Open Access
Add to BibSonomy
Abstract
In this study, a three-dimensional (3D) laser micromachining system with an integrated sub-100 nm resolution in-situ measurement system was proposed. The system used the same femtosecond laser source for in-situ measurement and machining, avoiding errors between the measurement and the machining positions. It could measure the profile of surfaces with an inclination angle of less than 10°, and the measurement resolution was greater than 100 nm. Consequently, the precise and stable movement of the laser focus could be controlled, enabling highly stable 3D micromachining. The results showed that needed patterns could be machined on continuous surfaces using the proposed system. The proposed machining system is of great significance for broadening the application scenarios of laser machining.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Many optical devices, such as artificial compound eye structures [1, 2] and hybrid refractive-diffractive optical elements, can be prepared by machining micro/nanostructures on curved surfaces [3–5]. As a mature, high-precision three-dimensional (3D) machining technology [6–8], laser direct-writing has been widely used by researchers in the machining of curved surfaces [9–12]. Because the height undulation of curved surface is much larger than the laser focus depth, it can be difficult to achieve uniform and consistent machining of an unknown surface profile. Consequently, obtaining surface profile information is a prerequisite for high-precision 3D surface machining.
Researchers have put considerable effort into the laser machining of complex curved surfaces. Wang et al. efficiently processed texture patterns on a freeform surface by dividing it into subregions, sublayers, and subblocks to ensure a uniform machining effect [13]. Ai et al. developed a laser direct-writing system that could perform rapid and μm-precision fabrication on curved surfaces [14]. By combining a high-speed galvanometer with an XYZ stage, the system could machine microstructures on large curved surfaces.
However, in the above methods, 3D measurement and machining are separate. Moreover, 3D measurement equipment is used to measure the profile before machining, and it can be difficult to align the machining area with the measurement area. Earlier, Diaci et al. integrated a 3D measurement system into a 3D laser-marking system [15], enabling in-situ inspection and machining without the hassle of aligning samples. However, they did not elaborate on the exact method of realization. Li et al. constructed a 3D in-situ laser machining system with integrated laser measurement using a 3D galvanometer scanner and an industrial camera [16]. They evaluated the accuracy of the 3D measurements in detail and processed 3D patterns on different complex surfaces. The above method had the advantage of being able to quickly perform 3D measurements and machining over a large area. However, the disadvantage was that its measurement accuracy was insufficient (of the order of millimeters).
To address these problems, a 3D laser micromachining system with an integrated in-situ measurement system was constructed. The system measured the coordinates of a number of points on the surface and reconstruct the 3D surface profile using a triangulation algorithm. The laser focus could be controlled near the surface according to the 3D surface profile for stable machining results. For the experiment itself, a school emblem was machined on a curved surface to demonstrate the machining capability of the proposed 3D laser micromachining system for curved surfaces.
2. 3D laser micromachining system
The workflow of the proposed 3D laser micromachining system is shown in Fig. 1, and comprises two parts, that is, in-situ measurement and in-situ machining systems. In the integrated system, the measurement and machining light sources are the same. First, the coordinates of the measurement points in the in-situ measurement area are interpolated to fit the 3d surface profile. Subsequently, the 2D pattern to be machined is algorithmically mapped onto the surface to form the 3D pattern to be machined. Finally, the laser is tuned to an appropriate power level to machining. During the in-situ measurement process, the laser power is low, and no damage is done to the material. During in-situ machining, the laser power can be increased as needed to accomplish the machining goal.
2.1 In-situ measurement
In-situ measurement of the profile of the area to be machined on a surface by acquiring surface point cloud data. The area to be measured was then divided into grids at fixed intervals on the XY-plane, and the 3D coordinate of each grid point was recorded as point-cloud data. The X and Y axis coordinates are the coordinates of the displacement stage corresponding to each point. The method for measuring the Z-axis coordinate at each point was based on a previously published focus measurement method [17]. However, the deformation of the laser spot image obtained by the charge-coupled Device (CCD) increases with the reflection angle of the curved surface. To solve this problem, we propose a new and improved method to process the CCD images of samples with different inclination angles.
