Open Access
Add to BibSonomy
Abstract
Aspheric cylindrical lenses, including fast axis collimators (FACs), are commonly used to collimate laser beams in the fast axis direction. Precision glass molding (PGM) is applied in the production of these optical lenses due to its high accuracy and efficiency. However, the profile errors and surface topography transferred from the mold reduce the optical performance of aspheric cylindrical lenses. In this paper, the surface errors of a FAC fabricated by combining ultraprecision diamond cutting and precision glass molding are analyzed. An optical simulation model is then established to qualitatively analyze the effects of tool marks on the optical defects, and the numerical calculations are carried out to determine the relative intensity distribution of light spots. Experiments are conducted to verify the theoretical results, which prove that the tool marks cause diffractive fringes and that the geometric parameters of the tool marks that are caused by cutting conditions affect the distribution of the fringe line defects. Finally, the critical conditions to eliminate diffractive fringes and improve the optical performance of the FAC are determined based on the experimental results.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Aspheric lenses have been widely applied in collimating systems because of their high optical performance, compactness, and structural simplicity. In the high-power diode laser industry, plano-aspheric cylindrical fast axis collimators (FACs) are integrated with laser diodes to transfer high intensity and power to application zones with low energy loss [1]. In the optical manufacturing industry, precision glass molding (PGM) is a feasible method to produce highly precise and efficient FACs [2,3]. In the PGM process, the profile of the mold is duplicated onto the lens under a high pressing load at a temperature that is above the transition temperature of the glass [4]. In recent years, numerous scholars have explored how to optimize the molding parameters to improve molding accuracy [5–7]. In terms of the accuracy of the molded lens, surface errors are often divided into three categories according to their spatial frequencies: form error, structured tool mark, and roughness. Various methods have been investigated to eliminate errors at different spatial frequencies. Li et al. [8] identified surface form distortion caused by the machining error and established an error compensation method based on the multi-body system theory. Beaucamp et al. [9] proposed a circular pseudo-random path polishing method to reduce the mid-spatial frequency errors on aspheric and freeform optics. The results showed that the random path could effectively suppress the material removal tracks on the surface. Lu et al. [10] introduced a dual-axis wheel polishing technology, using a rigid wheel combined with dual-axis rotational movements to reduce the surface roughness to the nanometer level. However, the requirements for surface accuracy in optical systems are also different for various applications. Most of the above-mentioned methods are also time-consuming and not universally applicable, even if they can reduce corresponding errors effectively. Thus, how to define a reasonable critical condition of the surface errors based on the evaluation of optical performance remains challenging. To reveal the effects of surface errors with different spatial frequency on optical performance, some theoretical analyses have been performed. Among them, Liu et al. [11] proposed a novel method to compensate form error based on wavefront aberrations by directly analyzing the relationship between optical performance and manufacturing errors. Noll found that roughness caused critical surface scatter defects in optical imaging systems [12]. The effects of form error and roughness on optical performance have been comprehensively studied, and corresponding approaches to eliminate the optical defects were proposed. Meanwhile, the effect of structured tool marks on optical performance is more complex than form error and roughness. He et al. [13,14] pointed out that the tool marks on diamond-turned optics will cause diffraction, which can be eliminated by controlling tool edge quality, material defects, and processing parameters. Liu et al. [15,16] and Chen et al. [17] studied the incident laser modulation induced by tool marks and claimed that the modulation degree was determined by the period of tool marks, while the height of tool marks has a slight impact on the modulation degree. Fang et al. [18] analyzed the scattering phenomenon of a conical reflector fabricated by single-point diamond turning. The results showed that the scattering characteristic had a close connection with tool marks, which relied on machining conditions, and selecting the proper feed rate could achieve a conical reflector with eligible reflecting performance. Zhang et al. [19] analyzed the surrounding circle defects in the collimation system caused by mid-frequency errors based on diffraction theory and introduced a polishing procedure to improve lens quality. At present, most research work about optical manufacturing is focused on the improvement methods of surface errors and the relationship between surface errors and their impacts on optical performance. Little work was reported to investigate the influence of machining condition on the geometrical distribution of tool marks and build up their direct influence on optical performance.
