Visual method for measuring the roughness of a grinding piece based on color indices

Huaian Yi; Jian Liu; Peng Ao; Enhui Lu; Hang Zhang

doi:10.1364/OE.24.017215

1. Introduction

Surface quality control in precision component processing is very strict, especially with respect to workpiece surface roughness, which has a significant impact on the friction wear, working precision, compatibility, fatigue resistance, and corrosion resistance of the workpiece. The methods used to measure surface roughness are generally categorized into contact and non-contact types. The main contact method is the stylus-based method, the precision of which is significantly impacted by the stylus’s radius and linear sampling range, its inability to function inline, and its low efficiency. Moreover, measuring using the stylus-based method inevitably scratches the workpiece’s surface and, therefore, is not suitable for measuring workpieces with high-quality surfaces. The main non-contact measuring methods include optical, electronic, and machine vision techniques. Optical measurement requires expensive equipment and has an extremely small single measurement area. In addition, optical measurement is easily influenced by environmental conditions and has a low operating efficiency [1,2]. Electronic measurement usually uses electrodes that move without making contact with the workpiece’s surface and capture the characteristics of the workpiece’s surface morphology within the range they cover, which is represented by the feedback signal obtained by its capacitive sensors. The measurement’s reliability is affected by the electrode’s radius and speed and by the equipment’s sensitivity, and its measuring efficiency is also quite low [3,4]. Machine vision measurement is based on optical imaging principles; surface images are collected by industrial cameras, and indices characteristic of the surface roughness parameter are extracted from them. The unknown surface roughness is then projected from known characteristic indices of the image. The measurement process is very efficient and can be easily automated. In addition, this method can support inline measurement and therefore, continually attracts more attention from researchers

Based on differences in light sources, machine vision measurement methods can be roughly categorized into two types. The first is vision measurement using laser light sources, which can provide very high precision. For example, Lu et al. obtained laser spot images by studying laser irradiation on a grinding surface and discovered that the surface roughness and the characteristic energy of the gray level co-occurrence matrix (GLCM) have a very well-defined monotonic relationship [5]. Angelsky et al. studied the feasibility of diagnosing the rough surfaces with roughness exceeding the wavelength of the probing radiation by transforming the longitudinal coherence function for a polychromatic field [6].The drawbacks of this method are that laser optical systems are very expensive, the measurement equipment is complex in structure, and optical path adjustment is rather difficult [7–9]. The other machine vision roughness measurement method is to use ordinary light sources (such as incandescent bulbs or light-emitting diodes (LEDs)). Methods of this type are further divided into micro-vision and macro-vision methods based on the size of the imaging area. Micro-vision methods collect magnified images of the surface to be measured, which can be used to observe its morphology and texture. Luk et al. used a machine micro-vision method in an early study of surface roughness and discovered that the ratio of the standard deviation to the root mean square distribution of the gray level histogram is a nonlinear increasing function of the surface roughness, Ra [10]. Ramamoorthy et al. studied the gray level histogram of a magnified image of a workpiece surface that had been processed by grinding, milling, and shaping and explored the use of a GLCM to distinguish different types of processed surface; they determined that the smoother the surface was, the more evenly the GLCM was distributed and that the trend is to move along the diagonal [11]. Gadelmawla used some parameters of the GLCM to characterize different roughnesses by extracting characteristics of the texture of a workpiece’s surface by processing trace morphology micro-images [12]. Liu et al. used the GLCM and a model based on a support vector machine (SVM) to project the roughness of the R-surface in deep hole [13]. In addition, Kamguem et al. [14] proposed a novel surface roughness measurement method based on gradient factors from threshold equations. However, due to their small imaging areas, micro-vision measurement methods cannot make overall assessments of workpiece surfaces. Macro-vision measurement directly collects images of a workpiece surface under ordinary lighting; because the measurement area of each image is large, this is an effective way of making low-cost automatic measurements of mechanical parts. In terms of macro-vision measurements, Younis measured the roughness of a workpiece’s surface by establishing a simple linear relationship between the roughness and the average gray level coefficients of an image [15]. Kumar et al. projected the surface roughness using regression by establishing a multivariate linear relationship between the surface roughness, the algebraic average gray level of an image, and the mechanical processing parameters [16]. Lee, Priya, and Palani injected the frequency spectrum of the Fourier transform of an image of a workpiece’s surface into a neural network to establish a relationship between the spectrum’s characteristics and the roughness and then projected the surface roughness [17–19], respectively. All of these macro-vision methods extract roughness-related assessment indices from grayscale images. However, grayscale images are degraded images; the sensitivity of the image index to surface roughness parameters is reduced by a certain amount. In addition, whereas the Fourier transform of the frequency spectrum is quite robust in representing textures with periodic features, when assessing the surface roughness of a grinding workpiece with a very random texture, its sensitivity is rather weak. In addition, the projection accuracy of an artificial neural network is significantly influenced by factors such as the size of the training sample, the training parameters, and the network’s structure [17,20]; therefore, it cannot guarantee an accurate projection when the sample size is small. In addition, a very important and objective factor that impacts the accuracy of roughness measurements that has been neglected in the abovementioned studies is that workpiece surfaces become contaminated with oil during the production process, and surface stains or rust on the learning calibration samples are formed by the environment over time.

