Gravitational Effects on Optical Lens Fabrication: First Insides on Earth- and Microgravity Experiments

Almost every production process is influenced by gravity. We are accustomed to adjusting processes to Earth’s environment, but, e.g., gravity changes significantly when going to space. However, independent of space, processes used on Earth are generally affected by gravity. In-space manufacturing (ISM) presents revolutionary opportunities for producing parts in space. A key advantage is to manufacture on-site to reduce the high transportation costs. Another advantage is the novel variety of materials available, as well as the conditions with very low gravity are advantageous for surface roughness and geometrical stability of components [1]. This holds promise for more cost-effective manufacturing and the creation of large-scale or intricate structures that may be challenging to produce on Earth. A cost-effective alternative to flights into space is offered by drop towers, which can create a microgravity (⁠$μ$g) condition on Earth for a limited period of time. Using the Einstein-Elevator, the first third-generation drop tower in operation, in which the gondola with the experimental setup inside is accelerated by a linear drive (first: pure vacuum tubes/shafts, second: vacuum tube/shaft with catapult), it is feasible for the first time to investigate the influence of gravity on new production processes efficiently and with quick access [2,3]. The 40 m high facility with a drop height of 20 m enables the subjection of large experimental setups (⁠$Ø1.7$ m, 2 m height, 1,000 kg) to both microgravity and various partial gravitational forces in the range of 0.1–1 $g$ [4]. The structure of the Einstein-Elevator is illustrated in Fig. 1 and the experimental setup on the experiment carrier in Fig. 4. The synergy between ISM and utilizing low gravity opens up new frontiers for space research and development.

Traditional fabrication of lenses relies upon precise techniques such as grinding and polishing of glass or polymer substrates. These processes require specialized craftsmanship and advanced machinery to achieve the desired optical properties. By selectively modifying the material surface, light rays are refracted, reflected, or diffracted to produce the desired optical effects. In the PhoenixD Cluster of Excellence, scientists from various disciplines, such as physics, chemistry, and engineering, collaborate to explore novel, cost-effective manufacturing processes for integrated optics. Integration of lenses into photonic components requires a high level of production effort regarding surface roughness, roundness, and precision during assembly. In addition, adapting the properties in small batches or for individual production is only economically feasible to a limited extent. Nowadays, lenses can also be created directly on component ends by dispensing, for example. However, the possibilities of adapting the radii of curvature are only possible with additional effort via conditioning lines or adapted surface roughness.

Kamal et al. have previously shown the manufacturing process and design of a portable imaging system. In this regard, silicone lenses produced using a dispenser are compared with commercial lenses in terms of their surface characteristics, revealing that the root mean square (RMS) value of surface roughness can be reduced by a factor of approximately five [5]. Additionally, Sun et al. have studied microlenses and arrays derived from them. This work demonstrated the cost-effectiveness of this manufacturing method and highlighted the ability to control droplet size by tuning forming parameters [6]. Technical applications for such arrays of dispensed lenses have been elucidated by Yu et al., where an array of many individual dispensed lenses was employed to increase the conversion efficiency and power generation of solar cells by 4.82% [7]. Regarding the contact angle depending on gravity over 1 g, experiments have been conducted by Liu et al. [8]. It was observed during dynamic visual monitoring in a centrifuge with a diameter of 6 m that the contact angle of a water droplet on various substrates continuously decreases between 1 and 8 g. In this case, the droplet is not solidified; it remains in a liquid state.

To the best of our knowledge, the effect or variation of gravity during the fabrication process, including dispensing and curing of integrated optical components, has only been carried out in small numbers on the International Space Station (ISS) for macroscopic freestanding lenses under microgravity [9]. Thus far, investigations into additive manufacturing processes in the Einstein-Elevator regarding the influence of gravity below Earth gravity (< 1 g) have been conducted [10,11] and are now being transferred to the production of optical components.