Typical defects caused by surface errors in a laser diode collimating system include poor residual divergence angle, diffractive fringes, and stray light. To address the above-mentioned research gap, this study aims to understand the optical defects caused by surface errors and their relationship with the diamond cutting process in order to manufacture high-quality FACs. In Section 2, an FAC is designed based on the practical application conditions. The entire manufacturing process, including mold manufacture and glass molding, is described in Section 3, and the surface errors of the FAC are measured by a tactile method. Based on the measured results of the FAC, the possible causes of optical defects in collimating are discussed. An optical simulation model and numerical calculation are conducted to analyze diffractive fringes caused by structured tool marks and analyze their relationship with machining parameters. Experiments are then carried out in Section 4 to define the critical parameters that can minimize diffractive fringes. The study provides a thorough analysis of the machining process and evaluation of optical performance and is helpful for the manufacturing of FACs.
2. Design and manufacture of the FAC
2.1 Optical design
The collimation of a high-power laser diode bar in the fast axis direction is the most challenging aspect of the design due to the large divergence angle (full angle of 40–60°) and small output, light size (∼1 µm) [20]. In this research, a FAC is designed as a plano-aspheric cylindrical lens with a high numerical aperture to meet the fast axis collimation requirements, as shown in Fig. 1(a). The laser spot is collimated into a narrow line shape in the fast axis, as shown in Fig. 1(b). The equation of the aspheric surface is defined by the even aspheric polynomial as follows:
2.2 Mold machining and precision glass molding processes
As the emitting area of a laser diode is small, the FAC is also designed with a small size and is normally in the sub-millimeter range. However, the fabrication of small individual lenses with conventional techniques is challenging. Instead of using conventional individual molding techniques to produce a FAC, in this study, FACs are integrated into a FAC array to ensure machining accuracy, consistency, and productivity increase. Figure 2 provides an illustration of the entire manufacturing process. Firstly, the mold profile is calculated based on the optical design of the FAC with consideration of the thermal expansion issues. The mold is then machined via the single-point diamond cutting method on an ultra-precision machine. Secondly, the FAC array is produced by precision glass molding under optimized molding parameters. A tactile method is then applied to evaluate the surface errors. The measured data is then used to compensate for form errors until peak-valley values meet the geometric requirements (PV < 0.5 µm). The last step is to separate the FAC array. As shown in Fig. 2(d), a dicing method is used to separate the FAC array into an individual FAC lens that can be used for fast axis collimation.
Fig. 2. Machining process of FAC: (a) Mold manufacture; (b) Precision glass molding; (c) Measuring; (d) Dicing.
2.3 Surface errors of the molded FAC
Figure 3(a) shows the original surface errors of the molded FAC. There are different components of surface errors in the FAC, whose effect on the optical performance varies from one component to another. It is most effective to analyze the source of these components and their effect on the optical performance individually. Thus, the surface errors are divided into three parts based on different spatial frequencies: form error, structured tool marks, and roughness, as shown in Fig. 3(b)–(d), respectively.
Fig. 3. Surface errors of the molded FAC and its components: (a) Surface errors; (b) Form error; (c) structured tool marks; (d) Roughness.
