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Abstract
A single-pixel optical system, equipped with a multicolor filter, is proposed for the screening inspection of the surfaces of objects in manufacturing processes. The optical system can identify sub-microscale roughness and detect a microscale defect in a focus-free setting through the color-mapping of reflectance direction fields, as validated by experiments.
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1. INTRODUCTION
In various manufacturing processes, inspections of microscale and even sub-microscale structures on product surfaces are needed. These inspections include detecting defects, surface roughness [1], scratches, dents, and foreign material adhesion. Microscale structure inspections are commonly conducted using high-speed, non-contact optical inspection cameras [2–6]. These camera-based inspection methods provide precise and efficient detection of surface irregularities without physical contact. There has recently been a global push to integrate the cameras into the Internet of Things (IoT), transforming them into smart devices capable of transferring captured images directly to computers. This integration facilitates automated inspection through advanced artificial intelligence (AI) image analysis, enhancing the speed and accuracy of defect detection. However, despite these advances, microscale defects characterized by small height variations often appear indistinct when captured by conventional cameras. Sub-microscale defects, therefore, are even more indistinct. Consequently, AI-based analysis systems may sometimes fail to detect such subtle defects. Thus, the inspection of microscale defects still heavily relies on the keen visual and tactile assessment skills of experienced workers, highlighting a gap in current technological capabilities.
The angle-resolved distribution of light rays reflected from a surface is effectively characterized by the bidirectional reflectance distribution function (BRDF) [7–15]. The BRDF is sensitive to even minor variations in the surface condition of an object, making it a valuable tool in precision surface inspection. Thus, an accurate assessment of surface conditions can potentially be realized through meticulous BRDF measurements. Figure 1 shows a schematic view of the conventional method for measuring the BRDF of the light rays scattered by a microscale structure on an object surface using a goniometric method. The parallel illumination, which includes a specific wavelength represented by color contours, is incident on the object. The photodetector, integrated into the goniometric method and moving to capture the light rays from various directions, measures the BRDF of the scattered light rays. However, this conventional BRDF measurement method, which involves moving the optical receiver to capture light from multiple directions, is notably time-intensive and laborious.
Fig. 1. Schematic view of the conventional method for measuring the BRDF of the scattered light rays using a goniometric method. The parallel illumination, which includes a specific wavelength represented by color contours, is incident on the object. The photodetector, integrated into the goniometric method and moving to capture the light rays from various directions, measures the BRDF of the scattered light rays.
Fig. 2. Conceptual view of an optical inspection system using a single-pixel (SPix) spectrometer. A reflectance direction distribution described by the BRDF will be color-mapped based on its reflectance angle $\theta$, defined by the angle between a light ray’s direction and the optical axis of the system. This color-mapping process is referred to here as the OneShotCRDF (one-shot color-mapping of reflectance direction field). The color-mapped light rays are then collected onto the SPix spectrometer.
To overcome this time-intensive problem, an imaging system has been developed that can instantaneously capture the reflectance direction field of the light rays as color information in one shot [16–21]. This imaging system employs a specially designed multicolor filter that has distinct wavelength transmission regions. This multicolor filter effectively color-maps the field of the light ray directions, enabling the detection and categorization of microscale surface structures. The imaging system is referred to here as a one-shot BRDF imaging system or one-shot BRDF for brevity. However, accurately detecting a microscale structure, especially one with a small width within a field of view, often necessitates capturing an image with high pixel density. Achieving this level of granularity typically requires an image sensor with an exceedingly large number of pixels, which may be impractical. Even if such an image sensor were to be developed, the processing time needed to analyze the high-resolution image for defect detection would be substantially increased, presenting a significant bottleneck in rapid inspection processes.
On the other hand, to simply detect the presence or absence of a microscale defect within a field of view, a process known as screening inspection, is often more essential than pinpointing the exact location of the defect. Therefore, an optical screening inspection system using a single pixel (SPix) that captures a reflectance direction field through color-mapping is proposed. Designed to efficiently detect the existence of defects without requiring high-resolution imaging, this inspection system significantly reduces data processing requirements. Moreover, it facilitates focus-free inspection. In this paper, this inspection system is referred to as the SPixCRDF (SPix color-mapping of reflectance direction field) system, or SPixCRDF for short. The remainder of this paper is organized as follows. First, the concept of the SPixCRDF, which can capture a light-reflectance direction field using SPix through color-mapping, is described. This is followed by a specific description of the structure of the SPixCRDF. Secondly, experimental validations of the SPixCRDF are conducted using its prototype. Lastly, discussions and conclusions are presented.
