Correlation of Optical Microstructure and Macroscopic Intensity of Defects on Steel Strip Surface

Abstract

Low contrast defects which originate from inclusions under the surface layer are often observed as patterns of shallow bright streaks with the exception of exposed inclusions on the surface of steel strips. These defects also appear brighter than the normal part under most optical conditions. In this research, the relationship between the macroscopic intensity of the defective parts and the defect microstructure was studied in detail with galvannealed (iron–zinc alloy) steel strips. The following points were observed: 1) Defective parts contain a number of microscopic flat portions which have mirror reflection parallel to the surface, and the reflected intensity of these micro-flat portions is dominant in specular reflection. 2) A clear correlation exists between the specular reflected intensity in the macroscopic images of the defective part and the unit area ratio of the microscopic flat portions. 3) When the intensity from macroscopic observations can be estimated while considering the polarized reflection characteristics of the defect and treating the flat portion as a mirror facet, it agrees with the measured intensity.

The results of this study led to a better understanding of the reason why defects originating from inclusions under the surface layer appear slightly brighter than the normal area on steel strips.

1. Introduction

Many types of surface defects occur on steel strips. Excluding defects originating from adhesion of foreign substances, these can be classified into two categories: defects due to the inner makeup of the material and defects occurring during manufacturing.

Surface defects originating from inclusions under the surface layer are critical from the standpoint of quality assurance. Such inclusions consist of powder from the casting process or oxides in slabs clustering under the surface layer of the strip.¹⁾ Depending on the inclusion size and the rolling state, obvious irregularities and abnormalities can originate from inclusions being exposed at the surface.

Figures 1(a) and 1(b) show an exposed and an unexposed inclusion, respectively. In both examples, the inclusions are streak-like, thinly stretched, around 1 mm-to-10 m length and 1 mm-to-1 cm width, and show many variations. However, the targeted defects in this study are limited to cases in which inclusions are located under the surface layer and the defects are not directly exposed on the surface, as shown in Fig. 1(b).

Fig. 1.

Sectional image of inclusion-originated defects (top) and their macroscopic appearance (bottom) on steel strip surface.

This type of defect (hereafter, simply referred to as “defect”) can also be observed on the surface of galvannealed (hereafter “GA”) steel strips. GA is a type of high-grade iron-zinc alloy coated steel strip which is widely used in automotive outer panels. Thus, serious damage can occur if the inner walls of the press equipment become scratched by small inclusions.

To inspect defects that are hidden in inclusions located under the surface layer, the authors developed an automatic surface inspector assuming a simple optical model.^2,3,4,5)

Although we were successful in the development and application, the physical relationship between the outer appearance of the macroscopically observed defects and their microcharacteristics has not been sufficiently understood.

Although the relationship between the characteristics of the steel strip surface and appearance has been studied in the past,⁶⁾ studies to explain the intensity or contrast of those defects have not been carried out.

In the present research, we attempt to clarify the physical and quantitative relationships between the microcharacteristics and specular reflection characteristics of this type of defect by microscopic observation and optical analysis.

2. Microcharacteristics of Defects

Figure 2(a) shows a scanning electron microscope (SEM) image of a normal GA surface. This is a rough surface in which the dense microcrystalline alloy has grown in random directions. In contrast, our previous observations revealed that defects contain micro-flat regions (flat portions). An example of this can be seen in Fig. 2(b).

Fig. 2.

SEM images of galvannealed steel strip surface, showing a normal part (left) and a defective part (right).

The areas where inclusions exist are thicker and harder than the normal parts. Therefore, when such an area passes through the rolls in the steel strip manufacturing process, the protrusion will gradually flatten out, forming groups of flat portions (micro-components of defects). Figure 3 shows an image of the formation process of the flat portions.

Fig. 3.

Mechanism of forming “micro-mirrors”.

A cross section in the width direction of the defective part was also examined. Figure 4(a) shows a cross-sectional SEM image of the normal part, while Fig. 4(b) shows a defective part where inclusions are present.

Fig. 4.

