# Automatic measurement of wood surface roughness by laser imaging. Part I: Development of laser imaging system.

Abstract

Producing the proper surface finish is an important part of the wood machining process. The surface finish is closely related to wood adhesion, friction, coating, post-processing cost, and aesthetic appearance. A contact method based on stylus is commonly used in laboratories and off-line for measurements of wood surface roughness. The need for improved flexibility, productivity, and product quality in a modern wood machining environment highlights the need for a non-contact, high-speed, in-process surface roughness measurement system. In this study, a laser imaging system was developed to automatically determine wood surface roughness using a two-dimensional Gaussian function model. The results have shown that the image processing system is effective and suitable for determining wood surface roughness for wood specie such as Japanese beech. The correlation between the full width at half maximum of Gaussian function and wood surface roughness coincides with a linear relationship. In other words, the full width at half maximum of Gaussian function is suitable for automatically evaluating wood surface roughness. However, further study is recommended on the influences of wood properties such as anatomical structure, density, and color on measuring accuracy.

**********

Producing the proper surface finish is an important part of the wood machining process. The surface finish is closely related to wood adhesion, coating, post-processing cost, and aesthetic appearance. In order to ensure that machined parts have been manufactured with the desired surface roughness, a sample of the parts is typically examined after machining. The primary disadvantage of post-machining inspection is that it does not allow corrections to be made during machining. The need for improved flexibility, productivity, and product quality in a modern wood machining environment highlights the need for high-speed in-process surface roughness measurement systems. In-process inspection of surface roughness during a machining process can provide better and faster feed back, indicating if the surface finish of the machined part is within a predefined tolerance, without disrupting the production process. An in-process inspection system is the key to successfully controlling product surface quality in an adaptive controlled wood machining environment (Hu et al. 2004).

Conventional contact methods based on stylus are commonly used for in-process inspection in laboratories and off-line roughness measurements of the wood surface. There are, however, disadvantages to using these methods in industry production including low measuring speed, surface damage, and single line traces (Devoe et al. 1992). Additionally variation can be caused by static tip characteristics (dimension, shape, flank angle, and weight) (Radhakrishnan 1970, Whitehouse 1974, Funck et al. 1992) and tip dynamic properties (tilting and vibrating of the stylus hold arm) (Nakamura 1996).

Several non-contact methods have been suggested as alternatives for in-process wood surface roughness measurement. For instance, laser scan method (LSM) (Lendberg and Porankiewicz 1995), optical triangulation measurement method (OTM) (Jakub et al. 2003, 2004; Lemaster 1997), and an image processing method (Timothy 1987, Hagman 1997) can achieve faster measurement speed than the stylus method. Image processing techniques are based on measuring the intensity of light reflected from the surface. These methods, however, suffer from low resolution, effects of wood anatomical structure, and wood properties such as wood density and color on light reflecting, and an inability to characterize the entire surface topography. The ideal measurement system should combine the speed of laser-based systems, the accuracy of contact profiling techniques, and the ability to characterize a two-dimensional region of the surface found in area-based topographic techniques to eliminate the distortion of light reflecting.

The primary focus on this work is on how to make an area-based system using optical image processing technology capable of measuring wood surface roughness which addresses each of the above-mentioned concerns. Kuba et al. (2003, 2004) have investigated two types of laser displacement sensors to characterize a wood surface. The detector was fixed to a position with a reflecting angle. It was reported that measurements were affected by wood properties and the highest resolution was only around 70 [micro]m. Analysis showed that surface topologies and unusual properties would change the detected light intensity for a fixed reflecting angle. The accuracy was questionable and results were not repeatable. In this study, an optical imaging system is proposed to overcome these drawbacks. It was also suggested that the distribution of the reflecting light intensity from surface roughness is a Gaussian function (Zhao et al. 1994, Deng et al. 2001). So a two-dimensional Gaussian model was used to approximate the light reflecting spot and a pair of its full width at half maximum was computed. Then the computed full width at half maximum were compared to the roughness measured by a stylus to build the correlation between the full width at half maximum and wood surface roughness.

