Optical performance of commercial liquid lens assemblies in microgravity

Abstract. Focus-tunable liquid lenses are used in various applications due to their compact size, light weight, low power consumption, and cost effectiveness. They have the potential for use in space applications, such as focus compensation, optical communications, and imaging systems. However, liquid lenses have not yet been evaluated for use in the space environment. This work focuses on characterizing operational differences of commercially available liquid lenses from Corning Varioptic and Optotune between Earth gravity, microgravity, and hypergravity environments. Results show a linear drift in the tip/tilt of 0.80 and 4.20 mrad going from 1 to 0 g for the Corning Varioptic A-39N0 lens and Optotune EL-16-40-TC-VIS lens, respectively, with lower optical aberrations in microgravity. Additionally, a significant but small increase in focal power going from 1 to 0 g by 0.02 D is observed for the Optotune lens. No significant change in focal power is observed for the Corning Varioptic lens tested in this experiment. Additionally, potential multi-beam interference is observed in defocus patterns of the Corning Varioptic lens tested during the experiment.


Introduction
Focus-tunable liquid lenses are compact nonmechanical focus-tunable lenses that use a liquid to change their focal length. 1 Due to their compact size, light weight, low power consumption, and cost effectiveness, they are attractive for space applications, such as focus compensation, optical communications, and others.However, liquid lenses have not been fully evaluated for use in the space environment.Previous work has subjected liquid lenses to thermal vacuum (TVAC) testing, 2,3 but other space environment testing such as ionizing radiation and microgravity has not yet been conducted.This work presents results using commercially available liquid lenses from Corning Varioptic and Optotune on a microgravity flight to characterize differences in operation between Earth gravity and microgravity.Microgravity testing is especially important for liquid lenses as the optical fluid sags in gravity, causing an increased wavefront error and aberrations. 4his work is part of the development for the miniature optical steered antenna for intersatellite communication (MOSAIC) project, which aims to utilize liquid lenses for a hemispherically steering lasercom terminal for small satellites, for which reliable operation in the space environment is required.The MOSAIC project seeks to construct a compact, nonmechanical lasercom transceiver with integrated beam steering for small satellites using liquid lenses. 2,3,5,6The transceiver design is based on a previous design by Zohrabi 7 that utilizes a single on-axis liquid lens for divergence control and two additional liquid lenses offset in x and y for 2D steering; it was initially proposed for light detection and ranging (LIDAR).

Background
Liquid lenses utilize an optical fluid to refract light as opposed to traditional solid materials like glass or plastic. 8Liquids offer several potential advantages: by tuning the liquid properties such as the surface tension and contact angle, optical properties can be precisely tuned without requiring traditional time-consuming and expensive optical manufacturing. 1 However, by the same virtue of exploiting liquid properties, gravity causes the optical fluid to sag and deform, causing aberrations, especially for larger liquid lenses. 9,10For this reason, liquid lenses offer a potential method through which large, next-generation space telescopes could be constructed. 11,12he added flexibility of liquid lenses can also be used to change the lens propertiesmanipulating the shape of the fluid droplet allows for, for example, focus tuning or wavefront control. 13Many methods for manipulating the droplet have been demonstrated, but the main methods are through electrowetting and hydraulic displacement. 1Electrowetting-based lenses, otherwise known as electrowetting-on-dielectric, work through changing the contact angle of a fluid droplet on a dielectric by changing the applied electric field. 1,14,15A diagram of how electrowetting causes a fluid droplet to displace is shown in Fig. 1.Hydraulic displacement, otherwise known as pressure-based liquid lenses, uses an actuator to displace fluid into an elastic membrane. 1The elastic membrane acts similarly to how surface tension causes fluid droplets to produce spherical shapes, creating a near-ideal spherical lens.
Focus tunable liquid lenses have applications in machine vision, 4,16,17 phone cameras, 18 microscopy, 19 optical communications, 9,[20][21][22][23][24] and more due to their compactness and, depending on the lens technology, low power.Optotune and Corning Varioptic are two companies manufacturing commercial liquid lenses, each producing lenses with different operating principles.Corning Varioptic's liquid lenses employ electrowetting technology, 16 whereas Optotune's lenses function based on pressure, with a voice coil causing fluid to displace into the center of a membrane. 4Diagrams of how Corning Varioptic's and Optotune's lenses work are shown in Figs. 2 and 3, respectively.Optotune's lenses come in a larger form factor due to the ease of scaling up pressure-driven lenses, and they contain more fluid mass as a result.
For satellite lasercom terminals, evaluating liquid lens performance in the space environment, including zero gravity testing, is important.Previous work has shown that liquid lenses can survive and operate in other space environment conditions, including TVAC testing, 2,3 with the Optotune lenses used in this study having an increased root mean square (RMS) wavefront error of 2.5 waves tested at 532 nm in Earth gravity conditions, as listed by the manufacturer, 4 and measured by placing the lens in different orientations.If this RMS wavefront error was purely in tip/tilt, it would result in a tip/tilt angle of 0.33 mrad using the result that for a linear tip/tilt the RMS wavefront error is half the peak value for a circular aperture. 25haracterizing liquid lens performance under zero gravity conditions is crucial for space applications.Previous work on evaluating the effects of gravity on focus-tunable liquid lenses has been conducted by changing the lens orientation, but this technique cannot eliminate the effects of gravity entirely. 9Liquid lenses utilizing ferrofluid actuation have been flown on parabolic flights and show an improvement in wavefront error from 27 to 17 waves in microgravity. 10his work presents zero gravity data from parabolic aircraft testing to understand the effects on optical performance.