(a) Sectional SEM image of normal part, (b) Sectional SEM image of defective part.

As can be seen, microscopic flat portions appear to have formed in multiple places within the surface of the steel strip in the areas where inclusions were present.

This is the basic components of the “micro-mirror” facets that are present in the defective part. From Fig. 2(b), it can be seen that each of the flat portions has a diameter in the range of 10–50 micrometers. From the above work, we were able to confirm the presence of groups of microscopic flat portions in defective parts.

The presence of microscopic mirror facet components in defective parts can also be confirmed by other optical experiments. Figure 5 is a schematic drawing of an experiment in which images are taken while changing the reflection receiving angle, where the angle of incidence of the light source is fixed at 60°.

Fig. 5.

Schematic of the experimental optical system.

Figure 6 shows the resulting images. The defect appears brighter than the normal area when the reflection angle is between specular reflection and surface normal, whereas the same defect appears darker at the back-scattering angle. This is because the incident light on defective parts is reflected forward compared to the normal area, and it does not enter to the camera. This simply proves the presence of mirror facet components with higher reflectance in the defective part compared to the normal areas.

Fig. 6.

Images of defects by line-sensor camera at various reflection angles.

3. Reflectance of Defective Part

From the observation described above, it can be concluded that the main elements of the specular reflection from the defect are the micro-flat portions.

Let us assume there are many micromirrors with average reflectance of R_a present on a strip surface with reflectance R_N. The area density of these micromirrors is set at g (0 < g < 1). Intensity in an image is proportional to the energy of the light received. Thus, intensity is proportional to g. Then, the energy of the reflected light E_ref from the surface can be calculated by the following equation when assuming the energy of incident light E_in:   

$$E_{ref}=E_{in}\left(g\cdot R_a+(1-g)R_N\right)$$(1)

Therefore, the effective reflectance R_eff can be expressed as (2).   

$$R_{eff}=\frac{E_{ref}}{E_{in}}=g\cdot R_a+(1-g)R_N$$(2)

If the reflectance for the flat portion R_a and its area density g can be determined, it is possible to estimate the effective reflectance R_eff of the defective part.

Then, the relative intensity ratio, i.e., C of the defective part is calculated by the following formula, in which R_N is the reflectance of the normal portion.   

$$C=\frac{R_{eff}}{R_N}$$(3)

4. Reflectance of Flat Portion

Let us first calculate the reflectance of GA. The Fresnel coefficients r_p and r_s for p and s polarization are described as follows:   

$$r_p=\mathrm{\hspace{0.17em} }\left|r_p\right|e^{i{\delta }_p}$$(4)

  

$$r_s=\mathrm{\hspace{0.17em} }\left|r_s\right|e^{i{\delta }_s}$$(5)

Where, δ is the relative phase shift and i is an imaginary unit. The polarization component p is parallel to the incident plane and component s is parallel to the strip surface. As reflectance is described as an absolute value of the Fresnel coefficient, the reflectance of the two components can be expressed as (6) and (7) for incident angle at θ when light enters from air with a refractive index of 1.0 to a GA surface with a reflective index of N:   

$$R_p={\left|r_p\right|}^2=\frac{{\left|N^{2}cos\theta -\sqrt{N^2-{sin}^2\theta }\right|}^2}{{\left|N^{2}cos\theta +\sqrt{N^2-{sin}^2\theta }\right|}^2}$$(6)

  

$$R_s={\left|r_s\right|}^2=\frac{{\left|cos\theta -\sqrt{N^2-{sin}^2\theta }\right|}^2}{{\left|cos\theta +\sqrt{N^2-{sin}^2\theta }\right|}^2}$$(7)

GA is a Fe–Zn alloy and the average refractive index of the mirror facets of the sample was N = 2.2 + 2.0i based on actual measurements (around 500–600 nm) with an ellipsometer.⁹⁾

The calculated reflectance for the p and s polarization is shown in Fig. 7 when using the horizontal axis as the angle of incidence. The combined total reflectance R_a is expressed using the average value of R_p and R_s, as described in (8).   

$$R_a=\frac{I_r}{I_0}=\frac{R_p+R_s}{2}$$(8)

where I₀ is incident intensity and I_r is reflected intensity.