Therefore, the aim of this research is to examine the adaptation of lenses, including the height and contact angle between carrier substrate and fluid, during the manufacturing process with the aid of gravity. For this purpose, a photopolymer is to be applied to a substrate under specially defined gravitational conditions using a jet dispenser and polymerized using a UV lamp. A robust camera system is used for detailed process observation. In order to be able to carry out statistical tests on the manufactured lenses under a specific gravitational environment, a movable substrate holder is provided using a linear axis. By using the Einstein-Elevator for the variation of gravity during a manufacturing process, this fundamental parameter can be researched in detail for the first time. A geometric characterization of the manufactured lenses is conducted using contact angle measurements, confocal microscopy, and scanning electron microscopy (SEM). In the future, this will enable the integration and adaptation of lenses on conventional photonic components individually and more economically, e.g., for integrated lenses on fiber ends, to eliminate complex alignment processes.

In drop morphology, a distinction is made between pendant and sessile drops, as different forces act on them depending on their position in relation to the surface. Due to the manufacturing process of our lenses under variable gravitational conditions, only sessile drops are considered in more detail below. Sessile drops are placed on a surface and, as shown in Fig. 2, are pushed toward the solid substrate by gravity. The visible and measurable effect of gravity correlates with the volume of the drop. The larger and heavier the droplets, the more influence gravity has on the morphology of the droplets.

Under Earth-like conditions, the capillary length is in the order of a few millimeters, but can be drastically changed by varying the engraving environment. To increase $κ−1$ by a factor of 10 to 1,000, it is necessary to work in an environment with microgravity, as density and surface tension cannot be varied to the same extent.

Equation (3) clearly shows that $hr∝g−1/2$ and thus the maximum height is inversely proportional to gravity, which theoretically describes the previously mentioned deformation to smaller heights with increasing gravity.

However, the edge areas of the drop cannot be described using this equation, as the forces there are not horizontal to each other. For a detailed description, a differential equation must be solved. Additionally, boundary effects occur, which cannot be described with sufficient accuracy by this solution. For a more precise description of the interface, the three-region model from Fig. 3 was developed. This consists of an outer capillary region dominated by capillarity and gravity, an inner molecular region where molecular interactions give rise to disjoining pressure and spatially varying interfacial free energies, and a transition region where surface tension is assumed constant. It is in the transition region where disjoining pressure competes with hydrostatic pressure, film curvature is negligible, and the vapor–liquid interface is almost linear. The interaction of these regions, including an analytical solution for the shape of the vapor–liquid interface, was explained in more detail by Elena Diaz et al. [14] and further experimentally investigated by Liu et al. [15] using hypergravity. They showed that the measured contact angle $θ$ varies with gravity, which contradicts the theory. An explanation for the decrease in $θ$ with increasing gravity was provided using the established three-region model because the measured apparent contact angle $θ$ differs from the actual contact angle $θ0$⁠. The angle is rather the angle of inclination of the liquid–vapor interface away from the solid surface (see Fig. 3). Accordingly, the measured contact angle depends on the resolution of the measuring system for optical measuring methods.

Finally, the description of drop morphology is the subject of current research, both in the field of hypergravity and microgravity, in order to describe and predict the influence of gravity more precisely. Especially in the field of microgravity, the limitation so far has been the generation of the environment/accessibility. Classical drop towers, parabolic flights, or suborbital flights allowed only little statistics and successive improvements of the measurement system so that discrepancies between the respective results cannot yet be conclusively explained.

For the fabrication of lenses under adjustable gravity conditions, it is first necessary to develop and build an experimental setup that is compatible with the corresponding microgravity device, in this case, the Einstein-Elevator. The Einstein-Elevator offers many advantages for the rapid integration of small to medium-sized experiments. The system provides a number of essential interfaces and media, thus reducing the effort required to fly a fully functional experiment. But even if the Einstein-Elevator already provides some interfaces, such as a power supply, communication with the experiment, and trigger signals, the experimental setup still has to be automated. This enables rapid repetition of the experiment and, therefore, statistical analysis in a short time.