Microgravity Simulation
Microgravity flights, otherwise known as parabolic flights, are flights in which pitching maneuvers are used to simulate microgravity conditions experienced in space.During parabolic flight maneuvers, an aircraft traces a parabolic trajectory.As the aircraft begins pitching up, objects    16 inside the aircraft experience increased gravity, peaking at around 1.8 g. 26 This hypergravity phase is felt throughout the entire upward arc up to an inflection point.After reaching this inflection point and as the aircraft starts to pitch over, everything inside begins to experience a brief period (typically 20 to 30 s) of microgravity.Microgravity then persists throughout the entire downward arc until the next inflection point, where the aircraft begins to pull out of the descent and objects inside the aircraft experience hypergravity until the aircraft completes its maneuver and levels out.Parabolic flights are between alternative microgravity simulation methods, such as drop towers and suborbital flights, in terms of duration of microgravity, and equipment on these methods is not exposed to extreme acceleration unlike the other two methods. 27The microgravity flight in this work is conducted on a Boeing 727-227F aircraft operated by Zero Gravity Corporation, organized by the MIT Media Lab.In this work, we refer to anything less than 0.1 g as 0 g or microgravity, 0.9 to 1.1 g as 1 g or Earth gravity, and anything greater than 1.5 g as hypergravity.

Experimental Setup
The experiment consists of two independent optical trains, each operated by a dedicated Raspberry Pi.The optical trains contain a portable fiber tester, FC/PC to FC/PC single-mode patch fiber cable, and laser collimator, which shines through the liquid lens and neutral density (ND) filter onto an image sensor.One optical train is for the Corning Varioptic lens, and the other is dedicated for the Optotune lens.The collimator uses an asphere lens factory aligned at the experiment wavelength, and the liquid lens is situated approximately at the waist distance of 10.72 mm from the collimator, which indicates that the wavefront should be near-planar at the liquid lens and significantly less than the wavefront error indicated in previous work. 4,10A block diagram of one of these optical trains is shown in Fig. 4, and a diagram of the optical components is shown in Fig. 5, with further details about the hardware used in the experiment given in Table 1.A photograph of the experiment on the aircraft is shown in Fig. 6.
During operation, lens commands are swept through, and the resulting spot on a detector is imaged.Measurements are taken for 64 lens commands surrounding the focus, from 49.5 to 53.5 V for the Corning Varioptic lens and 70 to 110 mA for the Optotune lens.The fastest data capture rate of every 300 ms and the 15 to 25 s parabola duration guide this quantity, with 64 points being approximately the number of points that can be captured in a single parabola, giving a complete sweep.20 ms of delay is added between setting the lens command and capturing the image, based on the settling time of the fluid in the lenses.Optotune specifically recommends 25 ms of settling time, which can be reduced by 50% if the input is a low frequency step, as in this experiment, 4 and previous laboratory experiments have shown on the order of 1 ms settling times for these particular Corning Varioptic lenses. 2 The measured quantities include the image, acceleration (three-axis), gyro (three-axis), magnetometer (three-axis), and temperature.A flowchart of the software is shown in Fig. 7.