Materials and methods

A schematic diagram of the optical imaging system is shown in Figure 1. It consists of a He-Ne laser source (Edmund Optics. NT61332, [lambda] = 628 nm), 5x beam expander (Edmund Optics, NT55577), a cubic beam splitter (Edmund Optics, NT32503), a CCD-camera (Victory KY-F350, Victor JVC) with a micro lens, a two-dimensional moveable table, some ancillary holding parts, and a host computer fitted with image processing software developed and installed by the authors. The materials selected for the experiment were Japanese beech (Fagus crenata blume) conditioned to approximate 10 percent moisture content. Samples were prepared by means of sanding paper with different grit (grit No. 80, 180, 220, 320, 400, and 600). All samples were checked by a stylus instrument (Taylor Hobson Ltd, Taylor Surtronic 3+) and scanned by the optical system shown in Figure 1. Considering processing efficiency, the scattering image was captured at 500 dpi (dots per inch) by adjusting the working distance and the focus length of the CCD-camera. Then the optical evaluation parameters (standard deviations [[sigma].sub.x], [[sigma].sub.y]) were automatically computed using the image processing program, which was written in Matlab 6.5 as code resource. Its flow chart is shown in Figure 2. How to process the scattering image and compute the pair of standard deviation is described in the following section.

Optical evaluation parameters

In the light incoming plane, i.e., x - y plane, the reflecting light intensity can be expressed by two-dimensional Gaussian function as shown (Deng et al. 2001):

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

I(w, y) = A exp(-a[x.sup.2] + bx - c[y.sup.2] + dy + exy + 1) [1]

where:

A, a, and c are real positive constants,

b, d, and e are arbitrary real constants, and

I(x, y) is the distribution of reflecting light intensity.

In order to determine the above coefficients using least square fitting method, Equation [1] can be rewritten as:

z = ln I(x, y) = -a[x.sup.2] + bx - c[y.sup.2] + dy + exy + f [2]

where:

f = ln A + 1.

The residual summation of Equation [2] can be expressed as:

S = [n.summation over (k=0)](-a[x.sub.k.sup.2] + b[x.sub.k] - c[y.sub.k.sup.2] + d[y.sub.k] + e[y.sub.k][y.sub.k] + f - [Z.sub.k])[.sup.2] [3]

where:

S = the summation of residuals;

k = 1,2..., n; p([x.sub.k], [y.sub.k]) is a arbitrary point inside this plane.

The coefficients of Equation [2] can be computed when the following equation is constrained.

[[partial derivative]S]/[[partial derivative]a] = [[partial derivative]S]/[[partial derivative]b] = [[partial derivative]S]/[[partial derivative]c] = [[partial derivative]S]/[[partial derivative]d] = [[partial derivative]S]/[[partial derivative]e] = [[partial derivative]S]/[[partial derivative]f] = 0 [4]

Equation [4] can be rewritten by its numerical expression shown by Equation [5]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [5]

Therefore,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [6]

Equation [1] can be rewritten as Equation [7] after translating the origin of the relative coordinates to the center of scattering spot.

I(x, y) = A exp(-[alpha][x.sup.2] - [beta][y.sup.2]) [7]

where:

[alpha] = a [cos.sup.2] [theta] + c [sin.sup.2] [theta] - e sin [theta] cos [theta],

[beta] = a [sin.sup.2] [theta] + c [cos.sup.2] [theta] + e sin [theta] cos [theta], and

[theta] = [1/2] arctan[e / (c - a)]

[theta] = the angle between the old and new coordinate axes (x and x').

The variance of Equation [6] at the x and y directions ([[sigma].sub.x.sup.2], [[sigma].sub.y.sup.2]) can be expressed as:

[[sigma].sub.x.sup.2] = [[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]]I(x, y)dxdy]/[[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]]I(x, y)dxdy] [8]

[[sigma].sub.y.sup.2] = [[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]][y.sup.2]I(x, y)dxdy]/[[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]]I(x, y)dxdy] [9]

Substituting the expression of Equation [7] into Equations [8] and [9], the following equations are created:

[[sigma].sub.x.sup.2] = [[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]][x.sup.2] A exp(-[alpha][x.sup.2] - [beta][y.sup.2])dxdy]/[[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]] A exp(-[alpha][x.sup.2] - [beta][y.sup.2])dxdy] = 1/[2[alpha]] [10]

