- Email: [email protected]
Validated simulations of diffuse optical transmission measurements on produce
Computers and Electronics in Agriculture 134 (2017) 94–101
Contents lists available at ScienceDirect
Computers and Electronics in Agriculture journal homepage: www.elsevier.com/locate/compag
Original papers
Validated simulations of diffuse optical transmission measurements on produce Nathan Tomer a,⇑, Andrew McGlone a, Rainer Künnemeyer b a b
Plant & Food Research, Private Bag 3230, Waikato Mail Centre, Hamilton 3240, New Zealand School of Engineering, University of Waikato, Private Bag 3105, Hamilton 3240, New Zealand
a r t i c l e
i n f o
Article history: Received 29 April 2016 Received in revised form 4 January 2017 Accepted 8 January 2017
Keywords: NIRFast Spatially resolved spectroscopy Onions Optical property Inverse adding doubling
a b s t r a c t We have compared simulations of the diffuse optical transport in fresh whole brown onions (Allium cepa) with real measurements. To ensure the accuracy of the computer simulations, a structured light scanner was used to record the three dimensional shape of the produce as well as the locations of light source and detectors. The light transport within the produce was simulated by the NIRFast finite element method using the mesh created by the 3D scanner. Results collected from 10 fresh onions showed general agreement between experiments and simulations when appropriate absorption and scattering values were used with the computer mesh models. Onion tissue absorption coefficients measured by the inverse adding doubling method are five times larger than those required to recreate the experimental transmission readings. The absorption values used are close to those reported in the literature using different measurement methods, such as time-resolved reflectance spectroscopy on apples. Simulations using mesh models with internal regions suggested inhomogeneous optical property distributions influenced the transport of light within the onions. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Near-infrared (NIR) spectroscopy is a widely used tool for non-destructive quality measurement of fresh produce (Nicolaï et al., 2007). Typically broad spectrum NIR illumination is directed at produce over a large surface area. Transmitted light is then collected with a spectrometer and used to create predictive models for quality measurements of the produce. Quality measures includes sugar content and the presence of defects like internal rot. However, measuring transmission using a wide area illumination averages contributions from a large amount of tissue. In that case small localized defects or features can escape detection. Onions are an example of a produce that can exhibit small localized defects, particularly small rots in the neck region. Focused and localized NIR illumination and light collection might be used to increase signal from more defined internal volumes. For example, using tightly collimated source(s), and collecting light with focused optics could make this possible. A design issue then arises where to illuminate and where to measure. In the general case, where a rot position is completely arbitrary, the
⇑ Corresponding author. E-mail addresses: [email protected] (N. Tomer), Andrew. [email protected] (A. McGlone), [email protected] (R. Künnemeyer). http://dx.doi.org/10.1016/j.compag.2017.01.006 0168-1699/Ó 2017 Elsevier B.V. All rights reserved.
answer is probably the more measurement locations the better. That answer may be also be appropriate to specific cases too, such as neck rot detection, since orientation of the onion to the measurement system may be arbitrary. Whichever case, it may be possible to select fewer illumination and detection positions for the same detection efficiency. Accurate simulation of diffuse light transport within produce is one approach to evaluating designs with fewer sparse light measurement locations. There has been much prior work on the simulation of diffuse light transport, mainly in the medical field but more recently also in agriculture. For instance, Qin and Lu (2009) and Wang and Li (2013) used Monte Carlo simulations to evaluate optical light transport in apples and onions respectively. Monte Carlo methods are accurate but can be slow, depending on the complexity of the simulation. A faster alternative approximates light transport using a light density diffusion equation (DE) which can be solved using the finite element method (FEM). The FEM uses a mesh structure to approximate the volume of the produce where the light density distribution will be estimated. Each node in the mesh holds its own optical properties to govern the light diffusion in the small surrounding region. The DE approximation is fast to solve and accurate away from the source. However, the solution is less accurate near the source and due to the nature of the approximation it is unable to model features on the scale of the reduced scattering length (ls0 ) or smaller. A popular
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101
FEM tool for diffuse light transport simulation in the medical optics field is NIRFast (Dehghani et al., 2009). Accurate optical properties in light transport simulations are crucial to accurately recreate light density distributions. One popular method for measuring the reduced scattering (ls0 ) and absorption (la) coefficients of biological materials is the Inverse Adding Doubling (IAD) method (Prahl, 2013). The IAD method’s inputs include diffuse transmission and diffuse reflection measured with an integrating sphere setup. A simulation of light through a thin sample with varied optical properties is then compared with the measurements. The optical properties which most closely reproduce the measurements are the output of the algorithm. The IAD method is popular as it requires relatively simple equipment, is fast and can target specific tissue samples. However the method is not failsafe and accuracy can depend on various experimental parameters, such as sample thickness, port diameter, and the value of the optical properties (Zhu et al., 2007). Wang et al. (2012) measured optical properties of onion samples using the IAD method in the wavelength range of 550–850 nm with typical values of la = 0.2 cm1 and ls0 = 10 cm1. We are not aware of other published studies on measuring the diffuse optical properties of onion tissue, so we made additional IAD measurements to confirm or otherwise the limited literature results. The objectives of the research reported here were to validate computer simulations of accurately localized NIR transmission measurements through individual onions. Accurate correspondence between simulation and experiment was achieved in a novel but convenient way by precisely registering fibre optic source and detector locations to a 3D scanned surface mesh model of the onion (Tomer et al., 2015). The scanned surface mesh models were turned into full body FEM meshes using one of two types of internal optical property distributions. The first distribution was a single uniform region, and the second was multiple uniform internal regions created using information from known structures in the dissected onions and taking into account the known light transmission patterns. Optical absorption and scattering values were selected for the internal regions based on IAD measurements. They were later changed based on the difference between the simulation results and onion transmission measurements. 2. Materials and methods 2.1. Mesh 3D model capture Ten onions were procured from a local produce retailer. The onions were blemish free, medium size (7.0 ± 1.0 cm in diameter) and estimated to be 2–11 months old. Some were fresh from the new season and some from previous year’s season. Eighteen locations were each defined at the intersections of optical registration grid lines (Figs. 1 and 2). There were 6 columns spaced approximately 60° apart (marked by an ‘arrow’ and A, B, C, D, E on their right) and 3 rows (bottom, middle and top). For each onion a structured light scanner (SLS) (SLS-1, DAVID Vision Systems) was used to capture the 3D shape and create a complete surface mesh. Then each location where a fibre optic probe would either gather or deliver light was highlighted with a small laser dot and individually scanned. A SLS is a calibrated camera/projector pair. The projector sends a structured pattern of light onto the object being scanned and the camera captures the image of the light on the surface. The cameraprojector pose, the patterns of light and the camera are all calibrated which allows triangulation of the surface of the object. The accuracy of using a SLS to capture the fibre optics locations on the surface mesh was previously evaluated, and the method records the locations of interest to within an error of 1% of the onion diameter, typically less than 0.1 cm (Qin and Lu, 2009).