This paper presents a dispensing process for the production of polymer lenses in different gravity environments (⁠$μ$g and 1 g). The dispensed polymer is jet-dispensed on a glass substrate carrier and then cured by a UV lamp. The dispensing and curing procedure is remotely monitored by a camera to check functionality during the flights within the Einstein-Elevator. The therefore developed setup is shown in Fig. 4. This paper focuses exclusively on comparing the differences between microgravity and Earth gravity. But future experiments in, e.g., lunar and Martian gravity are already being planned to specifically evaluate the effects of different gravitational environments on the manufacturing of polymer lenses.

A key component of the considered process is the dispenser system. Here, the jet dispenser TS9800-TT15-H by TECHCON is used. It consists of the jet valve and the corresponding controller. The jet valve has an ultra-fast piezo actuator, which enables it to dispense with up to 1,500 Hz maximum burst and very small shot volumes of 0.5 nl. During the conducted experiments, a tappet with a size of 0.7 mm and a nozzle with a diameter of 400 $μ$m were used. The controller is parameterized by the experiment control system and sets the process parameters for the jet valve. In this case, six different parameters have to be controlled: rise time, open time, fall time, nozzle lift, temperature, and pressure.

The material used is OrmoComp^® by microresist technology, a transparent polymer that cures under UV light and which is commonly used for microlenses, microlens array, and micro-optical components based on advanced design concepts. It has excellent transparency properties from visible and near UV spectrum down to 350 nm, is extremely thermally stable (up to 300 $∘$C), and has a high mechanical strength of the cured material. A special feature is the very fast UV curing (500–1,500 mJ/cm²), which is important due to the short microgravity phases of 4 s in the Einstein-Elevator.

To cure the polymer, a precisely controllable UV lamp is used. It is important that at least the outer shape of the lenses solidifies during flight before braking. During braking, up to 5 g are applied to the whole setup, including the produced lenses. Here, a bluepoint light-emitting diode (LED) eco UV lamp system by Hönle is used. It can deliver a maximum UV-A intensity of up to 20,000 mW/cm². The LED power is adjustable in 1% steps (between 10% and 100%), and the irradiation time can be controlled between 0.01 and 9,999 s. All process parameters are set by the experiment control system automatically.

The lenses are dispensed on standard glass substrate carrier (currently without special properties like hydrophobia, but foreseen in future experiments). To be able to produce several samples in succession more quickly, the substrate carrier is mounted on a plate on top of a controllable axis. The axis moves the substrate carrier to create distances between the lenses of 5 mm. This allows the production of 12 lenses without direct access to the experimental setup. In addition to saving time, this is necessary due to the avoidance of dust ingress and the influence of ambient conditions.

The dispenser, the UV lamp, the axis as well as the camera to monitor the dispensing process during flight and the pneumatic system are connected to the experiment control system. It consists of an industrial PC with connected input and output terminals and serial interfaces. Currently, the only manual adjustment in the experimental setup is the pressure control to provide for the dispenser needed and reduced air pressure, which is stored in the pressure tank for several dispensing processes and flights. But with all the other actuators and sensors connected to the experiment control system, automatic executions are enabled. The industrial PC is also linked to the control room to provide parameter changes when needed. The whole setup is mounted on a special experiment carrier level with an overall size of $800×800×400$ mm and a total weight of 290 kg.

The experimental setup described above in Sec. 3.1 is mounted on the experiment carrier of the Einstein-Elevator. In addition to the mechanical attachment, the interfaces are also connected. The different control systems of the carrier and the experiment hardware are then connected so that initial checks of the remote control of the experiment functions can be carried out. The center of gravity of the experiment carrier, including the experimental setup, is then balanced prior to the flight in the Einstein-Elevator. Once the carrier has been transported into the gondola, it is bolted to the floor of the gondola for the experiments carried out here, as the pressure hull has been dispensed with in favor of faster access. This means that the experimental setup in the gondola is also in a normal atmosphere at a room temperature of 20 $∘$C.