This method is suitable for materials with low surface roughness, including glass, crystals, metals, etc. High surface roughness can lead to diffuse reflections, making the CCD image irregular, or even the CCD failing to collect the image. Materials with low surface roughness enable specular reflection, allowing the reflected beam to return the way originally intended, which is necessary for in-situ measurements.
Figure 2 shows the basic principle of the in-situ measurement method. A brief optical path of the in-situ measurement system is shown in Fig. 2(a). Incident linear polarization changes to circular polarization after passing through a quarter-wave plate (QWP). The reflected circular polarization from the sample passes through the QWP again and changes into linear polarization perpendicular to the incident light. It is then reflected to the other side by a polarizing beam splitter prism (PBS) and focused on the CCD. The computer reads out the image data on the CCD for analysis and processing, after which the relative position of the laser focus and the sample surface can be obtained.
Fig. 2. Principle of in-situ measurement. (a) Brief schematic of the in-situ measurement system. (b) Processing of CCD images for horizontal samples. (c) Processing of CCD images for inclined samples.
The CCD images and data processing for the measurements of the samples with different inclination angles are shown in Fig. 2(b) and (c). When the refractive rate of the material is different or the inclination angle of the sample is changed, the power density of the reflected light will change, and we will change the exposure time and gain of the CCD to keep the gray intensity of the CCD image at a certain value. The above method enables CCD images to be standardized. Here, a 3D form of the laser spot was used instead of a 2D form for data processing. The gray intensity of the 2D image was converted to the height of the 3D image and redrawn. When converted to a 3D image, the gray intensity of each pixel of the 2D image is normalized by the maximum value of the image's gray intensity. Subsequently, the normalized 3D image was sliced at a fixed height and fitted to an ellipse. Due to the interference of environmental light and other interferences, the gray intensity of the pixels near the spot in the CCD image is not zero, and if the height value of the slice is low, the cut plane may not be elliptical for subsequent processing. The slice height was uniformly determined to be 0.3 in order to be applicable to CCD images acquired at all inclinations.
When measuring a horizontal sample without inclination, the laser spot extraction profile is circular, at which time σL = σS. When measuring a sample with inclination, the laser spot extraction profile is elliptical, and the long axis (σL) is larger than the short axis (σS). Differences exist in the ellipse parameters fitted to the laser spot images formed by reflections at different angles, which can be used as the basis for measurements.
Ellipticity data was acquired by taking measurements at different defocus positions from 0–10° of reflection angle, where σL denotes the long axis of the fitted ellipse and σS denotes the short axis of the fitted ellipse, as shown in Fig. 3. Combined with the intensity information, the position of the laser focus at different reflection angles can be determined, thus the surface profile can be measured.
To investigate the axial resolution of the proposed method, test samples were placed at a 10° inclination and the measurement points were scanned along the z-axis in steps of 150 nm, 100 nm and 50 nm, respectively. The measured Z-axis axial resolution results are shown in Fig. 4(a), (b), and (c). The results show that the method has a sub-100 nm axial resolution and can satisfy practical measurement requirements.
2.2 In-situ micromachining
When the distance between the focus and the sample surface is 0, the position of the Z-axis displacement stage is recorded as the Z-axis coordinate of the point on the surface. After acquiring the surface point-cloud data of the area to be machined, the local surface profile could be obtained using an interpolation method based on a triangulation algorithm. Before 3D in-situ machining, parallel projection was used to map the 2D pattern to the 3D surface. The height coordinates were added to the 2D machining data based on the corresponding 3D surface profile, and the 3D surface machining was then performed using the motion of the 3D displacement stage. In practice, the laser focus would always remain on the 3D surface for high-precision and high-stability machining.