95
Fig. 1. Onion model example.
Fig. 2. Onion model surface for Onion-3.
2.2. Transmission measurements Laser light source locations were all on the ‘arrow’ column (left most column in Fig. 2). For each source location (top, middle and bottom) light transmission readings were collected only at locations on the same row (once at each of location A, B, C, D, E approximately 60°, 120°, 180°, 240°, 300° transmission angle, respectively). The optical measurements were made using a 15 mW, 785 nm continuous wave laser as the light source and a spectrometer (MMS1, Zeiss, Germany) as the detector. The laser output power was monitored for stability using an optical power meter (71582, Oriel Newport, Irvine, USA). The laser light was delivered via a fibre optic cable (200 lm core diameter) which was aligned to the correct location and held in contact with the surface by mechanical arms (Fig. 3). A similar arrangement (400 lm core diameter) was used to collect and deliver the transmitted light to the spectrometer. To capture variance in optical fibre placement, the whole process was repeated three times to create a set of skin-on transmission measurements. Holes were then cut into the skin of the onion (Fig. 4), taking care not to damage the underlying flesh, and a set of skin-off transmission measurements was made through the holes. The integration time was varied between 6.5 s and 0.2 s depending on the separation distance between the source and collection fibre ends and whether or not the skin of the onion was removed for the measurement. After all optical measurements were recorded, the onions were dissected and images were taken of cross sections to aid interpretation of the optical measurements.
96
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101
Fig. 3. Illustration of data acquisition stages. The left side of the onion shows one of the projected patterns used by the David SLS to calculate the onion surface shape. In the centre a laser dot highlights one of the optical fibre locations. On the right, the fibre optic cables are aligned in contact with the surface of the onion, and held in place by the mechanical arms.
Fig. 4. Holes cut in the skin for ‘skin-off’ measurements.
The IAD method used by the authors to estimate the optical properties of onions is described in detail in Rowe et al. (2014). A single integrating sphere was used. The onion tissue samples were thin (5 mm) longitudinal slices taken parallel to the stem-root axis and from a zone about 10 mm in towards the central core from the surface. The slices were at least 40 mm in diameter, held between two 1.12 mm borosilicate glass slides. The integrating sphere sample port diameter was 38.1 mm. The IAD program version 3.9 105 was used to calculate the optical properties. The system was validated using 20% Intralipid diluted to concentrations of 0.5%, 1.0%, 1.5%, 2.0%. The results agreed to theoretical scattering values within 11.1% (Rowe et al., 2014), consistent with validation results found in literature.
Fig. 5. Simulations for all onion meshes (green, yellow) and measured transmission measurements at 785 nm (blue) normalized to the overall lowest transmission, lines are linear interpolation of logarithmic scale data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
locations, and the optical properties for each node were formatted to be suitable for input to NIRFast (Dehghani et al., 2009). NIRFast is a widely used and thoroughly tested toolbox which uses the finite element method to solve the diffusion equation approximation to the radiative transfer equation. The finite element method is capable of solving the diffusion equation over arbitrary regions. It is used to predict how the light density will diffuse through the onion mesh model. The mesh quality and density determines how accurate the simulation result is. Mesh generation parameters were investigated to determine the minimum size of an internal region which can be represented using Iso2Mesh meshes with NIRFast. We were unable to model optical effects of structures smaller than 2 mm in thickness, like for example skin, or volume elements of less than 1 mm (Fang and Boas, 2009) as the accuracy degrades or the simulations become unstable. Two approaches for modelling internal regions in the onion meshes were studied. In the first each onion mesh was composed of a single optically uniform region. For the second internal regions of differing optical properties were added. These regions compensate for the difference between the uniform mesh transmission results and the measured transmission results. Various shapes for the internal structures have been tested and we have settled on a procedure for generating the internal regions which works well for all the onions. The internal regions are kept close to being cylindrically symmetric where it was possible or are based on the shape observed in the dissected onion. The internal regions in the mesh keep the reduced scattering property of the surrounding region while the absorption properties were adjusted to effect the attenuation of light. These decisions were made to simplify the process of tuning the optical properties and selecting region shapes. The optical properties and shape of the internal regions were iteratively updated by hand to tune the simulation results to be in good agreement with the transmission measurements and cross section images of the dissected onions.
2.3. Simulation mesh creation and diffuse optics simulations 2.4. Data processing and analysis The SLS software produced a high resolution triangular surface mesh for each onion. The surface mesh was processed using Iso2Mesh (Fang and Boas, 2009) to create a lower resolution tetrahedral volumetric mesh. The volumetric mesh, the fibre optics
Three spectral measurements were averaged for each measurement, and dark current measurements were made throughout the experiment. The resulting readings were then adjusted
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101
97
Fig. 6. Optical properties of onion samples from three different onions, measured using the Inverse Adding Doubling Method. (a) Absorption, (b) reduced scattering.
dispersed over that range on the spectrometer (FWHM approx. 15 nm). The resulting transmission measurements were processed and analysed in the same way as the simulation output from NIRFast. The measurement and simulation results were normalized to their respective transmission readings at location C (approx. 180° transmission) through the middle of the onion to make the simulation and real measurements more easily comparable. The distance from the source to the collection fibre for each particular transmission measurement was calculated using the surface mesh model. These distances were paired with the associated transmission value to create light level versus transmission distance plots. The results for individual onions can be plotted with measurements grouped by row or column label to see how transmission through the onion changes across different directions.
3. Results 3.1. Validation of all onions with one optical region
Fig. 7. Image of a cross section of the volumetric mesh model of Onion-3 with added internal regions.
for differing integration times, laser stability, and electronic dark current. The wavelength range between 765 nm and 804 nm was integrated for the optical transmission signal, since the laser was
The outer dry skin of the onions has a non-uniform attenuation over the onion, in general attenuating more near the top and less near the bottom of the onion. The FEM diffusion approximation is unable to simulate small features like the skin. Therefore, skinoff measurements were first compared with the FEM simulation results to evaluate the validity of the mesh models and optical properties. Results for each measurement on all ten onions with skin removed are plotted in Fig. 5. We used the recorded source
Fig. 8. Simulation results for Onion-3 with internal regions as per Fig. 7, both plots present the same data. (a) has readings grouped by column and is labelled with ‘t’, ‘m’, ‘b’ to show which readings were taken on the top, middle and bottom rows, respectively. (b) is grouped by rows, and labelled with ‘a’ through ‘e’ to show which readings were taken on columns A through E.