As shown in Fig. 3(b), the form error of the FAC has a relatively low spatial frequency, which can be described as the PV error. Major factors that affect PV error include tool edge, tool path, and machine positioning errors in the mold machining process, as well as thermal effects in PGM. The form error of the FAC can be improved by compensating for the profile error on the mold and optimizing molding conditions in PGM [21,22]. Roughness refers to small irregularities on the optical surface and is usually described as Ra. As the single-point diamond turning technique can achieve an optical finish on a Ni-P surface, the roughness of the FAC can easily be guaranteed by controlling the random factors, such as applying an edge quality-controlled diamond tool and performing spindle balancing to reduce vibrations. In addition to form error and roughness, the study of structured tool marks remains inconclusive and requires further analysis. Deterministic machining methods like single point diamond cutting leave structured tool marks on the generated surfaces. The spatial frequencies of the tool marks tend to be lower than those of surface roughness and higher than those of form errors. In this section, the origin of the structured tool marks in the above-mentioned machining process is constructed. As shown in Fig. 2(a), the diamond tool moves along the cutting direction and tends to leave periodical residual tool marks on the workpiece surface. In conventional machining processes, the tool marks are relatively large in size and can be considered as ideal circular arcs and approximately calculated based on the diamond tool radius and processing parameters [23]. However, in the micro-cutting process, the tool marks are affected by many influencing factors, including tool edge waviness, material properties, machining parameters, and environmental factors [24]. The peak-to-valley value of the tool marks changes drastically under different processing conditions, while the period of the tool marks is approximately dependent on the feed rate. For simplification, the tool marks can be numerically constructed with a sinusoidal function:
where Rt is the amplitude of the tool marks, which can be represented by the peak-to-valley surface roughness, d is the distribution period of the tool marks, which is theoretically equal to the feed rate. The comparison between the simulated sinusoidal function and the actual tool marks is performed in Fig. 3(c).3. Analysis of diffractive fringes
3.1 Cause of diffractive fringes
In a laser diode collimating system, typical optical defects include poor residual divergence angle, diffractive fringes, and stray light. Obviously, the above-mentioned optical defects have a close connection with the surface errors of the molded FAC. From the optical performance point of view, the form error will cause obvious distortion of the center spot and lead to a poor divergence angle, while the randomly distributed roughness will scatter the laser light at large angles and cause stray phenomena [25]. The above-mentioned problems can be easily improved by adopting the profile error compensation method and optimizing molding parameters, which is not the focus of this study. Compared to the form error and roughness, the structured tool marks are more structured and will diffract the collimating light at angles small enough to cause diffractive fringes [26], as shown in Fig. 4. These first-order diffractive lights will influence the energy distribution of the center spot, which makes the molded FAC unacceptable for practical use.
To achieve a defect free FAC with single-point diamond cutting and precision glass molding, the relationship between the distribution of diffracted light and the structured tool marks should be analyzed in detail.
3.2 Optical simulation of diffractive fringes
In order to study the influence of tool marks on the collimating performance, optical simulations were conducted using VirtualLab Fusion software. To simplify the study, the laser source is considered as a Gaussian beam with different divergence angles in fast axis and slow axis directions. The wavelength and divergence angles were set the same (915nm, 25 degrees in fast axis) as the practical condition. As the focus of this study is the optical performance of the FAC, only collimation quality in the fast axis is studied, and the collimation effect in the slow axis direction is not considered. The diagram of the simulation model is illustrated in Fig. 5. The detect screen is placed 100 mm away from the exit surface of FAC, which locates in the Fraunhofer region (L>>λ), to characterize the light spot in the far-field. First, a FAC with an optimally designed aspheric profile is imported to obtain an ideal collimating result. As shown in Fig. 6(a), the ideal light spot is clear and without any diffractive fringes in the fast axis.
A sinusoidal grating is then placed next to the ideal FAC to simulate the effect of tool marks on the light spot. The geometrical parameters of the sinusoidal grating are set to be the same as the size of the tool marks. The simulated light spot is shown in Fig. 6(b). In addition to the center light spot, two diffractive fringes are parallel to the center spot and distributed in the fast axis direction, which coincides with our speculation in Section 3.1. This implies that the tool marks will work as a diffraction grating to impress a periodic variation onto the incident laser beam and cause fringe line defects on the light spot. As the structured tool marks are confirmed to be the cause of diffractive fringes, it is necessary to simulate how the geometric parameters of tool marks affect the position and intensity of diffractive fringes.