3. Experimental analysis and results
3.1 Experimental device
The system used a femtosecond laser (Light Conversion) with a wavelength of 1030 nm and a pulse width of 231 fs for measurement and machining. The laser power can be adjusted arbitrarily for measurement (low-power) and machining. The objective lens with NA = 0.6 was placed on the vertical stage, the sample was placed on the horizontal XY-axis stage, and the three-axis coordinated motion was controlled using an Aerotech controller. The travel distance of the XY-axis stage was 160 mm, and the resolution was 1 nm. The Z-axis stage had a travel distance of 60 mm and a resolution of 1 nm.
3.2 Influence of laser incident angle on machining results
When the laser acts on a curved surface, the shape and energy distribution of the laser spot change compared with those on a flat surface. In this study, the change in spot shape and energy distribution at different angles were theoretically and experimentally analyzed to determine their effect on machining. As the size of the focus spot was much smaller than that of the surface to be machined, the tangent plane approximation of the surface was used instead of the surface for our analysis. When the incident beam was not vertically irradiated onto the material surface, the light spot formed by the beam on the material surface was distorted into an ellipse, as shown in Fig. 5(a). Here, ω0 denotes the beam radius, θ denotes the angle of incidence, $\mathrm{\omega}_y=\mathrm{\omega}_0 / \cos \mathrm{\theta}$ denotes the long semi-axis of the elliptical spot, ωx = ω0 denotes the short semi-axis of the ellipse, and F0 denotes the peak energy density of the laser focus spot. The energy distribution of the laser focus spot on the tangent plane can be expressed as follows [13, 18]:
Fig. 5. (a) Distortion of the laser spot on a curved surface. (b) Energy distribution along the x-direction and (c) the y-direction of the laser spot projection at different angles.
It is evident from Eq. (1) that the distribution of the energy density of the laser focus spot on the curved surface is a function of the incident angle, which still approximately obeys a Gaussian distribution. The distribution of the laser focus spot energy densities on the X- and Y-axes are shown in Fig. 5(b) and 5(c), respectively. As the incident angle increases, the peak energy density of the laser focus spot decreases. When the material machining threshold is constant, the machining size in the X-axis direction decreases with increasing laser incident angle, whereas the machining size in the Y-axis direction changes in the opposite direction. However, the difference in the peak energy density between a spot at 0° inclination and a spot at 10° inclination is 2%, and the change in the machining size in the XY-plane is less than 1%, which has almost no effect on the machining.
This was verified by experimental results on laser machining at different angles of incidence. The energy density of the laser focus spot on the surface of the material was different at different positions along the Z-axis of the laser focus spot, decreasing from the center of the focus spot to the sides. As shown in Fig. 6(a), with the other conditions fixed, we can define the Z-axis threshold range. Surface can be damaged when the distance between the laser focus and the surface is less than the Z-axis threshold range. The laser scans lines at 50 nm intervals from top to bottom along the Z-axis. The Z-axis threshold range was obtained by multiplying the number of machined lines by 50 nm.
Fig. 6. (a) Schematic diagram of the Z-axis threshold range. (b) SEM image of the machining line segment when the laser incidence angle is 0°. (c) Z-axis threshold range under different laser incidence angles.
A femtosecond laser (power was 125 mW, repetition rate was 1000kHz) was used to explore the Z-axis threshold range on the sapphire surface at 0–10° incident angle. Figure 6(b) shows the SEM image of the processed line segment when the laser incident angle was 0°. As shown in Fig. 6(c), under the laser incident angle of 0–10°, the Z-axis threshold range is concentrated around 3.6 μm, and there is no obvious decreasing trend. This shows that at a laser incidence angle of less than 10°, the energy density change of the laser at the same Z-axis position on the material surface is very small, so the laser incidence angle has almost no impact on the machining effect.