98
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101
T:
and a very poor fit to the experimental transmission data. The simulations fitted the experimental data much better if an absorption coefficient la = 0.03 cm1, slightly higher than that of pure water, was used, which resulted in an effective attenuation coefficient of 1.12 cm1 (Fig. 5). 3.2. Individual onion validation
M:
B:
Fig. 9. The top (T), middle (M) and bottom (B) cross sections of Onion-3. The source locations are on the bottom of each cross section with a–e locations counter clockwise around the onion from the source at approximately 60° spacing.
and detector locations on the volumetric meshes from the scanned onions to create corresponding simulations of the transmission results. Various absorption and scattering properties were investigated and two are plotted for comparison (Fig. 5). The effective attenuation coefficient, the slope from a linear regression of the log scale data for all onions with the skin off is 1.09 cm1. Our IAD results, from measurements on tissue slices excised from three onions (Fig. 6) determined la = 0.15 cm1 and 10 cm1 6 ls0 6 15 cm1 at 785 nm. The values were in good agreement with other published IAD measurements on onion tissue (Wang et al., 2012). However, these values combined to deliver a much higher attenuation coefficient of 2.17 cm1 for the lower ls0 = 10 cm1
Simulation results using all meshes with a single uniform optical property followed the collective attenuation trend of all the onions. We achieved better re-creation of the attenuation for each onion by adjusting the optical properties in each mesh individually. Optical values for the bulk of each uniform onion mesh were in the range of 7 cm1 6 ls0 6 12 cm1 and 0.028 cm1 6 la 6 0.035 cm1. We investigated the addition of internal regions to the meshes where absorption values were chosen based on the differences between the real and simulated transmissions. Most of the onions’ transmission results were simulated well by adding two types of internal structure to the mesh. One was an outer bowl-shaped region of uniform thickness at the bottom of the onion, and the other was a core structure consisting of either one or two cylindrical cores near the centre of the onion. Each region has its own optical properties. There were three or four regions per mesh, each with absorption coefficients tailored to re-create the transmission readings. It was also observed that some of the onions showed a similar but lower attenuation for the top row as in the bottom row, and thus had an upside down bowl shape region of different attenuation at the top of the onion. Detailed graphical results for simulating and validating transmissions through Onion-3 are presented in Figs. 7–9. The outer layer bowl shape at the bottom of the mesh (Fig. 7) re-created the attenuation observed on the bottom row (Fig. 8, right), while the core structure re-created the offset of the C column from the trend line for the middle and top rows (Fig. 8, left). The core in the Onion-3 mesh (Fig. 7) was in a location between the 2 cores seen in the cross section images (Fig. 9) of Onion-3. Detailed results for Onion-4, as presented in Figs. 10–12, illustrate that onions with widely diverging double cores have different attenuation features to those with a single core or close double cores, like Onion-3. The transmission data for Onion-4 gave more divergent patterns, from location to location, than those of Onion-3. The readings for Onion-4 followed broader, more scattered attenuation curves (Fig. 11) than the equivalent for Onion-3 transmission readings (Fig. 8), which followed straighter well defined trend lines. This strongly suggested more inhomogeneity in the optical properties through Onion-4. When we added appropriate regions and absorption values to the Onion-4 mesh (Fig. 10), based on cross section images (Fig. 12, contrast enhanced showing onion cores), we obtained very good agreement between simulation results and real measurements. 4. Discussion Using optical properties determined with the IAD method should allow to accurately recreate light transmission through a registered simulation model. The simulations using IAD values however show transmission of light much lower than what is measured, indicating either scattering or absorption (or both) are overestimated. The experiment and the simulations here were done at a wavelength of 785 nm where the absorption of fruit and vegetable tissue is very low, i.e. an onion is rather transparent. It is known that there are potential inaccuracies with the IAD method for materials with low absorption values (Prahl, 2011). In particu-
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101
Fig. 10. Rendering of the surfaces separating the volumes in the Onion-4 model. Viewed from the direction of the source column.
lar, light that leaks out the sides of the sample is not necessarily accounted for in the IAD simulation. The result can be that absorption values are overestimated, despite Monte Carlo simulations in the IAD code intended to correct that. Zhu et al. (2007) simulated light loss out the sides of a sample in a double integrating sphere setup and examined the effect on estimated optical properties. They concluded the IAD method will work best on samples with relatively high absorption (>2.0 cm1) and scattering (>160 cm1) properties – not the properties typical of produce in the shortwave near infrared range from 700 to 1000 nm. Saeys et al. (2008) used the IAD to measure optical properties in the 650–1000 nm wavelengths on apples with typical values near la = 0.5 cm1 and ls0 = 30 cm1 away from water absorption peaks. When they compared their results with the alternative method of time-resolved reflectance spectroscopy (Cubeddu et al., 2001) (TRRS) the IAD measured optical absorption properties were nearly an order of magnitude higher than results from TRRS values, near la = 0.05 cm1 and ls0 = 20 cm1. The literature also indicates that the scattering coefficient is more reliably determined by the IAD method than the absorption coefficient (Saeys et al., 2008). The observed decrease in attenuation can be explained by a decrease
99
in scatter or absorption. Following the above argument, we concluded that our IAD measured scattering coefficient is correct, but the absorption coefficient is overestimated by a factor of 5 and is much closer to that of water. Comparing the simulations with real transmission measurements, we detect attenuation from non-uniform internal structure in the onion, however we cannot know for certain which attenuating features (absorption, scattering, location) effect the light transmission. The CW transmission measurements that we made cannot be used to separate scattering and absorption properties. The nodes with independent optical properties in the FEM mesh and a small number of transmission measurements creates a massively under determined system of equations. Internal regions reduce the number of optical properties from nodes to the number of regions. The internal regions introduced are based on physical boundaries in the onions and simulations using them recreate the transmission results very well. For simplicity we have opted to use only those regions which are required to recreate the measured transmission measurements, and which are based on features in the onions. We expect these regions to be similar in shape to the ones which produced the measured light transmissions. However, it cannot be ruled out that other attenuating structures affected light transmission, such as the multilayer structure of the onion. Only variation in the absorption coefficients have been used to model attenuation of internal structures since it eliminates a degree of freedom in the model. For example, if we use increased absorption values, we can compensate by using decreased scattering values to keep a very similar effective attenuation coefficient. It was surprising to us that the structure at the bottom of the onion was a bowl shape rather than a lump that might better match the physical shape of root mass at the bottom of the onion. We are not sure what causes this, though it would imply that the optical properties of the outer layer of tissue near the base of the onions are different to that of the rest of the outer tissue of the onions we measured. The distribution of optical properties within this bowl shape, and to some extent within any of the internal mesh regions, is not likely to be uniform as they are in the current finite element meshes. As some onions needed a bowl shaped region on the top as well as the bottom of the mesh, it may be better to approximate these regions with a continuously varying outer layer. In addition, the validation results for Onion-4 suggest that there are non-uniform optical properties in the core structures. Further experimental and simulation work is warranted to improve the understanding of light transport in onions. In particular, work on the influence of different internal regions and their optical properties, possibly enhanced by having more readings at
Fig. 11. Simulation results for Onion-4 with internal regions as per Fig. 10. (a) has readings grouped by column and is labelled with ‘t’, ‘m’, ‘b’ to show which readings were taken on the top, middle and bottom rows, respectively. (b) is grouped by rows, and labelled with ‘a’ through ‘e’ to show which readings were taken on columns A through E.
