Ultra-fast 3D printing of assembly—free complex optics with sub-nanometer surface quality at mesoscale

Complex-shaped optical lenses are of great interest in the areas of laser processing, machine vision, and optical communications. Traditionally, the processing of complex optical lenses is usually achieved by precision machining combined with post-grinding or polishing, which is expensive, labor-intensive and difficult in the processing of ultra-complex optical lenses. Additive manufacturing is an emerging technology that provides significant advantages in producing highly intricate optical devices. However, the layer-by-layer method employed in such manufacturing processes has resulted in low printing speeds, as well as limitations in surface quality. To address these challenges, we apply tomographic volumetric printing (TVP) in this work, which can realize the integrated printing of complex structural models without layering. By coordinating the TVP and the meniscus equilibrium post-curing methods, ultra-fast fabrication of complex-shaped lenses with sub-nanometric roughness has been achieved. A 2.5 mm high, outer diameter 9 mm spherical lens with a roughness value of RMS = 0.3340 nm is printed at a speed of 3.1 × 104 mm3 h−1. As a further demonstration, a complex-shaped fly-eye lens is fabricated without any part assembly. The designed spherical lens is mounted on a smartphone’s camera, and the precise alignments above the circuit board are captured. Upon further optimization, this new technology demonstrates the potential for rapid fabrication of ultra-smooth complex optical devices or systems.

The manufacturing efficiency of optical components, especially optical lenses, is usually determined by the printing speed and surface smoothness. Digital light processing (DLP) [9][10][11][12][13] which uses a single layer as the basic manufacturing unit is considered to be a more productive method for the fabrication of polymer lenses in comparison with dot printingbased two-photon polymerization [14,15], fused deposition modeling [16], direct ink writing [17], and stereolithography (SLA) [18]. However, most of the processing time is consumed in reapplying new light-curing resin to ensure uniformity between layers. The continuous liquid interface production (CLIP) process [19], which eliminates the time-consuming recoating step, offers an opportunity to increase manufacturing speed significantly. However, although CLIP dramatically increased the printing speed, the surface quality of optical lenses obtained is still constrained by the step effect. Therefore, the methods of mechanical oscillation assistance [10], grayscale polymerization method [12], post-coating [20], and meniscus equilibrium post-curing method [11,[21][22][23][24] have been developed for reducing the roughness of the surface down to the nanometer level. Among them, meniscus equilibrium post-curing method which requires no extra-facility is a convenient and effective way to improve the surface quality.
Tomographic volumetric printing (TVP) has several advantages for printing high-viscosity resin materials at ultrahigh speed. During the printing process, little relative motion is observed between the liquid resin and the manufactured object, which facilitates the accuracy of light dose delivery to the target space. Therefore, high-viscosity precursor materials can be used. The process guarantees a high surface quality of the surface while printing complex geometric structures in a single light pass. Furthermore, no sacrificial solid support structure is required since the 3D object is formed inside the viscous precursor material during printing. Given the unique advantages, TVP is desirable for fabricating complex optical devices. However, very few research results have been reported concerning the study of TVP in the optical manufacturing field.
In this work, we explore the viability of utilizing the TVP process further to improve the 3D printing speed of complex optical lenses. For a direct building of a centimeter-scale optical lens with sub-nanometer surface quality, the TVP technology first generates the lens structure in a few seconds. After extracting the manufactured object from the container, the resin film remaining on its surface is further cured to feature an ultra-smooth surface at the sub-nanometer scale. Fabrication of several examples of optical lenses will be illustrated about the advance of our developed process.