In response to the abovementioned drawbacks of roughness measurement methods and because color is a sensitive descriptive factor that simplifies target extraction and identification [21–23], the present paper proposes a macro-vision roughness measurement method based on a color index. The proposed method is based on the monotonic decrease in the difference between the red and green values of each pixel as the roughness increases and uses a model based on SVM projection to measure surface roughness. Comparing with the three indices used for assessment, i.e., the algebraic average of the image’s gray levels, Ga, the entropy, En, and the square of the main component of the frequency spectrum, F2, indicates that the proposed method exhibits a high correlation between the assessing index and the roughness, requires simple testing equipment, provides high measurement accuracy, and is able to reject interference and make inline measurements.

The remaining portion of the present paper is organized as follows: Section 2 describes the theoretical foundation of color index-based measuring the roughness of grinding workpiece surfaces and the mathematical method used to extract the color index. Section 3 introduces the experimental design, which includes the experimental procedure, sample preparation, and the design of the equipment and the color block. In Section 4, the robustness of the correlation between the color index and the roughness is evaluated by comparing with the three indices, Ga, En and F2; then, the roughness is projected using an SVM-based model. The factors that impact the color index are analyzed and discussed in Section 5, and the conclusions are stated in Section 6.

2. Theoretical analysis of color index-based measurement of grinding workpiece surface roughness

2.1 Light reflection by and imaging of a rough surface

According to the law of light reflection, the light irradiating a target object is reflected to a plane mirror, which reflects it into the human eye; this allows people to see a virtual image of the object in the mirror. By the same principle, viewing the grinding surface as a plane mirror and the camera as a human eye, target object A forms a virtual image on the grinding surface as shown in Fig. 1.

Fig. 1 Diagram of rough surface imaging. (a) Impact of a rough surface on imaging. (b) Vertical impact of a rough surface on imaging.

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When light shines on the surface of target object A, it can be viewed as a point light source. When two light rays are emitted from point A, as shown in Fig. 1(a), and arrive on the reflective surface of the grinding workpiece, they diverge after being reflected by the rough surface and only partially enter the imaging region. When the camera’s focus is fixed and the reflected light passes through the lens, which is precisely focused on the imaging plane, a clear point is produced. However, because the reflection is diffuse, the same point produces multiple virtual images with lower intensities, that is, multiple images of the same object, such as A1′ and A2′. If the reflected ray of light passing through the lens is not focused on the imaging plane, regardless of whether the focal point is in front of or behind the imaging plane, a fuzzy point appears on the plane, and the greater the distance from the focal point to the plane is, the fuzzier the image is [24]. In addition, Zhu et al. [25] believed that as the angle between the light source and the camera’s optical axis, $θ$ (<90°), increases, the divergent area, S, of the point on the target object’s in the imaging plane is directly proportional to roughness height, ΔZ, as shown in Fig. 1(b). Therefore, a virtual image in the imaging plane reflects variations in the rough surface and its height, ΔZ, and its quality, I(i, j) is related to the luminance, L(i, j), the surface character, F(i, j), and the reflectivity, R(i, j), at position (i, j) [26, 27], where i = 1, 2, …, M, j = 1, 2, …, N and M × N is the image size.

I (i, j) = f (L (i, j), F (i, j), R (i, j))

The quality, I(i, j), of a grayscale image is expressed by gray value; the quality of a color image is expressed by the values of its R, G, and B components in RGB color space. The luminance, L(i, j), refers to the intensity of the light shining on the grinding surface, which is the visible light energy received per unit area. The surface character, F(i, j), includes the surface’s roughness, and texture direction, etc. The reflectivity, R(i, j), refers to the ability of the rough surface to reflect light.

2.2 Theoretical analysis of the color index

The RGB color model commonly used in digital image processing can be expressed as shown in Eq. (2),

F (x, y) = R (x, y) \vec{r} + G (x, y) \vec{g} + B (x, y) \vec{b}

where F(x, y) represents the color vector at pixel (x, y) of the image; R(x, y), G(x, y), and B(x, y) represent the red, green, and blue values, respectively, at (x, y); and

\vec{r}

,

\vec{g}

, and

\vec{b}

are unit vectors along the positive R, G, and B axes, respectively.

Obviously, there are many more light rays emitted from point A in Fig. 1, and therefore, after it has been reflected by the rough surface, the size of the virtual image formed on the camera’s imaging plane varies with the roughness of the reflecting surface. Due to the conservation of energy, the rougher the reflecting surface is, the more virtual images of point A form, and the larger the divergent area is, and the lower the average brightness of the spot formed by the virtual images is; this is precisely the theoretical foundation of the gray level information-based method of measuring surface roughness. When there are red and green point light sources A and B, the divergent virtual image reflected by the surface whose roughness is to be measured forms an ideal circle, as shown in Figs. 2(a) and 2(b).

