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Wood grain direction measurement from spatial reflection with linear method Pan, Qi 2017

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WOOD GRAIN DIRECTION MEASUREMENT FROM SPATIAL REFLECTION  WITH LINEAR METHOD  by  Qi Pan B.E., Ningbo University, 2015   A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIRMENT FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE  in The Faculty of Graduate and Postdoctoral Studies  (Mechanical Engineering)   THE UNIVERSITY OF BRITISH COLUMBIA   (Vancouver)    August 2017  © Qi Pan, 2017   ii  Abstract Wood grain direction is a very important quality control feature in wood industry because it is a good indicator of wood strength and uniformity.  It is a three-dimensional quantity that is defined by its angles within and into the plane of the measured surface. These are respectively called the surface and dive angles.  An interesting method to measure these angles involves measuring the spatial reflection from the wood surface when illuminated by concentrated light.  The cellular shape of the wood microstructure causes the light reflection to be greatest perpendicular to the wood grain.  This effect allows the surface and dive angles to be determined by analyzing the spatial variation of the reflected light.  The conventional method for doing this involves sampling the reflection intensities around a circle above the wood surface.  However, this method is effective only for small dive angles.  A new method is described here where light reflection intensity variation is measured along two parallel lines on either side of the illuminated area.  It is able to measure the full ranges of surface and dive angles that occur in practice.  A laboratory device for making the required spatial reflection measurements is described and experimental results are presented. Based on the linear method, an equipment can be developed for industrial purpose, which consists of two parallel lines of sensors sparsely distributed along the longitudinal axis of lumber. To investigate this proposed arrangement of sensors, an interpolation study was undertaken on the associated low-resolution data, with the results compared with those from high-resolution full-field data. With the proposed sensor arrangement, grain angle measurements can be made at very high speed, which makes the equipment suitable for industrial use in sawmills and wood products factories.       iii  Lay Summary Measurement of wood grain direction is a very important in the wood industry because it provides a good indicator of wood strength and uniformity.  An interesting method to measure the 3-dimensional grain angle involves measuring the spatial reflection from the wood surface when illuminated by concentrated light.  The cellular shape of the wood microstructure causes the light reflection to be greatest perpendicular to the wood grain.  A new method is described here where light reflection intensity variation is measured along two parallel lines on either side of the illuminated area.  It is able to measure the full ranges of grain angles that occur in practice.  A laboratory device for making the required spatial reflection measurements is described and experimental results are presented.                    iv  Preface This dissertation is originally suggested by Dr. Gary Schajer, and the work presented henceforth was conducted in the Renewable Resources Lab at the University of British Columbia, Vancouver campus. With Dr. Gary Schajer’s techniques, I was the lead investigator, responsible for all major areas of concept formation, equipment development, data collection and analysis, as well as manuscript composition.  A version of chapter 1, 2, 3 and 4 has been published at the Forest Products Society 71st International Convention and it won the 1st prize of the 2017 Forest Product Society Wood Award. I was the lead investigator for all major areas of concept formation, data collection and analysis, and manuscript edits. Dr. Gary Schajer was involved for concept formation, algorithm development and contributed to manuscript edits.    v  Table of Contents  Abstract .......................................................................................................................................... ii Lay Summary ............................................................................................................................... iii Preface ........................................................................................................................................... iv Table of Contents .......................................................................................................................... v List of Figures .............................................................................................................................. vii Acknowledgements ...................................................................................................................... ix Dedication ...................................................................................................................................... x 1    Introduction ............................................................................................................................. 1 1.1 Wood grain ............................................................................................................................ 1 1.2 Surface angle and dive angle ................................................................................................ 4 1.3 State of art ............................................................................................................................. 4 1.4 Overview ............................................................................................................................... 6 2    Directional Reflection ............................................................................................................. 8 2.1 Specular, diffuse reflection and lobes ................................................................................... 8 2.2 Introduction to directional reflection .................................................................................... 9 2.3 Hyperbola model of the specular reflection ........................................................................ 11 2.4 Concluding remarks ............................................................................................................ 15 3    Theory .................................................................................................................................... 16 3.1 Circle method ...................................................................................................................... 16 3.1.1 Dive angle δ ................................................................................................................. 16 3.1.2 Surface angle α ............................................................................................................. 18 3.1.3 Discussion .................................................................................................................... 18 3.2 Linear method ..................................................................................................................... 19 3.2.1 Surface and dive angle ................................................................................................. 20 3.2.2 Simplified equations .................................................................................................... 21 3.2.3 Correction equations .................................................................................................... 22 3.3 Concluding remarks ............................................................................................................ 25 4    Experiments ........................................................................................................................... 26 4.1 Experimental procedure ...................................................................................................... 26 4.2 Scaling on directional reflection ......................................................................................... 27 4.3 Results -- Circle method ..................................................................................................... 29 4.3.1 Dive angle .................................................................................................................... 29 vi  4.3.2 Surface angle ................................................................................................................ 31 4.4 Results -- Linear method ..................................................................................................... 32 4.4.1 Dive angle .................................................................................................................... 32 4.4.2 Surface angle ................................................................................................................ 33 4.5 Concluding remarks ............................................................................................................ 34 5    Earlywood, Latewood and Surface Finishing .................................................................... 36 5.1 Early wood and late wood ................................................................................................... 36 5.2 Different surface finishing .................................................................................................. 38 5.3 Discussion ........................................................................................................................... 40 6    Industrial Concept of Linear Method ................................................................................. 41 6.1 Equipment design ................................................................................................................ 41 6.2 Interpolation study .............................................................................................................. 42 6.2.1 11-point parabola curve fitting around peaks .............................................................. 42 6.2.2 3-point parabolic curve fitting on the 7 data points ..................................................... 42 6.2.3 Comparison with other interpolations .......................................................................... 43 6.2.4 Localized interpolation ................................................................................................ 46 6.3 Results ................................................................................................................................. 48 6.4 Discussion ........................................................................................................................... 52 7    Conclusions and Future Work ............................................................................................. 54 7.1 Conclusions ......................................................................................................................... 54 7.2 Future work ......................................................................................................................... 56 Bibliography ................................................................................................................................ 