TVP system
The delivery of light dose is accomplished by irradiating the 2D light patterns into the rotating resin vial, as shown in figure 1(a). In TVP, each voxel in the target space has only two states-whether it reaches the gel point. A popular way to calculate the sets of TVP projection images is by using gradient-descent optimization algorithm [28], which is a better method to optimize the reconstructed optical dose. In our study, the TVP system primarily consists of a computer for processing control, a projector, a precision rotating stage, a charge coupled device (CCD) camera, a red light emitting diode (LED) and a cylindrical resin container. The specific model of the TVP hardware is detailed in section 5. To reduce the refraction of the light beam, we immersed the container in a rectangular tank containing the index-matching fluid, as shown in figure S1 of supplementary materials. Figure 1(a) illustrates that the serialized 2D light patterns are projected into the cylindrical container containing the mixed acrylic resin and photoinitiator (see details in section 5). The inset shows a frame of the projection. To observe the process of solidification of the target object, a red-light source illuminates the inside of the container during printing. The red-light source is orthogonal to the light from the projector, with the intersection point located at the center of the cylindrical container. Intensity spectra of the blue channels of the projector and red led are obtained using a spectrometer, as shown in figure S2. A CCD camera is used to observe the contents of the container.
At the beginning of printing, the liquid resin does not experience a cross-linking reaction after the brief stimulation of the projection light. The reason for this nonlinear solidification behavior in the target space is the presence of oxygen inhibition in the free radical polymerization process. The consumption of oxygen molecules by the radicals in the intended resin region is essential before photopolymerization can commence. Therefore, before photopolymerization occurs, the target region must absorb a minimum dose of light energy. After the accumulation of multi-angle projection doses, the target structure cures at once, as illustrated in figure 1(b) and movies S(1)-(2) of the supplementary materials.

Light dose calibration
In material systems for volumetric additive manufacturing, the concentration of the photoinitiator is a critical parameter. As an example, we used two acrylates polymerized via a free radical mechanism for printing. Specific material proportions can be seen in section 5. In the early period of printing, the activation of light leads to the production of free radicals that are rapidly suppressed and deactivated by oxygen, which is necessary to produce a 3D dose in a given space. It is important to note that in TVP process, the entire build volume must be processed through each light pattern for the object to be reconstructed accurately. This function sets the upper limit of the photoinitiator concentration. From the spectrophotometer measurements shown in figure 2(a), the absorbance value of the 3:1 BPAGDA/PEGDA mixture is pretty low at the peak illumination wavelength of 405 nm, which is sufficient for binary printing in our system. Lower absorption is more conducive to light penetration in the resin without the photoinitiator.
A high-viscosity resin is required to counteract the printed object's sedimentation. In TVP, the increase in density of the liquid resin after solidification leads to its settling in the resin tank. It also benefits the resolution of the print since the diffusion blur of the dose distribution is reduced. The viscosity of this polymer mixture was measured by a rheometer, as shown in figure 2(b). The viscosity is about 5.5 Pa·s in the range of shear strain rate 10 s −1 to 100 s −1 . Using the CCD camera observations, no significant precipitation (see figure  S3 and movies S(1)-(2) of supplementary materials) could be measured within the manufacturing time, indicating a negligible effect on the print resolution in our current setup. Figure 2(c) shows the adjustment of the induction period measured by using real-time Fourier transform infrared (FTIR) photorheology. The system solidifies when the storage modulus exceeds the loss modulus (G ′ > G ′′ ). The experiments were conducted at a light intensity of 7 mW cm −2 , and the gelation point corresponds to a time of approximately 45 s in our acrylic resin system. We further explored the effect of light intensity on the induction period. As shown in figure S4 of supplementary materials, with the increasing light intensity, the reaction gelation point time was accelerated along with a slight increase in the conversion rate of vinyl. As demonstrated in figure 2(d), the binary printing histogram primarily comprises two parts. 'In part' voxels (blue) inside the target space should exceed the dose corresponding to the gelation point. And 'Out of part' voxels (red), outside the target space, should remain in the liquid state. The projection sequence is optimized iteratively to maximize the separation between 'partial' and 'extra-partial' groups, which facilitates improved tolerance of imperfect optics and material [35].