A series of optical simulations were designed and performed to establish the relationship between the geometric parameters of the tool marks and the optical performance of the FAC qualitatively. Firstly, the amplitude of tool marks was set as constant (50 nm), and the period of tool marks varied from 5, 10, and 20 µm. The simulated results of the light spots are shown in Fig. 7. It can be observed that the distance D between the diffractive and the spot center decreases along with the period of tool mark increments. This result indicates that the distance between fringe line defects is inversely proportional to the feed rate. Another phenomenon is that the brightness of the diffractive fringes is maintained at a close level because the amplitude of tool marks is set as the same. It could thus be concluded that the amplitude of tool marks will influence the energy distribution of diffractive fringes. To confirm this finding, the periods of tool marks were set as a constant (5 um), and the amplitude of tool marks varied from 10 to 50 and 100 nm. The simulated results are shown in Fig. 8.
Fig. 7. Simulated light spots of FAC with different tool mark distribution periods: (a) 5 µm; (b) 10 µm; (c) 20 µm.
Fig. 8. Simulated light spots of FAC with different amplitudes of tool marks: (a) 10 nm; (b) 50 nm; (c) 100 nm.
From the simulation results in Fig. 8, when the amplitude of tool marks is 100 nm, two obviously diffractive fringes are distributed on the both side of center light. As the amplitude of tool marks decreases to 50 nm, the brightness of the diffractive fringes decreases. Furthermore, when the amplitude of tool marks decreases to 10 nm, the diffractive fringes are almost invisible and the light spot is close to ideal. For larger amplitudes, the energy intensity of diffractive fringes increases with a higher amplitude of tool marks, and the position of the diffractive fringes remains unchanged.
3.3 Numerical calculation of diffractive fringes
The simulation results can only give a fundamental qualitative analysis of the position and energy distribution of diffractive fringes. To precisely analyze the energy distribution of the collimated light spot and determine the critical conditions for practical use, a numerical calculation based on diffraction theory and Fourier optics is conducted. For a cylindrical lens, the optical power is only along the fast axis direction. Hence, only a 1D situation in the fast axis direction is considered in this case.
As discussed above, the distribution of the structured tool marks can be described as a harmonic component. Assuming the laser beam is perfectly collimated by the FAC when the light reaches the exit surface of FAC, the complex amplitude distribution on the exit surface can be written as:
With $\delta {\rm{ = }}\frac{{2\pi d}}{\lambda }\sin \theta = 2\alpha$, the above formula can also be written as:
If the distance between the exit surface of the FAC and the detect screen L is much larger than the distribution period of tool marks d, the intensity distribution can be simplified and considered as the sum of three diffraction orders, which corresponds to the 0 and ${\pm}$ 1 orders:
The distribution of relative intensity can be plotted as in Fig. 9. According to the grating equation [27], the diffraction angle is given by:
The distance between diffractive fringes can be approximately expressed as:
Fig. 9. The distribution of relative intensity considering diffractive fringes caused by tool marks.
The above equations illustrate that the intensity depends on the parameters of the generated surface, laser wavelength, and the position of the detect screen. The relative distribution of intensity of the +1 and −1 order diffractive fringes is proportional to the power of the amplitude of the surface texture, and the position of the diffractive fringes is inversely proportional to the distribution period of the tool marks. That is to say, the primary solution for minimizing the diffractive fringes defect is to reduce the amplitude and distribution period of the tool marks.
4. Experiments and results
4.1 Mold manufacture and glass molding
The FAC in this work was designed to be a cylindrical lens with an aperture and thickness of 0.6 and 0.53 mm, respectively, and a numerical aperture of 0.85 NA. The glass material was DZ-LaF52 LA with a refractive index of 1.81, produced by CDGM Glass Company Ltd.
The detailed coefficients are summarized in Table 1.
Table 1. Designed coefficients of the aspheric FAC.