57               vii  List of Figures  Fig. 1. 1 Wood cell structure. Source: [1]. ...................................................................................... 1 Fig. 1. 2 Structure of straws ............................................................................................................ 2 Fig. 1. 3 Effect of grain angle on wood strength. Source: [5]. ........................................................ 3 Fig. 1. 4 Pedestal is strongest when grain is parallel to its longest dimension. Source: [6]. .......... 3 Fig. 1. 5 Grain direction definition. ................................................................................................ 4  Fig.2. 1 Specular and diffuse lobes. ................................................................................................ 8 Fig.2. 2 Reflectance distribution on a cylinder. .............................................................................. 9 Fig.2. 3 Specular reflection from a cylindrical wood cell. ............................................................ 10 Fig.2. 4 Reflection from an illuminated wood specimen with zero surface and dive angle. ........ 11 Fig.2. 5 Reflection from wood surface. ........................................................................................ 11 Fig.2. 6 Reflection in cone shape intersects viewing plane with a pair of hyperbola. .................. 12 Fig.2. 7 Hyperbolas. ...................................................................................................................... 13  Fig.3. 1 Specular reflection in a prospective view. ....................................................................... 16 Fig.3. 2 Geometric graphs in two views. ...................................................................................... 17 Fig.3. 3 Geometric drawing in top view of specular reflection with non-zero surface angle. ...... 18 Fig.3. 4 Intersections between the sensor circle and the specular component of reflection. ........ 19 Fig.3. 5 Intersections between the sensor lines and the specular component of reflection. ......... 19 Fig.3. 6 Geometric illustration of linear method........................................................................... 20 Fig.3. 7 Geometric illustration of the simplified linear method. .................................................. 22 Fig.3. 8 The approximation of straight line from hyperbola changes measurement y1and y2. ... 23 Fig.3. 9 Dive angles computed from the simplified equations increasingly deviate as ‘g’ and ‘δ’ increases. ....................................................................................................................................... 24 Fig.3. 10 Corrected dive angles by correction equation 41. ......................................................... 24  Fig.4. 1 Experimental apparatus. .................................................................................................. 26 Fig.4. 2 Wood specimens used for grain angle measurements. Surface angle α = 0° for all........ 27 Fig.4. 3 Directional reflection maps of three specimens. ............................................................. 27 Fig.4. 4 Lambert’s cosine law. ...................................................................................................... 28 Fig.4. 5 Reflection intensity scaled using (Q/h)2.5. ....................................................................... 29 Fig.4. 6 Circle method on reflection intensity scaled using (Q/h)2.5. ............................................ 29 Fig.4. 7 Reflection intensity measured around a circle with R1=15mm and h=30 mm. ............... 30 Fig.4. 8 Reflection intensity measured around a circle with R2=30 mm and h=30mm. ............... 30 Fig.4. 9 Angular errors for measurements made over surface angle range 0° < α < 20°.............. 32 Fig.4. 10 Linear method on reflection intensity scaled using (Q/h)2.5. ......................................... 32 Fig.4. 11 Angular errors for measurements made over surface angle range 0° < α < 20°, linear method........................................................................................................................................... 34  Fig.5. 1 Transitions from earlywood to latewood. Source: [30]. .................................................. 36 Fig.5. 2 Specimen with earlywood and latewood marked out. ..................................................... 37 Fig.5. 3 Unscaled reflection maps of earlywood and latewood of specimen in Fig. 5.2. ............. 37 Fig.5. 4 Three kinds of surface finishing. ..................................................................................... 38 Fig.5. 5 Surface finishing on specimen. ........................................................................................ 38 viii  Fig.5. 6 Unscaled reflection maps from varnished surface. .......................................................... 39 Fig.5. 7 Unscaled reflection maps from sanded surface. .............................................................. 39 Fig.5. 8 Sanding creates more diffuse reflection. ......................................................................... 40  Fig.6. 1 Design of the equipment based on the linear method. ..................................................... 41 Fig.6. 2 61 data points intensity curves, linear method, g = 15 mm. ............................................ 42 Fig.6. 3 3-points parabolic curves, g = 15 mm. ............................................................................ 43 Fig.6. 4 Interpolation comparison on specimen with 0° dive angle.............................................. 44 Fig.6. 5 Interpolation comparison on specimen with 6° dive angle.............................................. 45 Fig.6. 6 Interpolation comparison on specimen with 10° dive angle............................................ 45 Fig.6. 7 Localized 3-point parabolic interpolation with 90% subtraction of the smallest value .. 47 Fig.6. 8 Reflection maps of specimen with 0° dive angle, h =30 mm. ......................................... 48 Fig.6. 9 Surface and dive angle results of the specimen with 0° dive angle with variable ‘g’. .... 49 Fig.6. 10 Reflection maps of specimen with 6° dive angle, h =30 mm. ....................................... 50 Fig.6. 11 Surface and dive angle results of the specimen with 6° dive angle with variable ‘g’. .. 50 Fig.6. 12 Reflection maps of specimen with 10° dive angle, h =30 mm. ..................................... 51 Fig.6. 13 Surface and dive angle results of the specimen with 10° dive angle with variable ‘g’. 52 Fig.6. 14 Intensity curves plotted in one diagram for the rotated 0° dive angle specimen. .......... 53 Fig.6. 15 Dive angle results of the specimen with 10° dive angle with variable ‘g’ by using simplified linear method without corrections. .............................................................................. 53                    ix  Acknowledgements  First of all, I would like to give my sincere gratitude to my supervisor -- Dr. Gary Schajer, for his guidance and support all along. He is not only an intelligent individual but also an amicable friend, who takes care of his students like his own children. Without him, I wouldn’t be able to come this far. I am glad that I had the opportunity to come to UBC, thank you, Dr. Schajer! Also, many thanks to Hermary Optoelectronics Inc. and the Natural Science and Engineering Research Council of Canada (NSERC) for funding the project. Moreover, I would like thank my lab mates at the Renewable Resources Lab of UBC, Filipe Zanini Broetto, Juuso Heikkinen, Harsh Pokharna, Charles Karassowitsch for helping and supporting me.   Thanks to the former member of the Renewable Resources Lab -- Darren Sutton, for his kind experimental help and instructive foundational research work. Special thanks to Glenn Jolly from the Electronics lab for helping me on electronics issues. Finally, I’d like to express my gratitude to my parents for providing me with continuous encouragement and financial support throughout years of study, this accomplishment would not be achieved without them. Thank you!                    x  Dedication    To family   1  1    Introduction 1.1 Wood grain Wood grain describes the longitudinal arrangement of fibres in wood. There are at least 50 types of grain in different categories, while the term ‘grain’ alone is often a description of the dominant longitudinal cells in a tree [1]. Fig. 1.1 shows micrographs of the cell structure for both hardwood and sorftwood. The elongated cells are in the shape of tubes, which resemble a structure of numerous straws tied along the same direction in Fig. 1.2.   Fig. 1. 1 Wood cell structure. Source: [1]. (a) Hardwood (Red oak); (b) Softwood (Eastern white pine).  Unlike the softwoods, however, the structure of hardwoods is more complex. In hardwoods, vessel elements are usually large in diameter but with thin walls. These are responsible for water conduction [2]. Fibres, on the other hand, are smaller in diameter and shorter than the tracheids but make up the largest part of the structure of hardwood and contribute the most strength to the wood [1].  Vessel elements Tracheids Fibres (a) (b) 2   Fig. 1. 2 Structure of straws   Wood is a natural material that has large variations in structure, mostly due to the presence of knots and spiral grain. For example, wood fibres in softwood often form a spiral along the trunk. In many trees in the northern hemisphere the grain twists from left to right handed direction [3]. The mechanical and physical properties of wood fibres are strongly affected by the direction of the polymers, such as cellulose microfibrils, because they have anisotropic properties [4]. Consequently, the strength of wood is affected by the variations in wood grain (fibre) direction; even a small deviation in grain direction significantly weakens the lumber.  For example, a 15°deviation of the grain direction can almost reduce as much as half the strength of a lumber, see Fig. 1.3 [5].   3   Fig. 1. 3 Effect of grain angle on wood strength. Source: [5].  Another typical example, the pedestal in Fig. 1.4 (a) is the strongest compared to that in Fig. 1.4 (b) and (c), since in (a) the grain runs parallel to its longest dimension [6].                   Fig. 1. 4 Pedestal is strongest when grain is parallel to its longest dimension. Source: [6].  In general, grain direction is a good indicator of wood strength model. It provides critical information for strength rating of the lumber and it plays an important role in quality grading. It’s also been found that the grain angle standard deviation is more closely related to strength than the average grain angle when the measurement is conducted along a line on the lumber [3].  Thus, for product quality control, it is important to be able to measure wood grain direction. In this way, grades of lumber with more uniform and assured strength properties can be produced. Thus, lumber with specific characteristics can be best utilized to fit their design purpose.   