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Abstract
This study aims to resolve the trade-off between the constraints and capabilities of ultra-precision machining to achieve ophthalmic Fresnel lenses. A general Fresnel lens pattern has a narrow variable pitch and curved grooves. However, we obviate the limitations of the tool nose radius constraint and the long tool path via ultra-precision machining of the modified Fresnel lens, ensuring a constant pitch of 0.1 mm and varying the height of straight grooves from 0 to 11 µm. Photorealistic raytracing visualization and MTF simulation verified the compatibility of the lens pattern with human perception sensitivity. Copper-coated mold was fabricated using a diamond tool with a tool nose radius of 5 µm. The replicated flexible Fresnel lens demonstrated a relative MTF imaging performance of 89.1% and was attached to the goggles for the qualitative assessment. The proposed Fresnel lens design and fabrication approach can be extended to applications in the visual and infrared ranges as well.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Since Augustin-Jean Fresnel constructed a lens that combined concentric rings, Fresnel lenses have been applied in a range of optical devices. Optical-grade surfaces of ultra-precision lens [1], Fresnel lens [2,3], and optical prism [4] exemplify the versatile optical technologies for X-ray imaging systems [5], fish-eye lens [6], solar concentrators [7], light illumination [8], and infrared camera [9]. Among these highly functional optical surfaces, the Fresnel lens has gained a competitive advantage because of its low weight and high power, relative to its bulky counterparts [10,11]. Recently, there has been an increasing amount of research on Fresnel lenses because they possess advantages such as reduced weight, cost-effective production, and using less material than conventional lenses. Fresnel lens can be employed as the critical component for 3D view systems [12], zooming applications [13], and infrared imaging systems [14].
Several earlier publications have introduced the Fresnel lens in ophthalmology. The use of Fresnel and ophthalmic prisms for persons with hemianopic visual field loss [15], presbyopia correction [16], the polymethylmethacrylate (PMMA) Fresnel lens for treatment of strabismus [17,18], and light filters for Fresnel microprisms [19] has been proposed. The Fresnel liquid crystal lens [20,21] is considered for near-to-eye applications. However, there are still many challenges to improve the groove's quality of the Fresnel lens in these lenses.
On the other hand, versatile manufacturing techniques have realized optical-grade surfaces, including deep reactive ion etching [22,23], ultra-precision machining [24–26], E-beam lithography [27], LIGA process [28], two-photon polymerization [29], inkjet printing [30]. However, ultra-precision machining is the most prominent technique among all the manufacturing techniques owing to its universal one-step process and the non-requirement of any post-processing, even for millimeter-scale optics. Freeform and complex optics have been realized via highly accurate ultra-precision machining, particularly single-point diamond turning (SPDT) [31]. SPDT enables the generation of complex optical surfaces via manipulation of the depth of the cut in the micrometer range because of the highly sharp cutting-edge tool [32]. Owing to its inherent tool nose radius, clearance angle, and rake angle, the tool geometry plays a critical role in achieving an appropriate surface structure, particularly in optical-grade applications. An effective tool path generation strategy for complicated optical surfaces has been proposed based on the unique tool geometry [33]. The Fresnel lens pattern comprises the grooves or facets of the concentric annular ring. The slope, draft, and angle of the facet define the optical efficiency [34]. Considering the manufacturing factors, the Fresnel lens sidewall design can affect the imaging system performance [35]. Conventionally, annular rings have been designed and fabricated with a variable pitch and constant height [12,14]. The narrowest groove meets the tool-nose-radius limitation in the constant-height, variable-pitch design of the Fresnel lens with a high sag. A micro tool nose radius tool wears rapidly, traversing the curved groove of the large-diameter lens.
Considering these stringent requirements, we have suggested a manufacturing-friendly novel design of Fresnel lens with a constant pitch and variable height based on ultra-precision machining [36]. And, to overcome these above limitations, the design and simulation through the NX and Zemax commercial software were done. And then, fabrication and testing processes of the feasibility of ophthalmic Fresnel lenses are shown in this paper. This study aims to manipulate the ultra-precision machining capabilities to realize optical Fresnel lens surfaces. In contrast to the conventional notion of variable pitch and constant height of concentric annular grooves, we have explored the constant pitch and variable height options to realize an ultra-precision-machined Fresnel lens mold. The proposed design obviates the inherent tool nose radius constraints and the limitation of traversing the curved tool path. To our knowledge, this is the first study to address these problems of the Fresnel lens in ophthalmic applications.