Results and discussions
Binary printing satisfies the simultaneous curing of target points in space and has ultra-fast printing speed while ensuring a smooth surface. To verify that the TVP-printed samples have excellent surface quality, we printed the same model (Thorlabs, LA1472) using SLA, DLP, and TVP as shown in figures 3(a)-(c), under the same layer thickness (50 µm), respectively, with the printing parameters shown in table S1 of supplementary materials. TVP was performed in a highviscosity resin. The lower fluidity ensures that the sample is in suspension, thus avoiding the challenges of a printing process that requires support, as illustrated in figures 3(a)-(c). That is highly beneficial for printing optics, eliminating the limitation of damaging the surface of the optics during the removal of the support.
In addition, TVP has an absolute advantage in terms of printing speed. To quantify and compare printing times, we printed the above model, which has a volume of ≈ 128.6 mm 3 , then scaled down by 0.5× and up by 1.5× (volumes of ≈ 16.1 mm 3 and 434.1 mm 3 , respectively). All TVP-printed models were completed within almost the same printing time (50 s), and in SLA, the print time increased rapidly with the scale factor. In contrast, in the DLP process, the print time grows linearly with increasing build height, regardless of the area to be printed in every layer ( figure 3(d)). We compared the surface morphology using scanning electron microscopy (SEM) to characterize the same model printed with SLA, DLP, and TVP in figures 3(e)-(g). The apparent step effect can be found in figures 3(e) and (f), but not reflected in figures 3(g) and (h). The samples fabricated by TVP have excellent surface topography compared with the other two printing methods. However, we also noticed that the surface of the printed lens was damaged after cleaning, as shown in figure 3(g) and figure  S5(b) of supplementary materials. As a demonstration, the lens fabricated with TVP after meniscus coating shows excellent light transmission performance and enables a clear view of the background image shown in figure S5(a).
The 3D morphology of the TVP-printed lens was quantitatively characterized by a white light interferometer with a pixel size of 0.19 nm. The results tested from the TVP-printed lens combined with the meniscus equilibrium post-curing method are shown in figures 4(a)-(g). Using the 50× objective lens of the white light interferometer, a randomly selected area over the vertex shown in figure 4(a) was used to compute the surface roughness. Figures 4(b) and (c) illustrate the enlarged forms of the two regions of the center (Region I) and the edge (Region II) extracted from figure 4(a). In figures 4(d) and (e), by statistical analysis, root mean square roughness (RMS) and the mean roughness (Sa) values at the center region I were found to be 0.3340 nm and 0.4898 nm, respectively. The corresponding values in edge region II were 0.4096 nm and 0.5372 nm, which are considerably smaller compared to the wavelength of visible light, indicating that TVP process can produce optical devices with excellent surface quality when combined with the meniscus equilibrium post-curing method. In addition, the cross-sectional profiles in figures 4(f) and (g) extracted from figures 4(d) and (e) show a variation within ±4 nm without special features, which is very well suited for optical applications.
To demonstrate the significance of utilizing the meniscus equilibrium post-curing method to improve the surface finish of lenses manufactured through the TVP process, we removed the resin liquid film with isopropyl alcohol and characterized its surface quality. The cleaned surface is significantly rougher, as illustrated in figures 4(h)-(j).  satisfy the strict λ/20 criterion. To verify the print versatility of the meniscus equilibrium post-curing method combined with TVP in optical devices, the same sphere lens was also printed using another resin (see the details in section 5). As shown in figure S6 of supplementary materials, the values of two roughness parameters, RMS and Sa, were obtained through statistical analysis as RMS = 0.3340 nm and Sa = 0.5199 nm, suggesting the meniscus equilibrium effect well-smoothed surface topography. It was noticed that the the resin film remaining on TVP-printed lens did not fully post-cure. After extracting the target structure from the resin, the photoinitiator is almost consumed in the resin film, making it difficult to perform a fully post-cured treatment.