2. OPTICAL INSPECTION SYSTEM UTILIZING A SINGLE PIXEL
Figure 2 shows a conceptual view of an optical inspection system using a single-pixel (SPix) spectrometer, specifically the SPixCRDF. A reflectance direction distribution that can be described by the BRDF will be color-mapped based on its reflectance angle $\theta$, defined by an angle between the direction of a light ray and the optical axis of the system. This color-mapping process is referred to here as the OneShotCRDF (one-shot color-mapping of reflectance direction field). The color-mapped light rays are then collected onto the SPix spectrometer. The BRDF of a microscale structure typically differs from that of a flat surface. Consequently, the spectra of the microscale structure and the flat surface become distinct. This distinction enables the detection of the microscale structure.
Figure 3 shows a schematic view of a specific structure of the SPixCRDF that realizes its concept. The SPixCRDF is mainly composed of an illumination system and a photodetection system. The illumination system generates parallel light rays from the light source of a white LED (light-emitting diode). The photodetection system captures the spectra of the light rays reflected off an object, which is illuminated by the parallel light rays.
Fig. 3. Schematic view of an optical inspection system using a SPix spectrometer, specifically the SPixCRDF. The parallel light rays, generated from the light source of a white LED using a pinhole and a freeform lens, are incident on the surface of an object via a beam splitter. These light rays are then scattered by a microscale structure on the object surface. The BRDF of the scattered light rays is color-mapped based on their directions using a focusing lens and a multicolor filter placed at the focal plane of the lens. The light rays are then diffused by a diffuser and collected onto the SPix by a concentrator.
The illumination system has a pinhole and an illumination lens that can convert the diverging light rays emitted from the LED to the parallel light rays toward the surface of the object via a beam splitter. The illumination lens is designed based on Hamiltonian optics [22–25]. The photodetection system has a focusing lens and a multicolor filter that consists of multiple different transmission spectral regions. The multicolor filter is coaxial with the optical axis of the focusing lens and is placed at the focal plane of the lens at a distance $f$ from the principal plane of the lens. The multicolor filter is set parallel to the $xy$ plane in a Cartesian coordinate system. The origin $O$ of the coordinate system is set in the multicolor filter. The reflected light rays pass through the multicolor filter, with their colors determined by their directions. The light rays are then diffused by a diffuser and collected onto the SPix by a TIR (total internal reflection) concentrator. Thus, the light rays collected onto the SPix have distinct spectra based on their directions. The design of the TIR concentrator is crucial for efficiently collecting the light rays [26–30]. The diffuser, placed at the bottom of the TIR concentrator, is designed to reduce efficiency variation in transmitting light rays toward the SPix. This variation depends on the direction of the incident light rays and arises from the returning light rays from the outlet of the TIR concentrator.
With this setup, a light ray reflected from the object’s surface in a direction parallel to the optical axis of the focusing lens passes through the center region of the multicolor filter (represented by the blue region in Fig. 3). On the other hand, a light ray reflected from the surface with an angle, $\theta$, inclined to the optical axis passes through the outer regions of the multicolor filter (represented by the red, yellow, and green regions in Fig. 3). As a result, the larger the angle, $\theta$, of a light ray with respect to the optical axis, the more outer region of the multicolor filter it passes through. The light rays thus become different colors depending on their directions, regardless of the reflection location on the surface. Consequently, the direction of a light ray reflected at any point on the object can be identified by its color. Therefore, the SPixCRDF can enable the detection of subtle differences in the direction of the light rays. Specifically, the BRDF of the microscale structure differs from that of the flat surface. This difference enables the SPixCRDF to detect the existence of the microscale structure through its unique specular spectrum.