An ultra-precision machine (Freeform, AMETEK Precitech Inc., USA) with high stability was used for FAC mold manufacturing. The cutting process is shown in Fig. 10. The mold was mounted on the C-axis by a vacuum chunk, and the diamond tool was mounted on the Z-axis slide. Before machining, the position of the workpiece and the diamond tool were adjusted by rotating the C-axis and B-axis to avoid setting errors. In the cutting process, Y-axis and Z-axis slides were driven simultaneously to feed, and the X-slide axis was driven to remove the material. The machining instrument was a diamond round-nosed tool with a radius of 0.245 mm and a sharp blade edge. To explore the influence of the tool marks on diffractive fringe line defects, different feed rates were used in the cutting process. Detailed machining parameters are provided in Table 2.
Table 2. Cutting conditions for FAC mold machining.
A 300 µm thick nickel-phosphorus (Ni-P) plated mold was chosen as the mold plating material due to its high hardness, wear, and corrosion resistance. A Ta-N coating was then deposited on the mold to prevent adhesion between the glass and mold.
The molding experiment was conducted on a PGM machine (PFLF7-60A) by SYS Co., Ltd with a molding temperature of 594 °C and a pressing load of 0.15 MPa. The molding process was carried out under the protection of pure nitrogen to prevent oxidation of the mold. The detailed molding conditions are shown in Table 3.
Table 3. Molding conditions for FAC.
The fabricated mold and corresponding molded FAC array are shown in Fig. 11.
4.2 Evaluation of surface topography
After performing glass molding, the fabricated FAC array was measured by a Taylor Hobson PGI measuring instrument. For all conditions, the surface measurements were performed perpendicular to the cutting direction. The measured surface errors were separated into the three components of form error, structured tool marks, and roughness by a secondary Gaussian filter and the cutoff parameters were selected as 0.08 mm and 0.0025 mm according to the procedures requested in ISO 25178-2:2021. The obtained results are displayed in Fig. 12. According to the measured results, even though the feed rate is increased from 5 to 20 µm, the PV values are maintained at around 0.5 µm, illustrating that the feed rate has no significant effect on form error. The applied raster cutting method and glass molding process facilitate the stable production of high precision FAC lenses. However, the surface morphology of these lenses, including tool marks, are different and show a close connection to the machining parameters observed by SEM, as displayed in Fig. 13. The surface of Lens 1 is very smooth and without any visible tool marks, with a peak-to-valley surface roughness Rt of 9.97 nm. Meanwhile, periodical structured tool marks can be observed on Lens 2 and Lens 3. In Fig. 13(b), tool marks are approximately 10 µm in period and 30.26 nm in height. In Fig. 13(c), tool marks are approximately 20 µm in period and 125.73 nm in height. The periods of tool marks are precisely consistent with the feed rate, indicating that the machining parameters directly determine the tool marks.
Fig. 12. Surface errors, tool marks, and roughness of molded FACs with parameters in Table 2: (a) Lens 1: PV 0.4541 µm and no obvious tool marks; (b) Lens 2: PV 0.4494 µm and tool marks in 10 µm period; (c) Lens 3: PV 0.4974 µm and tool marks in 20 µm period.
Fig. 13. SEM photographs of molded FACs with parameters in Table 2: (a) Lens 1: no obvious tool marks; (b) Lens 2: tool marks in 10 µm period; (c) Lens 3: tool marks in 20 µm period.
4.3 Evaluation of optical performance
Figure 14 shows the setup for detecting the collimating performance of the FAC. A single emitter diode laser (Focuslight Technologies Inc.) was applied as an optical source. The laser source was a Gaussian beam with 25 degrees of half-angle divergence in the fast axis direction and 10 degrees in the slow axis direction. We only investigated the optical performance in the fast axis in this work. The wavelength of the laser source was 915 nm, and the FAC was mounted on the fixture and could be fine-adjusted by five-axis displacement adjusters to meet the focal length. A beam analyzer (CINOGY CMOS 1201) was placed after the FAC to measure the real-time light spot size in the far-field. The distance between the exit surface of FAC and the beam analyzer was set the same as that in optical simulation. A 1/12 filter was used to protect the beam analyzer from being damaged by the laser energy.