Fig. 2 Target object and its virtual image on (a) low-roughness surface and (b) high-roughness surface.

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In Fig. 2, A1 and A2 and B1 and B2 are ideal virtual images of light sources A and B, respectively, formed on different rough surfaces. The energies of the rays of light from points A and B are denoted by E_A and E_B, respectively, and it is assumed that no energy is lost. In Fig. 2(b), the red and green virtual images overlap in the region shown in yellow. The radii of virtual images A1, B1, A2, and B2 are denoted by $r_{A 1}$ , $r_{B 1}$ , $r_{A 2}$ and $r_{B 2}$ , respectively, where $r_{A 1} \leq r_{A 2}$ and $r_{B 1} \leq r_{B 2}$ ; the overlapping region in Fig. 2(b) is denoted by $A 2 \cap B 2$ . The single-pixel RGB value of virtual image A1 is denoted by $(R_{A 1 (i, j)}, G_{A 1 (i, j)}, B_{A 1 (i, j)})$ , and that of A2 is denoted by $(R_{A 2 (i, j)}, G_{A 2 (i, j)}, B_{A 2 (i, j)})$ , where $B_{A 1 (i, j)} = B_{A 2 (i, j)} = 0$ . $L_{(A 2 \cap B 2) (i, j)}$ represents the brightness of the overlapping region in Fig. 2(b). Then, the following relations can be obtained:

R_{A 1 (i, j)} \propto \frac{E_{A}}{r_{A 1}^{2}} \geq R_{A 2 (i, j)} \propto \frac{E_{A}}{r_{A 2}^{2}}

G_{B 1 (i, j)} \propto \frac{E_{B}}{r_{B 1}^{2}} \geq G_{B 2 (i, j)} \propto \frac{E_{B}}{r_{B 2}^{2}}

G_{A 1 (i, j)} = R_{B 1 (i, j)} = 0

L_{(A 2 \cap B 2) (i, j)} = R_{A 2 (i, j)} + G_{B 2 (i, j)} \propto \frac{E_{A}}{r_{A 2}^{2}} + \frac{E_{B}}{r_{B 2}^{2}}

Therefore, one has

| R_{A 1 (i, j)} - G_{A 1 (i, j)} | \geq | R_{A 2 (i, j)} - G_{A 2 (i, j)} |

| G_{B 1 (i, j)} - R_{B 1 (i, j)} | \geq | G_{B 2 (i, j)} - R_{B 2 (i, j)} |

The absolute difference in the values of the red and green components of each point is called the color difference, and CD is used to represent the average color difference of the M × N pixels in the range of the image. Then, the following correlation between the color index described in this paper, CD, and the roughness is established:

C D = \frac{1}{M \times N} \sum_{i = 1}^{M} \sum_{j = 1}^{N} | R_{(i, j)} - G_{(i, j)} |

It is easy to see from Eqs. (7) and (8) that the mathematical relationship between CD and the surface roughness should be such that when the surface roughness is minimized, CD is maximized, and as the roughness increases, CD decreases monotonically and gradually approaches a relatively small constant. Therefore, the following mathematical model of the surface roughness, Ra, and the average image color index, CD, is established:

R a = f (C D)

3. Experimental design

3.1 Sample preparation and experimental equipment

Forty 50 × 50 mm² test samples made of 45# steel are processed using a manual plane surface grinder. A JB-4C stylus-based roughness measuring instrument is used to measure the roughness at nine evenly distributed locations; the results are shown in the Appendix, Table 5. It can be seen from Table 5 that the stylus-based roughness measurements are affected by the location, length, and number of measurements.

The target object shown in Fig. 1 is a red and green color block, which forms a virtual image on the test sample’s surface. To allow the virtual image of the color block captured by the camera to reflect the maximum variation in roughness, as shown in Fig. 1(b), the test sample’s measurement plane is placed perpendicular to the workbench, and the color block forms a 45° angle with the workbench; the camera is parallel to the color block to ensure that the virtual image is perpendicular to the camera’s optical axis, as shown in Fig. 3. Because the test sample’s texture influences the reflected light in a certain way [28], the experiment is discussed on the basis of the texture of surface being oriented perpendicular to the workbench and horizontally.

Fig. 3 Experimental model.

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The camera used is a 2448 × 2050 pixel Basler color CCD camera fitted with a five megapixel lens. The light source is a white LED (model OPT-LI21222) whose brightness is controlled by a lighting controller (model OPT-DPA1024E-4, maximum level 255). Digital images are captured through a data bus and stored using Pylon 4. To reduce vibration of the test equipment during the imaging process, a precision optical platform is used as workbench. The light source’s brightness is controllable during the experiments, the locations of the camera and the color block locations, and the test sample is fixed to an iron plate with magnets; the entire experimental setup is shown in Fig. 4.