Initial tests are conducted at a standstill under 1 g to determine the parameters. Subsequently, microgravitational samples can be produced during the flight of the experiment as well as the comparison samples at 1 g at standstill with the identical production parameters and timings. To perform the microgravity experiments, the gondola, together with the experimental setup, is accelerated to 20 m/s at 5 g. This only takes 0.5 s. The vertical parabolic flight then takes place for 4 s, during which the lenses are dispensed and cured (Fig. 5).

To monitor the repeatability of the dispensed lenses, always a combination of $μ$g- and 1 g-samples are produced on the same glass substrate carrier in quick succession.

For a qualified determination of the influence of gravity on the geometric properties of the lenses, it is essential to first define suitable process parameters. The process parameters determined in advance are then kept constant during the experiments. It is necessary to find parameters which, on the one hand, enable good quality lenses in 1 g and, on the other hand, are in the expected order of size (see Sec. 2). In order to influence the size of the volume of the dispensed lenses, several parameters can be adjusted, including the stroke of the tappet (lift), the timings during the dispensing process of the tappet (rise time, open time, and fall time), the pressure applied to the material leading to the tappet, and the temperature adjustable via the heating element, which affects the viscosity of the material. The volume can also be increased by quickly applying several drops to form a lens (max. 1,500 Hz dispensing frequency).

The footprint/diameter of the droplet is also influenced by the distance of the nozzle to the substrate, which can apply additional velocity in the 1 g experiments by its accelerated fall. But again, the temperature of the nozzle changes the viscosity of the polymer and, with it, the flow behavior. Also, the interaction between the liquid and the solid surface, as well as the surface tension, affects the shape of the droplets, including the contact angle.

For the later experiments, the following parameters were set because they showed the best repeatability and quality in production:

• The tappet times are set to 1,000 $μ$s rise time, 300 $μ$s open time, and 80 $μ$s fall time with 100% nozzle lift.

• The distance between the nozzle and the substrate is 6 mm.

• The dispenser temperature in the nozzle is set to 60 $∘$C.

• The operating pressure for the dispenser is set to 3 bar.

• The UV light intensity is set to 60% (12,000 mW/cm²) for an irradiation time of 4 s.

Theoretically, the required curing time for OrmoComp^® with a recommended UV-exposure dosage of 500–1,500 mJ/cm² and the used UV lamp with 12,000 mW/cm² is only 42–125 ms. To ensure full curing of the lens and stability in shape, a longer exposure time was specified. Experimentally, dimensional stability was achieved with an exposure time of less than 1 s. With these parameters established, the test campaign commences. Upon manual initiation by operators from the control room, the internal timing of the experiment control system is automatically activated. The timing of the experimental sequence relative to the movement of the Einstein-Elevator is depicted in Fig. 5 (see also Sec. 3.2). The dispensing process initiates with a delay of 1.5 s after launch. Following dispensation, a shield promptly rotates in front of the nozzle within 400 ms to protect it from the UV lamp, preventing polymer curing inside the nozzle. Subsequently, the irradiation process commences 1 s later, ensuring solidification of the lens before the free-falling experiment is decelerated at 5 g. However, the irradiation process concludes at the preset time, even after the system has reached the parking position.

Following the production of lenses under both microgravity and Earth gravity conditions within the controlled environment of the Einstein-Elevator, the fabricated lenses undergo evaluation. The utilization of suitable measurement techniques adhering to standardized methodology is crucial for facilitating the planned statistical analysis of the acquired data. This approach plays a pivotal role in mitigating measurement variance and ensuring the reliability and robustness of the subsequent analysis.

The evaluation of the $μ$g and 1 g experiments takes place in several stages. First, all lenses produced are subjected to an optical inspection using a Leica DM LM System microscope (Leica Microsystems Inc., Wetzlar, Germany). The roundness of the droplets, the amount of air inclusions, and the absence of dust are checked. To determine the uniformity of the lenses, their diameters are measured in two orthogonal directions (⁠$xy$-plane of the glass substrate) using the internal camera system of the system microscope and the Leica Application Suite X (las x) software. An example can already be found in Fig. 6.

