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Abstract
In this work, we present the methods of fabrication and characterization of biconvex spherical and aspherical lenses with 25 and 50 mm diameters that have been created via additive technology using a Formlabs Form 3 stereolithography 3D printer. After the prototypes are postprocessed, fabrication errors $\le\! 2.47{\rm{\%}}$ for the radius of curvature, the optical power, and the focal length are obtained. We show eye fundus images captured with an indirect ophthalmoscope using the printed biconvex aspherical prototypes, proving the functionality of both the fabricated lenses and the proposed method, which is fast and low-cost.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
Recently, advances in the manufacturing industry using 3D technology have been progressing more and more each time, so this technology is becoming an affordable alternative for the fabrication of prototypes and components in the scientific, technological, and medical areas [1–15]. For example, in medicine, additive technology is being used for the fabrication of orthotics and prosthetics, reducing costs from thousands to hundreds of dollars [7–9]. In the automotive industry, 3D printing is changing the logistics of prototype fabrication, which can be scaled and customized, allowing designers to make a great variety of designs and reach the maximum performance of the car parts that they want to fabricate [16–18]. In optical fabrication, the use of 3D printing enables the design and fabrication of optical lenses, such as spherical lenses with diameters $\le {25.4}\;{\rm{mm}}$ [19–21], aspherical lenses with diameters $\le {{3}}\;{\rm{mm}}$ [22,23], and freeform lenses with diameters $\le {{3}}\;{\rm{mm}}$ [24–26]. Much smoother surfaces for improved imaging resolution can be printed in a customized micro-stereolithography printer combined with grayscale photopolymerization, allowing for colorful fine details in images [22]. The design and fabrication of lenses using a custom optics 3D inkjet printer for irradiance distribution and imaging quality were developed by Assefa et al. [24,25,27]. Spin coating and glass curing methods for the final finish of spherical surfaces printed in a Form 2 commercial lithographic printer (Formlabs) were presented by Berglund and Tkaczyk [28]. As can be seen, the use of 3D printing in the optics field is becoming more common because it allows for the easy manufacturing of optical components for instruments, reducing fabrication times, weight, and cost. However, it is worth mentioning that until this moment, the works reported in the literature have fabricated components with dimensions of only a few millimeters ($\le \!{12.7}\;{\rm{mm}}$); thus, in most cases, additional postprocessing to reach the design parameters is not necessary, but it is when larger surfaces are fabricated, as shown in this work. In our case, additional postprocessing is carried out to eliminate print stretch marks and obtain smoother and clearer surfaces. Before we can obtain surfaces that meet the design parameters, fabrication and characterization processes must be established, and it is for all these reasons that, in this work, we present fabrication and characterization methods for biconvex spherical and aspherical lenses with diameters of 25 mm and 50 mm printed in a Formlabs Form 3 stereolithography 3D printer, and then ground and polished by hand. The work is organized as follows: a brief introduction about the importance that additive manufacturing has reached in recent days in optical fabrication has been presented in Section 1; the methods of fabrication and characterization are described in Section 2; the results and application of the fabricated lenses are shown in Section 3; and, finally, Section 4 presents the conclusions and final comments.
2. MANUFACTURING PROCESS
In this section, we describe the steps of the fabrication process for lenses printed in a Form 3 printer using Clear Resin (Formlabs). In a previous work [29], we described the printer’s printing parameters as the radius of curvature, thickness, roundness, and angles, as well as the refractive index and the absorbance and transmittance of the resin. The fabrication error for the radius of curvature was $\le {1.5}\%$ for convex surfaces and $\le {{2}}\%$ for concave surfaces; for thickness, it was $\le {0.52}\%$; for roundness, $\le {0.67}\%$; and for the angles, ${\lt}{{2}}\%$. The measured values for the resin included 1.505 for the refractive index and a transmittance for the UV (330–400 nm), visible (400–700 nm), and IR (700–1020 nm) of 50.93%, 81.23%, and 93.50%, respectively.