Fig. 4 Machine vision-based roughness measurement setup.

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3.2 Color block design

Based on an analysis of the virtual images of points A and B in Fig. 2 on the test sample’s surface, considering the target object is a block of two different colors, the color difference of each pixel in the virtual image decreases monotonically as the surface roughness increases. Because the human eye is more sensitive to green light than to light of the other two primary colors and is also sensitive to the color yellow, which is a mixture of red and green, the experiment combines the sensory capabilities of the human eye by creating an ideal color block in red and green.

To study the impacts of the texture’s direction and the color block’s density on the color index, four combinations of red and green are designed. Figure 5 show 150 × 150 mm² color blocks that are evenly divided into two, four, 64, and 256 small blocks, respectively; their common property is alternating regions of red and green, which resemble a chess board. When light is reflected from the color block onto the test sample’s surface, it becomes red and green. Due to variations in the test sample’s surface roughness and the abovementioned mechanism governing reflection from rough surfaces, the virtual red and green images on the test sample’s surface should be clearly and distinctly red and green if the surface is smooth or a mixture of red and green if the surface is rough.

Fig. 5 Color block design. From left to right, the number of color block is two, four, 64 and 256.

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3.3 Experimental procedure

To construct a mathematical model of the relationship between CD and the roughness, 15 test samples with small standard deviations, evenly distributions in roughness, as shown in Table 5, are selected. Images with a resolution of 1201 × 1001 dpi are captured and used to calculate CD; furthermore, the robustness of the correlation between CD and the roughness is evaluated. Finally, the 32 test samples listed in Table 5 are used for training the SVM-based method, and the other eight samples are used to verify the feasibility of CD as a measure of roughness. The experimental procedure is shown in Fig. 6, and the roughnesses of the 15 samples are listed in Table 1.

Fig. 6 Experimental procedure flow chart

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Table 1. Roughnesses of the 15 Test Samples (Unit: μm)

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4. Experiment for comparing the roughness assessment indices

The main indices for assessing roughness used in macro-vision measurement methods include the algebraic average of the image’s gray levels, Ga [16], and the square of the main component of the image’s Fourier transform, F2 [17–19]. In addition, in the GLCM and the image matrix, the entropy, En, represents the image’s information content [13,29,30]. According to Shannon information theory, the amount of information is greatest when the entropy is maximized. It is believed that a higher value of En means the image is clearer, and virtual images are obviously clearer on smooth surfaces than on rough ones. Therefore, the correlations of the other three indices used for comparison with the roughness are

G a = \frac{1}{M \times N} \sum_{i = 1}^{M} \sum_{j = 1}^{N} | I (i, j) - I_{m}) |

F 2 = λ

E n = - \sum_{i = 1}^{m} \sum_{j = 1}^{n} I (i, j) I n [I (i, j)]

where

I_{m} = \frac{1}{M \times N} \sum_{i = 1}^{M} \sum_{j = 1}^{N} I (i, j)

and λ is the largest eigenvalue of the covariance matrix of the normalized power spectrum.

Because calibration and training models need to be constructed as part of machine vision-based roughness measurement and mechanical parts are easily contaminated during the manufacturing process, the components of the surface imaging conditions may differ from those of the calibration model during inline measurement. In addition, because the calibration test samples are prone to contamination by dust and air pollution, there is also a problem with inconsistent imaging conditions for the calibration sample and the inline measured sample. The question of whether the roughness assessment index is robust to such contamination has not been investigated in past studies of vision-based roughness measurement. Therefore, the values of the four indices, Ga, En, F2, and CD, for the 15 test samples are compared before and after contamination to determine how robustly they represent the roughness. Figure 7 shows the virtual image formed on the surface before and after contamination.

Fig. 7 Images before (a) contamination and (b) after contamination.

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4.1 Correlation comparison

Because the units are different, the values of CD, Ga, En, and F2 are normalized. It needs to be specially noted that the values of CD, Ga, and En decrease as the roughness increases, whereas F2 increases. For convenience of comparison, the following process is performed during the normalization:

C D_{n o r m a l} (i) = C D (i) / \max (C D)

F 2^{*} (i) = 1 - F 2 (i) / \max (F 2)

F 2_{n o r m a l} (i) = F 2^{*} (i) + (1 - \max (F 2^{*}))

where i = 1, 2, …, 15, CD, Ga, and En are normalized in the same way and F2 exhibits variations in the same direction as those of CD, Ga, and En after normalization.

Figures 8(a) and 8(b) are the curves representing the four indices, CD, Ga, En, and F2, on clean and contaminated surfaces, respectively; the goodness of fit is judged by the coefficient of determination, R², of each fitted curve. The principle underlying the curve fitting is to ensure that the relationship between the indices and the roughness is monotonic first and then to fit the data to the same type of curve before and after contamination. The method of calculating R² is shown in Eq. (17), and the R² values are listed in Table 2;

R^{2} = 1 - \frac{S S E}{S S T} = 1 - \frac{\sum {(y - y *)}^{2}}{\sum {(y - \bar{y})}^{2}}

where SSE is sum of squares for error, SST is sum of squares for total, y is the measured value,

\bar{y}

is the average measured value, and y* is the predicted regression value.