100
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101
T:
M:
The light density diffusion approximation inherently has limitations on the size of optical features that can be approximated. Using NIRFast means we cannot accurately model the optical transport through the skin, or light propagation near the source location(s). This means the method is not accurate for investigating diffuse reflection near the source, when Monte Carlo methods are potentially very useful. This is also why we did not use the skinon measurements to validate our simulations. A second limitation of the FEM comes from the complexities of creating and using a mesh structure for the geometry of the problem domain, the full solution of which is a research topic for itself. Despite these limitations, using the NIRFast toolbox worked very well to approximate the transmission of diffuse light through the bulk of the onion. The FEM also has a key advantage over potentially more accurate Monte Carlo simulation methods, which is speed. Diffuse light density tends to follow an exponential decay with distance from the source. Re-creating this exponential decay accurately over increasing transmission distance with a Monte Carlo method would similarly require an exponential increase in the number of photons and simulation time. The average simulation time for one NIRFast onion mesh is only about one minute for the high resolution 1 mm tetrahedral volume models, several orders of magnitude faster than a comparable Monte Carlo simulation. 5. Conclusions
B:
We have validated simulations of diffuse optical transmission measurements on whole onions. We created computer models of the onions and their optical properties using a 3D capture method and post processing to provide accurate geometric mesh models. FEM software running in Matlab was successfully used to estimate the light transport distribution in the onion. Two types of structures, the core and an outer layer, were introduced inside the onion meshes. These structures had elevated optical absorption coefficients to re-create the measured light transmission data at different measurement locations on each onion. There was good agreement with measurement and simulation using these optical properties and mesh structures. Comparison of measurements on onions with simulations using the onion meshes strongly suggest that the optical absorption coefficient of onion flesh reported from IAD measurements at 785 nm are approximately a factor of 5 too high. Acknowledgements The authors would like to acknowledge financial support from the New Zealand Ministry of Business Innovation and Employment (MBIE) Sensing Produce Programme C11X1208. References
Fig. 12. Contrast enhanced images of the top (T), middle (M) and bottom (B) cross sections of Onion-4. The source locations are on the bottom of each image with A–E locations counter clockwise around the onion from the source at approximately 60° spacing.
a finer spatial resolution, or with frequency modulated light sources and phase delay measurements. More measurement locations would allow less ambiguous reconstruction of internal regions in the onion mesh, and theoretically allow reconstruction of smaller regions. Frequency modulation and phase delay measurements in theory allow some discrimination between the absorption and scattering properties within the onion.
Cubeddu, R., D’Andrea, C., Pifferi, A., Taroni, P., Torricelli, A., Valentini, G., Dover, C., Johnson, D., Ruiz-Altisent, M., Valero, C., 2001. Nondestructive quantification of chemical and physical properties of fruits by time-resolved reflectance spectroscopy in the wavelength range 650–1000 nm. Appl. Opt. 40, 538–543. http://dx.doi.org/10.1364/AO.40.000538. Dehghani, H., Eames, M.E., Yalavarthy, P.K., Davis, S.C., Srinivasan, S., Carpenter, C. M., Pogue, B.W., Paulsen, K.D., 2009. Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction. Commun. Numer. Methods Eng. 25, 711–732. http://dx.doi.org/10.1002/cnm.1162. Fang, Q., Boas, D., 2009. Tetrahedral mesh generation from volumetric binary and gray-scale images. Proc. IEEE Int. Symp. Biomed. Imag. 2009, 1142–1145. http:// dx.doi.org/10.1109/ISBI.2009.5193259. Nicolaï, B., Beullens, K., Bobelyn, E., Peirs, A., Saeys, W., Theron, K., Lammertyn, J., 2007. Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: a review. Postharvest Biol. Technol. 46, 99–118. http://dx.doi. org/10.1016/j.postharvbio.2007.06.024. Prahl, S., 2011. Everything I Think You Should Know About Inverse AddingDoubling. Oregon Med. Laser Center, St. Vincent Hosp.
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101 Prahl, S., 2013. Inverse Adding-Doubling Program.
101
Tomer, N., McGlone, A., Künnemeyer, R., 2015. A Method of Registering Optical Measurements to Computer Models”. IEEE ICST2015 December 8–December 10 2015, Auckland, NZ. Wang, W., Li, C., 2013. Measurement of the light absorption and scattering properties of onion skin and flesh at 633 nm. Postharvest Biol. Technol. 86, 494– 501. http://dx.doi.org/10.1016/j.postharvbio.2013.07.032. Wang, W., Li, C., Gitaitis, R., Tollner, E.W., 2012. Optical Properties of Healthy and Sour Skin-infected Onion Tissues in Vis-NIR Region. ASABE July 29–August 1 2012, Dallas, Texas. Paper No. 121338380. Zhu, D., Lu, W., Zeng, S., Luo, Q., 2007. Effect of light losses of sample between two integrating spheres on optical properties estimation. J. Biomed. Opt. 12, 064004. http://dx.doi.org/10.1117/1.2815691.