A position vector, ${\boldsymbol r}$, when projected onto the multicolor filter, represents the position where a light ray with an angle $\theta$ to the optical axis passes in the multicolor filter. This projected position vector, ${\boldsymbol r}$, represented in two dimensions, can be derived based on the geometrical optics using the focal length $f$ and a two-dimensional angle vector, ${\boldsymbol \Theta}$, having two components of ${\Theta _x}$ and ${\Theta _y}$ as
Fig. 4. (a) CAD image of a SPixCRDF prototype and (b) photographic image of the fabricated prototype. The focal length of the focusing lens (Nikon, AF-S, Nikkor, F/1.4) is set to 105 mm. The SPix spectrometer is set to a Czerny—Turner fiber spectrometer (Thorlabs, CCS100). The cross-sectional diameter of the parallel illumination is designed to be 12 mm.
Fig. 5. Side view of the TIR concentrator. The TIR concentrator is designed with a diameter of 22 mm for the inlet and 2.7 mm for the outlet. The length along the optical axis is set to 101 mm. The maximum acceptance angles are set at ${\alpha _{{\rm in}}}$ of 7° for the inlet and at ${\alpha _{{\rm out}}}$ of 80° for the outlet.
3. EXPERIMENTAL RESULTS
Experiments are performed to validate the SPixCRDF function using its prototype. Sub-microscale surface roughness and a microscale ridge are chosen as test samples.
A. Experimental Setup
Figure 4 shows the prototype of the SPixCRDF. On the left-hand side, (a) shows the CAD image of the prototype. On the right-hand side, (b) shows the photographic image of the fabricated prototype. The pinhole used for generating the parallel illumination has a diameter of 0.4 mm. The divergence half-angle of the parallel illumination is set to 0.12 deg. The cross-sectional diameter of the parallel illumination is designed to be 12 mm. The focal length of the focusing lens (Nikon, AF-S, Nikkor, ${\rm F}/\;{1.4}$) is set to 105 mm. The SPix spectrometer is set to a Czerny—Turner fiber spectrometer (Thorlabs, CCS100). The multicolor filter is designed to have an outermost diameter of 22 mm and features 22 color regions from the center to the outermost radius. A diffuser, set on top of the multicolor filter, has a divergence half-angle of 5 deg.
Figure 5 shows a side view of the TIR concentrator. The TIR process can effectively collect light rays onto the SPix, as it can reflect the light rays without any loss due to the absence of absorption [26]. A compound parabolic concentrator, which utilizes the TIR process, is thus designed to collect the light rays from the multicolor filter onto the SPix. The cross-sectional diameters of the TIR concentrator are set as ${R_{{\rm in}}}$ at the inlet and ${R_{{\rm out}}}$ at the outlet. The maximum acceptance angles from the optical axis are set as ${\alpha _{{\rm in}}}$ at the inlet and ${\alpha _{{\rm out}}}$ at the outlet. The following equation can then be derived based on the etendue conservation:
It should be noted that some light rays will be reflected at the outlet surface of the TIR concentrator, thus preventing their transmission through the concentrator to the SPix. This leads to variation in the collection efficiency of the TIR concentrator, depending on the directions of the incident light rays at the inlet. Therefore, the diffuser, placed at the bottom of the TIR concentrator, is designed to reduce this efficiency variation and to ensure that at least some of the diffused light rays can pass through to reach the SPix.
B. Relationship between Light Ray Direction and its Spectrum
A relationship between the direction of a light ray and its spectrum, captured by the SPixCRDF, can be measured using an optical mirror and a goniometric method. Figure 6(a) shows the multicolor filter in the $xy$ plane with reflectance angles $\theta$ indicated by solid circle lines. Figure 6(b) shows a reflectance direction caused by the optical mirror in the $xz$ plane, where the mirror can be inclined by the goniometric device. Figure 6(c) shows the wavelength spectra for each reflectance angle $\theta$. These spectra establish relationships between each light ray direction (i.e., reflectance angle) and each spectrum, which are measured by the SPixCRDF prototype using the optical mirror with the goniometric device. These spectra show that each reflectance angle $\theta$ is distinguishable based on its corresponding spectrum.
Fig. 6. (a) Multicolor filter in the $xy$ plane with reflectance angles $\theta$ indicated with solid circle lines. (b) Reflectance direction caused by an optical mirror in the $xz$ plane, where the mirror can be inclined by a goniometric device. (c) Wavelength spectra for each reflectance angle. These spectra establish relationships between each light ray direction and each spectrum.