2. Design and simulation
2.1 Design
The Fresnel lens pattern in Fig. 1(a) has a spherical lens profile with a radius of 250 mm, and the patterned area over the lens mold of the developed Fresnel lens is 50 mm circumscribed by an outer non-patterned flat area with an optical-grade surface finish of Ra 1 nm. The schematic at the top of Fig. 1(a) illustrates the Fresnel lens pattern with a constant height and variable pitch, and the outermost ring has the narrowest groove to be machined with considerable difficulty using a diamond tool with a conventional tool nose radius. The schematic at the bottom of Fig. 1(a) shows the new Fresnel design pattern with a constant pitch and variable height. In the new lens design, the height of the annular Fresnel rings was varied from 0 to 11 µm from the center to the outermost ring. During the proof-of-concept studies of the proposed design, it was revealed that concentric annular rings with a pitch of 0.1 mm have the competitive advantage of being compliant with human perception sensitivity. Figure 1(b) highlights the inherent tool nose radius and compares the curved path with the straight path to develop the new Fresnel lens design.
Fig. 1. Schematic of the Fresnel lens pattern. (a) Two Fresnel lens profile conversions: (top) constant height and variable pitch; (bottom) constant pitch and variable height. (b) Tool path on the profile, left side: inherent characteristic of tool nose radius, right side: comparison of curved tool path versus straight tool path adopted for optimal machining. (c) Schematic of the Fresnel lens profile conversion.
Figure 1(c) shows the schematic of the Fresnel lens profile conversion. The conventional concave lens (with the radius of curvature R) is divided into several concentric rings. The spherical profile of the lens (OG) is divided down to the flat base (OPn). In this study, the Fresnel lens has a diameter d of 50 mm, and is made of n grooves radiating out from the optical axis (origin O). Therefore, the Fresnel lens profile of each groove can be determined by points: $O,{A_1},{A_2}, \ldots {A_n},{\; }{P_1},{P_2}, \ldots {P_n}$. Each groove is of equal width, called pitch (p), and their x-coordinates are given as follows:
The sag height of the points ${A_i}({{x_i},\; {z_i}} )$ of the Fresnel lens is found using the height of the spherical lens. Thus, the sag height of the Fresnel lens is determined by the following equation:
By substituting ${x_i}$ from Eq. (2) into Eq. (3), the sag height of each groove becomes:
From Eq. (4), the Fresnel lens profiles (the curved and straight paths on the Fresnel lens) are obtained with the sag height from 0 to 11 µm.
2.2 Photorealistic ray tracing visualization
Photorealistic raytracing visualization can evaluate virtually reflective scenes well for complex optical surfaces, thereby complementing the design and optimization process [37]. Figure 2(a) illustrates a photorealistic raytracing visualization schematic for comparing the constant pitch design iterations through the commercial software NX.
Fig. 2. (a) Schematic of photorealistic raytracing visualization [30]. (b–g) Photorealistic raytraced visualization of Fresnel design pattern with constant pitches: (b, c, d) curved path, (e, f, g) preferable straight path for machining.
Figure 2(b, c, d) show the ideal reflective scenes from the reference image in Fig. 2(a) to the curved groove path of the pitches of 0.5, 0.2, and 0.1 mm, respectively. Therefore, the Fresnel lens pattern ideally requires curved grooves that are not preferable owing to the long tool path and tool wear characteristics in this study. Hence, we propose a new viable option by following a straight path. Figure 2(e, f, g) depicts the reflective scenes corresponding to the Fresnel design pattern for the machinable straight path with pitches of 0.5, 0.2, and 0.1 mm, respectively. The presence of serrated edges over the entire reflective scene for a pitch of 0.5 mm in Fig. 2(e) indicates that the pitch of the concentric annular rings needs to be further reduced. Here, the decrease in the pitch from 0.5 mm to 0.1 mm facilitates overcoming serrated edges in the reflective scene. The pitch improved the distorted image of edges for the yellow parking lines in Fig. 2(e) from 0.5 to 0.1 mm in Fig. 2(f, g). Owing to the resolution of the limitations of the tool nose radius and the requirement of following the curved tool trajectory, this result also highlights the significance of the machinable straight path in Fresnel lens design with 0.1 mm pitch. Additionally, the Fresnel lens pattern with annular rings (pitch 0.1 mm) and a straight path is comparable to a curved groove and is acceptable based on human perception sensitivity.
2.3 Optical performance
In the imaging systems, the beams first pass through the Fresnel lens and are then focused on the image plane. To analyze the optical performance, the Fresnel lens is designed using sequential and non-sequential components in Zemax software [38]. Zemax visualization affords the advantage of effectively simulating and visualizing optical images for various curved surfaces. Figure 3 shows the sagittal modulation transfer function (MTF) values for the Fresnel lens.
Fig. 3. MTF simulation (a) straight groove and (b) curved groove with the constant pitch p of each groove.