STRONG (b) (a) (c) 4  1.2 Surface angle and dive angle Grain direction can be defined by two angles respectively called the surface angle ⍺ and dive angle δ. Ideally, clear wood would be considered as the highest grade when all fibres are parallel to the longitudinal direction. When the spiral grain, knots or other defects exist, the grain deviates from the longitudinal axis and the material becomes weaker. The surface angle ⍺ is the angle between the grain direction and the longitudinal axis on the viewing surface ‘A’ of the lumber, as shown in Fig 1.5(b); the dive angle δ is the tilting angle of the grain direction with respect to the surface ‘A’ [7], see Fig 1.5 (c).   Fig. 1. 5 Grain direction definition. (a) ⍺ = 0°, δ = 0°; (b) ⍺ ≠0°, δ = 0°; (c) ⍺ = 0°, δ ≠ 0°.  1.3 State of art In wood industry, lumber grain direction has traditionally been determined by visual inspection by skilled graders, typical inspection criteria includes knots detection, grain direction, heart wood and sapwood, pitch pockets, etc. [8]. It is a time-consuming process with low consistency because of the high degree of personal judgment required. Followed by visual inspection, nondestructive machine rating is carried out for better sorting material for specific application in Engineering [9]. Grain deviations substantially reduce the strength of the lumber, so (b) (a) (c) 5  an accurate and fast determination of the grain direction is needed to improve wood grading performance and to add to the efficiency of the machine sorting system.  There are several modern techniques of measuring wood grain direction, each with its particular features. The longitudinal arrangement of wood fibers, causes lumber to be anisotropic in various physical properties. For example, the dielectric anisotropy of wood can be exploited to allow non-contact measurements of surface angle in real time using radio frequency [10] and microwave [11] measurements. The radio frequency based grain angle indicator has also been applied not only to lumber, but also to distinguishing flake arrangement in structural three layer flakeboard [12], where in that case the alignment of the flakes in the board is a critical factor to the stiffness of the board. An X-ray diffractometry approach has also been used to measure the grain angle, but the samples require very delicate preparation [13].    Light illumination has been popularly used as a method of measuring wood grain direction. For example, based on the observation that light transmits axially along the tracheids of wood, the spiral grain angle can be determined by measuring the deflection of ambient daylight transmitting through a disc of a lumber [14].  Among other light illumination techniques, laser scanning provides an alternative practical method for measuring wood grain angle due to its characteristics of directionality and high intensity. Most laser-scanning techniques are based on the so-called ‘tracheid effect’.  When a wood surface is illuminated by a concentrated light source such as a laser, the light tends to spread along the wood fibers or tracheids at the surface to form an elliptical illuminated spot [3] [15] [16]. The tracheid effect can also be obtained by transillumination imaging [17], where a near infrared laser light source illuminates a wood sample from behind and the light transmitted through the sample is captured by a camera at the front of the sample.  Taking the concept of long-wavelength illumination a step further, the tracheid effect has been implemented commercially to detect the presence of knots by locally heating the wood surface and measuring the response using a thermal camera [18].  A limitation of the tracheid method is that it measures surface angle only. An attempt has been made also to infer the dive angle [19], but the measurement resolution is very low.    In addition to the within-surface spreading of light due to the tracheid effect when wood is illuminated by a concentrated light source, light also reflects from the wood surface to form a spatial pattern shaped by the wood grain direction.  At the microscopic scale, wood material is 6  composed of many parallel cylindrical cells [20].  When incident light strikes the surface of the cylindrical cells, the reflection preferentially fans out perpendicular to the grain [21], which happens to any tubular objects that have cylindrical surfaces. Matthews and Soest [22] developed a system that samples the reflected light around a circular path to determine both the surface and the dive angles of the wood. An alternative approach is to reverse the actions of the light source and sensor and instead rotate the light source around the wood sample and measure the reflected light normal to the wood surface [23]. The ability to measure both surface and dive angles is a particular feature of the light reflection method that distinguishes it from other wood grain angle measurement techniques that measure surface angle only [3] [10] [11] [12][16] [18] [24].    A limitation of the method of making measurements around a circular path is that it can measure only smaller dive angles, typically < 5-10°.  The research here describes a new approach to enable measurements of larger dive angles, thereby giving the technique a wider range of applicability.    1.4 Overview The subsequent chapters in the present work are organized as follows. Chapter 2 explains the mechanism of the directional reflection when a piece of lumber is illuminated by a concentrated light source, such as laser. The reflection changes its pattern in terms of the coordinate relation between the fibre and the incident laser beam. Chapter 3 introduces the Circle Method [22] and the linear method. In the circle method, measurements are taken around a circular path on the reflected light off the surface of a lumber. As described previously, the Circle Method is limited to measuring small dive angles. This feature is discussed in this chapter with speculations on the reasons. The limitation of the circle method brings the newly developed Linear Method which uses measurements along two parallel lines on each side of the laser spot. This enables measurements of large dive angles.  Chapter 4 shows the surface and dive angle results from both circle and linear method. It meets the expectation in Chapter 4 that the circle method is indeed limited to small dive angles. When the dive angle is large, the sensor circle became too tangential with the specular reflection component which makes difficult to detect the two peaks. More details are presented in this 7  chapter. The results of the linear method shows its advantage on measuring larger dive angle. Since the results of the linear method are from the simplified equations where it assumes the specular reflection as a straight line, following correction equations for the simplified equations are presented at the end of this chapter. Chapter 5 presents how the results differ from various woods and surface finish. Since the characteristics of the fibres are different in various woods, and also for early wood and late wood of the same specimen, the reflection under laser illumination will also vary. The higher density of the fibre makes the reflection sharper. Also, surface finishing plays another important role for the quality of the measurement. Well-planed wood surface gives more reflective signals. However, finishing like sanding greatly disrupts the fibre arrangement near the surface and seriously impairs optical grain angle measurement. Chapter 6 presents the final equipment based on the Linear Method. It consists of two parallel lines of sensors above the lumber, with a laser beam that is scanned across the lumber at very high speed. The equipment is designed for application in a production line in sawmills. The equipment also opens opportunities to detect defects on the lumber such as knots, split, and check, etc. Experimental results are presented with this equipment as well as validation.  Chapter 7 draws conclusions for the research and discusses the potential work that can be done in the future.    8  2    Directional Reflection 2.1 Specular, diffuse reflection and lobes When an incident beam impinges on a surface, the reflection of the light can be either specular or diffuse or a combination depending on the characteristic of that surface. Specular reflection is a mirror-like reflection where the angle of incidence and reflection are equal; all light rays are reflected in the same direction.  This is the familiar characteristic of a mirror. Diffuse reflection occurs when light impinges on an optically rough surface, causing reflection over a wide range of angles. This type of reflection can occur either at or within a thin layer near the surface [25], where a fraction of incident light enters into the material, is absorbed and scattered, and eventually exits the material with an angle different from the incidence angle. This subsurface reflection is the most general mechanism of diffuse reflection.  The diffuse reflection can be described by Lambert’s Law [26], I    =    I0  cosθ                                                               (1) where I is the reflected light intensity at angle θ and I0 is the incident light intensity.  The equation indicates that the reflected light intensity is maximum normal to the illuminated surface and diminishes as θ increases.  Most surfaces are neither fully specular nor fully diffuse, but a mixture of the two. The reflection lobes in Fig.2.1 illustrate the ways that light is reflected at different surfaces. Fig.2.1 (a) shows pure specular reflection from a mirror and Fig.2.1(c) shows the pure diffuse reflection from a diffuse surface.  Fig. 2.1(b) shows the mixture of specular and diffuse reflection that occurs, for example, in glossy magazine paper [27] [28].  Fig.2. 1 Specular and diffuse lobes. (a) Mirror reflection; (b) Specular reflection; (c) Diffuse reflection; (d) Mixture. (a) (b) (c) Specular peak (d) 9  2.2 Introduction to directional reflection   When a concentrated and collimated light source is vertically incident on a wood surface the reflection is a mixture of specular reflection and diffuse reflection. In addition, the pattern of the reflection depends on the wood grain direction. The wood cellular structure is composed mainly of tracheids whose length is hundred times their diameter. The wood grain direction follows the longitudinal axis of those long narrow cylindrical tubes. When light illuminates these tubes, the reflection tends to reflect perpendicular to the tubes. This phenomenon can be described by the Bidirectional Reflectance Distribution Function (BRDF), which defines the spatial distribution of light that reflects from an opaque surface [28]. In Fig. 2.2 (a), light scatters at the surface of a cylinder, which creates the fan shaped reflection shown in Fig. 2.2 (b).  Fig.2. 2 Reflectance distribution on a cylinder.  If the fiber direction is parallel to the wood surface, as in Fig.2.3 (a), the fan of specularly reflected light is planar. If a flat plane is imagined parallel to the wood surface, the fan of light would intersect it to form a straight line, and the line rotates as the surface angle varies in Fig.2.3 (b). If however the fiber direction dives into the wood surface, as in Fig.2.3(c), then the fan of specularly reflected light forms a slightly conical shape and the intersection with the plane becomes curved. Figure 2.3 illustrates the response of the specular component of the reflected light. The diffuse component combines with the specular component to give a more spread out reflection, as shown in Figure 2.4 and Fig. 2.5.  (a) (b) 10                          (a)Cell parallel to wood surface; (b) Non - zero surface angle; (c) Cell diving into wood surface (Non - zero dive angle). Plane Plane (a) Plane Plane (b) Plane Plane (c) Fig.2. 