Figure 15 shows the detected light spots from the beam analyzer. The center light spots are very similar in shape and size. The only difference is that the light spot of Lens 1 is clear and without any diffractive fringes. The light spots from Lens 2 with a 10 µm feed rate and Lens 3 with a 20 µm feed rate have obvious fringe line defects (marked in the red dashed box). The distance between the fringe line defects and the center of the light spot decreases as the feed rate increases, obeying the previous theoretical and simulation analysis. For the 5 µm FAC lens, the fringe line defects are unobservable. The first reason for this is that the height of the tool marks is much lower with a 5 µm feed rate than that of those at 10 and 20 µm, and so its corresponding influence on light spots is negligible. Thus, the fringe line defects cannot be detected on screen. Secondly, the fringe line defects are too far away from the center of the light spot and cannot be measured as they are outside of the detected area of the beam analyzer.
Fig. 15. Light spots on beam analyzer: (a) Feed rate in 5 µm; (b) Feed rate in 10 µm; (c) Feed rate in 20 µm.
As demonstrated in Fig. 12(a) and Fig. 15(a), with proper feed rate, the amplitude of the tool marks less than 10 nm is achieved, and under this condition the diffractive fringes cannot be observed anymore. Combine considering the simulation results and experimental results, decreasing amplitude of tool marks, the diffractive fringes gradually weaken, and when the amplitude of the tool marks is controlled below a certain level, the optical performance will be considered acceptable. In this case, reducing the amplitude of tool marks to under 10 nm can generate an optical surface similar to that shown in Fig. 15(a). To confirm this, the light spot of tool marks with an amplitude of 10 nm and the distribution period of 10 and 20 µm was further simulated. The simulated results are shown in Fig. 16.
Fig. 16. Simulated light spots of FACs with different tool marks: (a) Amplitude of 10 nm and period of 10 µm; (b) Amplitude of 10 nm and period of 20 µm.
As the simulation results show, when the amplitude of the tool marks is equal to 10 nm, no diffractive fringe can be observed for various distribution periods, which means only if the amplitude of tool marks is equal or below 10 nm, an acceptable optical performance can be achieved. Therefore, a reasonable critical condition for eliminating the diffractive fringes of molded FACs is a peak-to-valley surface roughness of less than 10 nm.
4.4 Critical conditions for elimination of diffractive fringes
As discussed above, the key to ensuring the optical performance of the FAC is to achieve tool marks with small amplitudes. As reported by He et al. [13], the surface topography generated by single-point diamond turning with a waviness-controlled diamond tool is significantly influenced by the process parameters. Meanwhile, the Ni-P is an amorphous plating material without significant material defects like hard inclusions and voids. Thus, the generated surface topography is mainly decided by the machining parameters. The relationship between the peak-to-valley surface roughness of the molded FAC and feed rate was experimentally analyzed to determine the appropriate machining parameters to control the amplitude of tool marks. The results are shown in Fig. 17. The experimental result shows that with the decrease in feed rate, the peak-to-valley surface roughness presents a trend of first decreasing and then increasing. This is because when the feed rates are in relatively high values, the feed rate and the tool edge radius play a key role in the formation of tool marks. When the feed rate is reduced to a certain value, the material properties like plastic side flow and material spring back will dominate the tool marks forming process. A low feed rate will lead to a high plastic side flow, while the peak-to-valley surface roughness will increase. The results demonstrate that in order to obtain a FAC with good optical performance, the feed rate parameter needs to be carefully selected to achieve peak-to-valley surface roughness that can satisfy the requirement. In this case, the suggested feed rate is between 3 to 6 µm.