Contents lists available at ScienceDirect
Computers and Electronics in Agriculture journal homepage: www.elsevier.com/locate/compag
Original papers
Validated simulations of diffuse optical transmission measurements on produce Nathan Tomer a,⇑, Andrew McGlone a, Rainer Künnemeyer b a b
Plant & Food Research, Private Bag 3230, Waikato Mail Centre, Hamilton 3240, New Zealand School of Engineering, University of Waikato, Private Bag 3105, Hamilton 3240, New Zealand
a r t i c l e
i n f o
Article history: Received 29 April 2016 Received in revised form 4 January 2017 Accepted 8 January 2017
Keywords: NIRFast Spatially resolved spectroscopy Onions Optical property Inverse adding doubling
a b s t r a c t We have compared simulations of the diffuse optical transport in fresh whole brown onions (Allium cepa) with real measurements. To ensure the accuracy of the computer simulations, a structured light scanner was used to record the three dimensional shape of the produce as well as the locations of light source and detectors. The light transport within the produce was simulated by the NIRFast finite element method using the mesh created by the 3D scanner. Results collected from 10 fresh onions showed general agreement between experiments and simulations when appropriate absorption and scattering values were used with the computer mesh models. Onion tissue absorption coefficients measured by the inverse adding doubling method are five times larger than those required to recreate the experimental transmission readings. The absorption values used are close to those reported in the literature using different measurement methods, such as time-resolved reflectance spectroscopy on apples. Simulations using mesh models with internal regions suggested inhomogeneous optical property distributions influenced the transport of light within the onions. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Near-infrared (NIR) spectroscopy is a widely used tool for non-destructive quality measurement of fresh produce (Nicolaï et al., 2007). Typically broad spectrum NIR illumination is directed at produce over a large surface area. Transmitted light is then collected with a spectrometer and used to create predictive models for quality measurements of the produce. Quality measures includes sugar content and the presence of defects like internal rot. However, measuring transmission using a wide area illumination averages contributions from a large amount of tissue. In that case small localized defects or features can escape detection. Onions are an example of a produce that can exhibit small localized defects, particularly small rots in the neck region. Focused and localized NIR illumination and light collection might be used to increase signal from more defined internal volumes. For example, using tightly collimated source(s), and collecting light with focused optics could make this possible. A design issue then arises where to illuminate and where to measure. In the general case, where a rot position is completely arbitrary, the
⇑ Corresponding author. E-mail addresses: [email protected] (N. Tomer), Andrew. [email protected] (A. McGlone), [email protected] (R. Künnemeyer). http://dx.doi.org/10.1016/j.compag.2017.01.006 0168-1699/Ó 2017 Elsevier B.V. All rights reserved.
answer is probably the more measurement locations the better. That answer may be also be appropriate to specific cases too, such as neck rot detection, since orientation of the onion to the measurement system may be arbitrary. Whichever case, it may be possible to select fewer illumination and detection positions for the same detection efficiency. Accurate simulation of diffuse light transport within produce is one approach to evaluating designs with fewer sparse light measurement locations. There has been much prior work on the simulation of diffuse light transport, mainly in the medical field but more recently also in agriculture. For instance, Qin and Lu (2009) and Wang and Li (2013) used Monte Carlo simulations to evaluate optical light transport in apples and onions respectively. Monte Carlo methods are accurate but can be slow, depending on the complexity of the simulation. A faster alternative approximates light transport using a light density diffusion equation (DE) which can be solved using the finite element method (FEM). The FEM uses a mesh structure to approximate the volume of the produce where the light density distribution will be estimated. Each node in the mesh holds its own optical properties to govern the light diffusion in the small surrounding region. The DE approximation is fast to solve and accurate away from the source. However, the solution is less accurate near the source and due to the nature of the approximation it is unable to model features on the scale of the reduced scattering length (ls0 ) or smaller. A popular
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101
FEM tool for diffuse light transport simulation in the medical optics field is NIRFast (Dehghani et al., 2009). Accurate optical properties in light transport simulations are crucial to accurately recreate light density distributions. One popular method for measuring the reduced scattering (ls0 ) and absorption (la) coefficients of biological materials is the Inverse Adding Doubling (IAD) method (Prahl, 2013). The IAD method’s inputs include diffuse transmission and diffuse reflection measured with an integrating sphere setup. A simulation of light through a thin sample with varied optical properties is then compared with the measurements. The optical properties which most closely reproduce the measurements are the output of the algorithm. The IAD method is popular as it requires relatively simple equipment, is fast and can target specific tissue samples. However the method is not failsafe and accuracy can depend on various experimental parameters, such as sample thickness, port diameter, and the value of the optical properties (Zhu et al., 2007). Wang et al. (2012) measured optical properties of onion samples using the IAD method in the wavelength range of 550–850 nm with typical values of la = 0.2 cm1 and ls0 = 10 cm1. We are not aware of other published studies on measuring the diffuse optical properties of onion tissue, so we made additional IAD measurements to confirm or otherwise the limited literature results. The objectives of the research reported here were to validate computer simulations of accurately localized NIR transmission measurements through individual onions. Accurate correspondence between simulation and experiment was achieved in a novel but convenient way by precisely registering fibre optic source and detector locations to a 3D scanned surface mesh model of the onion (Tomer et al., 2015). The scanned surface mesh models were turned into full body FEM meshes using one of two types of internal optical property distributions. The first distribution was a single uniform region, and the second was multiple uniform internal regions created using information from known structures in the dissected onions and taking into account the known light transmission patterns. Optical absorption and scattering values were selected for the internal regions based on IAD measurements. They were later changed based on the difference between the simulation results and onion transmission measurements. 2. Materials and methods 2.1. Mesh 3D model capture Ten onions were procured from a local produce retailer. The onions were blemish free, medium size (7.0 ± 1.0 cm in diameter) and estimated to be 2–11 months old. Some were fresh from the new season and some from previous year’s season. Eighteen locations were each defined at the intersections of optical registration grid lines (Figs. 1 and 2). There were 6 columns spaced approximately 60° apart (marked by an ‘arrow’ and A, B, C, D, E on their right) and 3 rows (bottom, middle and top). For each onion a structured light scanner (SLS) (SLS-1, DAVID Vision Systems) was used to capture the 3D shape and create a complete surface mesh. Then each location where a fibre optic probe would either gather or deliver light was highlighted with a small laser dot and individually scanned. A SLS is a calibrated camera/projector pair. The projector sends a structured pattern of light onto the object being scanned and the camera captures the image of the light on the surface. The cameraprojector pose, the patterns of light and the camera are all calibrated which allows triangulation of the surface of the object. The accuracy of using a SLS to capture the fibre optics locations on the surface mesh was previously evaluated, and the method records the locations of interest to within an error of 1% of the onion diameter, typically less than 0.1 cm (Qin and Lu, 2009).