Considering all these parameters, we define the steps of the fabrication protocol for printing biconvex lenses with diameters $\ge {{25}}\;{\rm{mm}}$ as follows: (1) the design, (2) the printing, and (3) the postprocessing. For the prototype design, we used Zemax OpticStudio and Autodesk AutoCAD software; however, any computer-aided design software for generating an “.STL” file can be used. When the design file is finished, is sent to the 3D printer to start the printing process. Depending on the printer model, some printing parameters can be modified, such as orientation, layer thickness, supports, rotation, etc., in order to improve the prototype finish and/or reduce the printing time. It is important to mention that varying these parameters can improve or worsen the prototype finish; in our case, the samples were printed with a layer thickness of 25 µm, and to avoid layer errors in the final sample, a rotation angle of 35º was set. Additionally, supports were generated at the edges of the sample in such a way that the printer did not create stretch marks at its center, to avoid damaging the images we wanted to generate with these prototypes. When all these parameters have been set and saved in the printer software, the printing process starts. The waiting time depends on the samples’ size and complexity, as well as the input printing parameters; in our case the fabrication time was ${\sim}{{2}}\;{\rm{h}}$ per inch of diameter. The final step of the fabrication process is the postprocessing of the printed samples, which consists of an isopropyl alcohol (IPA) bath and a post-curing of the samples that are made, to eliminate the resin waste that remains on the surface and to maximize the properties of the material, respectively. In our case, the times for alcohol bath and the post-curing of the samples were 10 min for the IPA bath and 15 min to 60°C for the post-curing of the sample. When the three steps of the fabrication process were finished, the prototypes that we obtained were not smooth and transparent; therefore, we decided to add two more steps to the protocol: the grind and polish of the two surfaces of the prototype. The grind and polish of the prototype were done completely by hand in 5 min steps for each with micro-graded wet/dry polishing paper. For the grind, we used three-stage filtered water and 30 µm silicon carbide micro-graded polishing paper, while for the polish we used three-stage filtered water and 15, 9, 3, 2, and 1 µm aluminum oxide micro-graded polishing paper. In the next section, we show the results we obtained during the fabrication process.
3. OPTICAL PERFORMANCE
We fabricated one biconvex spherical lens prototype and three biconvex aspherical lenses prototypes to prove the functionality of the proposed method. The design of the spherical prototype was the same as the Thorlabs LB1761-A commercial glass lens, to which we made a direct comparison. To validate the biconvex aspherical lenses prototypes, we compared the design with the experimental parameters measured at the laboratory (radius of curvature, conic constant, focal length, thickness, and diameter). Next, we give the design parameters and the results obtained for each prototype.
A. Biconvex Spherical Lens Prototype
The design parameters for the biconvex spherical lens prototype were 25.4 mm diameter, 25.4 mm focal length, 24.5 mm radius of curvature for both surfaces, and 9 mm thickness. In Fig. 1 are some images of the biconvex spherical prototype’s postprocessing, post-curing, grinding, and polishing steps. Note the great difference that exists between the post-curing spherical prototype [Fig. 1(a)] and the finished spherical prototype [Fig. 1(e)]. When the prototype comes out of the post-curing step, it is completely opaque and some printing stretch marks can be observed on the surface, while after the grinding and polishing steps, a completely transparent and smooth surface is obtained.
Fig. 1. Biconvex spherical lens prototype: (a) post-curing, 15 min to 60 °C; (b) 30 µm silicon carbide grinding; (c) 15 µm, (d) 9 µm, and (e) 1 µm aluminum oxide grinding.
Figure 2 shows a comparison of the design and the experimental radius of curvature for the two surfaces of this spherical prototype. The experimental diameter and thickness were 25.38 mm and 9.91 mm, respectively, with a maximum percentage error of 0.7%.
Figure 3 shows a visual comparison of the Thorlabs LB1761-A commercial lens and the biconvex spherical lens prototype fabricated using our protocol. As can be easily seen in Fig. 3, the images obtained with the Thorlabs lens and the prototype are very similar; you can only observe a small difference in magnification between the two images.