Fig. 8 Curves relating each index to the roughness of (a) clean surface and (b) contaminated surface.

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Table 2. R² Values of the Curves Fitted to the Four Indices before and after the Sample is Contaminated

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It can be seen from Fig. 8 and Table 2 that the roughness’s correlation with the proposed index, CD, is more robust than its correlation with any of the other three indices is. Regardless of whether contamination has occurred, the coefficient of determination, R², of the fitted curve the most for CD, and the difference between the values before and after contamination is small, which indicates that CD is not sensitive to contamination and is able to resist interference rather well. The value of R² for F2 is the worst and changes the most in response to contamination, which indicates that the Fourier transform-based method does not measure highly random grinding surfaces well. Because the images used to evaluate Ga, En and F2 are all grayscale images, contamination on the test sample’s surface is seen as information relating to the roughness during gray level processing. In contrast, the proposed index, CD, is based on color information, and therefore, contamination is less important to the evaluation process. In addition, it can be seen that CD is more sensitive to roughness than the other three indices are; for the same difference in roughness, the change in CD is much greater than the change in any of the other three; moreover, CD changes more monotonically with the roughness than any of the other three indices do.

4.2 Measurement performance comparison

Although the fitted curves’ coefficients of determination, R², illustrate the correlation between the roughness and each index, correlation does not necessarily indicate strong predictive ability; therefore, the ability of CD to measure roughness must be verified experimentally. The SVM-based method proposed by Vapnik is a learning method that uses the training error as a constraint and minimization of the confidence range as an optimization target; its ability to generalize is obviously higher than that of traditional learning methods, such as neural networks [13,31]. In addition, when using an SVM-based regression model, only a small number of samples is needed to construct a function for estimating the regression, which significantly reduces the amount of data required. Therefore, this study uses an SVM-based regression model in the experimental verification.

The standard deviation of the 15 roughness values measured using a stylus shown in Table 1 is small, and theoretically, these values are ideal for use in an SVM. However, at the same time, they are also ideal for use as verification test samples. Therefore, eight of the 15 samples are selected for verification; the verification range is from 0.127 μm to 2.245 μm. The other seven samples and the 25 samples in listed in Table 5, i.e., a total of 32 samples, are used for training. Then, the four indices, CD, Ga, En and F2, are used to make comparable predictions before and after contamination; the results and the error rates are listed in Table 3, where P1 and P2 refer to the predicted roughness values before and after contamination, respectively, and $δ$ is the error rate relative to stylus measuring value. The cuckoo optimization algorithm [32] is used to optimize the two main parameters of the SVM, c and g, which refer to the penalty factor and the Gaussian kernel function, respectively. Two goals must be achieved; one is high precision without overlearning, and the other is that the regression data must decrease monotonically with the roughness, as shown in Fig. 9. The error rate $δ$ is calculated as follows:

Table 3. Prediction Results and Errors Rate of Four Indices

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Fig. 9 Raw data and regression data. Left: Ga index. Right: CD index.

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δ = \frac{| p r e d i c t i o n - s t y l u s m e a s u r e d v a l u e |}{s t y l u s m e a s u r e d v a l u e} \times 100

It can be seen from Table 3 that the CD’s predictions are obviously more accurate than those of the other three indices are. The mean and standard deviation of the error rate of CD are both the smallest; the average error rate is 6.77%, and the standard deviation is 5.70% before contamination; after contamination, they are, respectively, 10.47% and 7.92%; these values are far smaller than those of the other three indices, Ga, En, and F2. Compared to the other three indices, Ga, En, and F2, the average error rate of CD provides reductions of 24.94%, 28.33%, and 26.60%, respectively, before contamination and 13.59%, 9.01%, and 45.52%, respectively, after contamination; the standard deviation is reduced by 19.54%, 24.97%, and 22.02%, respectively, before contamination and by 14.40%, 23.24%, and 33.68%, respectively, after contamination.

Therefore, using CD to measure roughness not only results in a high accuracy of approximately 90% but also provides smaller error fluctuations. Its measurement performance is quite stable and is able to resist interference relatively well, and it is able to make measurements over a wide range. To emphasize CD’s ability to resist interference, contaminated samples are used in the rest of this study unless otherwise noted.

5. Estimation and analysis of factors that impact CD

5.1 Impact of the color block design on CD

The four color block designs shown in Fig. 5 are compared experimentally using the 15 test samples listed in Table 1. The curves relating CD and the roughness are shown in Fig. 10; an SVM-based regression model is used with the eight samples listed in Table 4 for verification purposes.

Fig. 10 Color index versus roughness.