After the exclusion of defective or improperly manufactured lenses from the dataset, the lenses are subjected to examination utilizing a Surftens Basic contact angle instrument (OEG GmbH, Hessisch Oldendorf, Germany). The contour is observed laterally, and with suitable illumination, contours can be precisely focused and assessed using automated image analysis with surftens automatic 4.7 software. Through this method, the apparent contact angles, the mean of the left contact angle $θl$ and right contact angle $θr$⁠, and the volumes of the lenses are determined. In Fig. 7, a capture of the contact angle measurement is depicted. The intersection area of the horizontal blue line, which matches the specific glass plane on which the lens was made, and the circle segment, which mimics the outer contour between the lens and its surroundings, is the manufactured lens. Below the horizontal blue line is the shadow of the lens, which resembles a mirror image of the lens.

Following the determination of contact angles, the height of the lenses is assessed utilizing the microsurf custom confocal microscope (NanoFocus AG, Oberhausen, Germany). To this end, the difference between the initial position where the lens adheres to the glass substrate and the apex of the lens is determined. For improved visualization and validation of measurement results, lens samples are examined sporadically using SEM. Specifically, a three-dimensional scan of the lens is generated using the FlexSEM 1000 II scanning electron microscope (Hitachi High-Tech Corporation, Tokyo, Japan) and subsequently analyzed utilizing the hitachi map 3d light 8.1 software. SEM-3D scans of lenses fabricated under $μ$g and 1 g are depicted in Fig. 8.

Out of the total 24 lenses manufactured as part of the study, 18 lenses (nine from the microgravity group and nine from the Earth gravity group) were selected for detailed statistical analysis. Six lenses could not be automatically evaluated by the image analysis software for contact angle measurements due to at least one of the following critical aspects was not being met:

• Roundness of droplets: The shape and symmetry of the manufactured droplets were assessed to ensure that they had a uniform shape and that there were no unwanted process artifacts in the analysis.

• Absence of air bubbles: Lenses were inspected for air bubbles or inclusions that could affect optical quality.

• Absence of dust particles: As dust particles can affect the optical properties of the lenses, the absence of dust on the lens surface was ensured.

• Uniform volume: Each selected lens was tested to confirm that all samples were uniform in volume for comparability.

The impact of gravitational forces on the contact angles and height of the lenses throughout the manufacturing process is evaluated by employing the statistical software jmp^® 17.2 (sas Institute Inc., Cary, NC, USA). The data were analyzed using the method of least squares. The analysis reveals that gravity exerts a statistically significant influence (⁠$P$-value $<0.05$⁠) on the shape of the lenses, as evidenced by a $P$-value below 0.0001 for both the contact angle and the height of the lenses.

As shown in Table 1, the lenses manufactured under microgravity conditions exhibited, on average, a contact angle steeper by 1.48 deg at 47.56 deg compared to an average of 46.08 deg for lenses manufactured under 1 g conditions, with an approximately equal volume of about 140 nl (141.4 nl for $μ$g and 139.8 nl for 1 g). Concurrently, the average lens height for lenses manufactured in microgravity, at 274.94 $μ$m, was 7.57 $μ$m higher than lenses manufactured under 1 g conditions, which averaged 267.37 $μ$m in height. Figure 8 provides a comparative visualization of scanning electron microscope (SEM) images with color-coded height profiles of lenses manufactured under $μ$g and 1 g conditions. The comparison of the two SEM images provides additional support for the conclusions drawn from the measurement data obtained from the confocal microscope, suggesting that lenses with similar diameters exhibit varying heights. This observation is evident through the consistent z-color scaling apparent in both images.