Fig. 3. Visual comparison of (a) the Thorlabs LB1761-A lens and (b) the biconvex spherical lens prototype.
Fig. 4. Analysis of resolution using the 1951 USAF resolution target: (a) the Thorlabs LB1761-A lens, (b) the biconvex spherical lens prototype.
Figure 4 shows our analysis of the resolution of both lenses using a standard USAF 1951 resolution target and an Edmund Optics OE-18112 18.1 megapixel camera. In the intensity graphs in Fig. 4, you can easily see that the images formed by the Thorlabs lens have a slightly greater contrast than the images formed by the biconvex spherical lens prototype at the central part of the images. For the Thorlabs lens, the maximum resolution obtained was 64 lpi, since the bars of group 6, element 1, can be perceived [Fig. 3(a)]. On the other hand, for the spherical lens prototype, the maximum resolution obtained was 50.8 lpi, since the bars of group 5, element 6, can be perceived [Fig. 3(b)]. These results prove what we visually noted in the above figures: the images formed by the Thorlabs lens have a slightly greater contrast than the images formed by the biconvex spherical lens prototype. Nevertheless, this analysis of resolution demonstrates the good performance of the printed lens, and therefore we can say that the resolution of both lenses is comparable.
Because of the good results obtained with the biconvex spherical lens prototype, we decided to increase the difficulty of the problem. Thus, we designed, fabricated, and tested aspherical lenses, which are very challenging to fabricate due to the complexity of their surface shape. The results obtained in our analysis are shown in the next section.
B. Biconvex Aspherical Lens Prototypes
To demonstrate the printer’s ability to print complex optical elements, we designed three biconvex aspherical lenses for the construction of an indirect ophthalmoscope at a low cost. The lenses’ characteristics were as follows: prototype 1, lens diameter 50 mm and 20D optical power; prototype 2, lens diameter 42 mm and 20D optical power; and prototype 3, lens diameter 42 mm and 30D optical power. The radius of curvature and the conic constant obtained from the optimization are shown in Table 1, and the refractive index of the resin was $n = {1.505}$. These prototypes were designed in Zemax OpticStudio based on the Arizona eye model described by Schwiegerling [30], with a stop diameter of 6 mm, considering that the instrument works as a mydriatic fondus camera [31].
Table 1. Radius of Curvature and Conic Constant of the Biconvex Aspherical Lenses
These three prototypes were fabricated following the protocol described in Section 2; to characterize them, we measured the profile of each lens surface. For this, we used a 12.7 mm max range Mitutoyo ABSOLUTE Digimatic indicator ID-S, with 1 µm resolution and a needle point stainless steel rod with R = 0.2 mm.
After the lenses’ profiles were measured, the discrete data were fitted to the conics equation [Eq. (1)] to obtain the radius of curvature ($r$) and the conic constant ($k$) for each of the printed prototypes:
The percentage error shows a varied behavior between the surfaces; as was mentioned before, this is due to the manual postprocessing of the prototypes. Regardless of these variations, we proved that it is possible to fabricate biconvex aspherical lenses with a percentage error of $\le {2.47}\%$ for the radius of curvature. It is worth mentioning that the smallest error was 0.93%, for prototype 3.
Figure 6 shows the comparison of the design and experimental conic constants and the percentage error of each prototype. In Fig. 6, we can see that the greatest error for the conic constant was 6.58%, for prototype 2, but we can also note that for this prototype the percentage error for the radius of curvature was 1.78%. The smallest error for the conic constant was 1.04%, for prototype 1.
Table 2 shows the design and experimental diameter and thickness of each prototype.
Note that the diameter and thickness errors are below 0.4%, replicating the data obtained in [29]. Table 3 shows the design data for the optical power and focal length of each prototype.
Table 2. Diameters and Thickness: Design versus Experimental Data
Table 3. Optical Power and Focal Length Prescription
Figure 7 shows the graphs for the optical power, the differences, and the percentage error for the design and the experimental data.