95
Fig. 1. Onion model example.
Fig. 2. Onion model surface for Onion-3.
2.2. Transmission measurements Laser light source locations were all on the ‘arrow’ column (left most column in Fig. 2). For each source location (top, middle and bottom) light transmission readings were collected only at locations on the same row (once at each of location A, B, C, D, E approximately 60°, 120°, 180°, 240°, 300° transmission angle, respectively). The optical measurements were made using a 15 mW, 785 nm continuous wave laser as the light source and a spectrometer (MMS1, Zeiss, Germany) as the detector. The laser output power was monitored for stability using an optical power meter (71582, Oriel Newport, Irvine, USA). The laser light was delivered via a fibre optic cable (200 lm core diameter) which was aligned to the correct location and held in contact with the surface by mechanical arms (Fig. 3). A similar arrangement (400 lm core diameter) was used to collect and deliver the transmitted light to the spectrometer. To capture variance in optical fibre placement, the whole process was repeated three times to create a set of skin-on transmission measurements. Holes were then cut into the skin of the onion (Fig. 4), taking care not to damage the underlying flesh, and a set of skin-off transmission measurements was made through the holes. The integration time was varied between 6.5 s and 0.2 s depending on the separation distance between the source and collection fibre ends and whether or not the skin of the onion was removed for the measurement. After all optical measurements were recorded, the onions were dissected and images were taken of cross sections to aid interpretation of the optical measurements.
96
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101
Fig. 3. Illustration of data acquisition stages. The left side of the onion shows one of the projected patterns used by the David SLS to calculate the onion surface shape. In the centre a laser dot highlights one of the optical fibre locations. On the right, the fibre optic cables are aligned in contact with the surface of the onion, and held in place by the mechanical arms.
Fig. 4. Holes cut in the skin for ‘skin-off’ measurements.
The IAD method used by the authors to estimate the optical properties of onions is described in detail in Rowe et al. (2014). A single integrating sphere was used. The onion tissue samples were thin (5 mm) longitudinal slices taken parallel to the stem-root axis and from a zone about 10 mm in towards the central core from the surface. The slices were at least 40 mm in diameter, held between two 1.12 mm borosilicate glass slides. The integrating sphere sample port diameter was 38.1 mm. The IAD program version 3.9 105 was used to calculate the optical properties. The system was validated using 20% Intralipid diluted to concentrations of 0.5%, 1.0%, 1.5%, 2.0%. The results agreed to theoretical scattering values within 11.1% (Rowe et al., 2014), consistent with validation results found in literature.
Fig. 5. Simulations for all onion meshes (green, yellow) and measured transmission measurements at 785 nm (blue) normalized to the overall lowest transmission, lines are linear interpolation of logarithmic scale data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
locations, and the optical properties for each node were formatted to be suitable for input to NIRFast (Dehghani et al., 2009). NIRFast is a widely used and thoroughly tested toolbox which uses the finite element method to solve the diffusion equation approximation to the radiative transfer equation. The finite element method is capable of solving the diffusion equation over arbitrary regions. It is used to predict how the light density will diffuse through the onion mesh model. The mesh quality and density determines how accurate the simulation result is. Mesh generation parameters were investigated to determine the minimum size of an internal region which can be represented using Iso2Mesh meshes with NIRFast. We were unable to model optical effects of structures smaller than 2 mm in thickness, like for example skin, or volume elements of less than 1 mm (Fang and Boas, 2009) as the accuracy degrades or the simulations become unstable. Two approaches for modelling internal regions in the onion meshes were studied. In the first each onion mesh was composed of a single optically uniform region. For the second internal regions of differing optical properties were added. These regions compensate for the difference between the uniform mesh transmission results and the measured transmission results. Various shapes for the internal structures have been tested and we have settled on a procedure for generating the internal regions which works well for all the onions. The internal regions are kept close to being cylindrically symmetric where it was possible or are based on the shape observed in the dissected onion. The internal regions in the mesh keep the reduced scattering property of the surrounding region while the absorption properties were adjusted to effect the attenuation of light. These decisions were made to simplify the process of tuning the optical properties and selecting region shapes. The optical properties and shape of the internal regions were iteratively updated by hand to tune the simulation results to be in good agreement with the transmission measurements and cross section images of the dissected onions.
2.3. Simulation mesh creation and diffuse optics simulations 2.4. Data processing and analysis The SLS software produced a high resolution triangular surface mesh for each onion. The surface mesh was processed using Iso2Mesh (Fang and Boas, 2009) to create a lower resolution tetrahedral volumetric mesh. The volumetric mesh, the fibre optics
Three spectral measurements were averaged for each measurement, and dark current measurements were made throughout the experiment. The resulting readings were then adjusted
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101
97
Fig. 6. Optical properties of onion samples from three different onions, measured using the Inverse Adding Doubling Method. (a) Absorption, (b) reduced scattering.
dispersed over that range on the spectrometer (FWHM approx. 15 nm). The resulting transmission measurements were processed and analysed in the same way as the simulation output from NIRFast. The measurement and simulation results were normalized to their respective transmission readings at location C (approx. 180° transmission) through the middle of the onion to make the simulation and real measurements more easily comparable. The distance from the source to the collection fibre for each particular transmission measurement was calculated using the surface mesh model. These distances were paired with the associated transmission value to create light level versus transmission distance plots. The results for individual onions can be plotted with measurements grouped by row or column label to see how transmission through the onion changes across different directions.
3. Results 3.1. Validation of all onions with one optical region
Fig. 7. Image of a cross section of the volumetric mesh model of Onion-3 with added internal regions.
for differing integration times, laser stability, and electronic dark current. The wavelength range between 765 nm and 804 nm was integrated for the optical transmission signal, since the laser was
The outer dry skin of the onions has a non-uniform attenuation over the onion, in general attenuating more near the top and less near the bottom of the onion. The FEM diffusion approximation is unable to simulate small features like the skin. Therefore, skinoff measurements were first compared with the FEM simulation results to evaluate the validity of the mesh models and optical properties. Results for each measurement on all ten onions with skin removed are plotted in Fig. 5. We used the recorded source
Fig. 8. Simulation results for Onion-3 with internal regions as per Fig. 7, both plots present the same data. (a) has readings grouped by column and is labelled with ‘t’, ‘m’, ‘b’ to show which readings were taken on the top, middle and bottom rows, respectively. (b) is grouped by rows, and labelled with ‘a’ through ‘e’ to show which readings were taken on columns A through E.