3 Specular reflection from a cylindrical wood cell. 11  In Figure 2.4, the wood grain is purely longitudinal, with zero surface and dive angles. This produces the horizontal symmetrical reflection seen in Fig.2.4 (d). A non-zero surface angle causes the reflection to rotate, as shown in Fig.2.5 (a), while a non-zero dive angle causes the reflection to move sideways, away from the center, as shown in Fig.2.5(b).   Fig.2. 4 Reflection from an illuminated wood specimen with zero surface and dive angle.  (a)Wood illumination; (b) Specular reflection; (c) Diffuse reflection; (d) Combined reflection.  Fig.2. 5 Reflection from wood surface.  (a)Non-zero surface angle; (b) Non-zero dive angle.  2.3 Hyperbola model of the specular reflection With non-zero dive angle, the intersection between the cone shaped specular component reflected light and the viewing plane can be modeled as a pair of hyperbola, as shown in Fig. 2.6 (a).  In Fig. 2.6, incident ray AG impinges on wood surface perpendicularly. Due to the dive angle δ, light is reflected in a conical with axis parallel to the wood cell, i.e., inclined at angle δ.  (d) (c) (b) (a) Plane Plane Plane Plane (a) (b) (c) Plane Plane Plane Plane (d) 12  Only the upper half of the cone is illuminated and the lower half exits only mathematically. Also mathematically only, a second cone AGE can be constructed with common axis with angles δ in the opposite direction. In terms of math theory, these two cones intersects the view plane above as a pair of hyperbolas at point C and A, marked in red in Fig. 2.6 (a).                   Fig.2. 6 Reflection in cone shape intersects viewing plane with a pair of hyperbola. (a) Photographic geometry; (b) Schematic geometric drawing. (a) (b) 13   The equation for a symmetrical hyperbola is as follows, x2a2 −  y2b2= 1.                                                                      (2)  Fig.2. 7 Hyperbolas.  (a) Symmetrical hyperbolas; (b) Hyperbolas shifted to the right.  Where ± a are the x-axis intersects. The gradients of the two asymptotes are  𝑦𝑥= ± 𝑏𝑎  .                                                                    (3) As shown in Fig 2.7 (b), the hyperbola are shifted to the right a distance ‘a’ so that the left hyperbola passes through the origin, and equation (2) now can be re-written as follows, (𝑥 − 𝑎)2𝑎2−𝑦2𝑏2= 1                                                               (4) ⇒  𝑥2𝑎2−2𝑥𝑎−𝑦2𝑏2= 0.                                                         (5) Where ‘a’ can be determined from distance AC = 2a according to Fig. 2.6 (b) as follows,  𝐴𝐶 = ℎ ∙ 𝑡𝑎𝑛2𝛿 =  2ℎ ∙ 𝑡𝑎𝑛𝛿1 − 𝑡𝑎𝑛2𝛿= 2𝑎                                               (6) (a) -b b -b b (b) 14  ⇒   𝑎 =  ℎ ∙ 𝑡𝑎𝑛𝛿1 − 𝑡𝑎𝑛2𝛿                                                              (7) where ‘h’ is the distance between viewing plane and laser spot on the wood surface, and ‘b’ can be determined from 𝑏𝑎= 𝑃𝑟𝑜𝑗𝑒𝑐𝑡𝑒𝑑 𝑐𝑜𝑛𝑒 𝑎𝑛𝑔𝑙𝑒 𝑖𝑛 𝑣𝑖𝑒𝑤𝑖𝑛𝑔 𝑝𝑙𝑎𝑛𝑒.  If the reflection cone axis were parallel to the viewing plane, the asymptote gradients would be 𝑏𝑎=  ± 1𝑡𝑎𝑛𝛿=  𝐶𝐹𝐺𝐹=  𝐽𝐿𝐺𝐹.                                                     (8) However, the reflection cone axis is inclined at angle 𝛼  to the viewing plane. In consequence, distance GF appears as GH and JL as IK. 𝑦𝑥 =  𝐼𝐾𝐺𝐻. Let r = cone radius at C. ⇒ 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐶𝐹 = 𝐹𝐷 = 𝐽𝐿 = 𝐼𝐿 = 𝑟. 𝐺𝐹 = 𝑟 ∙ 𝑡𝑎𝑛𝛿                                                                   (9)  ⇒ 𝐻𝐹 = 𝐺𝐹 ∙ 𝑡𝑎𝑛𝛿 = 𝑟 ∙ 𝑡𝑎𝑛2𝛿 = 𝐾𝐿.                                               (10) According to Pythagoras: 𝐾𝐿2 + 𝐼𝐾2 =  𝑟2, ⇒ 𝐼𝐾 =  √𝑟2 − 𝑟2𝑡𝑎𝑛4𝛿 = 𝑟√1 − 𝑡𝑎𝑛4𝛿                                      (11) ⇒ 𝐺𝐻 =  𝐺𝐹𝑐𝑜𝑠𝛼=  𝑟 ∙ 𝑡𝑎𝑛𝛿𝑐𝑜𝑠𝛿= 𝑟 ∙ 𝑡𝑎𝑛𝛿 ∙ √1 + 𝑡𝑎𝑛2𝛿 .                                (12) By using: 𝑠𝑒𝑐2𝛿 = 1 + 𝑡𝑎𝑛2𝛿, 𝑏2𝑎2=  𝐽𝐿2𝐺𝐹2=  𝑟2 ∙ (1 − 𝑡𝑎𝑛4𝛿)𝑟2 ∙ 𝑡𝑎𝑛2𝛿 ∙ (1 + 𝑡𝑎𝑛2𝛿) =  (1 − 𝑡𝑎𝑛2𝛿) ∙ (1 + 𝑡𝑎𝑛2𝛿)𝑡𝑎𝑛2𝛿 ∙ (1 + 𝑡𝑎𝑛2𝛿) =  1 − 𝑡𝑎𝑛2𝛿𝑡𝑎𝑛2𝛿   (13) ⇒  𝑏2 =  𝑎2 ∙1 −  𝑡𝑎𝑛2𝛿𝑡𝑎𝑛2𝛿= (ℎ ∙ 𝑡𝑎𝑛𝛿1 − 𝑡𝑎𝑛2𝛿)2∙1 − 𝑡𝑎𝑛2𝛿𝑡𝑎𝑛2𝛿=  ℎ211 − 𝑡𝑎𝑛2𝛿                  (14) 𝑥2𝑎2− 2𝑥𝑎−𝑦2𝑏2 =  0                                                         (15) 15  ⇒  (1 − 𝑡𝑎𝑛2𝛿)2ℎ2 ∙ 𝑡𝑎𝑛2𝛿∙ 𝑥2 −2(1 − 𝑡𝑎𝑛2𝛿)ℎ ∙ 𝑡𝑎𝑛𝛿𝑥 −1 − 𝑡𝑎𝑛2𝛿ℎ2𝑦2 = 0.                          (16) Multiplying by ℎ2𝑡𝑎𝑛2𝛿1−𝑡𝑎𝑛2𝛿  on both sides gives (1 − 𝑡𝑎𝑛2𝛿)𝑥2 − 2ℎ𝑥𝑡𝑎𝑛𝛿 − 𝑡𝑎𝑛2𝛿 ∙ 𝑦2 = 0.                                  (17) Equation 17 shows that the specular reflection is a part of a hyperbola that varies with different dive angle δ and distance h, when δ ranges from 0 to 45°.  2.4 Concluding remarks In general, due to the longitudinal arrangement of the fiber in wood, when wood is illuminated by a concentrated light source, light reflected off the wood surface is directional. The reflection is mixture of specular light and diffuse light. Specular reflection is a mirror like reflection as light is reflected in one direction. When the viewing plane is intersecting the cone-shape specular reflection, the intersection can be interpreted as a part of a pair of hyperbola. The shape and the position of the hyperbola is affected by the dive angle of the illuminated wood specimen and the distance ‘h’ between the viewing plane and the wood.     16  3    Theory  In 1986, Matthews and Soest [22] developed a system to detect wood grain angle by using a series of light sensors arranged around a circular path. This arrangement is described here as the Circle method. The sensors are mounted above a wood specimen that is illuminated by a concentrated light source. The advantage of the circle method is that it is able measure both surface and dive angle of wood.  3.1 Circle method 3.1.1 Dive angle δ Figure 3.1 shows an incident light ray AG illuminating a point G on the surface of a piece of wood. The tubular cell structure of the wood causes the light to be reflected in a plane perpendicular to the wood surface grain direction, as described in sections 2.2 and 2.3. In the case of diving grain, the specular reflection ECF intersects with the sensor circle at point E and F on the viewing plane.                                 Fig.3. 1 Specular reflection in a prospective view.  17  Consider the side view plane ABC in Fig. 3.2 (a), GB is the normal to the wood cell surface. Angle AGB = δ. The light is reflected a further angle δ to C. For a part of ray AG that reaches an oblique part of the wood cell, the light is also reflected around the local normal. The locus of all such normal is a plane perpendicular to the wood cell length. This plane intersects the sensor plane along the straight line BD, where distance AB = h tan δ. Consider a particular oblique ray GE that happens to reach the sensor circle at E. Ray GE reflects at angle β around the normal line GD, as shown in oblique view A-D-E in Fig. 3.2 (b).                   Fig.3. 2 Geometric graphs in two views. (a)Side view A-B-C; (b) Oblique view A-D-E.  𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐴𝐸 = ℎ tan 2𝜃 = 𝑅 .                                       (18) where R is the radius of the sensor circle. From above, angle θ can be obtained as follows, tan 2𝜃 =  𝑅ℎ .                                                                 (19) Also, 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐴𝐵 = ℎ tan 𝛿                                                        (20) 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐴𝐷 =  𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐴𝐵𝑐𝑜𝑠𝜑=   ℎ𝑡𝑎𝑛δ𝑐𝑜𝑠𝜑                                        (21) ⇒ 𝑡𝑎𝑛𝜃 =  𝐴𝐷ℎ=  𝑡𝑎𝑛δ𝑐𝑜𝑠𝜑  .                                                           (22) (b) (a) 18  Thus, the dive angle δ can be obtained from equation as follows, 𝑡𝑎𝑛𝛿 = 𝑡𝑎𝑛𝜃 ∙ 𝑐𝑜𝑠𝜑.                                                               (23)  3.1.2 Surface angle α When the surface angle α is non-zero, as shown on the viewing plane in Fig. 3.3, the surface angle can be calculated as follows based on the measurements of angle 𝜑1 and 𝜑2, 𝛼 =  𝜑1 + 𝜑22− 90° .                                                            (24)                                                Fig.3. 3 Geometric drawing in top view of specular reflection with non-zero surface angle.  3.1.3 Discussion The circle method has an advantage of measuring both surface and dive angle, which makes it stand out of other wood grain direction measurement techniques. It is also a very efficient and reliable method due to its concise equations and the directness of the measurement method for angles 𝜑1 and 𝜑2 can be easily obtained. However, the circle method will be limited to small dive angles because when the dive angle is large, the specular component of the reflection becomes too tangential to the sensor circle so that only one intersect appears, as shown in Fig 3.4, which will fail the circle method since two intersects are needed to complete the calculation. A solution will be using a sensor circle with larger radius, but the reflection intensity will be reduced at longer distance which makes it difficult to have distinct intersects.   In general, the circle method has the capability of measuring both surface and dive angle.  However, it cannot measure large dive angles because they cause the specular reflection to become 19  tangential to the measurement circle, as in Fig.3.4b. Therefore, the linear method is introduced as follows that has a better range of measurement on dive angle.           Fig.3. 4 Intersections between the sensor circle and the specular component of reflection. (a) Small dive angle; (b) Large dive angle.  3.2 Linear method The linear method is introduced here to keep the measurement lines more perpendicular to the line of maximum light intensity and thereby avoid the tangential response of the circle method. In Fig3.5, the two sensor lines always have a perpendicular cut on the specular component of refection as dive angle varies.             Fig.3. 5 Intersections between the sensor lines and the specular component of reflection. (a) Small dive angle; (b) Large dive angle.   (a) (b) (a) (b) 20  3.2.1 Surface and dive angle In the linear method, measurements are made along parallel lines at distance g at either side of the illuminated spot. The measurement plane is distance h above the wood surface. The axial distances of the light intensity peaks from the centerline, 𝑦1 and 𝑦2, replace the previously measured angles 𝜑1 and 𝜑2 . In section 2.3, it is shown that the specular reflection from a cylindrical surface is a part of a hyperbola, as shown in Fig.3.6. There are two circles in terms of the intersections 𝑦1 and 𝑦2, and by using Equation (1) twice, two new equations can be established as follows,                       Fig.3. 6 Geometric illustration of linear method.  𝑡𝑎𝑛𝛿 = tan𝜃12𝑐𝑜𝑠𝜑𝑅1 = 𝑡𝑎𝑛𝜃12cos (𝜋2− 𝛽1 + 𝛼) = 𝑡𝑎𝑛𝜃12sin(𝛽1 − 𝛼)         (25) 𝑡𝑎𝑛𝛿 = 𝑡𝑎𝑛𝜃22𝑐𝑜𝑠𝜑𝑅2 =  𝑡𝑎𝑛𝜃22cos (𝛽2 −𝜋2− 𝛼) = 𝑡𝑎𝑛𝜃22sin(𝛽2 − 𝛼).       (26) Equation 4 and 5 can be obtained to give the surface angle α as, 𝑡𝑎𝑛𝛼 =  𝑡𝑎𝑛𝜔1𝑠𝑖𝑛𝛽1 − 𝑡𝑎𝑛𝜔2𝑠𝑖𝑛𝛽2𝑡𝑎𝑛𝜔1𝑐𝑜𝑠𝛽1 − 𝑡𝑎𝑛𝜔2𝑐𝑜𝑠𝛽2                                     (27) 21   where 𝑡𝑎𝑛𝜃1 =  𝑅1ℎ, 𝑡𝑎𝑛𝜃2 =  𝑅2ℎ, 𝜔1  =  𝜃12, 𝜔2 =  𝜃22                 (28 − 31) and 𝑡𝑎𝑛𝜃 =  2𝑡𝑎𝑛𝜃21 − 𝑡𝑎𝑛2𝜃2=  2𝑡𝑎𝑛𝜔1 − 𝑡𝑎𝑛2𝜔  .                                 (32) Combining equations 28 -32 into surface angle formula (27), the surface angle becomes: tan 𝛼 =𝑄1 − ℎ𝑅1∙𝑦1𝑅1− 𝑄2 − ℎ𝑅2∙𝑦2𝑅2𝑄1 − ℎ𝑅1∙𝑔𝑅1+𝑄2 − ℎ𝑅2∙𝑔𝑅2=  (𝑄2 + ℎ)𝑦1 − (𝑄1 + ℎ)𝑦2𝑔(𝑄1 + 𝑄2 + 2ℎ) .              (33) From equations (25 - 26) and (18), the dive angle can be obtained as:  tan 𝛿 =𝑔(𝑦1 + 𝑦2)√(𝑦12 + 𝑔2)(𝑄2 + ℎ)2 + (𝑦22 + 𝑔2)(𝑄1 + ℎ)2 + (𝑄1 + ℎ)(𝑄2 + ℎ)(2𝑔2 − 2𝑦1𝑦2). (34)  where 𝑄 =  √𝑦2 + 𝑔2 + ℎ2  .                                                (35)  3.2.2 Simplified equations Equations (33) and (34) are too complex for practical use. To simplify the algorithm, the specular reflection marked in red in Fig. 3.6 is approximated as a straight line, as shown in Fig. 3.6 (a). Theoretically, the specular reflection is a part of a hyperbola.   22              Fig.3. 7 Geometric illustration of the simplified linear method. (a) Plane view; (b) Side view.  Under the approximation, in Fig. 3.7 (a), the surface angle can be determined as follows, 𝛼 = 𝑎𝑡𝑎𝑛𝑦1 − 𝑦22𝑔.                                                                      (36) From Fig.3.7 (b), the dive angle can be determined as, 𝑡𝑎𝑛2𝛿 =𝑦ℎ                                                                          (37)       where, 𝑦 =𝑦1 + 𝑦22∙ 𝑐𝑜𝑠𝛼.                                                                (38)       Thus, the dive angle can be expressed as follows, 𝛿 = 0.5𝑎𝑡𝑎𝑛 ( 𝑦1 + 𝑦22ℎ𝑐𝑜𝑠𝛼).                                                     (39)  3.2.3 Correction equations The simplified linear method is based on the approximation of considering the specular reflection as a straight line, which in fact is a part of hyperbola. By doing so, the dive and surface angle computed from the simplified equations deviates from the true values that are based on a (b) (a) 23  hyperbola. Thus, it is necessary to use corrections on the simplified linear method to compensate for this deviation. For the dive angle, the two main factors that influence the dive angle computation are the parameter ‘g’ and the computed dive angle δ itself. In Fig. 3.8, when parameter ‘g’ increases from 15 mm to 30 mm, the measurements y1 and y2 (black intersection dots) move sideways along the parabola, which increases the measurement ‘y’ in the simplified equations. This increment of ‘y’ then slightly enlarges the computed dive angle. Also, when parameter ‘g’ remains at a constant value but the dive angle δ increases, the curvature of the hyperbola (specular reflection) will be larger. Due to this change, measurement ‘y’ will also increase because the approximated straight line deviates away from the vertex of the hyperbola as the curvature changes.  Fig.3. 8 The approximation of straight line from hyperbola changes measurement y1and y2.  Fig. 3.9 shows how dive angle and parameter ‘g’ affect the simplified linear method. When the surface angle is zero and dive angle computed in terms of the hyperbola increases from 0 to 15°, the dive angle from the simplified equations in terms of the approximated straight line is not only increasing but also gradually deviates from the true dive angle. In Fig.3.9 (c), the deviation is the biggest due to the larger parameter ‘g’, which is 45 mm. 24   Fig.3. 9 Dive angles computed from the simplified equations increasingly deviate as ‘g’ and ‘δ’ increases. (a) g = 15mm; (b) g = 30 mm; (c) g = 45 mm.  A correction equation for the dive angle can be postulated as follow: 𝛿𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 =  𝛿𝑠𝑖𝑚𝑝𝑙𝑖𝑓𝑖𝑒𝑑 ∙ (1 − 𝑐 ∙ (𝑔ℎ)2∙ 𝛿𝑠𝑖𝑚𝑝𝑙𝑖𝑓𝑖𝑒𝑑2).                           (40) where, ‘δ’ is the dive angle, ‘c’ is a constant to be determined, ‘g’ is the distance from each sensor line to the reflection center and ‘h’ is the normal distance from the specimen to the sensor plane.  After a few tests using example numbers it was found that the the influence of the dive angle ‘δ’ was less than expected and that it could be removed from the adjustment factor. \After some further investigations the finlaized correction equation was chosen as: 𝛿𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 =  𝛿𝑠𝑖𝑚𝑝𝑙𝑖𝑓𝑖𝑒𝑑 ∙ (1 − 0.14 ∙ (𝑔ℎ)1.5).                                   (41)  Fig.3. 10 Corrected dive angles by correction equation 41.  (a) g = 15mm; (b) g = 30 mm; (c) g = 45 mm. (a) (c) (b) (a) (b) (c) 25  Fig. 3.10 shows the corrected results compared to the original results in Fig. 3.10.  The corrected dive angle is the green line, which closely follows the true dive angle line in red.  A similar approach can be taken to correct the surface angle.  After many tests, it is found that the influences of dive angle and parameter g are both modest. Fig. 3.12 shows a comparison of the surface angle computed using the simplified approach and “exact” calculations using the full hyperbola geometry, the difference between them is very small.    3.3 Concluding remarks The circle and linear methods provide non-contact measurements for both surface and dive angles, which makes them stand out among other techniques that measure the surface angle only. The ideal condition for the circle and linear methods is when the specular reflection line intersects the line of sensors perpendicularly.  For the circle method this occurs when the dive angle is small, and for the linear method when the surface angle is small.  Performance deteriorates when the angles are not small.  Thus, the two methods have opposite strengths, the circle method for measuring large surface angles and the linear method for measuring large dive angles.  It turns out that the linear method has a greater capacity for measuring surface angle than the circle method has for measuring dive angle.  The linear method is also more extendable to the case of multiple measurement spots, so is the preferred choice here.   Approximate equations were developed to simplify the mathematical solutions for the angles determined by the linear method. A further correction equation for the dive angle for developed and found to be effective. On the other hand, the surface angles computed from the approximate method directly give good results, so not further correction equation is required.    26  4    Experiments 4.1 Experimental procedure Figure 4.1 schematically illustrates the apparatus used for the wood grain angle measurements reported here.  Each wood specimen was mounted on an optical table and illuminated by a laser diode removed from a 5mW 660nm laser pointer.  In order not to obstruct the viewing area adjacent to the wood surface, the laser diode was mounted remotely at the side of the wood specimen.  The light beam was reflected onto the wood surface by a 45° mirror, as shown in the diagram.  This mirror was made very small, < 2mm across, to minimize its obstruction of the viewing area.  In addition, it was mounted on a glass plate so that its mechanical support would not cause any further optical obstruction.  Light reflection measurements were made using an OPT101 photodiode (Texas Instruments, Dallas, TX, USA) connected to a custom-made signal conditioner.  The photodiode was mounted to a 3-axis motorized table so that it could move in a controlled manner within the space adjacent to the wood surface. The photodiode could then be moved systematically to measure a detailed map of the surface reflection pattern radiating from the illuminated spot on the wood specimen.    The three example wood specimens shown in Figure 4.2 were prepared.  They are all of Englemann spruce (Picea engelmannii), a prominent commercial species in the local wood industry.  The three specimens, 50x15x5 mm, were prepared so that they all had parallel surface grain directions, α = 0°, but different dive angles, δ = 0°, 6° and 10°, as observed microscopically.  The bold black lines in Figure 4.2 indicate the dive angles.               Fig.4. 1 Experimental apparatus.   (a) Schematic diagram; (b) Photographic view. (a) Tiny mirror Specimen Laser Glass sheet Photodiode Motorized table (b) 27                    Fig.4. 2 Wood specimens used for grain angle measurements. Surface angle α = 0° for all.  (a) Dive angle δ = 0°; (b) Dive angle δ = 6°; (c) Dive angle δ = 10°.  4.2 Scaling on directional reflection Figure 4.3 shows the directional reflection map measured by scanning the sensor, column by column, to form an image.  The smoothly varying light intensity indicates that the reflected light is a mixture of specular and diffuse components.  As the dive angle of the specimen increases from 0 to 10°, the brightest part of the reflection displaces sideways.    Fig.4. 3 Directional reflection maps of three specimens.  (a) Dive angle δ = 0°; (b) Dive angle δ = 6°; (c) Dive angle δ = 10°.  The large diffuse component in the reflected light causes the specular peaks to become indistinct. An effective way was developed to separate the diffuse effect from the specular effect by scaling the data to flatten out the diffuse reflection component. The various points within the reflection intensity maps in Figure 4.3 have differing distances Q from the illuminated spot on the δ=6°  δ=10°  (a) (b) (c) (a) (b) (c) 28  wood surface (Equation 35), causing the measured light intensity to vary according to the inverse square law as follows, Light intensity ∝  1distance2.                                                   (43) This effect then can be compensated for by multiplying the measured light intensities by (Q/h)2.                               Fig.4. 4 Lambert’s cosine law.  An additional effect occurs because the light reflection from a diffuse surface varies with direction according to Lambert’s Law (Equation 1), which states that the luminous intensity observed by the sensor from any surface depends on the incident angle θ [29], as shown in Fig.4.4. At the same height ‘h’, sensor 1 receives the maximum intensity and it decreases as sensor 2 moves away as distance ‘y’. The incident angle θ can be determined as follows, I    =    I0  cosθ                                                              (44) cos 𝜃 =  ℎ𝑄.                                                                     (45) In terms of equation 44 and equation 45, thereby it requires an additional compensation factor Q/h.  Combining these gives a required compensation factor (Q/h)3.  The light sensor used here also had some directional dependence. After some tests using plane diffuse surfaces, it was found that the flattest response was achieved from the sensor measurements by scaling by (Q/h)2.5.  Figure 4.5 shows the scaled reflection intensity maps for the measurements shown in Figure 4.3. It can be seen that the scaling is very effective at flattening the diffuse reflection 29  component and thereby making the specular component more visible against that flat background. The specular component also extends sideways to a much greater extent, thus making it easier to identify. These effects greatly add to the quality of the feature extraction.   Fig.4. 5 Reflection intensity scaled using (Q/h)2.5.  (a) Dive angle δ = 0°; (b) Dive angle δ = 6°; (c) Dive angle δ = 10°.  4.3 Results -- Circle method  4.3.1 Dive angle In Fig. 4.6, the motorized table was programmed to move the sensor in 72 x 5° steps around a circle at radius R1 = 15 mm, at a distance h = 30 mm above each specimen surface.  Figure 4.7 shows the measured reflected light intensity curves.  Fig.4. 6 Circle method on reflection intensity scaled using (Q/h)2.5. R1=15mm, R2=30mm, h=30mm.  (a) Dive angle δ = 0°; (b) Dive angle δ = 6°; (c) Dive angle δ = 10°. (c) (b) (a) R1 R2 R1 R2 R1 R2 (c) (b) (a) 30   Fig.4. 7 Reflection intensity measured around a circle with R1=15mm and h=30 mm.  (a) Dive angle δ = 0°; (b) Dive angle δ = 6°; (c) Dive angle δ = 10°.  