The image plane was set 1020 mm away from the lens, with an object height of 25 mm, and illuminated with the light of standard visible spectrum wavelengths. Here, due to the MTF values in the tangential and sagittal directions are almost similar, only the MTF values in sagittal were plotted to avoid the overlap with the tangential direction. For both the straight and curved groove Fresnel lenses, the MTF values are reduced by increasing the pitch size. However, regardless of the pitch size, the curved groove Fresnel lenses always achieve improved MTF results. For the spatial frequency range, there is considerable contrast variation in straight groove Fresnel lenses, particularly for large pitch sizes. Furthermore, the MTF values of these responses increase as the pitch decreases. For the straight Fresnel lens, the difference in the MTF values is significant between each pitch size. At a spatial frequency of 5 lp/mm, a contrast of approximately 30% can only be achieved by the straight Fresnel lens with a pitch of 0.1 mm.
For the Fresnel lenses shown in Fig. 3(b), all MTF traces increase significantly, particularly those with a large pitch size. However, for smaller pitch sizes, the difference in the shape of the curved groove Fresnel lens does not significantly affect the lens performance. Additionally, all Fresnel lenses with straight grooves achieved MTF values lower than those of the Fresnel lens with curved grooves with a pitch of 0.1 mm. Using the simulation option in Zemax with the imaging object of the USAF 1951 chart, Fig. 4 shows these comparisons.
Fig. 4. Image simulation. Upper row: straight groove Fresnel lens for (a) p = 0.1, (b) p = 0.2, and (c) p = 0.5 mm. Lower row: curved groove Fresnel lens for (d) p = 0.1, (e) p = 0.2, and (f) p = 0.5 mm.
The influence of pitch size on the image simulation quality is shown in Fig. 4. The results show that a decrease in pitch size leads to improved image quality. The larger pitch size images contain several ghost circles that result in blurred images and reduce the image quality. The image quality in Fig. 4(a) and (d–f) are mostly similar, although they have different pitch sizes and shapes. This corresponds to the MTF values shown in Fig. 3. For exceedingly small pitch sizes, the image quality improvement is marginal in both configurations. Notably, the image quality is considerably low, even with a small pitch size. However, few object details can be detected, suggesting that this Fresnel lens may have few low-cost applications.
3. Fabrication
3.1 Ultra-precision machining of the Fresnel mold
A Fresnel lens mold of the copper coating on the steel with a concentric annular ring pattern was achieved through the single-point diamond turning process using an ultra-precision 5-axis CNC turning machine (FG350, Moore Nanotech) and the dedicated diamond tool. Figure 5 shows the ultra-precision machining process for manufacturing the Fresnel lens mold.
Fig. 5. Ultra-precision machining of Fresnel lens mold. (a) Ultra-precision machine (FG350, Moore Nanotech). Inset displays the micrograph of the SPDT tool nose radius of 5 µm. (b) Ultra-precision machined mold. It demonstrates the same role as that of the concave mirror of magnifying the object. (c) White-light interferometer (NV6300, Zygo) surface map of the mold (Ra 1 nm). (d) Straight path profile (pitch 0.1 mm) of Fresnel lens mold (VK9700, Keyence).
The inset of Fig. 5(a), captured at 1500× magnification, displays the unique diamond tool characteristics of the tool nose radius of 5 µm during ultra-precision machining. Figure 5(b) illustrates that the ultra-precision machined mold has a spherical mirror performance; the imaging capability of the Fresnel lens pattern area versus that of the no-pattern counterpart is highlighted. The equivalent concave shape of the Fresnel lens mold magnifies the object successfully. Additionally, the white-light interferometer (NV6300, Zygo) surface map of the developed ultra-precision Fresnel mold is illustrated in Fig. 5(c), highlighting the achieved surface roughness, Ra 1 nm of the mold. Figure 5(d) shows the measured surface profile (VK9700, Keyence), and the short peaks represent the tool marks developed during the ultra-precision machining because of the characteristic tool nose radius of 5 µm. For a large tool nose radius, for example, 30 µm, we can expect smoother profiles, but side wall loss of the pitches is caused. A method to reduce the side wall loss was proposed by modifying the orientation of the side walls [35]. Therefore, the lens design with a constant pitch of 0.1 mm and variable height provides an optical-grade surface with a tool nose radius of 5 µm. With the concave ophthalmic lens superimposed on the machined Fresnel lens pattern, Fig. 6(a, b) shows the image capturing capability of the developed Fresnel lens.
Fig. 6. Image of the myopic ophthalmic lens superimposed on the Fresnel mold. (a) Lateral direction. (b) Coronal direction.