[[sigma].sub.y.sup.2] = [[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]][y.sup.2] A exp(-[alpha][x.sup.2] - [beta][y.sup.2])dxdy]/[[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]] A exp(-[alpha][x.sup.2] - [beta][y.sup.2])dxdy] = 1/[2[beta]] [11]

Therefore, the standard deviations at the x and y directions ([[sigma].sub.x], [[sigma].sub.y]) can be expressed as:

[[sigma].sub.x] = 1/[square root of 2[alpha]] [12]

[[sigma].sub.y] = 1/[square root of 2[beta]] [13]

Generally, the full width at half maximum is used to evaluate Gaussian function instead of its standard deviation. The full width at half maximum can be expressed as:

FWH[M.sub.x] = 2[square root of (ln 2[[sigma].sub.x])] = 2[square root of (ln 2)] / [square root of (2[alpha])] [14]

FWH[M.sub.y] = 2[square root of (ln 2[[sigma].sub.y])] = 2[square root of (ln 2)] / [square root of (2[beta])] [15]

In this study, full width at half maximum (FWH[M.sub.x], FWH[M.sub.y]) were used to evaluate the reflecting light from the wood surface so that the wood surface roughness could be evaluated directly.

Results and discussion

The image of the laser light scattering spot captured by the optical imaging system shown in Figure 3 is a quasi-ellipse. This phenomenon is considered to be affected by the tracheid effects (Hu et al. 2004) and machining direction. The quasi-ellipse is gradually fading from its center to edge. The scattering spot also increases when surface roughness increases.

[FIGURE 3 OMITTED]

The scattering laser intensity distributions of Figure 3 are shown in Figure 4. They are obviously two-dimensional Gaussian distributions. Zhao et al. (1993) have reported that wood surface roughness after machining obeyed a one-dimensional Gaussian function by using a one-dimensional optical sensor. Deng et al. (2001) reported similar findings in a metallic field. Comparing the images shown in Figures 3 and 4, the three-dimensional plots show the more obvious variations. As surface roughness becomes more coarse, the maximum scattering light intensity decreases and the diameter of the intensity distribution projecting on the x-y plane increases. The maximum scattering light intensity decreased from 142 to 118 when surface roughness varied from 24.5 to 78.3 [micro]m.

[FIGURE 4 OMITTED]

In order to approximate the scattering light intensity distribution using a two-dimensional Gaussian function, the original images (Fig. 3) were put into an image processing course developed by authors. The detected binary images of the scattering spots are shown in Figure 5. The white area is the scattering spot and the black area is the background. As shown in Figure 5, the scattering spot was correctly detected. The images in Figure 5 show the same tendency as the images shown in Figure 3. The scattering light is fading from the center to the edge. The scattering spot increases where the wood surface roughness is coarser.

Pixels of detected scattering spot were passed to a least square curve fitting analysis to approximate the scattering light intensity distribution and determine the full width at half maximum. The approximated intensity distributions of scattering light at different surface roughness are shown in Figure 6. It can be clearly observed that they coincide with the measured intensity distribution shown in Figure 4. The maximum scattering light intensity decreases from 142 to 118 [micro]m when the surface roughness increased from 24.5 to 78.3 [micro]m. The width of the distribution increases according to the increase of surface roughness. Figure 6e is included as a representative distribution graph on the minor axis at a surface roughness 78.3 [micro]m. This also shows that it coincides with a Gaussian function.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

The correlation between the full width at half maximum (FWH[M.sub.x] and FWH[M.sub.y]) and surface roughness is shown in Figure 7. It can be observed that there is an almost linear relationship between full width at half maximum and surface roughness on both the major and minor axis. The regression expressions at major and minor axis are y = 0.0024x + 1.3681 with [r.sup.2] value 0.7828, and y = 0.0035x + 1.071 with [r.sup.2] 0.9185, respectively. Considering the statistical theory, the result on the minor axis is more credible than that on the major axis because the [r.sup.2] value on the minor axis is greater than that on the major axis. As previously mentioned, this may be the result of the tracheid effect and/or machining direction. The influence of wood properties such as its anatomical structure, color, and density should also be studied and discussed in future study.

Conclusions

In this study, a laser imaging system was developed to automatically determine wood surface roughness using two-dimensional Gaussian function model. The results have shown that the image processing system is effective and suitable for determining wood surface roughness. The correlation between the full width at half maximum of Gaussian function and wood surface roughness coincides with a linear relationship. In other words, the full width at half maximum is suitable to automatically evaluate wood surface roughness for wood specie such as Japanese beech.