Additionally, regression analysis was performed to further explain the relationship between gravitational conditions and lens characteristics. Figure 9 illustrates the contact angles obtained from experiments conducted under both $μ$g and 1 g conditions, along with the corresponding regression line. The regression analysis yielded a root mean square error (RMSE) of 0.5143 and an $R2$ value of 0.70, indicating a strong correlation between gravitational conditions and contact angles. Similarly, Fig. 10 presents the lens heights obtained from experiments conducted under $μ$g and 1 g conditions, along with the associated regression line. The regression analysis for lens heights resulted in an RMSE of 0.0027 and an $R2$ value of 0.69, indicating a high degree of correlation between gravitational conditions and lens heights. However, it is important to critically assess these results due to the limited sample size of only 18 lenses (nine per gravitational condition). With such a small sample, there is a risk of overfitting or obtaining results that are influenced by random variation rather than true underlying relationships. Therefore, to ensure the robustness and validity of these findings, it is planned to replicate the experiments using a larger sample size and under additional gravitational conditions such as lunar gravity (0.17 g) and Martian gravity (0.38 g) in future studies. This would provide more reliable evidence regarding the influence of gravitational conditions on lens characteristics and validates the regression analyses.

A theoretical introduction to the behavior of drop height and contact angle as a function of gravity was given. Based on this, it is expected that gravity has no significant influence on the shape of very small drops. For larger drops, however, the maximum drop height is expected to be inversely proportional to gravity. To the best of our knowledge, the application and subsequent curing of sessile droplets in microgravity has never been performed before. The Einstein-Elevator is ideally suited for this purpose, and the experimental setup and test procedure have been described in detail above, including all materials and equipment used, as well as the timing during the 4 s microgravity phase between the payload control system and the dispensing process. The properties of the lenses produced were analyzed geometrically. In particular, the parameters height of the lens and contact angle to the glass substrate were measured and evaluated. We found that the contact angle increased by $1.5±0.7$ deg with decreasing gravity, and the maximum height of the droplet also increased with decreasing gravity by $7.6±3.9μm$ from 267.37 $μ$m to 274.94 $μ$m. In order to reduce the variance of the measurements and to ensure the robustness and validity of these results, the experiments will be repeated in the future with a larger number of samples. Scattering of the height and contact angle parameters with identical process parameters can be attributed to a possible material film at the nozzle outlet; furthermore, the substrate carrier surface is not of identical quality, which leads to a local surface energy variation.

In terms of the optical properties, relevant parameters can already be identified under the microscope, which still need to be investigated in more detail. These include future measurements of radius of curvature, surface roughness, and optical characteristics like focal point and light transmission. This new knowledge will enable quantifying the influence of gravitation in the production process of dispensed sessile drops for use as microlenses, thus contributing to the development of gravity-adapted lenses. Potential reasons for the formation of an apron at the outer end may be caused by shrinkage during curing and/or contraction after accelerated impact due to fluid viscosity. Air bubbles, which can be seen in Fig. 6, are due to the repeated refilling of the polymer; in addition, there is no vacuum in the process chamber, which must be taken into account in further testing.

In the future, the parameter space will also be extended. For example, the study will be expanded to include different lens sizes (particularly interesting for larger lenses, where the influence of gravity is expected to be greater). Furthermore, tests with other material combinations, e.g., other UV-curing materials with lower viscosity or hydrophobic substrate surfaces, can be performed without major modifications to the experiment. It is also possible to vary the gravity using other specific different gravity conditions. Of particular importance for ISM are lunar gravity (0.17 g) and Martian gravity (0.38 g).

In conclusion, this is the first time that gravity has been considered as a process parameter in optical manufacturing technology. This opens up a previously inaccessible parameter space that will be used to improve fundamental understanding of manufacturing processes and transfer to novel applications on Earth and in space.

This research was financially supported by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453). The authors would also like to thank the DFG and the Lower Saxony state government for their financial support for building the Hannover Institute of Technology (HITec) and the Einstein-Elevator (NI1450004, INST 187/624-1 FUGB) as well as the Institute for Satellite Geodesy and Inertial Sensing of the German Aerospace Center (DLR-SI) for the development and the provision of the experiment carrier system.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

g =

Earth’s gravity (⁠$1g=9.81$ m/s²). It is written in italics to avoid confusion with the unit gram (“g,” not written in italics).

ISM =

in-space manufacturing

ISS =

International Space Station

$μ$g =

microgravity

RMS =

root mean square

RMSE =

root mean square error

SEM =

scanning electron microscope