-term study. The overall cost of construction was still comparatively low compared to other diffuse optical tomographs. This approach also hints toward the potential of conducting multi-spectral tomography, and by combining with well-established chemometric techniques, the possibility of mapping the concentration of specific chemical components. The optical tomography setup described was intended for laboratory use as a research tool. In the short-term, we think this is its most likely application. The approach of mixing commercial and custom components was successful in that it allowed a simple low-cost evaluation system to be constructed quickly, although the final design was far from optimal. In hindsight the performance could be improved through a more judicial choice of optical components and the mechanical scanning arrangement could have been better designed. Similarly, the image quality could have been improved by not restricting the detector positions to half the available space. We were interested in seeing how the signals changed with angular distance from the detector, and although in principle measurements from opposite positions could be synthesised, in practice it would be easier to have measured over a greater angular range. However we hope that this report will provide a simple guide to those interested in evaluating this technique. One likely research application is for comparing the sensitivity of various source-detector configurations to detect internal features. For simplified sample geometries, comparing measurements taken before and after the introduction of an internal target
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can provide convincing evidence of the ability to detect internal aberrations. For single source-detector geometries this change may be small, since the signal will be sensitive to varying degrees throughout a relative large spatial region. Tomographic modelling methods potentially provide an analytical framework for combining data collected from multiple locations to pull out these subtle changes. Essentially, this can be considered as taking a set of measurements and then transforming them to a new domain to provide better discrimination. Using simple phantoms is of course far removed from the various difficulties that will need to be overcome in real life situations. These problems include: irregular shape and sizes, and their associated 3D effects; skin and dirt on the surface; smaller contrasts between the optical properties of healthy and diseased tissue; variations in detection limits with position from the surface; and constraints on the time available for data acquisition and processing. To address these now would be highly speculative and so we will restrict ourselves to some general comments. These problems are common to all NIR sensors, and so it may be possible to adopt some of the current methods of overcoming them. For example, adopting the approach described by Krivoshiev et al. (2000) for accommodating peel in potatoes. Methods developed by Dahm and Dahm (1999) could be used to model the interactions within the tissue. These are known to involve both absorption and scattering, which may be separated using approaches described in a pair of papers by Leonardi and Burns (1999a,b). Where there is little dispersion the scattering properties, which depend on differences in the refractive index, will not vary significantly with wavelength. In such instances scatter corrections based at a single wavelength can be applied across a spectrum, using an approach described in Leonardi and Burns (1999b). Here time resolved measurement were used to characterise the scattering properties, although steady-state methods, such as those described by Birth (1978), and updated by Lu (Lu, 2004; Peng and Lu, 2006) may be used instead. Finally, although optical tomography systems have been built that operate at high-acquisition rates, these were for studying certain processes confined to a fixed geometry, such as gas flow in bubble columns. For agricultural produce, additional size and shape information would be required. This could be acquired by projecting light patterns onto the object, which are then viewed by cameras—a technique called structured light. Combining this information during the image reconstruction is a potential time bottle neck, and so this technique may well first be restricted to supermarket applications rather than the, say 10 fruit/s, requirements of a conveyer line. Acknowledgment The authors thank the EPSRC, grant reference GR/ S71323/01, for funding this work, and the referees for their helpful comments. References Arridge, S., 1999. Optical tomography in medical imaging. Inverse Probl., R41–R93.
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