In conclusion, the results obtained were listed in table S2 of supplementary materials and three other cases of 3D printing using projection stereolithography printing. Energy modulation using the volumetric method has a definite advantage in printing speed. However, the single-angle volumetric energy modulation [21] necessitates a support structure to house the printed lens. In our work, multi-angle projection (figure S7) in a high-viscosity resin for light dose delivery can generate the target body simultaneously after reaching the energy threshold, as shown in figure S8. Furthermore, the layerwise approach and TVP process make it easier to control the printing shape. However, the layer-based printing method inevitably has a step effect, which requires additional complex processes to eliminate the step effect (supplementary table S3). Since TVP prints all the basic points of the entity at the same time, there is no step effect as shown in figures 3(g) and (h).
Other complicated lenses (figures 5(a)-(c)) and a lens set (figure 5(d)) were also printed using the TVP process. As shown in figure 5(e), we used a simple setup to test the functional properties of the TVP-printed lens. As illustrated in figure 5(f), without a 3D printing lens, the light from the green laser pointer displayed a dot on the wall. Figure 5(g) shows the results after the laser passes through the y-direction in figure 5(a). The spot diameter changes significantly after the beam passes through the biconvex lens. More interestingly, as the beam passes along the Z-direction in figure 5(c), the wall shows enlarged light and dark streaks, indicating the fly-eye lens with a wide-angle field of view ( figure 5(h)). This suggests that the optics fabricated by TVP combined with the meniscus equilibrium post-curing method can be more functional with a different design. To investigate the dimensional accuracy acquired by the TVP, we have designed several standard structures to compare the geometric measurements of the printed parts with the CAD models, as illustrated in figure S9(a). Figure S9(b) shows the geometric dimensions of the printed samples (3:1 BPAGDA/PEGDA) deviate from the design values by about 2.2% to 8.0%.
Upon successfully validating the improved surface quality of the TVP-printed lens in combination with the meniscus equilibrium post-curing method, we further explored TVP's ability to customize imaging lenses, using a spherical lens as a representative example. As shown in figure S10, the cured part shows an excellent transmittance of nearly 90% in the visible range measured by a UV-vis spectrophotometer. Figure S11 illustrates the refractive index values (N) of the photopolymerized acrylate resin at different wavelengths, which were measured using a spectroscopic ellipsometer. The geometry and optical properties of a typical spherical lens were designed and optimized in Zemax using a complex refractive index as input. The insert in figure S11 of supplementary materials illustrates optical simulation of the imaging properties for the optimized design of the spherical lens.
To demonstrate the optical property of the TVP-printed lens, an experimental setup in figure 6(a) used a resolution test target (GCG-020601, Daheng New Epoch Technology, Inc.) which has eight groups of patterns from 0 to +7. Figure 6(b) shows the target image captured by the CCD. Figure 6(c) shows that the bars in element 6 of group 3 can be seen. The TVP-printed spherical lens was attached to a smartphone, shown in figure 6(d), for a quick demonstration. Figure 6(e) shows an image of the surface of the Arduino Mega 2560 taken through a smartphone without using the printed lens. Two magnified images of the surface of the Arduino Mega 2560 were captured through the smartphone by using a spherical lens, as shown in figures 6(f) and (g). We can visualize the component type in focus and the line with a width of 500 µm. Here, we employed a coordinate line as an object shown in figure 6(i). The fabricated fly-eye lens was directly mounted onto a smartphone shown in figure 6(h), and we found that magnified object image was observed in figure 6(j). The imaging magnification was due to the function of a convex lens for magnified imaging, and the formation of two blurred coordinate lines showed that we could get the image from the ommatidium, which had been reported in the earlier studies [36,37]. The testing results confirmed that the TVP-printed lens could be effectively utilized in commercial smartphones to deliver high-quality images.