3.2 Replication of the flexible PDMS Fresnel lens
The replication of the polydimethylsiloxane (PDMS) Fresnel lens was accomplished using a Fresnel lens mold. Figure 7 shows the PDMS replication process of the Fresnel lens. PDMS was prepared by vigorously mixing the elastomer and curing agent (Slygard184, Dow Corning) in a 10:1 weight ratio. The resulting air bubbles were removed by placing the mixture in a vacuum desiccator for 30 min. PDMS was thereafter poured over the Fresnel lens mold. The mold was subsequently placed in a vacuum desiccator to remove air bubbles to prevent the emergence of pinholes in the subsequent curing process. Thereafter, the curing process of the PDMS Fresnel lens was performed at 90°C for 3 hours. Finally, the cured PDMS Fresnel lens was delaminated from the ultra-precision Fresnel lens mold.
4. Testing
4.1 MTF experimental setup
Figure 8(a) illustrates the setup used to evaluate the relative imaging performance of the Fresnel lens using a digital Basler USB 3.0 color camera. The camera was set in front of the lens and connected to a computer through a USB cable connector. Figure 8(b, c) represents the images captured using the Basler camera with and without the Fresnel lens. The background color of the image captured was adjusted from green to white.
Fig. 8. (a) Configuration to test the imaging performance of the replicated Fresnel lens. The object distance from the lens position was varied by 25 cm. (b, c) Images against USAF 1951 chart with and without Fresnel lens, respectively. Inset depicts the relative imaging performance of 89.1% based on the USAF 1951 resolution calculator.
Here, the distance x between the object and the lens was set to 25 cm to ensure near vision. Moreover, the distance between the camera and the Fresnel lens positions was fixed at 5 cm during the tests. However, the focus has been manually adjusted based on the lens of the Basler camera; therefore, it is probably not the best focus.
4.2 MTF experimental results
The maximum spatial resolution of an optical system can be determined by identifying the largest group and element pair of the non-distinguishable bars, both vertical and horizontal bars. In terms of the imaging object of the USAF 1951 chart in Fig. 8(b, c), the image capture clearly shows Element 1 in Group 3 at maximum resolution without the Fresnel lens, and the Fresnel lens image shows the limitation of Element 6 of Group 2. The image through the Fresnel lens demonstrated blur, but captured the resolution features of the USAF 1951 chart. Using the 1951 USAF resolution calculator [39], the equivalent image resolutions were found to be 8 lp/mm (Group 3, Element 1) and 7.13 lp/mm (Group 2, Element 6). This does not indicate the absolute resolution of the images. However, the Fresnel lens camera has a relative imaging performance of 89.1% (7.13 lp/mm to 8 lp/mm). A replicated IR Fresnel lens [14] has shown a low-range resolution against the modulation transfer function. Our experimental results confirm the proof of concept of Fresnel lens design and fabrication based on constant pitch and straight grooves.
4.3 Qualitative assessment
To conduct a qualitative assessment of the imaging quality of the lens, a Fresnel lens was attached to the goggles, as shown in Fig. 9. The object was captured at a distance of 25 cm. The blurred image was captured on the left side of the goggles, and few object details were identified with acceptable image quality. Additionally, there is an increase in the field of view of imaging. This characteristic of a flexible Fresnel lens can be useful for developing imaging systems with a wide field of view.
Fig. 9. Image of testing the Fresnel lens using goggles. (a) Flexible PDMS Fresnel lens. (b) Fresnel lens pattern cutting. (c) A photograph of the goggles with the Fresnel lens pattern attached only on the left side, taken at a distance of 25 cm under visible light.
5. Conclusion
To summarize, an optical-grade Fresnel lens surface was successfully realized using an ultra-precision machined mold with a diameter of 50 mm and a spherical radius of 250 mm. The MTF values improved with the decreasing pitch size; overall, the Fresnel lenses with curved grooves produced images with an improved resolution. Additionally, at extremely small pitch sizes, other design parameters of the Fresnel optical surface had a negligible effect on the imaging performance. The replicated flexible Fresnel lens can be utilized in a wide range of applications, including ophthalmic devices. The new Fresnel lens design is compatible with human perception sensitivity and overcomes the tool nose radius constraint of 5 µm and the limitation of the long trajectory associated with ultra-precision machining. The surface roughness was Ra 1 nm with a uniform pitch of 0.1 mm and straight grooves. In addition, the replicated Fresnel lens demonstrated object magnification and exhibited inherent blur characteristics. This shows that the flexible Fresnel lens has an imaging performance of 89.1% in comparison with cameras without the Fresnel lens. It demonstrates the potential capabilities of the Fresnel lens in ophthalmic devices.
Funding
Research funded by Hanbat National University (2020).
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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