Fig. 7.

Reflectance of p and s polarization and average reflectance of GA surface.

Figure 7 shows the calculated result of R_p and R_s, and the solid line represents R_a. For example, when the incident angle is 60°, the average reflectance for the flat portion of GA is R_a = 0.40.

5. Area Ratio of Mirror Facet Flat Portion

Next, let us obtain the area ratio of the flat portions in defective parts. Here, an extraction method is needed.

Figure 8 shows an image of targeted defects captured by a line scan camera. The angle of incident light and the receiving angle are both 60°.

Fig. 8.

Specular reflective image of sample defects, and analyzed area for extraction of flat portions.

A microscope capable of coaxial episcopic illumination was used to extract the flat portions on the GA surface. An outline of the optical system is shown in Fig. 9. When the surface is observed from the normal line direction, it can be seen that the illuminated light is irradiated onto the steel strip coaxial and parallel to the optical axis.

Fig. 9.

Coaxial episcopic imaging system for extraction of flat portions.

In this optical system, angular range of 1.2 degree to the vertical axis is observed bright as mirror reflection. This range is substantially the same to the acceptable angular range as specular reflection to the camera lens in Fig. 5.

Therefore, because the flat portions in the defective part with near-mirror reflection had a comparatively higher reflected intensity than the normal part, pixels of flat portions can be readily extracted in intensity histogram. Figure 10 is a typical histogram of an image of defective part. Extremely bright region can be seen in the right end of it, and threshold is drawn at the first lowest frequency level from the right end. Then flat portions are extracted by binarization of the image.

Fig. 10.

Typical intensity histogram of coaxial episcopic image.

The processing technique was performed in the rectangular area specified in Fig. 8 on defect “B”. An example of the result is shown in Fig. 11. The images in the top row are those by the coaxial episcopic system, and the white areas in the bottom row are the extracted flat portions.

Fig. 11.

Coaxial episcopic images of GA surface (top), and extracted mirror-facets (bottom).

As seen here, the area ratio of the flat portion of the defective part (left) is higher than that of the normal part (right).

6. Results

6.1. Correlation between Area Ratio of Flat Portions and Intensity in Defective Parts

The intensity profile of Fig. 8 and the area ratio of the flat portion are plotted in Fig. 12. The area ratio is extracted by the aforementioned procedure and is the ratio of the total number of pixels extracted as flat portions to the total number of pixels in the images.

Fig. 12.

Intensity profile of defects and corresponding area ratio of micro-flat portions: The contrast of defect “B” is 1.22 to the normal level of 127.

In Fig. 11, the correlation between the intensity (solid line) and the area ratio (gray line) can be seen well, and it is understood that the main factor of the contrast of a defect originates from the area ratio of its flat portion.

For a clearer understanding, the correlation plotting between the area ratio and the image intensity is shown in Fig. 13. The value of intensity level for the normal part is set to 127 in a 256 grayscale.

Fig. 13.

Area ratio of micro-flat portions versus intensity level.

Figure 13 shows approximately linear correlation, and it satisfies formula (1) for parts with area ratios of the flat portion over 2%. Similar correlations were also observed for other places, including defect “A” in Fig. 8.

6.2. Comparison of Calculated Contrasts of Defects and Measured Values

Here, the effective reflectance R_eff can be calculated, and the contrast (relative intensity) between the defective part and the normal area will be estimated using formulas (2) and (3).

The measured and calculated values through the procedure to estimate the effective reflectance of defect “B” are shown in Table 1.

Table 1. Values for estimation of contrast of defect “B” and result from specular reflective image (Fig. 8).