Further evaluation is recommended to study the influence of wood properties such as wood anatomical structure, density, and color on the measuring accuracy.

Literature cited

Devoe, D., L. Knox, and G. Zhang. 1992. An experimental study of surface roughness assessment using image processing. ISP Tech. Rept. 1992-28:1-6.

Funck, J.W., J.B. Forrer, D.A. Butler, C.C. Brunner, and A.G. Maristany, 1992. Measuring surface roughness on wood: A comparison of laser scatter and stylus tracing approaches. SPIE. 1821:173-184.

Hagman, O. 1997. Multivariate prediction of wood surface features using an imaging spectrograph. Holz als Roh- und Werkstoff. 55:377-382.

Hu, C.S., T. Chiaki, and T. Ohtani. 2004. On-line determination of the grain angle using ellipse analysis of the laser light scattering pattern image. J. Wood Sci. 50(4):321-326.

Hu, C.S., T. Chiaki, T. Ohtani, and R. Okai. 2004. An improved automatic control system of wood routing using ellipse analysis technology. Forest Prod. J. (in Press)

Jakub, S. and T. Chiaki. 2003. Evaluation of surface smoothness by laser displacement sensor 1: Effect of wood species. J. Wood Sci. 49:305-311.

Jakub, S., T. Chiaki, and T. Ohtani. 2004. Evaluation of surface smoothness by laser displacement sensor 2: Comparison of lateral effect photodiode and multielement array. J. Wood Sci. 50:22-27.

Lemaster, R.L. 1997. The use of optical profilometers to monitor product quality in wood and wood based products. In: Proc. of the National Particleboard Assoc. Sanding and Sawing Seminar. Forest Product Society, Madison, WI. pp. 33-42.

Lundberg, I.A. and S. Porankiewicz. 1995. Studies of non-contact methods for roughness measurements on wood surfaces Holz als Roh- und Wekstoff. 53(5):309-314.

Nakamura, G. 1966. On deformation of surface roughness curves caused by finite radius of stylus tip and tilting of stylus integration. Bulletin Japan Soc. Precis. Eng. 1:240-248.

Radhakrishnan, V. 1970. Effect of stylus radius on the roughness values measured with tracing stylus instruments. Wear. 16:325-335.

Timothy, D.F. 1987. Real time measurement of veneer surface roughness by image analysis. Forest Prod. J. 37(6):34-40.

Whitchouse, D.J. 1974. Theoretical analysis of stylus intergration. Ann CIRP. 23:181-182.

Xuezeng, Z., J. Jinman, and W. Maodi. 1994. Study on measurement of wood surface roughness by Fourier optical method. Scientia Silvae Sinicae. 30(5):458-463 (in Chinese).

Zhicong, D. and K. Masanori. 2001. Optical method for two-dimensional surface roughness measurement. J. of the Japan Society of Mechanical Engineers. 67(653):254-261 (in Japanese).

Chuanshuang Hu

Muhammad T Afzal*

The authors are, respectively, Postdoctoral Fellow and Associate Professor, Faculty of Forestry and Environmental Management, Univ. of New Brunswick, Frederiction, NB, Canada (chuanshuanghu@hotmail.com and mafzal@unb.ca). This paper was received for publication in November 2004. Article No. 9965.

*Forest Products Society Member.

Producing the proper surface finish is an important part of the wood machining process. The surface finish is closely related to wood adhesion, friction, coating, post-processing cost, and aesthetic appearance. A contact method based on stylus is commonly used in laboratories and off-line for measurements of wood surface roughness. The need for improved flexibility, productivity, and product quality in a modern wood machining environment highlights the need for a non-contact, high-speed, in-process surface roughness measurement system. In this study, a laser imaging system was developed to automatically determine wood surface roughness using a two-dimensional Gaussian function model. The results have shown that the image processing system is effective and suitable for determining wood surface roughness for wood specie such as Japanese beech. The correlation between the full width at half maximum of Gaussian function and wood surface roughness coincides with a linear relationship. In other words, the full width at half maximum of Gaussian function is suitable for automatically evaluating wood surface roughness. However, further study is recommended on the influences of wood properties such as anatomical structure, density, and color on measuring accuracy.