98
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101
T:
and a very poor fit to the experimental transmission data. The simulations fitted the experimental data much better if an absorption coefficient la = 0.03 cm1, slightly higher than that of pure water, was used, which resulted in an effective attenuation coefficient of 1.12 cm1 (Fig. 5). 3.2. Individual onion validation
M:
B:
Fig. 9. The top (T), middle (M) and bottom (B) cross sections of Onion-3. The source locations are on the bottom of each cross section with a–e locations counter clockwise around the onion from the source at approximately 60° spacing.
and detector locations on the volumetric meshes from the scanned onions to create corresponding simulations of the transmission results. Various absorption and scattering properties were investigated and two are plotted for comparison (Fig. 5). The effective attenuation coefficient, the slope from a linear regression of the log scale data for all onions with the skin off is 1.09 cm1. Our IAD results, from measurements on tissue slices excised from three onions (Fig. 6) determined la = 0.15 cm1 and 10 cm1 6 ls0 6 15 cm1 at 785 nm. The values were in good agreement with other published IAD measurements on onion tissue (Wang et al., 2012). However, these values combined to deliver a much higher attenuation coefficient of 2.17 cm1 for the lower ls0 = 10 cm1
Simulation results using all meshes with a single uniform optical property followed the collective attenuation trend of all the onions. We achieved better re-creation of the attenuation for each onion by adjusting the optical properties in each mesh individually. Optical values for the bulk of each uniform onion mesh were in the range of 7 cm1 6 ls0 6 12 cm1 and 0.028 cm1 6 la 6 0.035 cm1. We investigated the addition of internal regions to the meshes where absorption values were chosen based on the differences between the real and simulated transmissions. Most of the onions’ transmission results were simulated well by adding two types of internal structure to the mesh. One was an outer bowl-shaped region of uniform thickness at the bottom of the onion, and the other was a core structure consisting of either one or two cylindrical cores near the centre of the onion. Each region has its own optical properties. There were three or four regions per mesh, each with absorption coefficients tailored to re-create the transmission readings. It was also observed that some of the onions showed a similar but lower attenuation for the top row as in the bottom row, and thus had an upside down bowl shape region of different attenuation at the top of the onion. Detailed graphical results for simulating and validating transmissions through Onion-3 are presented in Figs. 7–9. The outer layer bowl shape at the bottom of the mesh (Fig. 7) re-created the attenuation observed on the bottom row (Fig. 8, right), while the core structure re-created the offset of the C column from the trend line for the middle and top rows (Fig. 8, left). The core in the Onion-3 mesh (Fig. 7) was in a location between the 2 cores seen in the cross section images (Fig. 9) of Onion-3. Detailed results for Onion-4, as presented in Figs. 10–12, illustrate that onions with widely diverging double cores have different attenuation features to those with a single core or close double cores, like Onion-3. The transmission data for Onion-4 gave more divergent patterns, from location to location, than those of Onion-3. The readings for Onion-4 followed broader, more scattered attenuation curves (Fig. 11) than the equivalent for Onion-3 transmission readings (Fig. 8), which followed straighter well defined trend lines. This strongly suggested more inhomogeneity in the optical properties through Onion-4. When we added appropriate regions and absorption values to the Onion-4 mesh (Fig. 10), based on cross section images (Fig. 12, contrast enhanced showing onion cores), we obtained very good agreement between simulation results and real measurements. 4. Discussion Using optical properties determined with the IAD method should allow to accurately recreate light transmission through a registered simulation model. The simulations using IAD values however show transmission of light much lower than what is measured, indicating either scattering or absorption (or both) are overestimated. The experiment and the simulations here were done at a wavelength of 785 nm where the absorption of fruit and vegetable tissue is very low, i.e. an onion is rather transparent. It is known that there are potential inaccuracies with the IAD method for materials with low absorption values (Prahl, 2011). In particu-
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101
Fig. 10. Rendering of the surfaces separating the volumes in the Onion-4 model. Viewed from the direction of the source column.
lar, light that leaks out the sides of the sample is not necessarily accounted for in the IAD simulation. The result can be that absorption values are overestimated, despite Monte Carlo simulations in the IAD code intended to correct that. Zhu et al. (2007) simulated light loss out the sides of a sample in a double integrating sphere setup and examined the effect on estimated optical properties. They concluded the IAD method will work best on samples with relatively high absorption (>2.0 cm1) and scattering (>160 cm1) properties – not the properties typical of produce in the shortwave near infrared range from 700 to 1000 nm. Saeys et al. (2008) used the IAD to measure optical properties in the 650–1000 nm wavelengths on apples with typical values near la = 0.5 cm1 and ls0 = 30 cm1 away from water absorption peaks. When they compared their results with the alternative method of time-resolved reflectance spectroscopy (Cubeddu et al., 2001) (TRRS) the IAD measured optical absorption properties were nearly an order of magnitude higher than results from TRRS values, near la = 0.05 cm1 and ls0 = 20 cm1. The literature also indicates that the scattering coefficient is more reliably determined by the IAD method than the absorption coefficient (Saeys et al., 2008). The observed decrease in attenuation can be explained by a decrease
99
in scatter or absorption. Following the above argument, we concluded that our IAD measured scattering coefficient is correct, but the absorption coefficient is overestimated by a factor of 5 and is much closer to that of water. Comparing the simulations with real transmission measurements, we detect attenuation from non-uniform internal structure in the onion, however we cannot know for certain which attenuating features (absorption, scattering, location) effect the light transmission. The CW transmission measurements that we made cannot be used to separate scattering and absorption properties. The nodes with independent optical properties in the FEM mesh and a small number of transmission measurements creates a massively under determined system of equations. Internal regions reduce the number of optical properties from nodes to the number of regions. The internal regions introduced are based on physical boundaries in the onions and simulations using them recreate the transmission results very well. For simplicity we have opted to use only those regions which are required to recreate the measured transmission measurements, and which are based on features in the onions. We expect these regions to be similar in shape to the ones which produced the measured light transmissions. However, it cannot be ruled out that other attenuating structures affected light transmission, such as the multilayer structure of the onion. Only variation in the absorption coefficients have been used to model attenuation of internal structures since it eliminates a degree of freedom in the model. For example, if we use increased absorption values, we can compensate by using decreased scattering values to keep a very similar effective attenuation coefficient. It was surprising to us that the structure at the bottom of the onion was a bowl shape rather than a lump that might better match the physical shape of root mass at the bottom of the onion. We are not sure what causes this, though it would imply that the optical properties of the outer layer of tissue near the base of the onions are different to that of the rest of the outer tissue of the onions we measured. The distribution of optical properties within this bowl shape, and to some extent within any of the internal mesh regions, is not likely to be uniform as they are in the current finite element meshes. As some onions needed a bowl shaped region on the top as well as the bottom of the mesh, it may be better to approximate these regions with a continuously varying outer layer. In addition, the validation results for Onion-4 suggest that there are non-uniform optical properties in the core structures. Further experimental and simulation work is warranted to improve the understanding of light transport in onions. In particular, work on the influence of different internal regions and their optical properties, possibly enhanced by having more readings at
Fig. 11. Simulation results for Onion-4 with internal regions as per Fig. 10. (a) has readings grouped by column and is labelled with ‘t’, ‘m’, ‘b’ to show which readings were taken on the top, middle and bottom rows, respectively. (b) is grouped by rows, and labelled with ‘a’ through ‘e’ to show which readings were taken on columns A through E.