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Table 4. Prediction Results and Error Rates for the Four Color Block Designs

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It can be seen from Fig. 10 that when the color block contains two, four, 64, or 256 sub-blocks, CD decreases as the roughness increases, which indicates the feasibility of the theory of using CD to measure roughness. In particular, the fluctuations in the data are consistent at every point, which indicates that the relationship between CD and the test sample’s roughness test. The measurement area should remain constant for all the designs, which indicates that the measured value of CD for each test sample is accurate, which shows that the proposed method is robust. For the same roughness level, CD is the largest for the two-block design and smallest for the 256-block design. In addition, the more sub-blocks there are, the more CD approaches an asymptote at zero; that is, the sensitivity of CD to the roughness decreases as the number of sub-blocks increases. The reason for this can be seen from Eq. (9): as the number of sub-blocks increases, the distribution of red and green becomes more even, and therefore, CD approaches zero; at this time, CD has no effect on the roughness.

The verification results listed in Table 4 correspond closely with the results shown in Fig. 10. If the number of sub-blocks reaches a certain value, the ability of CD to measure roughness decreases. Nonetheless, the average prediction error rate of CD first decreases and then increases as the number of sub-blocks increases. This result provides us with an idea about the optimal color block design, which will be the focus of follow-up studies.

5.2. Impact of lighting and texture

To increase the experimental efficiency, five samples with roughnesses of 0.052, 0.383, 0.826, 1.507, and 2.245 μm are selected from the abovementioned 15 samples based on how evenly the roughness is distributed.

The texture and lighting conditions are studied. The five test samples with evenly distributed roughnesses used in the experiment do not affect the assessment of the impacts of these two factors. The texture experiments are conducted in both vertical and horizontal orientations. With the lighting at a brightness of 110, the four color block designs are tested, and the results are shown in Fig. 11. The lighting impact experiment is conducted with the surface texture of the test sample perpendicular and horizontal to the workbench. The five test samples with different roughnesses are compared and discussed under different lighting conditions; see Fig. 12.

Fig. 11 Impact of the texture orientation of the grinding sample on CD (brightness of 110) when the color block contains sub-blocks of (a) two, (b) four, (c) 64 and (d) 256 respectively.

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Fig. 12 Relationship between lighting and CD. Surface texture is (a) perpendicular and (b) horizontal to the workbench respectively when the number of color block is two. Surface texture is (c) perpendicular and (d) horizontal to the workbench respectively when the number of color block is 256.

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It can be seen from Fig. 11 that the impact of the texture orientation on CD is quite large regardless of whether the two-, four-, 64-, or 256-block design is used. However, special attention should be paid to the difference between Fig. 11(a) and Figs. 11(b), 11(c), and 11(d). In Fig. 11(a), CD is larger for horizontally oriented textures than for vertically oriented textures, but Figs. 11(b), 11(c), and 11(d) show the opposite result, which indicates that the color block’s design can alter the impact of texture on CD.

Figure 12 provides two pieces of information: first, regardless of the orientation, CD is higher for lower roughnesses than for higher roughnesses, and second, the relationship between the lighting and CD is linear. Therefore, it is feasible to seek a mathematical model that can eliminate the impact of the lighting on this roughness index.

5.3 Discussion

When the number of sub-blocks is large, the mixing of red and green is based on a two-color block design. With a two-color block design, the color of the virtual image formed on the rough surface can be divided into two regions, one with pure colors and the other with mixed colors, as shown in Figs. 13(a), 13(b), and 13(c). However, the concentration points used to measure the roughness with CD are different in the two regions.

Fig. 13 CD measurement area with a roughness of (a) 0.052 μm and (b) 0.826 μm. (c) Color division model. (d) Color difference for the 0.052 μm sample (3D plot).

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In Fig. 2, the mechanism analysis shows that CD decreases monotonically as the roughness increases in both the pure and the mixed color regions. In the pure color region, the brightness has decisive significance for CD; in this situation, CD has the same mechanism as Ga. In the mixed color region, both the pixel location and the brightness of the lighting affect CD, and not only does the brightness of each pixel decrease as the roughness increases but the amount of scattering induced by differences in the roughness also directly affects the brightness of the region in which red and green overlap. It can be seen from Fig. 13(d) that the color difference in the mixed color region is minimized at the boundaries of the blocks and gradually increases toward the two sides. That is, the red-green color difference is only meaningful in the mixed color region; the red and green color values are closest at the boundary and become more different far from the boundary.

Therefore, even for the test sample with a low roughness of 0.052 μm, using CD provides an overall measurement; this is in agreement with the conclusion from Fig. 10, which is that the measurement area should remain constant for four designs. For very rough test samples, the overall red-green mix is more obvious, and the average color difference, CD, naturally decreases as the roughness increases.