**********

Producing the proper surface finish is an important part of the wood machining process. The surface finish is closely related to wood adhesion, coating, post-processing cost, and aesthetic appearance. In order to ensure that machined parts have been manufactured with the desired surface roughness, a sample of the parts is typically examined after machining. The primary disadvantage of post-machining inspection is that it does not allow corrections to be made during machining. The need for improved flexibility, productivity, and product quality in a modern wood machining environment highlights the need for high-speed in-process surface roughness measurement systems. In-process inspection of surface roughness during a machining process can provide better and faster feed back, indicating if the surface finish of the machined part is within a predefined tolerance, without disrupting the production process. An in-process inspection system is the key to successfully controlling product surface quality in an adaptive controlled wood machining environment (Hu et al. 2004).

Conventional contact methods based on stylus are commonly used for in-process inspection in laboratories and off-line roughness measurements of the wood surface. There are, however, disadvantages to using these methods in industry production including low measuring speed, surface damage, and single line traces (Devoe et al. 1992). Additionally variation can be caused by static tip characteristics (dimension, shape, flank angle, and weight) (Radhakrishnan 1970, Whitehouse 1974, Funck et al. 1992) and tip dynamic properties (tilting and vibrating of the stylus hold arm) (Nakamura 1996).

Several non-contact methods have been suggested as alternatives for in-process wood surface roughness measurement. For instance, laser scan method (LSM) (Lendberg and Porankiewicz 1995), optical triangulation measurement method (OTM) (Jakub et al. 2003, 2004; Lemaster 1997), and an image processing method (Timothy 1987, Hagman 1997) can achieve faster measurement speed than the stylus method. Image processing techniques are based on measuring the intensity of light reflected from the surface. These methods, however, suffer from low resolution, effects of wood anatomical structure, and wood properties such as wood density and color on light reflecting, and an inability to characterize the entire surface topography. The ideal measurement system should combine the speed of laser-based systems, the accuracy of contact profiling techniques, and the ability to characterize a two-dimensional region of the surface found in area-based topographic techniques to eliminate the distortion of light reflecting.

The primary focus on this work is on how to make an area-based system using optical image processing technology capable of measuring wood surface roughness which addresses each of the above-mentioned concerns. Kuba et al. (2003, 2004) have investigated two types of laser displacement sensors to characterize a wood surface. The detector was fixed to a position with a reflecting angle. It was reported that measurements were affected by wood properties and the highest resolution was only around 70 [micro]m. Analysis showed that surface topologies and unusual properties would change the detected light intensity for a fixed reflecting angle. The accuracy was questionable and results were not repeatable. In this study, an optical imaging system is proposed to overcome these drawbacks. It was also suggested that the distribution of the reflecting light intensity from surface roughness is a Gaussian function (Zhao et al. 1994, Deng et al. 2001). So a two-dimensional Gaussian model was used to approximate the light reflecting spot and a pair of its full width at half maximum was computed. Then the computed full width at half maximum were compared to the roughness measured by a stylus to build the correlation between the full width at half maximum and wood surface roughness.

Materials and methods

A schematic diagram of the optical imaging system is shown in Figure 1. It consists of a He-Ne laser source (Edmund Optics. NT61332, [lambda] = 628 nm), 5x beam expander (Edmund Optics, NT55577), a cubic beam splitter (Edmund Optics, NT32503), a CCD-camera (Victory KY-F350, Victor JVC) with a micro lens, a two-dimensional moveable table, some ancillary holding parts, and a host computer fitted with image processing software developed and installed by the authors. The materials selected for the experiment were Japanese beech (Fagus crenata blume) conditioned to approximate 10 percent moisture content. Samples were prepared by means of sanding paper with different grit (grit No. 80, 180, 220, 320, 400, and 600). All samples were checked by a stylus instrument (Taylor Hobson Ltd, Taylor Surtronic 3+) and scanned by the optical system shown in Figure 1. Considering processing efficiency, the scattering image was captured at 500 dpi (dots per inch) by adjusting the working distance and the focus length of the CCD-camera. Then the optical evaluation parameters (standard deviations [[sigma].sub.x], [[sigma].sub.y]) were automatically computed using the image processing program, which was written in Matlab 6.5 as code resource. Its flow chart is shown in Figure 2. How to process the scattering image and compute the pair of standard deviation is described in the following section.