For the first specimen with 0° dive angle, the two peaks in the intensity curve in Fig.4.7 (a) are distinct, giving a well-defined result δ = 0.6°.  For the second specimen with 6° dive angle, the two light intensity peaks in Fig.4.7(b) move closer and become a little less distinct, but the measurement was still successful to give δ = 7.8°.  However, for the third specimen with 10° dive angle, the light intensity peaks in Fig.4.7 (c) have moved so much together that they have merged into one.  Thus, it is not possible to identify individual angles ϕ1 and ϕ2, causing the measurement to fail.  The reason for the problem has been discussed in Chapter 3.3 and it can also be seen in Fig.4.6 (c), where the maximum reflection peak has moved to become tangential to the R1 circle.  As mentioned previously, a larger circle will ameliorate the tangential measurement problem, but the received light intensity will become reduced at the greater distance and the specular peaks less distinct.  Figure 4.8 shows the result when the radius of the sampling circle is increased to R2=30 mm.  As expected, the light intensity is about half of previously, and the measured peaks are less distinct, both factors making the angle evaluations more prone to measurement error.   Fig.4. 8 Reflection intensity measured around a circle with R2=30 mm and h=30mm.  (a) Dive angle δ = 0°; (b) Dive angle δ = 6°; (c) Dive angle δ = 10°. δ = 7.8° Failed δ = 0.6° (b) (c) (a) (a) (b) (c) δ = 3.6° δ = 8.3° δ = 13.1° 31  4.3.2 Surface angle Surface angle measurement capability was tested by doing a series of measurements where each of the three test specimens was rotated in 5° increments over the range 0° to 20°.  This range was chosen to span the sizes of surface angles commonly found in commercial lumber.   The Circle method was used to measure both surface and dive angle at each angular position with measurement radius R2 = 15mm. Figure 4.9 (a) shows the results, plotted in terms of the deviations from the expected angles.  These correspond to the measurement errors. Thus for a surface angle measurement, the plotted value equals the measured surface angle minus the specimen rotation angle.   In Figure 4.9 (a), the blue dashed line, green solid line and yellow dotted line with triangle marker refer to the results from specimen with 0°, 6° and 10° respectively.  For the small dive angle specimens, δ = 0° and δ = 6°, the circle method identifies the surface and quite well, error is within about 2°.  The large dive in the δ = 10° specimen made the angle evaluations challenging.  The circle method fails entirely due to its inability to resolve distinct reflection peaks.  Also, for a dive angle measurement during the rotation, the plotted value in Fig 4.9 (b) equals the measured dive angle minus the known dive angle of the specimen. And still the blue dashed line, green solid line and yellow dotted line refer to the results from specimen with 0°, 6° and 10° respectively. The results showed a good stability of the circle method on the dive angle when specimen is rotating, except for the large dive angle specimen.     -6-4-202460 5 10 15 20Measurement error / °Specimen rotation / °Dive angle δ = 0° Dive angle δ = 6°Dive angle δ = 10°(a) 32   Fig.4. 9 Angular errors for measurements made over surface angle range 0° < α < 20°.  (a) Surface angle measurement; (b) Dive angle measurement.   4.4 Results -- Linear method 4.4.1 Dive angle  Figure 4.10 shows the parallel arrangement of measurement lines used by the linear method.  These lines are much more perpendicular to the specular reflection line than the previous circle, so give more sharply defined peaks and thus better results.  The measurement lines in Fig.4.10 are used in symmetrical pairs, with g1=15mm and g2=30mm, corresponding to the two radius choices, R1=15 mm and R2=30mm shown in Fig.4.10.   Fig.4. 10 Linear method on reflection intensity scaled using (Q/h)2.5. R1=15mm, R2=30mm, h=30mm. (a) Dive angle δ = 0°; (b) Dive angle δ = 6°; (c) Dive angle δ = 10°. -6-4-202460 5 10 15 20Measurement error / °Specimen rotation /°Dive angle δ = 0° Dive angle δ = 6°Dive angle δ = 10°(b) (a) (b) (c) 33  By using the simplified equation 36, equation 39 and correction equation 41, the dive angles computed from the scaled reflection corresponding to g1=15mm are δ = 0.2°, 6.7° and 9.9°, which compare very well with the microscopically measured values 0°, 6° and 10°.  The successful 10° result is notable because the circle method failed when using R1=15mm.   With g2=30mm, the corresponding computed dive angles are δ = 0.8°, 6.1° and 9.6°, which also compare well with the microscopically measured values 0°, 6° and 10° and also are superior to the R2=30mm results from the circle method. These results demonstrate that the linear method is more robust and reliable than the circle method for measuring dive angle.   4.4.2 Surface angle  The surface angle measurement with linear method is also following the procedure as it is in the circle method. The specimens were rotated from 0° to 20° by 5° at each time. The distance between the measurement line and the center is g = 15 mm that is corresponding to R = 15 mm in the circle method. Results are still plotted as measurement error from expected rotation angles versus specimen rotation, and the blue dashed line, green solid line and yellow dotted line with triangle marker refer to the results from specimen with 0°, 6° and 10° respectively.                 -6-4-202460 5 10 15 20Measurement error / °Specimen rotation / °Dive angle δ = 0° Dive angle δ = 6°Dive angle δ = 10°(a) 34          Fig.4. 11 Angular errors for measurements made over surface angle range 0° < α < 20°, linear method.  (a) Surface angle measurement; (b) Dive angle measurement.  Fig. 4.11 shows the results. The specimens with 0° and 6° show good results, more stable than with the circle method. It also can be seen that the measurement error increases as the rotation increases, which indicates that the linear method is less effective at measuring large surface angles.  Grain angle evaluations were challenging with the 10° dive angle specimen. Dive angle measurement errors remain within 2° with the linear method, but the surface angle measurement errors reached up to 5°. The latter result is larger than with the smaller dive angle specimens, but still is much better than the circle method, which failed entirely due to its inability to resolve distinct reflection peaks.  4.5 Concluding remarks The circle method and linear method both provide practical techniques for measuring wood grain orientation. However, the circle method is limited to small dive angle less than 6°, because the measurement circle diagonally intersects with the specular component of reflection when dive angle is large, thereby causing detection difficulties. The proposed linear method replaces the measurement circle with two parallel lines that are more perpendicular to the specular reflection, thereby allowing a greater range of measurement of dive angles.  -6-4-202460 5 10 15 20Measurement error / °Specimen rotation / °Dive angle δ = 0° Dive angle δ = 6°Dive angle δ = 10°(b) 35  The scaling on the original reflection maps is also a critical step, since it removes the diffuse reflection and makes specular reflection more distinct. Therefore, it makes easier for the linear method to precisely predict the measurements 𝑦1  and 𝑦2 . However, the scaling has no influence on the circle method because all the distances Q of the measurement points to the illuminated spot on the wood surface are constant around a circular path. Thus, the circle method light intensity profiles shown in Fig.4.7 and 4.8 are simply scaled vertically by a uniform factor while the underlying shapes do not change. This means that the peak positions remain the same and so the previously computed dive and surface angle remain unchanged.   36  5    Earlywood, Latewood and Surface Finishing The measurement capabilities of both the circle method and linear methods are highly dependent on the quality of the directional reflections from the wood surface. A distinct specular reflection component helps both algorithms make accurate measurements.  However, the specular reflection is accompanied by a diffuse reflection.  The latter carries no directional information and acts as an impediment to the measurement of the specular reflection.  The relative size of the diffuse reflection depends on the wood surface finish, for example, a planed surface gives relatively low diffuse reflection and so the specular reflection is easy to measure. Conversely, a sanded surface gives high diffuse reflection and so poor measurement of the specular reflection,   this chapter discusses the effects of surface conditions, for example, variations in earlywood and latewood, planed surface, varnished surface and sanded surface.  All these conditions are influential on the reflections.   5.1 Early wood and late wood An annual growth ring in wood comprises a light color low-density layer of earlywood followed by a darker color high-density layer of latewood. The light and dark colors correspond to the different cells formed in the early and late growing season. Wood cells formed in the early growing season are large in diameter and have thin cell walls, while cells formed in the later growing season are small in diameter with thick cell walls [30].                                    Fig.5. 1 Transitions from earlywood to latewood. Source: [30].   Earlywood Latewood 37  Due to the microstructural difference of the earlywood and latewood, the reflections from those two woods are also different. For example, when the specimen in Fig. 5.2 is illuminated by a concentrated light source on the earlywood and latewood, the reflections are shown in Fig. 5.3.                                     Fig.5. 2 Specimen with earlywood and latewood marked out.    Fig.5. 3 Unscaled reflection maps of earlywood and latewood of specimen in Fig. 5.2.  (a) Earlywood; (b) Latewood.  In Fig. 5.3, the reflection of latewood is significantly sharper than that of earlywood, in other words, it is less affected by the diffuse effect.  This is most likely due to the denser fiber arrangement and larger thickness of cell walls in latewood.  Visual inspection of a planed surface shows the latewood layers to be somewhat shiny, while the earlywood layers appear as relatively diffuse. Latewood Earlywood (a) (b) 38  5.2 Different surface finishing The surface finishing also plays an important role in the wood grain direction measurement, because different surfaces reflect differently. In Fig.5.4, three different kinds of surface finishing were used on the specimen in Fig. 5.2.  Fig.5. 4 Three kinds of surface finishing.  (a) Planing; (b) Sanding; (c) Varnishing.   Fig.5. 5 Surface finishing on specimen.  (a) Planing; (b) Sanding; (c) Varnishing.  To ensure that the measurements were taken from the same spot on the specimen, and to avoid possible adverse effects of prior surface treatments, the measurements were done first on a planed surface, the a varnished surface and then a sanded, as shown in Fig. 5.5 (b).  Fig. 5.3 shows the reflection maps obtained from the planed surface. The reflection from the latewood is substantially more specular than from the earlywood, as seen by the more compact (a) (b) (c) (a) (b) (c) 39  reflection map.  After the planed surface is varnished, the fibres become more reflective so that the specular reflection component appears to be yet sharper as shown in Fig. 5.6.   