5. Conclusion
A novel production process of a fast axis collimator for a laser diode was introduced in this work. The surface errors of the FAC were studied, and corresponding effects on optical performance were analyzed. The main cause of diffractive fringes in the laser collimating system was found to be tool marks duplicated from the mold, which was fabricated by single-point diamond cutting. The relationship between the geometric parameters of tool marks and diffractive fringes was then established, and a critical condition to meet the optical performance was proposed. The main conclusions of this paper are drawn as follows:
- (1) In the fabrication of optical molds by single-point diamond cutting, the tool marks depend on the machining and geometrical tool parameters. The tool marks are then duplicated onto the lens surface during PGM. Periodically structured tool marks will cause diffractive fringes due to diffractions.
- (2) The position and energy intensity of diffractive fringes are determined by the geometric parameters of the tool marks. The distance between diffractive fringes and the center of the light spot decreases as the distribution period of tool marks increases. The smaller the height of the tool marks, the lower the energy intensity of diffractive fringes.
- (3) Removing tool marks on the optical surface is the key to eliminating the diffractive fringes of the FAC. Considering there is no effective way to eliminate tool marks entirely, selecting a diamond cutting tool with a larger tool edge radius and selecting an appropriate feed rate can effectively reduce tool marks on the fabricated surface to achieve an acceptable optical performance. The critical condition for obtaining molded FACs with acceptable optical performance is to ensure the height of the tool marks is below 10 nm. To achieve this value, the suggested feed rate is between 3 to 6 µm.
Funding
National Natural Science Foundation of China (51775046, 51875043); Beijing Municipal Natural Science Foundation (JQ20014).
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.
References
1. H. Rudiger, B. Bernhard, and Hans J. Tiziani, Advanced Optics Using Aspherical Elements (SPIE Press, 2008).
2. A. Y. Yi and A. Jain, “Compression Molding of Aspherical Glass Lenses-A Combined Experimental and Numerical Analysis,” J. Am. Ceram. Soc. 88(3), 579–586 (2005). [CrossRef]
3. T. Zhou, X. Liu, Z. Liang, Y. Liu, J. Xie, and X. Wang, “Recent advancements in optical microstructure fabrication through glass molding process,” J. Mech. Eng., Chin. Ed. 44(01), 46–65 (2008). [CrossRef]
4. T. Zhou, J. Yan, N. Yoshihara, and T. Kuriyagawa, “Study on Nonisothermal Glass Molding Press for Aspherical Lens,” J. Adv. Mech. Des. Syst. 4(5), 806–815 (2010). [CrossRef]
5. Y. Zhang, K. You, and F. Fang, “Pre-Compensation of Mold in Precision Glass Molding Based on Mathematical Analysis,” Micromachines 11(12), 1069 (2020). [CrossRef]
6. T. Zhou, J. Xie, J. Yan, K. Tsunemoto, and X. Wang, “Improvement of glass formability in ultrasonic vibration assisted molding process,” Int. J. Precis. Eng. Manuf. 18(1), 57–62 (2017). [CrossRef]
7. A. R. Abdul Manaf and J. Yan, “Improvement of form accuracy and surface integrity of Si-HDPE hybrid micro-lens arrays in press molding,” Precis. Eng. 47, 469–479 (2017). [CrossRef]
8. Y. Li, Y. Zhang, J. Lin, A. Yi, and X. Zhou, “Effects of Machining Errors on Optical Performance of Optical Aspheric Components in Ultra-Precision Diamond Turning,” Micromachines 11(3), 331 (2020). [CrossRef]