100
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101
T:
M:
The light density diffusion approximation inherently has limitations on the size of optical features that can be approximated. Using NIRFast means we cannot accurately model the optical transport through the skin, or light propagation near the source location(s). This means the method is not accurate for investigating diffuse reflection near the source, when Monte Carlo methods are potentially very useful. This is also why we did not use the skinon measurements to validate our simulations. A second limitation of the FEM comes from the complexities of creating and using a mesh structure for the geometry of the problem domain, the full solution of which is a research topic for itself. Despite these limitations, using the NIRFast toolbox worked very well to approximate the transmission of diffuse light through the bulk of the onion. The FEM also has a key advantage over potentially more accurate Monte Carlo simulation methods, which is speed. Diffuse light density tends to follow an exponential decay with distance from the source. Re-creating this exponential decay accurately over increasing transmission distance with a Monte Carlo method would similarly require an exponential increase in the number of photons and simulation time. The average simulation time for one NIRFast onion mesh is only about one minute for the high resolution 1 mm tetrahedral volume models, several orders of magnitude faster than a comparable Monte Carlo simulation. 5. Conclusions
B:
We have validated simulations of diffuse optical transmission measurements on whole onions. We created computer models of the onions and their optical properties using a 3D capture method and post processing to provide accurate geometric mesh models. FEM software running in Matlab was successfully used to estimate the light transport distribution in the onion. Two types of structures, the core and an outer layer, were introduced inside the onion meshes. These structures had elevated optical absorption coefficients to re-create the measured light transmission data at different measurement locations on each onion. There was good agreement with measurement and simulation using these optical properties and mesh structures. Comparison of measurements on onions with simulations using the onion meshes strongly suggest that the optical absorption coefficient of onion flesh reported from IAD measurements at 785 nm are approximately a factor of 5 too high. Acknowledgements The authors would like to acknowledge financial support from the New Zealand Ministry of Business Innovation and Employment (MBIE) Sensing Produce Programme C11X1208. References
Fig. 12. Contrast enhanced images of the top (T), middle (M) and bottom (B) cross sections of Onion-4. The source locations are on the bottom of each image with A–E locations counter clockwise around the onion from the source at approximately 60° spacing.
a finer spatial resolution, or with frequency modulated light sources and phase delay measurements. More measurement locations would allow less ambiguous reconstruction of internal regions in the onion mesh, and theoretically allow reconstruction of smaller regions. Frequency modulation and phase delay measurements in theory allow some discrimination between the absorption and scattering properties within the onion.
Cubeddu, R., D’Andrea, C., Pifferi, A., Taroni, P., Torricelli, A., Valentini, G., Dover, C., Johnson, D., Ruiz-Altisent, M., Valero, C., 2001. Nondestructive quantification of chemical and physical properties of fruits by time-resolved reflectance spectroscopy in the wavelength range 650–1000 nm. Appl. Opt. 40, 538–543. http://dx.doi.org/10.1364/AO.40.000538. Dehghani, H., Eames, M.E., Yalavarthy, P.K., Davis, S.C., Srinivasan, S., Carpenter, C. M., Pogue, B.W., Paulsen, K.D., 2009. Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction. Commun. Numer. Methods Eng. 25, 711–732. http://dx.doi.org/10.1002/cnm.1162. Fang, Q., Boas, D., 2009. Tetrahedral mesh generation from volumetric binary and gray-scale images. Proc. IEEE Int. Symp. Biomed. Imag. 2009, 1142–1145. http:// dx.doi.org/10.1109/ISBI.2009.5193259. Nicolaï, B., Beullens, K., Bobelyn, E., Peirs, A., Saeys, W., Theron, K., Lammertyn, J., 2007. Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: a review. Postharvest Biol. Technol. 46, 99–118. http://dx.doi. org/10.1016/j.postharvbio.2007.06.024. Prahl, S., 2011. Everything I Think You Should Know About Inverse AddingDoubling. Oregon Med. Laser Center, St. Vincent Hosp.
N. Tomer et al. / Computers and Electronics in Agriculture 134 (2017) 94–101 Prahl, S., 2013. Inverse Adding-Doubling Program.
101
Tomer, N., McGlone, A., Künnemeyer, R., 2015. A Method of Registering Optical Measurements to Computer Models”. IEEE ICST2015 December 8–December 10 2015, Auckland, NZ. Wang, W., Li, C., 2013. Measurement of the light absorption and scattering properties of onion skin and flesh at 633 nm. Postharvest Biol. Technol. 86, 494– 501. http://dx.doi.org/10.1016/j.postharvbio.2013.07.032. Wang, W., Li, C., Gitaitis, R., Tollner, E.W., 2012. Optical Properties of Healthy and Sour Skin-infected Onion Tissues in Vis-NIR Region. ASABE July 29–August 1 2012, Dallas, Texas. Paper No. 121338380. Zhu, D., Lu, W., Zeng, S., Luo, Q., 2007. Effect of light losses of sample between two integrating spheres on optical properties estimation. J. Biomed. Opt. 12, 064004. http://dx.doi.org/10.1117/1.2815691.