1	Reflectance of GA (Ideal mirror) Ra	0.40	Calculated by formula (6), (7), (8) using measured refractive index of GA mirror; N = 2.2 + 2.0 i
2	Area ratio of flat portion at peak intensity g	0.025	Measured value using coaxial episcopic imaging system.
3	Effective reflectance of defective part Reff	0.054	Calculated by formula (2).
4	Reflectance of GA (Normal part) RN	0.034	Measured by an experiment in Fig. 5. RN(s) = 0.059, RN(p) = 0.009, RN = (RN(s) + RN(p) ) / 2
5	Contrast of defect C = Reff / RN	1.60	Calculated by formula (3). through the procedure above.
6	Contrast of defect	1.22	Measured in the intensity profile in Fig. 11.

As the basic facts, the reflectance of a GA mirror is 40% (Row 1 in Table 1 from Fig. 7). The measured average specular reflectance of the normal rough surface is R_N = 3.4% (Row 4) and that for defect “B” was 5.4% (Row 3); therefore, the relative intensity ratio (contrast of defect “B”) is 1.60. On the other hand, at the measured intensity profile in Fig. 11, it is 1.22 (Row 5, 6).

For defect “A”, the estimated value is 1.28, while the measured value is 1.17.

6.3. Considerations

The estimated contrast values are higher than those of the measured values for both defects. The following may be suggested as reasons for this difference:

1) Diffusive elements remain on the rolled flat portions and cause the reflectance of the defective part to be lower than the calculated value.

2) In order to fit the model, the faces of all the flat portions must be oriented parallel to the strip surface; however, in reality, some deviation will inevitably exist.

3) The extraction method for flat portions is incomplete.

Two types of optical models are well known for diffusive modeling of the surface; Beckmann-Spizzichino model based on physical optics⁷⁾ and the Torrance-Sparrow model based on geometrical optics.⁸⁾ Though these theories predict effective information on reflective images from rough surface, precise consideration is needed for modeling of diffusive effects of mixed structure with micro-mirrors which include diffusive elements in themselves.

The above issues await further investigation.

Although there is a discrepancy of 9.4–31% between the calculated contrast and measured values, the results suggest that this procedure is almost satisfactory. It was confirmed that the effective reflectance of the defective part, which is estimated from the area ratio of the flat portion and its basic reflectance, are the main contributing factors to the contrast of the defective part in a macroscopic image.

6.4. Explanation of Macro Intensity of Defect

In many instances, defects appeared brighter than normal areas. The reason can be explained from the following:

1) The defective part contains micro-mirrors whose reflectance is far greater than the specular reflectance of the normal area; the ratio is 12.5 times for defect “B”.

2) Groups of micro-mirrors make the effective reflectance higher than that of the normal area, and as a result, slight contrast of a defect appears.

3) This is because more light from the area of the observer’s viewpoint returns back to the observer than that for the surrounding illumination. This does not change to a great degree even when observing a steel-strip from angles that deviate from the normal direction.

For example, if a mirror facet part (with nonzero reflectance) exists parallel to a zero reflectance surface, as shown in Fig. 14, then this mirror facet part should appear relatively bright when examined from any angle in uniform surrounding light. This is inferred to be the cause of the fact that defects appear brighter on a GA strip surface. The observed contrast depends on the ratio of reflectance between the defective part and the normal area.

Fig. 14.

Sight image of high reflectance part in low reflectance plane: Surrounding light that meets the specular angle to sight causes contrast of the high reflectance part.

7. Conclusions

The relationship of the micro- and macrostructure of surface defects of steel strips originating from inclusions was studied. The following conclusions were inferred from the findings:

(1) Flat portions parallel to the steel strip surface are present in defective parts and play an important role in specular reflection.

(2) The reflected intensity of a defective part in macroscopic observations depends on the area ratio of the flat portions. These defects appear brighter when observing the specular reflection and the surrounding incident reflection when the area ratio of the flat portions is large.

(3) The macroscopically observed intensity was estimated considering the polarized reflection characteristics of the defect and treating the flat portions as mirror facets. The calculated and experimental results were in good agreement.

We found no inconsistencies with previous optical models, and offered a quantitative explanation for the relationship between the intensity of the defective part and that of the normal area.

For further investigations, we plan to apply these methods and findings to other types of defects to reduce trial-and-error efforts to build surface inspectors with higher performance.

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