9. A. Beaucamp, K. Takizawa, Y. Han, and W. Zhu, “Reduction of mid-spatial frequency errors on aspheric and freeform optics by circular-random path polishing,” Opt. Express 29(19), 29802 (2021). [CrossRef]
10. A. Lu, T. Jin, Q. Liu, Z. Guo, M. Qu, H. Luo, and M. Han, “Modeling and prediction of surface topography and surface roughness in dual-axis wheel polishing of optical glass,” Int. J. Mach. Tools Manuf. 137, 13–29 (2019). [CrossRef]
11. X. Liu, X. Zhang, F. Fang, and Z. Zeng, “Performance-controllable manufacture of optical surfaces by ultra-precision machining,” Int. J. Adv. Manuf. Technol. 94(9-12), 4289–4299 (2018). [CrossRef]
12. R. J. Noll, “Effect of Mid- and High-Spatial Frequencies on Optical Performance,” Opt. Eng. 18(2), 182 (1979). [CrossRef]
13. C. L. He and W. J. Zong, “Diffraction effect and its elimination method for diamond-turned optics,” Opt. Express 27(2), 1326 (2019). [CrossRef]
14. C. L. He, W. J. Zong, C. X. Xue, and T. Sun, “An accurate 3D surface topography model for single-point diamond turning,” Int. J. Mach. Tools Manuf. 134, 42–68 (2018). [CrossRef]
15. Q. Liu, J. Cheng, Z. Liao, H. Yang, L. Zhao, and M. Chen, “Incident laser modulation by tool marks on micro-milled KDP crystal surface: Numerical simulation and experimental verification,” Opt. Laser Technol. 119, 105610 (2019). [CrossRef]
16. Q. Liu, J. Cheng, H. Yang, Y. Xu, L. Zhao, C. Tan, and M. Chen, “Modeling of residual tool mark formation and its influence on the optical performance of KH2PO4 optics repaired by micro-milling,” Opt. Mater. Express 9(9), 3789 (2019). [CrossRef]
17. M. J. Chen, J. Cheng, X. D. Yuan, W. Liao, H. J. Wang, J. H. Wang, Y. Xiao, and M.-Q. Li, “Role of tool marks inside spherical mitigation pit fabricated by micro-milling on repairing quality of damaged KH2PO4 crystal,” Sci. Rep. 5(1), 14422 (2015). [CrossRef]
18. F. Fang, K. Huang, H. Gong, and Z. Li, “Study on the optical reflection characteristics of surface micro-morphology generated by ultra-precision diamond turning,” Opt. Laser Eng. 62, 46–56 (2014). [CrossRef]
19. Y. Zhang, G. Yan, Z. Li, and F. Fang, “Quality improvement of collimating lens produced by precision glass molding according to performance evaluation,” Opt. Express 27(4), 5033 (2019). [CrossRef]
20. D. Kura, H. Moser, E. Langenbach, and M. Forrer, “Fast axis collimation for high power diode lasers,” in 2009 High Power Diode Lasers and Systems Conference (2009), pp. 1–2.
21. D. Yu, L. Yu, S. Wang, and Y. Tian, “Surface error analysis and online compensation method for increasing the large-sized cylindrical part’s quality,” Int. J. Adv. Manuf. Technol. 79(5-8), 1401–1409 (2015). [CrossRef]
22. C. Chen, C. Huang, W. Peng, Y. Cheng, Y. Yu, and W. Hsu, “Freeform surface machining error compensation method for ultra-precision slow tool servo diamond turning,” Proc. SPIE 8838, 88380Y (2013). [CrossRef]
23. W. A. Knight and G. Boothroyd, Fundamentals of Metal Machining and Machine Tools, (CRC Press, 2005).
24. C. He, W. Zong, and T. Sun, “Origins for the size effect of surface roughness in diamond turning,” Int. J. Mach. Tools Manuf. 106, 22–42 (2016). [CrossRef]
25. M. Forrer, H. Moser, D. Kura, M. Grössl, and H. Forrer, “Industrial performance analysis of the fast axis collimator,” Proc. SPIE 8963, 89630D (2014).
26. J. M. Tamkin and T. D. Milster, “Effects of structured mid-spatial frequency surface errors on image performance,” Appl. Opt. 49(33), 6522 (2010). [CrossRef]
27. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light. (Cambridge University, 2019).