3.3 Influence of DOF on machining results
Although the material can be machined when the laser focus is within the Z-axis threshold range, the different energy densities acting on the material result in different machining results. The Z-axis distance at which the focus beam has approximately the same intensity is referred to as the depth of focus (DOF) [13, 19]. When the distance between the laser focus and material surface is less than the DOF, very close machining results can be produced on the material. The formula for the DOF can be expressed as follows:
where M2 denotes the quality factor of the laser beam, λ denotes the laser wavelength, f denotes the focal length of the lens, and D denotes the diameter of the laser beam before the focusing transformation. In this paper, f is about 4.5 mm, M2 is 1.2, λ is 1.03 μm, and D is about 7.5 mm, and the DOF is calculated to be about ±1.149 μm.With a laser incident angle of 10°, different power lasers were chosen to machine the lines at different Z-axis heights and measure the depth and width of the lines, the results of which are shown in Fig. 7. The laser power settings were 200 and 300 mw, the repetition frequency was 1000 kHz, and the scanning speed was 3 mm/s. It is evident that the lines machined at the DOF exhibit a relatively consistent depth and width, decreasing when the focus deviates from the DOF. This demonstrates the stability of the laser machining in the DOF. Consequently, highly stable laser machining on curved surfaces can be achieved by controlling the distance between the laser focus and surface, which is always less than the DOF. The surface measurement accuracy of the proposed 3D micromachining system was considerably higher than this requirement.
Fig. 7. (a) depth and (b) Line width of machining lines with different z-axis heights when the laser incident angle is 10°.
3.4 Machining of patterns on curved surfaces
A school-emblem pattern was processed on the surface of a K9 glass lens using the proposed high-precision 3D laser micromachining system with an integrated in-situ measurement system. However, in-situ measurement method is applicable to surfaces with continuously varying curvature and is not applicable to irregular surfaces, and has some limitations.
First, an area of 0.36 mm2 was selected to measure the 3D profile; the interval was set to 60 μm, and 3D coordinate data of a total of 100 points were obtained. Before measurement, the displacement stage is scanned along the z-axis to find the approximate location of the brightest spot, so that the gray intensity of the CCD image at this time does not exceed 255, and then the measurement can be carried out. During measurement, a rapid scanning along the z-axis performed until the gray intensity of the CCD image is greater than 30 (higher than the background gray intensity of the CCD image). The scanning speed is then reduced to scan until the gray intensity in the CCD image is greater than 120, and the image is captured to fit the ellipse. The data of the long and short axes of the fitted ellipse are brought into Fig. 3 to find the coordinates of the nearest point and the exact focus position. It takes about thirty minutes to measure 100 points. The point-cloud data was then fitted via interpolation to obtain a 3D profile. Finally, the image of the Jilin University emblem was processed to generate 2D machining data, which were then mapped onto the 3D profile obtained to generate 3D machining data for in-situ machining. The laser power was then set to 25 mw and the repetition rate to 200 kHz. Figure 8(a) and (b) shows microscope and laser confocal 3D images of the 3D school-emblem pattern, demonstrating the machining capability of the high-precision 3D laser micromachining system with an integrated in-situ measurement system.
Fig. 8. (a) Micrograph and (b) laser confocal 3D images of the machined school emblem pattern on a curved surface.
However, if the method wants to be applied to industrial applications, the scanning process for each measurement point needs to be further optimized to reduce the measurement time. The system needs more optimization to be practically applied in industry.
4. Conclusion
A 3D laser micromachining system capable of in-situ inspection and machining was proposed. The in-situ measurement system reconstructed the surface profile by acquiring point-cloud data on a curved surface, the measurement resolution being better than 100 nm. The system could then generate 3D machining data based on the 3D surface profile for in-situ laser machining. The effects of the laser incidence angle and DOF on the surface machining process were then analyzed, the surface measurement accuracy of the system being shown to meet the demand for high-precision machining within an inclination angle of 10°. Consequently, the proposed machining system exhibits potential application value for the practical high-precision machining of microstructures on curved surfaces.
Funding
National Natural Science Foundation of China (61825502, 61827826, 62175086, 62131018); the Major Science and Technology Projects in Jilin Province (Grant No. 20220301001GX).
Disclosures
The authors declare that there are no conflicts of interest related to this paper.
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.