Optical evaluation parameters

In the light incoming plane, i.e., x - y plane, the reflecting light intensity can be expressed by two-dimensional Gaussian function as shown (Deng et al. 2001):

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

I(w, y) = A exp(-a[x.sup.2] + bx - c[y.sup.2] + dy + exy + 1) [1]

where:

A, a, and c are real positive constants,

b, d, and e are arbitrary real constants, and

I(x, y) is the distribution of reflecting light intensity.

In order to determine the above coefficients using least square fitting method, Equation [1] can be rewritten as:

z = ln I(x, y) = -a[x.sup.2] + bx - c[y.sup.2] + dy + exy + f [2]

where:

f = ln A + 1.

The residual summation of Equation [2] can be expressed as:

S = [n.summation over (k=0)](-a[x.sub.k.sup.2] + b[x.sub.k] - c[y.sub.k.sup.2] + d[y.sub.k] + e[y.sub.k][y.sub.k] + f - [Z.sub.k])[.sup.2] [3]

where:

S = the summation of residuals;

k = 1,2..., n; p([x.sub.k], [y.sub.k]) is a arbitrary point inside this plane.

The coefficients of Equation [2] can be computed when the following equation is constrained.

[[partial derivative]S]/[[partial derivative]a] = [[partial derivative]S]/[[partial derivative]b] = [[partial derivative]S]/[[partial derivative]c] = [[partial derivative]S]/[[partial derivative]d] = [[partial derivative]S]/[[partial derivative]e] = [[partial derivative]S]/[[partial derivative]f] = 0 [4]

Equation [4] can be rewritten by its numerical expression shown by Equation [5]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [5]

Therefore,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [6]

Equation [1] can be rewritten as Equation [7] after translating the origin of the relative coordinates to the center of scattering spot.

I(x, y) = A exp(-[alpha][x.sup.2] - [beta][y.sup.2]) [7]

where:

[alpha] = a [cos.sup.2] [theta] + c [sin.sup.2] [theta] - e sin [theta] cos [theta],

[beta] = a [sin.sup.2] [theta] + c [cos.sup.2] [theta] + e sin [theta] cos [theta], and

[theta] = [1/2] arctan[e / (c - a)]

[theta] = the angle between the old and new coordinate axes (x and x').

The variance of Equation [6] at the x and y directions ([[sigma].sub.x.sup.2], [[sigma].sub.y.sup.2]) can be expressed as:

[[sigma].sub.x.sup.2] = [[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]]I(x, y)dxdy]/[[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]]I(x, y)dxdy] [8]

[[sigma].sub.y.sup.2] = [[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]][y.sup.2]I(x, y)dxdy]/[[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]]I(x, y)dxdy] [9]

Substituting the expression of Equation [7] into Equations [8] and [9], the following equations are created:

[[sigma].sub.x.sup.2] = [[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]][x.sup.2] A exp(-[alpha][x.sup.2] - [beta][y.sup.2])dxdy]/[[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]] A exp(-[alpha][x.sup.2] - [beta][y.sup.2])dxdy] = 1/[2[alpha]] [10]

[[sigma].sub.y.sup.2] = [[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]][y.sup.2] A exp(-[alpha][x.sup.2] - [beta][y.sup.2])dxdy]/[[[integral].sub.-[infinity].sup.[infinity]][[integral].sub.-[infinity].sup.[infinity]] A exp(-[alpha][x.sup.2] - [beta][y.sup.2])dxdy] = 1/[2[beta]] [11]

Therefore, the standard deviations at the x and y directions ([[sigma].sub.x], [[sigma].sub.y]) can be expressed as:

[[sigma].sub.x] = 1/[square root of 2[alpha]] [12]

[[sigma].sub.y] = 1/[square root of 2[beta]] [13]

Generally, the full width at half maximum is used to evaluate Gaussian function instead of its standard deviation. The full width at half maximum can be expressed as:

FWH[M.sub.x] = 2[square root of (ln 2[[sigma].sub.x])] = 2[square root of (ln 2)] / [square root of (2[alpha])] [14]

FWH[M.sub.y] = 2[square root of (ln 2[[sigma].sub.y])] = 2[square root of (ln 2)] / [square root of (2[beta])] [15]

In this study, full width at half maximum (FWH[M.sub.x], FWH[M.sub.y]) were used to evaluate the reflecting light from the wood surface so that the wood surface roughness could be evaluated directly.