6. Conclusions

As a novel method of measuring surface roughness, the method proposed in this study is based on the high sensitivity of color information. Through comparison with Ga, En and F2, it is determined that the proposed index, CD, is more highly correlated with surface roughness and more robust to contamination. An SVM-based method is used with eight test samples with different roughnesses for verification; the verification range is from 0.127 μm to 2.245 μm. The verification proved that the measurement accuracy of CD is higher than that of Ga, En and F2; it reaches 90%. This method can also be used over a larger area. Through comparison of four color block designs, the feasibility of using CD to measure surface roughness is further verified; the results indicate that the color block design can alter the impact of the surface texture on CD. The linear relationship between CD and lighting and the robustness of CD to contamination make inline roughness measurement under various lighting conditions possible. However, it is true that we can’t ignore the influence of monochromatic interference. Because of the high roughness, specular component of the reflected radiation will decrease and the forward scattered part of the radiation will increase inversely, which may lead to monochromatic interference due to the phase delay between monochromatic lights [33,34]. Monochromatic interference can have impact on coloring, and it is therefore still need to conduct further search on whether coloring affect CD index which can be applied to evaluate the high roughness, especially for Ra larger than a wavelength.

Appendix

Table 5. Nine Roughness Measurement (Units: μm) Made Using a Stylus-based Method

View Table | View all tables in this article

Funding

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 71271078), and the Key Project of Science and Technology of Changsha (Grant No. K1307006-11-1).

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	F2	En	Ga	CD
R² before contamination	0.7634	0.8304	0.9050	0.9811
R² after contamination	0.5119	0.9205	0.8437	0.9677
Change (%)	32.94	10.85	6.77	1.37

No.	Stylus value	F2 prediction				En prediction				Ga prediction				CD prediction
No.	Stylus value	P1	$δ$	P2	$δ$	P1	$δ$	P2	$δ$	P1	$δ$	P2	$δ$	P1	$δ$	P2	$δ$
1	0.127	0.138	8.66	0.300	136.22	0.250	96.85	0.091	28.35	0.233	83.46	0.136	7.09	0.127	0.00	0.111	12.60
2	0.211	0.392	85.78	0.339	60.66	0.132	37.44	0.408	93.36	0.163	22.75	0.246	16.59	0.210	0.47	0.226	7.11
3	0.383	0.259	32.38	0.173	54.83	0.234	38.90	0.393	2.61	0.175	54.31	0.308	19.69	0.355	7.31	0.323	15.67
4	0.541	0.608	12.38	0.571	5.55	0.314	41.96	0.493	8.87	0.371	31.42	0.522	3.47	0.599	10.72	0.607	12.20
5	1.064	0.459	56.86	0.347	67.39	1.085	1.97	1.196	12.41	1.278	20.11	1.786	67.89	1.230	15.60	1.336	25.56
6	1.507	1.761	16.85	0.918	39.08	0.818	45.72	1.500	0.46	1.605	6.50	2.190	45.29	1.644	9.09	1.523	1.06
7	1.785	1.631	8.63	1.930	8.12	2.090	17.09	1.634	8.46	2.158	20.90	1.892	6.02	1.962	9.92	1.743	2.35
8	2.245	1.226	45.39	0.537	76.08	2.265	0.89	2.216	1.29	1.925	14.25	2.840	26.51	2.222	1.02	2.083	7.22
Average			33.37		55.99		35.10		19.48		31.71		24.06		6.77		10.47
St.dev			27.72		41.60		30.67		31.16		25.24		22.32		5.70		7.92

No.	Stylus value	Two-block	$δ$	Four-block	$δ$	64-block	$δ$	256-block	$δ$
1	0.127	0.111	12.60	0.131	3.15	0.127	0.00	0.124	2.36
2	0.211	0.226	7.11	0.236	11.85	0.220	4.27	0.382	81.04
3	0.383	0.323	15.67	0.364	4.96	0.369	3.66	0.251	34.46
4	0.541	0.607	12.20	0.726	34.20	0.534	1.29	0.374	30.87
5	1.064	1.336	25.56	1.063	0.09	1.355	27.35	1.245	17.01
6	1.507	1.523	1.06	1.569	4.11	1.424	5.51	1.436	4.71
7	1.785	1.743	2.35	2.036	14.06	1.812	1.51	1.809	1.34
8	2.245	2.083	7.22	2.429	8.20	2.512	11.89	2.250	0.22
Average			10.47		10.08		6.93		21.50
St.dev			7.92		10.78		9.03		27.59