References
1. D. Radtke, J. Duparre, U. D. Zeitner, et al., “Laser lithographic fabrication and characterization of a spherical artificial compound eye,” Opt. Express 15(6), 3067–3077 (2007). [CrossRef]
2. X. Q. Liu, S. N. Yang, L. Yu, et al., “Rapid Engraving of Artificial Compound Eyes from Curved Sapphire Substrate,” Adv. Funct. Mater. 29, 8 (2019). [CrossRef]
3. Y. J. Xie, Z. Q. A. Lu, F. Y. Li, et al., “Lithographic fabrication of large diffractive optical elements on a concave lens surface,” Opt. Express 10(20), 1043–1047 (2002). [CrossRef]
4. R. Tian, J. Liu, X. Li, et al., “Design and fabrication of complicated diffractive optical elements on multiple curved surfaces,” Opt. Express 23(26), 32917–32925 (2015). [CrossRef]
5. D. Radtke and U. D. Zeitner, “Laser-lithography on non-planar surfaces,” Opt. Express 15(3), 1167–1174 (2007). [CrossRef]
6. S. Kawata, H. B. Sun, T. Tanaka, et al., “Finer features for functional microdevices - Micromachines can be created with higher resolution using two-photon absorption,” Nature 412(6848), 697–698 (2001). [CrossRef]
7. M. Schumann, T. Bückmann, N. Gruhler, et al., “Hybrid 2D-3D optical devices for integrated optics by direct laser writing,” Light: Sci. Appl. 3(6), e175 (2014). [CrossRef]
8. K. Sugioka and Y. Cheng, “Femtosecond laser three-dimensional micro- and nanofabrication,” Appl. Phys. Rev. 1(4), 041303 (2014). [CrossRef]
9. A. D. Wang, L. Jiang, X. W. Li, et al., “Functionalization of freeform curved surfaces by shaped femtosecond laser pulses in the propagation axis,” Opt. Express 29(4), 5487–5496 (2021). [CrossRef]
10. Y. G. Kim, H. G. Rhee, and Y. S. Ghim, “Real-time method for fabricating 3D diffractive optical elements on curved surfaces using direct laser lithography,” Int. J. Adv. Des. Manuf. Technol. 114(5-6), 1497–1504 (2021). [CrossRef]
11. A. Michalek, A. Batal, S. J. Qi, et al., “Modelling ultrafast laser structuring/texturing of freeform surfaces,” Applied Surface Science Advances 2, 100036 (2020). [CrossRef]
12. X. Li, X. Y. Ren, X. S. Mei, et al., “In situ three-dimensional laser machining system integrating in situ measurement, reconstruction, parameterization, and texture mapping,” Int. J. Adv. Des. Manuf. Technol. 111(3-4), 673–684 (2020). [CrossRef]
13. X. Z. Wang, J. Duan, M. Jiang, et al., “Study of laser precision ablating texture patterns on large-scale freeform surface,” Int. J. Adv. Des. Manuf. Technol. 92(9-12), 4571–4581 (2017). [CrossRef]
14. J. Ai, Q. F. Du, Z. L. Qin, et al., “Laser direct-writing lithography equipment system for rapid and mu m-precision fabrication on curved surfaces with large sag heights,” Opt. Express 26(16), 20965–20974 (2018). [CrossRef]
15. J. Diaci, D. Bracun, A. Gorkic, et al., “Rapid and flexible laser marking and engraving of tilted and curved surfaces,” Opt. Lasers Eng. 49(2), 195–199 (2011). [CrossRef]
16. X. Li, B. Liu, X. S. Mei, et al., “Development of an In-Situ Laser Machining System Using a Three-Dimensional Galvanometer Scanner,” Engineering 6(1), 68–76 (2020). [CrossRef]
17. S.-J. Xu, Y.-Z. Duan, Y.-H. Yu, et al., “Machine vision-based high-precision and robust focus detection for femtosecond laser machining,” Opt. Express 29(19), 30952–30960 (2021). [CrossRef]
18. L. Overmeyer, J. F. Duesing, O. Suttmann, et al., “Laser patterning of thin film sensors on 3-D surfaces,” CIRP Ann. 61(1), 215–218 (2012). [CrossRef]
19. W. M. Steen and J. Mazumder, Laser material processing (springer science & business media, 2010).