C. Sub-Microscale Surface Roughness on a Metal Surface
For a test sample, a metal surface with sub-microscale roughness is captured by the SPixCRDF. Figure 7(a) shows sub-microscale surface roughness on the metal test piece, exhibiting two different Rz values, 0.2 and 0.4 µm, captured by a conventional camera. Figure 7(b) shows their height profiles along certain lines, where the horizontal axis indicates the distance along the line, and the vertical axis represents the height. The surface roughness, having an Rz value of 0.2 µm, exhibits a maximum height difference of 0.2 µm. On the other hand, the surface roughness with an Rz value of 0.4 µm exhibits a maximum height difference of 0.4 µm. These Rz values are based on the JIS (Japanese Industrial Standards).
Fig. 7. (a) Sub-microscale surface roughness on a metal test piece, exhibiting two different Rz values, 0.2 and 0.4 µm, captured by a conventional camera. (b) Height profiles of the surface roughness along certain lines, where the horizontal axis indicates the distance along the line, and the vertical axis represents the height. The surface roughness having an Rz value of 0.2 µm exhibits a maximum height difference of 0.2 µm. On the other hand, the surface roughness with an Rz value of 0.4 µm exhibits a maximum height difference of 0.4 µm.
Figure 8 shows the spectra for the Rz values of 0.2 and 0.4 µm at several $z$ positions, such as $\Delta z = - {5}$, 0, and ${+}{5}\;{\rm mm}$. These $\Delta z$ values are defined as the differences along the $z$ direction from the object plane, which is placed 100 mm away from the front surface of the focusing lens. The horizontal axis indicates the wavelength, and the vertical axis indicates the intensity in the arbitrary unit. The blue dashed line, black solid line, and red dotted line represent the $\Delta z$ values of ${-}{5}$, 0, and ${+}{5}\;{\rm mm}$, respectively.
Fig. 8. Spectra for the Rz values of 0.2 and 0.4 µm at several $z$ positions, such as $\Delta z = - {5}$, 0, ${+}{5}\;{\rm mm}$. These $\Delta z$ values are defined as the differences along the $z$ direction from the object plane, which is placed 100 mm away from the front surface of the focusing lens. The horizontal axis indicates the wavelength, and the vertical axis indicates the intensity in the arbitrary unit. The blue dashed line, black solid line, and red dotted line represent the $\Delta z$ values of ${-}{5}$, 0, and ${+}{5}\;{\rm mm}$, respectively.
From Fig. 8, it is clearly shown that the difference in the Rz values can be identified using the spectra captured by the SPixCRDF. Furthermore, the difference in the Rz values is almost entirely unaffected by the working distances, specifically the $\Delta z$ values. This indicates that the SPixCRDF can detect the difference between two surfaces with sub-microscale roughness in a focus-free setting.
D. Microscale Ridge on an Aluminum Plate
For the other test sample, an aluminum microscale ridge on a flat surface is selected. Figure 9(a) shows an image of the microscale ridge with a maximum height of 45 µm, captured by a conventional camera. The ridge is fabricated on a flat-surface aluminum plate. The outer diameter of the parallel illumination, which is 12 mm, is also shown. The center position of the ridge in the $xy$-coordinate system is set to ($\Delta x$, 0), where a $\Delta x$ of 0 corresponds to the center of the illumination. Figure 9(b) shows the height profile of the ridge that is measured by the scanning white light interferometric microscope.
Fig. 9. (a) Image of a microscale ridge with a maximum height of 45 µm, captured by a conventional camera. The ridge is fabricated on a flat-surface aluminum plate. The diameter of the parallel illumination is 12 mm. The center position of the ridge in the $xy$-coordinate system is set to ($\Delta x$, 0), where a $\Delta x$ of 0 corresponds to the center of the illumination. (b) Height profile of the ridge that is measured by the scanning white light interferometric microscope.
Figure 10 shows the spectra for the ridge and the flat surface at several $z$ positions, such as $\Delta z = - {5}$, 0, and ${+}{5}\;{\rm mm}$. These $\Delta z$ values are defined as the differences along the $z$ direction from the object plane, which is placed 100 mm away from the front surface of the focusing lens. The spectra for the ridge include several plots corresponding to the ridge placed at $\Delta x = - {4}$, 0, and ${+}{4}\;{\rm mm}$, where a $\Delta x$ of 0 corresponds to the center of the illumination. The horizontal axis indicates the wavelength, and the vertical axis indicates the intensity in the arbitrary unit. The blue dashed line, black solid line, and red dotted line represent the ridge placed at the $\Delta z$ values of ${-}{5}$, 0, and ${+}{5}\;{\rm mm}$, respectively. The orange dashed, solid, and dotted lines represent the flat surface placed at the $\Delta z$ values of ${-}{5}$, 0, and ${+}{5}\;{\rm mm}$, respectively.