We can see that the percentage error for the optical power is small, at $\le {1.33}\%$.
In Fig. 8, the graphs of the focal length for the design and experimental data, the differences, and the percentage error of these values are shown. As can be seen in these graphs, the percentage error for the effective focal length (EFL) is also small, at $\le {1.31}\%$, while the percentage error for the back focal length (BFL) is $\le {1.41}\%$ (Fig. 9).
It is clear that the lenses’ performance is affected very little by the errors in the fabrication of the conic constant, as the optical power and the focal length measured experimentally are very close to the design parameters. It is worth mentioning that the similarity between the design and the experimental data is fulfilled for all the prototypes, and thus we can say that all the fabricated lenses have good performance, proving that the proposed method is effective for the fabrication of biconvex aspherical lenses with diameters $\le {{50}}\;{\rm{mm}}$. Figure 10 shows the good finish we obtained with our fabrication method for the biconvex aspherical lens prototypes.
To prove the functionality and image quality of the prototypes, these lenses were mounted on an indirect ophthalmoscope to capture eye fundus images of a patient with a dilated pupil. For the patient’s examination, the ophthalmologist records a video of the patient’s retina with the ophthalmoscope, which is mounted on a cellphone. The optical power and diameter of the prototypes are two parameters that determine both the distance of separation between the instrument and the patient’s eye and the observation field over the retina. The illumination in this arrangement is provided by the cellphone’s LED light, which must be placed at the eye’s entrance pupil to produce homogeneous illumination over the retina [31]. Figure 11 shows preliminary images taken from a video that was recorded during the eye fundus imaging; each frame was captured at a different time and position of the instrument with respect to the patient.
In these images, we can observe the optic nerve, the macula, and the fovea of the patient, which demonstrates that the biconvex aspherical lenses fabricated with our method can be used for eye fundus imaging with an indirect ophthalmoscope that has both good quality and a low cost. Hence, we suggest that our biconvex aspherical prototypes could be used in applications such as illumination or other areas where the image quality requirements are within the values we obtained.
4. CONCLUSION
We presented the method of fabrication and characterization of biconvex spherical and aspherical lenses with diameters of 25 mm and 50 mm fabricated with additive technology using a Formlabs Form 3 3D printer. After the prototypes were postprocessed, smooth and transparent lenses with fabrication errors of $\le 2.47{\rm{\% \;}}$ were obtained. For the biconvex spherical lens prototype, the maximum resolution obtained was 50.8 lpi, proving its good image quality. For the biconvex aspherical lens prototypes, the greatest percentage errors were $\le {2.47}\%$ for the radius of curvature, $\le {6.58}\%$ for the conic constant, $\le {1.33}\%$ for the optical power, $\le {1.31}\%$ for the EFL, and $\le {1.41}\%$ for the BFL. We observed that the performance of the aspherical prototypes was affected very little by the errors in the fabrication of the conic constant, as the optical power and the focal length measured were very close to the design parameters. We obtained eye fundus images with an indirect ophthalmoscope using the printed aspherical prototypes and proved that the optic nerve, the macula, and the fovea of a patient with a dilated pupil could be observed, demonstrating the functionality of both the fabricated lenses and the proposed method of fabrication.
Comparing our method and molding or glass curing methods of lens production, the fabrication or purchase of additional elements such as molds and glass is not necessary with our method, and therefore fabrication times and costs are considerably reduced. Also, with our method, different lenses with complex shapes can be fabricated simultaneously, while with molding or curing methods only one lens can be obtained at a time.
Funding
Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México (IT100321); Consejo Nacional de Ciencia y Tecnología.
Acknowledgment
The authors of this paper are indebted to Mariana Cervantes Macías and Daniel Paniagua Herrera for their help in obtaining the eye fundus images. Dulce Gonzalez-Utrera acknowledges the grant from the CONACyT Estancias Posdoctorales por México at ICAT, UNAM, working under the supervision of Daniel Aguirre-Aguirre.
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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