Fig.5. 6 Unscaled reflection maps from varnished surface.  (a) Earlywood; (b) Latewood. Finally, the varnish was removed by sanding along the grain direction.  Reflection maps were measured from earlywood and latewood, as shown in Fig. 5.7. The reflections are dominant by the diffuse reflections in the shape of two circles.  Fig.5. 7 Unscaled reflection maps from sanded surface. (a) Earlywood; (b) Latewood. (a) (b) (a) (b) 40  5.3 Discussion In general, reflections from latewood are sharper and less affected by the diffuse effect than earlywood because the fiber of latewood is much more dense and uniform. Surface finishing substantially changes reflection character. A planed surface gives a more specular response. Varnishing enhances the specular reflection because it reduces the comparative size of the diffuse reflection. In contrast, sanding damages the wood surface structure by disarranging the fibers on the surface such that the longitudinal arrangement of fiber no longer exists. In Fig. 5.8 (b), since the fiber is disordered, the diffuse effect become greater as light gets reflected in random directions.                 Fig.5. 8 Sanding creates more diffuse reflection.  (a) Undamaged wood surface; (b) Sanded wood surface.         (a) (b) 41  6    Industrial Concept of Linear Method In the wood industry, lumber is commonly produced with small surface angle modest dive angle, which is the ideal condition for the linear method in practice. Therefore, an equipment is designed based on the linear method that is suitable for industrial use in sawmills and wood products factories.  6.1 Equipment design Based on the linear method, an equipment can be developed by arranging two parallel lines of sensors along the longitudinal axis of lumber, as shown in Fig. 6.1. The sensors are VBPW34S high speed sensitive photodiodes that are mounted on a printed circuit board with 10 mm of spacing next to each other. The laser on the top is designed to be able to scan along the length of the lumber while remains perpendicular to the measurement surface. It is a TTL laser diode that flashes up to 15 kHz and when the sensors receive reflected light, signals then go through the band pass filter on the printed circuit board which is modulated to filter out signals at any other frequencies. This allows the equipment to be immune to ambient light which is usually at 120 Hz for incandescent lamp.   Fig.6. 1 Design of the equipment based on the linear method.  (a) Schematic diagram; (b) 3D model.  Specimen Sensor array 1 Sensor array 2 Laser (a) (b) 42  6.2 Interpolation study During the previous experiments, the motorized table allows measurements with spacing between measurement points of 1 mm. Now in the new equipment the sensors have been arranged sparsely with intervals of 10 mm. Since the resolution is reduced, interpolation is needed to help find the location of highest intensity. 6.2.1 11-point parabola curve fitting around peaks In the linear method, during the previous measurements with the motorized table, there were 61 data points for each measurement line, as shown in Fig. 6.2. After collecting 61 data points, an 11-point parabola curve fitting was done around the highest intensity of the 61 data points. The vertex of these two fitted parabolas will be the measurements 𝑌1 and 𝑌2  in the proceeding linear method calculation.  Fig.6. 2 61 data points intensity curves, linear method, g = 15 mm. (a) Dive angle δ = 0°; (b) Dive angle δ = 6°; (c) Dive angle δ = 10°.  6.2.2 3-point parabolic curve fitting on the 7 data points In the circuit board set-up, 8 sensors are evenly spread out with spacing of 10 mm. A parabola passing through would be very close to the original 61 data points curve. In order to fit a parabola to find the vertex, at least 3 data points including the highest value are required. It is also known that the spacing is 10 mm that makes the 3 data points 20 mm long, which is enough predict the location of the vertex. The remaining data points are too far to influence the location of the vertex. The 3 selected data points are named as  𝑌1, 𝑌2 and 𝑌3 where 𝑌2 is the middle reading with the highest value. The units are in sensor spacing so to get mm multiply by 10, and by considering (a) (b) (c) 43  𝑌1 is the negative value ahead of 𝑌2 and 𝑌3 is the positive behind, the coordinates of these 3 points became [-1, intensity at 𝑌1 ], [0, intensity at 𝑌2 ] and [1, intensity at 𝑌3 ]. Substituting these 3 coordinates into a parabola, the vertex position can be written as follows, 𝑥𝑚𝑎𝑥 =  𝑌1 − 𝑌32(𝑌1 − 2𝑌2 + 𝑌3). In Fig.6.3, 7 data points were selected from the data presented in Fig.6.2, with spacing 10 mm next to each other. By finding three points containing the highest value 𝑌1, 𝑌2 and 𝑌3, the fitted parabolic curves can be obtained as shown in Fig. 6.3, the black dots are the vertexes of the parabolas as measurements 𝑦1 and 𝑦2.   Fig.6. 3 3-points parabolic curves, g = 15 mm.  (a) Dive angle δ = 0°; (b) Dive angle δ = 6°; (c) Dive angle δ = 10°.  6.2.3 Comparison with other interpolations  In addition to the 3-point parabola interpolation, there are also other interpolations in order to make a comparison, such as 4-point parabola interpolation, 4-point cubic interpolation and 5-point parabola interpolation. (a) (b) (c) 44  To keep the comparison clear, the original 61-points data is plotted in Fig.6.4 (a) with smoothing using a moving average filter. 4 kinds of interpolation have been tested as shown in Fig. 6.4 (b), (c), (d), (e) on the specimen with dive angle of 0 degree.  (a) Smoothed 61 data points; (b) 3-points parabolic interpolation; (c) 4-points parabolic interpolation; (d) 4-points cubic interpolation; (e) 5-points parabolic interpolation.  Fig. 6.5 and Fig.6.6 also show the comparisons for the specimen with 6 degrees of dive angle and 10 degrees of dive angle. It is easy to observe that the cubic interpolation is not a good choice because of the Runge’s phenomenon, in which oscillation occurs at the edges of an interval when the polynomial interpolation is at high degrees. It is also found that the interpolations of more than 3 points don’t necessarily improve the accuracy of peak detection since the data points at the edges have too little intensity to be influential.    (a) (c) (d) (e) (b) Fig.6. 4 Interpolation comparison on specimen with 0° dive angle. 45   Fig.6. 5 Interpolation comparison on specimen with 6° dive angle.  (a) Smoothed 61 data points; (b) 3-points parabolic interpolation; (c) 4-points parabolic interpolation; (d) 4-points cubic interpolation; (e) 5-points parabolic interpolation.  Fig.6. 6 Interpolation comparison on specimen with 10° dive angle. (a) (b) (c) (d) (e) (a) (b) (c) (d) (e) 46   (a) Smoothed 61 data points; (b) 3-points parabolic interpolation; (c) 4-points parabolic interpolation; (d) 4-points cubic interpolation; (e) 5-points parabolic interpolation.  6.2.4 Localized interpolation Fig. 6.4, 6.5 and 6.6 shows the main problem for the interpolation is that none of the interpolation functions fit the measured 61 points data perfectly. The reason could be that the 61-point curves show that there is a localized curvature at the peak, surrounded by comparatively straight sides. A parabola has more uniform curvature, therefore does not fit that well.  In order to have more concentrated curvature in the middle, we can fit the original 3-point parabola by 𝑦 = (𝑎 𝑥2 + 𝑏𝑥 + 𝑐)4 𝑜𝑟 ℎ𝑖𝑔ℎ𝑒𝑟. Also, another problem is that the intensity values around the peaks are all much the same, so in order to get a bigger variation, the chosen subset of three data points are all subtracted by the smallest value among them. After some tests using the subtraction, it was found that the peaks tend to move towards to smallest value side that is 0 after subtraction, and this can be resolved by subtracting 90% of the smallest value instead of 100%. The vertex position now becomes as follows, 𝑥𝑚𝑎𝑥 =  𝑌′1 − 𝑌′32(𝑌′1 − 2𝑌′2 + 𝑌′3) where, 𝑌′1 = √𝑌′1 − 90% ∙ 𝑌𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡4 𝑌′2 = √𝑌′2 − 90% ∙ 𝑌𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡4 𝑌′3 = √𝑌′3 − 90% ∙ 𝑌𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡4 𝑌𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 = min(𝑌1, 𝑌2, 𝑌3). The interpolated curves now become as shown in Fig. 6.7 (b), (d) and (f).    47      Fig.6. 7 Localized 3-point parabolic interpolation with 90% subtraction of the smallest value  (a) Smoothed 61-point data curve on specimen with dive angle = 0°;  (b) Localized 3-point parabolic interpolation on specimen with dive angle = 0°; (c) Smoothed 61-point data curve on specimen with dive angle = 6°;  (d) Localized 3-point parabolic interpolation on specimen with dive angle = 6°; (a) (b) (c) (d) (e) (f) 48  (e) Smoothed 61-point data curve on specimen with dive angle = 10°;  (f) Localized 3-point parabolic interpolation on specimen with dive angle = 10°.  6.3 Results In order to see the performance of the finalized 3-point parabolic interpolation, tests have been made with more data sets, because the previous test of only three examples does not necessarily give a general applicable conclusion.  The first set of data is still taken from the specimen with 0° dive angle by using the single-sensor scanning equipment with motorized table. The specimen was placed vertically where the fibers are parallel to the sensing columns, and the pixels obtained columns by columns form the reflection maps presented in Fig.6.8 (a). After that, the specimen is rotated counter-clockwise by 20 degrees, and the reflection map is shown in Fig. 6.8 (b). The surface and dive angle results with variable ‘g’ are shown in Fig. 6.9, ‘g’ is selected to vary from 10 mm to 29 mm.  Fig.6. 8 Reflection maps of specimen with 0° dive angle, h =30 mm.  (a) No rotation; (b) 20° rotation.     (a) (b) 49   Fig.6. 9 Surface and dive angle results of the specimen with 0° dive angle with variable ‘g’.  (a) Surface angle, no rotation on the specimen; (b) Dive angle, no rotation on the specimen;  (c) Surface angle, 20° rotation on the specimen; (d) Dive angle, 20° rotation on the specimen.  Repeated measurements are also made on the specimen with 6° of dive angle and 10° of dive angle. The reflection maps are presented in Fig. 6.10 and Fig. 6.12, and the results of surface and dive angle versus the variable ‘g’ is shown in Fig. 6.11 and Fig. 6.13.  (a) (b) (c) (d) 50   Fig.6. 10 Reflection maps of specimen with 6° dive angle, h =30 mm.  (a) No rotation; (b) 20° rotation.  Fig.6. 11 Surface and dive angle results of the specimen with 6° dive angle with variable ‘g’. (a) (b) (a) (b) (c) (d) 51   (a) Surface angle, no rotation on the specimen; (b) Dive angle, no rotation on the specimen;  (c) Surface angle, 20° rotation on the specimen; (d) Dive angle, 20° rotation on the specimen.   Fig.6. 12 Reflection maps of specimen with 10° dive angle, h =30 mm.  (a) No rotation; (b) 20° rotation.     (a) (b) (a) (b) 52   Fig.6. 13 Surface and dive angle results of the specimen with 10° dive angle with variable ‘g’.  (a) Surface angle, no rotation on the specimen; (b) Dive angle, no rotation on the specimen;  (c) Surface angle, 20° rotation on the specimen; (d) Dive angle, 20° rotation on the specimen.  