From Fig. 10, it is evident that the presence of the ridge at any value of $\Delta x$ can be detected using the spectra captured by the SPixCRDF. Furthermore, the spectral difference between the ridge and the flat surface is almost entirely unaffected by the working distances, specifically the $\Delta z$ values. These indicate that the SPixCRDF is capable of capturing microscale structures in a focus-free setting.
Fig. 10. Spectra for the ridge and the flat surface at several $z$ positions, such as $\Delta z = - {5}$, 0, and ${+}{5}\;{\rm mm}$. These $\Delta z$ values are defined as the differences along the $z$ direction from the object plane, which is placed 100 mm from the front surface of the focusing lens. The spectra for the ridge include several plots corresponding to the ridge placed at $\Delta x = - {4}$, 0, ${+}{4}\;{\rm mm}$, where a $\Delta x$ of 0 corresponds to the center of the illumination. The horizontal axis indicates the wavelength, and the vertical axis indicates the intensity in the arbitrary unit. The blue dashed line, black solid line, and red dotted line represent the ridge placed at the $\Delta z$ values of ${-}{5}$, 0, and ${+}{5}\;{\rm mm}$, respectively. The orange dashed, solid, and dotted lines represent the flat surface placed at the $\Delta z$ values of ${-}{5}$, 0, and ${+}{5}\;{\rm mm}$, respectively.
4. DISCUSSION
The experiments reveal that the SPixCRDF can obtain the difference of the microscale or even sub-microscale height variations on the metal surface from their corresponding spectra. Note that these spectra can be obtained in a focus-free setting. Differences in the spectra can then be quickly quantified through simple operations such as subtraction and ratios. This implies that the SPixCRDF can be applicable to the screening inspection of the surfaces of objects in manufacturing processes.
The function of the SPixCRDF, as proposed in its conceptual design, is qualitatively validated in experiments. Theoretically, the SPixCRDF is capable of detecting any minor defects, provided that their BRDFs differ from those of the reference surfaces. However, there may be quantitative limitations to this detection capability. Although further study is necessary to identify these limitations, they are primarily considered to stem from three major factors. The first of these factors is the angular resolution, which is influenced by the focal length of the focusing lens and the spatial resolution of the multicolor filter. When the BRDF of a defect closely resembles that of the reference surface, distinguishing between them becomes difficult. Improving the angular resolution, either by using a lens with a longer focal length or by employing a multicolor filter with finer spatial resolution, can aid in differentiating such similar BRDFs. The second factor relates to the spectral cutoff generated by the multicolor filter. Accurate detection requires that the spectra corresponding to different colors do not overlap. Ideally, the SPixCRDF can precisely detect any minor defects when the light rays passing through different color regions in the multicolor filter produce non-overlapping spectra. However, in practice, some degree of overlap is inevitable. Minimizing this overlap is thus crucial for improving detection accuracy. The third factor involves the sensitivity of the SPix spectrometer to light intensity. When dealing with smaller defects, the intensity of the scattered light rays might be too weak for the SPix spectrometer to detect. In such cases, a higher-sensitivity SPix spectrometer is necessary.
The SPixCRDF may also be applied to detect anomalies in various transparent media, including glass, water, and air. In these media, observing several physical properties, such as the refractive index field, temperature field, and stress tensor field, is important [31–33].
5. CONCLUSION
A single-pixel optical inspection system, namely, the SPixCRDF, equipped with a multicolor filter, is proposed for the screening inspection of the surfaces of objects in manufacturing processes. The SPixCRDF can identify sub-microscale roughness and detect a microscale defect in a focus-free setting through the color-mapping of reflectance direction fields, as validated by experiments. The SPixCRDF has the potential to enable faster inspection than traditional image inspection methods that handle a large number of pixels to inspect the entire surface. The wavelength spectrum obtained by SPixCRDF may allow for a detailed classification of defects. The SPixCRDF is focus-free and offers flexible installation options. Furthermore, the use of simple optical components should enable the construction of a compact and cost-effective optical system.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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