Conclusion
In this work, we have combined the meniscus equilibration post-curing method with the TVP process to reduce surface roughness of manufactured object to the nanometer level while maintaining high manufacturing speeds. The entire object was polymerized in a single step under the irradiation of a series of modulated UV light patterns. As a demonstration, centimeterscale spherical and complex lenses were printed directly in less than one minute. The spherical lens was printed at the speed of 3.1 × 10 4 mm 3 h −1 with an average roughness of RMS = 0.3340 nm. The printed components deviate from the design values by 2.2% to 8.0%. Mounting the TVP-printed lens directly onto the smartphone's rear camera and capturing a sharp picture of the Arduino Mega 2560 demonstrates the practicality of using TVP-printed lenses for optical imaging. The current design of the TVP printing technique is only feasible for high-viscosity materials, which can be dragged to rotate at almost the same speed as the motor. This limits the promotion of the printing speed threshold. Furthermore, applying a meniscus liquid film adhering to the printed surface is relied on oxygen-induced polymerization inhibition and causes incomplete curing of the printed 3D part. Process improvements should be further studied for higher speed, multi-material applications. In summary, the work presented in this paper shows the potential of TVP technology for applications in the optical field. It is predicted that TVP will become a powerful technology in fabricating complex optical devices.

Preparation of photocurable resin
The photocurable resin is prepared by mixing bisphenol A glycerolate (1 glycerol/phenol) diacrylate (refractive index = 1.557) and poly(ethylene glycol) diacrylate (refractive index = 1.463, average Mn = 250) at a mass ratio of 3:1. Camphorquinone (CQ) was used as the photoinitiator with a mass fraction of one-thousandth of the above-mixed resin. Ethyl 4-dimethylaminobenzoate (EDAB) of comparable mass to CQ was used as a co-initiator. These chemicals were purchased from Sigma-Aldrich (Shanghai) Trading Co., Ltd and can be used directly without further purification. In addition, an alternative alphatic urethane acrylate resin (WDS-3532) purchased from Wuxi Boqiang Polymer materials science and technology CO., Ltd with a viscosity range of 1.2-3.6 Pa·s was used to fabricate the sphere lens. To limit the attenuation of the optical path in the resin, the mass of CQ and EDAB is one-thousandth of the total mass, respectively. Figure 1(a) shows the hardware system design in this study. The process of TVP of complex-shaped lens was carried out using a DLP projector ((PRO4500, Wintech, China) with an optical lens (f = 150 mm). The UV projector was capable of providing a maximal projection area of 96 mm × 54 mm and a light intensity range of 0-34.7 mW cm −2 . The printing process (movies S(1)-(2) of supplementary materials) is captured via a CCD camera (MER2-503-36U3C, Daheng New Epoch Technology, Inc.) in the arrangement shown in figure 1. A 21 mm diameter cylindrical vial containing photosensitive resin was mounted to a motorized rotation stage (URS50BCC, Newport) with a custom-designed vial holder. A large rectangular vat containing the index-matching solution is outside the cylindrical vial. The wall of the vat is perpendicular to the incident beam.

TVP post-treatment
After printing, to reduce the viscosity of uncured material, the vials containing the uncured material and cured part were heated in a water bath at 60 • C for 10-20 s. After extracting the manufactured object from the resin container, the resin film remaining on its surface because of the wetting and capillary phenomena. The prints were subjected to post-curing using 405 nm light within a Formlabs Form Cure machine at a temperature of 60 • C for 20 min.

Characterization
The viscosity of the mixed acrylic resin solutions were characterized by a rheometer (HAAKE MARS, America) at room temperature. The absorption spectrum of the monomer and the transmission spectrum of the cured parts were recorded using a UV-vis spectrophotometer (UV1800, Shimadzu, Japan). As shown in figure S4, real-time FTIR rheological analysis was carried out under 405 nm light irradiation using a device combining rheometer (HAAKE MARS60, ThermoFisher) and ATR-FTIR (Nicolet iS10 series, ThermoFisher). A spectroscopic ellipsometer (ME-L, Wuhan Eoptics Technology Co., Ltd, China) measured the wavelength-dependent refractive index. The surface morphology of three 3D printed lenses was investigated using SEM (Sigma 300, ZEISS, Germany). An optical surface profiler based on white light interferometry (ER230, Atometrics, China) was utilized to catch the 3D morphology of the TVP-printed lens. Measurements were made with a 50x objective lens (Nikon 50x Mirau) to obtain the surface morphology.