6.4 Discussion In general, the results of the surface angle are noisier than for the dive angle because by looking at the equations, the dive angle is the average of the measurements 𝑦1 and 𝑦2, while the surface angle is proportional to the difference between the two measurements. Therefore, the signal to noise ratio of the surface angle is less than that of the dive angle.  In Fig.6.8 (c), the surface angles computed from the interpolation methods are unrealistic and vary rapidly when g changes. This occurs because the measurements 𝑦1 and 𝑦2 appear in the middle of two sensors that are 1 cm away from each other, as shown in Fig. 6.13. Fig. 6.13 shows the intensity curves of two parallel lines at each ‘g’. When g increases, the intensity curves become more flat due to the decease of intensity. This issue could be resolved by increasing another parameter ‘h’, which is the distance from the sensor to the illuminated spot. By doing so, the reflection would be enlarged and the effect from the spacing of sensors will be reduced. Compared to the unmodified 3-point interpolation, the finalized 3-point interpolation is generally effective for measuring both angles. The results computed from the original method that has 11-point parabolic fit around the peaks quite well.  (a) (b) 53                                               Fig.6. 14 Intensity curves plotted in one diagram for the rotated 0° dive angle specimen.  It also found in Fig. 6.13 that the dive angle decreases when parameter ‘g’ increases. This could be due to the specular reflection not being perfectly hyperbolic as it is expected to be, but more linear as shown in Fig. 6.12. In this case, the simplified equations will work without any corrections, since it’s based on the approximation of a straight line on the specular component of reflection. Fig. 6.15 shows that the straight line approximation does ameliorate the issue of decreasing dive angle.  Fig.6. 15 Dive angle results of the specimen with 10° dive angle with variable ‘g’ by using simplified linear method without corrections. (a) Dive angle, no rotation on the specimen; (b) Dive angle, no rotation on the specimen.   Small ‘g’s Large ‘g’s (b) (a) 54  7    Conclusions and Future Work 7.1 Conclusions The longitudinal fiber arrangement in wood contributes a lot to the strength of lumber. For example, a 15 degree of grain direction deviation reduces wood strength by 50%.  Thus, for lumber quality control purposes, a reliable technique to measure the woodgrain direction is needed. The light reflection method developed here provides a practical method for measuring wood grain orientation because it is capable of measuring both surface and diving grain angles. Due to the directional woodgrain arrangement of the lumber and the cylindrical shape of woodgrain, the reflection from a wood surface tends to be directional when it is illuminated by a concentrated light source such as laser. The surface angle results in rotation of the reflection by the same amount of the surface angle, and the dive angle moves the reflection sideways.  The reflection is a mixture of specular and diffuse components. The specular part is a mirror-like reflection that reflects from the cylindrical surface of the woodgrain.  It appears to be a line on the viewing. The diffuse light is mostly caused by the irregularity of the wood surface, and acts to blur the specular line. An important step to make the specular reflective light component more distinctive and easier to locate is to flatten the diffuse reflective light component by scaling the measured reflected light by factors that compensate for the operations of the Inverse Square Law and Lambert’s Law.  This scaling works very effectively and enables the superimposed specular light component to appear clearly as a distinctive line.   The established approach, the circle method, measures the reflected light around a circle concentric with the illumination point. When the collected reflected light is plotted as intensity curves, the two intersections between the specular reflection line and the sensor circle become the two peaks of the curves, measured in angles as 𝜑1 and 𝜑2. The surface angle makes the two peaks move sideways and the dive angle closes up the two peaks. The circle method is effective for measuring surface angle, but it was found to have limited capability to measure diving grain angles beyond about 6°.  This limitation occurs because larger dive angles cause the specular component of the wood surface reflection to become increasingly tangential to the measurement circle, thereby inhibiting the ability of the measurement method to distinguish local light intensity peaks. This is why the linear method is introduced.   55  The proposed linear method replaces the previous measurement circle with two parallel lines.  These remain more perpendicular to the specular component of the wood surface reflection over a much greater range of dive angles.  The intersections between the two lines and the specular reflection are measured in displacement from the center line as 𝑦1 and  𝑦2, corresponding to 𝜑1 and 𝜑2 in the circle method. Unlike the circle method, in the intensity curve graph, the surface angle separates the two peaks and the dive angle moves the peaks sideways. The proposed linear method was shown to be effective at measuring surface grain angles within 5° over the range 0° - 20°, and diving grain angles within 2° over the range 0° to 10°.   Furthermore, to simplify the linear method, the specular reflection is approximated to be a straight line from a hyperbola. The simplified equations with correction is found to be effective on dive angle. Also, the surface angle computed from the simplified equations is overall good so correction is not needed.  In general, the circle method is good at measuring surface angle and limited to large dive angle, while the linear method does a good job on measuring dive angle rather than surface angle. The characteristic of the wood grain makes a difference on the measurement. For example, reflections from latewood is sharper and less affected by the diffuse reflection than earlywood. This occurs because the wood grain in latewood is much more dense and uniform. The wood surface finish also plays an important role. It is found that varnishing gives best results compared to planing and sanding. On the other hand, sanding seriously damages the wood surface and makes the reflection highly diffuse. For industrial applications, an equipment that consists of two parallel lines of sensors was developed. The equipment is based on the linear method and is able to make a series of wood grain orientation measurements along the length of lumber. Since the sensors are sparsely distributed along the two lines with spacing of 10 mm for every two sensors, a 3-data-point parabolic interpolation was developed and was found to be effective for measuring both surface and dive angles. In the interpolation, a 90% subtraction of the smallest value was done to make the interpolated curve more concentrated near the peaks. This improved the results by locating the peaks more accurately. After many measurements to simulate the situation in the new equipment, it is found that the surface angle computed from the linear method with 3-point interpolation is noisier than the dive angle. This occurs because the surface angle calculation makes the noise a bigger portion to 56  the results, particularly when the measurements 𝑦1 and 𝑦2  appear to be in the middle of two sensors. A solution is to increase ‘h’, which is the distance from the sensor to the illuminated spot on the wood surface. It is also found that when the dive angle becomes as large as 10°, the specular reflection is actually not as hyperbolic as expected. This reduces the dive angle when parameter ‘g’ increases. In this case, the simplified linear method without correction alleviates the change of the dive angle.   7.2 Future work   It would be advantageous to improve the hardware in terms of speed. The current design of the equipment with two lines of sensors uses NI 6009 data acquisition, which allows 6000 scans per second when all 8 channels are connected to the sensors. A higher speed analog-to-digital converter would enable data acquisition to be integrated into the circuit boards together with the sensors. The advantage of making measurements at high speed is that it allows them to be made along the length of the lumber in a straight line. It would be even better if there were multiple measurement lines along the lumber so that further information could be gathered. Also, it is desirable that the circuit boards can be connected adjacent to each so that the measurement would not be constrained by length of the specimen.  In a longer term, it would be advantageous to make the equipment more suitable for industrial use. For example, making empirical algorithms according to different wood surface finishes and wood species. This would make the equipment more versatile, so that measurements can be made with higher accuracy.     57  Bibliography  [1]  H. R.Bruce, Understanding wood: A Craftsman's Guide To Wood Technology, Newton, CT, USA: The Taunton Press, 1980.  [2]  J. F. Siau, Transport Processes in Wood, Syracuse, NY, USA: Springer- Verlag Berlin Heidelberg, 1984.  [3]  M. Brannstrom, J. Manninen and J. Oja, "Predicting the strength of sawn wood by tracheid laser scattering," BioRsources , vol. 3, no. 2, pp. 437-451, 2008.  [4]  J. S. Stevanic and L. Salmen, "Orientation of the wood polymers in the cell wall of spruce wood fibres," Holzforschung, vol. 63, pp. 497-503, 2009.  [5]  D. E. 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A. Mclauchlan, J. A. Norton and D. J. Kusec, "Slope of Grain Indicator," Forest Products Journal, vol. 23, no. 5, pp. 50-55, 1973.  [11]  G. S. Schajer and F. B. Orhan, "Measurement of Wood Grain Angle, Moisture Content and Density using Microwaves," Holz als Roh - und Werkstoff, vol. 64, no. 6, pp. 483-490, 2006.  [12]  R. L. Geimer, K. A. McDonald, F. K. Bechtel and J. E. Wood, "Measurement of Flake Alignment in Flakeboard with Grain Angle Indicator," USDA Forest Products Laboratory, Vols. FPL-RP-518, p. 17, 1993.  [13]  C. Buksnowitz, U. Muller, R. Evans, A. Teischinger and M. Grabner, "The potential of SilviScan's X-ray diffractometry method for the rapid assessment of spiral grain in softwood, evaluated by goniometric measurements," Wood Science and Technology, vol. 42, no. 2, pp. 95-102, 2008.  [14]  M. Riddell, D. Cown, J. Harrington, J. Lee and J. Moore, "Assessing spiral grain angle by light transmission," IAWA Journal, vol. 33, no. 1, pp. 1-14, 2012.  [15]  E. Astrand, "Building a high-performance camera for wood inspection," 8 Nov 2011. [Online]. Available: http://www.eetimes.com/document.asp?doc_id=1279213. [Accessed 11 Dec 2016]. 58  [16]  J. Zhou and J. Shen, "Ellipse detection and phase demodulation for wood grain orientation measurement based on the tracheid effect," Optics and Laser in Engineering, vol. 39, no. 1, pp. 73-89, 2003.  [17]  S. Nieminen, J. Heikkinen and J. Raty, "Laser transillumination imaging for determining wood defects and grain angle.," Measurement Science and Technology, vol. 24, no. 12, p. 7, 2013.  [18]  V. Daval, G. Pot, M. Belkacemi, F. Meriaudeau and R. Collet, "Automatic measurement of wood fiber orientation and knot detection using an optical system based on heating conduction," Optical Society of America, vol. 23, no. 26, pp. 33529-33539, 2015.  [19]  S. P. Simonaho, J. Palviainen, Y. Tolonen and R. 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