Results and discussion

The image of the laser light scattering spot captured by the optical imaging system shown in Figure 3 is a quasi-ellipse. This phenomenon is considered to be affected by the tracheid effects (Hu et al. 2004) and machining direction. The quasi-ellipse is gradually fading from its center to edge. The scattering spot also increases when surface roughness increases.

[FIGURE 3 OMITTED]

The scattering laser intensity distributions of Figure 3 are shown in Figure 4. They are obviously two-dimensional Gaussian distributions. Zhao et al. (1993) have reported that wood surface roughness after machining obeyed a one-dimensional Gaussian function by using a one-dimensional optical sensor. Deng et al. (2001) reported similar findings in a metallic field. Comparing the images shown in Figures 3 and 4, the three-dimensional plots show the more obvious variations. As surface roughness becomes more coarse, the maximum scattering light intensity decreases and the diameter of the intensity distribution projecting on the x-y plane increases. The maximum scattering light intensity decreased from 142 to 118 when surface roughness varied from 24.5 to 78.3 [micro]m.

[FIGURE 4 OMITTED]

In order to approximate the scattering light intensity distribution using a two-dimensional Gaussian function, the original images (Fig. 3) were put into an image processing course developed by authors. The detected binary images of the scattering spots are shown in Figure 5. The white area is the scattering spot and the black area is the background. As shown in Figure 5, the scattering spot was correctly detected. The images in Figure 5 show the same tendency as the images shown in Figure 3. The scattering light is fading from the center to the edge. The scattering spot increases where the wood surface roughness is coarser.

Pixels of detected scattering spot were passed to a least square curve fitting analysis to approximate the scattering light intensity distribution and determine the full width at half maximum. The approximated intensity distributions of scattering light at different surface roughness are shown in Figure 6. It can be clearly observed that they coincide with the measured intensity distribution shown in Figure 4. The maximum scattering light intensity decreases from 142 to 118 [micro]m when the surface roughness increased from 24.5 to 78.3 [micro]m. The width of the distribution increases according to the increase of surface roughness. Figure 6e is included as a representative distribution graph on the minor axis at a surface roughness 78.3 [micro]m. This also shows that it coincides with a Gaussian function.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

The correlation between the full width at half maximum (FWH[M.sub.x] and FWH[M.sub.y]) and surface roughness is shown in Figure 7. It can be observed that there is an almost linear relationship between full width at half maximum and surface roughness on both the major and minor axis. The regression expressions at major and minor axis are y = 0.0024x + 1.3681 with [r.sup.2] value 0.7828, and y = 0.0035x + 1.071 with [r.sup.2] 0.9185, respectively. Considering the statistical theory, the result on the minor axis is more credible than that on the major axis because the [r.sup.2] value on the minor axis is greater than that on the major axis. As previously mentioned, this may be the result of the tracheid effect and/or machining direction. The influence of wood properties such as its anatomical structure, color, and density should also be studied and discussed in future study.

Conclusions

In this study, a laser imaging system was developed to automatically determine wood surface roughness using two-dimensional Gaussian function model. The results have shown that the image processing system is effective and suitable for determining wood surface roughness. The correlation between the full width at half maximum of Gaussian function and wood surface roughness coincides with a linear relationship. In other words, the full width at half maximum is suitable to automatically evaluate wood surface roughness for wood specie such as Japanese beech.

Further evaluation is recommended to study the influence of wood properties such as wood anatomical structure, density, and color on the measuring accuracy.

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Chuanshuang Hu

Muhammad T Afzal*

The authors are, respectively, Postdoctoral Fellow and Associate Professor, Faculty of Forestry and Environmental Management, Univ. of New Brunswick, Frederiction, NB, Canada (chuanshuanghu@hotmail.com and mafzal@unb.ca). This paper was received for publication in November 2004. Article No. 9965.

*Forest Products Society Member.

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Author: | Hu, Chuanshuang; Afzal, Muhammad T. |
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Publication: | Forest Products Journal |

Geographic Code: | 1USA |

Date: | Dec 1, 2005 |

Words: | 2872 |

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