No.	First	Second	Third	Forth	Fifth	Sixth	Seventh	Eighth	Ninth	Average	St.dev.
1	0.053	0.046	0.056	0.056	0.050	0.048	0.053	0.056	0.052	0.052	0.0036
2	0.121	0.130	0.110	0.108	0.114	0.111	0.106	0.109	0.112	0.113	0.0076
3	0.128	0.123	0.129	0.131	0.130	0.123	0.137	0.123	0.121	0.127	0.0052
4	0.147	0.126	0.13	0.18	0.123	0.127	0.169	0.127	0.141	0.141	0.0206
5	0.168	0.154	0.136	0.164	0.165	0.143	0.166	0.133	0.143	0.152	0.0139
6	0.172	0.13	0.121	0.202	0.166	0.157	0.173	0.139	0.132	0.155	0.0262
7	0.168	0.145	0.161	0.162	0.160	0.180	0.180	0.180	0.189	0.169	0.0138
8	0.162	0.151	0.151	0.208	0.199	0.150	0.187	0.195	0.177	0.176	0.0228
9	0.183	0.178	0.196	0.204	0.187	0.173	0.185	0.176	0.235	0.191	0.0192
10	0.204	0.201	0.192	0.227	0.208	0.206	0.216	0.229	0.220	0.211	0.0124
11	0.190	0.248	0.225	0.210	0.251	0.229	0.231	0.241	0.239	0.229	0.0193
12	0.203	0.214	0.238	0.191	0.232	0.291	0.193	0.202	0.312	0.231	0.0435
13	0.238	0.237	0.234	0.248	0.196	0.238	0.246	0.215	0.239	0.232	0.0165
14	0.290	0.348	0.282	0.338	0.373	0.310	0.290	0.342	0.315	0.321	0.0312
15	0.298	0.323	0.363	0.443	0.334	0.363	0.422	0.316	0.388	0.361	0.0492
16	0.378	0.385	0.365	0.395	0.393	0.383	0.386	0.356	0.406	0.383	0.0153
17	0.43	0.359	0.382	0.377	0.406	0.379	0.437	0.335	0.355	0.384	0.0342
18	0.316	0.440	0.337	0.389	0.410	0.326	0.441	0.498	0.362	0.391	0.0616
19	0.371	0.344	0.385	0.422	0.458	0.370	0.494	0.465	0.388	0.411	0.0514
20	0.469	0.48	0.465	0.527	0.446	0.417	0.46	0.445	0.479	0.465	0.0304
21	0.442	0.541	0.495	0.525	0.566	0.522	0.480	0.697	0.598	0.541	0.0746
22	0.737	0.636	0.718	0.827	0.894	0.707	0.877	0.826	1.019	0.805	0.1174
23	0.777	0.819	0.871	0.812	0.893	0.938	0.759	0.648	0.920	0.826	0.0913
24	0.968	0.781	0.810	1.051	0.842	0.848	1.002	0.809	0.844	0.884	0.0970
25	0.848	1.007	0.863	0.628	0.900	0.783	0.857	1.080	1.215	0.909	0.1717
26	1.202	1.125	1.014	1.068	1.130	0.912	1.112	1.038	0.972	1.064	0.0896
27	1.157	1.473	0.947	1.159	1.173	0.986	1.216	1.153	0.926	1.132	0.1676
28	1.055	1.274	1.019	1.305	1.183	1.019	1.113	1.106	1.331	1.156	0.1223
29	1.323	1.079	1.151	1.060	1.320	1.313	1.177	1.196	1.047	1.185	0.1123
30	1.781	1.421	1.246	1.894	1.282	1.119	1.657	1.373	1.095	1.430	0.2868
31	1.421	1.466	1.486	1.641	1.421	1.499	1.563	1.514	1.552	1.507	0.0708
32	1.722	1.558	1.611	1.649	1.617	1.408	1.731	1.675	1.436	1.601	0.1151
33	1.431	1.921	1.858	1.448	1.832	1.623	1.380	1.786	1.731	1.668	0.2045
34	2.086	1.748	1.749	2.109	1.618	1.664	2.138	1.468	1.484	1.785	0.2637
35	1.911	1.783	2.362	1.798	1.400	1.886	1.836	1.616	2.113	1.856	0.2740
36	2.099	1.943	2.029	1.929	2.094	2.04	2.149	2.139	2.083	2.056	0.0786
37	1.901	1.946	2.122	2.174	2.107	2.239	2.030	2.268	2.395	2.131	0.1581
38	1.652	2.486	2.367	1.598	2.491	2.450	1.645	2.545	2.508	2.194	0.4244
39	2.308	2.682	2.441	2.078	2.004	2.161	2.288	2.187	2.057	2.245	0.2142
40	2.463	2.051	2.571	2.664	2.369	2.293	2.654	1.799	2.185	2.339	0.2905

	F2	En	Ga	CD
R² before contamination	0.7634	0.8304	0.9050	0.9811
R² after contamination	0.5119	0.9205	0.8437	0.9677
Change (%)	32.94	10.85	6.77	1.37

Visual method for measuring the roughness of a grinding piece based on color indices

Abstract

1. Introduction

2. Theoretical analysis of color index-based measurement of grinding workpiece surface roughness

2.1 Light reflection by and imaging of a rough surface

2.2 Theoretical analysis of the color index

3. Experimental design

3.1 Sample preparation and experimental equipment

3.2 Color block design

3.3 Experimental procedure

4. Experiment for comparing the roughness assessment indices

4.1 Correlation comparison

4.2 Measurement performance comparison

5. Estimation and analysis of factors that impact CD

5.1 Impact of the color block design on CD

5.2. Impact of lighting and texture

5.3 Discussion

6. Conclusions

Appendix

Funding

References and links

Cited By

Figures (13)

Tables (5)

Equations (18)

Optics Express