Spot Analysis
Using the data, the imaged spots on the detector can be analzyed to understand operational differences between the gravity regimes.Prior work suggests that the wavefront error shifts significantly in different gravity regimes, 10 with significant amounts of coma.Conventionally, in  lasercom experiments, the beam quality is measured using a metric called M 2 , 28 which gives the difference in divergence from the ideal diffraction-limited beam, taken from a Gaussian fit on the beam sampled at multiple points along the optical axis.However, Gaussian beam fits can be more computationally intensive due to the additional parameters compared with a simpler measurement, such as encircled energy.Due to the number of samples taken in this experiment, we use encircled energy instead to provide a measurement of the overall beam diameter.A  comparison of these methods for a highly aberrated sample is shown in Fig. 8.The encircled energy is given as 29 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 7 ; 5 2 9 where r is the radius, I is the image of the sample, E is the total energy in I, and ρ and ψ are polar coordinates centered on the centroid of I.In practice, this is implemented in discrete samples as ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 7 ; 4 5 7 where KðrÞ is a binary mask that indicates whether a particular point in I around its centroid is within a specified radius.KðrÞ can also be anti-aliased to improve its correspondence to the continuous version, but to improve computational performance, we apply a 1 pixel Gaussian blur to K to approximate anti-aliasing.Additionally we use a small noise threshold and an areaof-interest (AOI) to mitigate against the effects of noise on the sensor and reflections in the optical train affecting the analysis.
To use the encircled energy as a measurement, we use a bisection search to find where the encircled energy of the samples is equal to 83.8%, corresponding to the same encircled energy at the first null of an Airy disk. 29We use the notation r 0.838 for this radius.The diffraction limits used in this work are the ideal 83.8% radii calculated with the ideal Gaussian beam propagation 30 of the measured collimator diameter, with corresponding adjustments going from the 1∕e 2 diameter to the 83.8% encircled energy radius.These adjustments make it so that the diffraction limits quoted are lower bounds for the 83.8% encircled energy.
A Gaussian beam's diameter will vary hyperbolically around its focus. 28,31Sampling the same beam with varying the lens focal length can be considered analogous to sampling a beam at different points along the optical axis.Because the focal length of these lenses varies linearly in the commands executed during the experiment, 4, 16 we can also expect the beam diameter to vary hyperbolically, which can then be examined to determine how the focal power changes during the experiment in different gravity regimes.

Limitations
Initially, this experiment was designed to use a phase retrieval algorithm, and the hardware was sized to optimize for a balance of point spread function (PSF) size as well as being able to image the pupil plane, at the collimator.Unfortunately, due to convergence issues, we were unable to successfully conduct phase retrieval with low enough error for usable results.For this reason, the collimator for the Optotune lens undersamples the full 16 mm aperture, but the collimator fully fills the Corning Varioptic lenses' 3.9 mm aperture beyond the 1∕e 2 diameter.
Additionally, this experiment utilizes a coherent source for the data to match our lasercom application, which may not be applicable for all cases.

Results and Discussion
In this section, measurements from the flight are used to understand how lens performance changes between zero gravity, Earth gravity, and hypergravity conditions.The spot analysis approach is used to understand how the lenses change in focal length, and centroiding is used to determine how the PSFs change for each condition.

Flight Profile and Measurements
The flight profile of the experiment is shown in Fig. 9.The profile shows all 20 parabolas, including the two parabolas each in Lunar and Martian gravity.The takeoff and landing phases are also clearly visible.Figure 9 shows a zoomed in view of the second set of five parabolas.
Measurements of hypergravity experienced during the ascent phases of each parabola are also recorded, providing additional data for comparison.A histogram of the recorded g-force for all samples is shown in Fig. 10.Approximately 20,000 samples were collected for both Corning Varioptic and Optotune lenses.

Spot Analysis
Figures 11 and 12 show individual focused samples from each gravity regime for the Corning Varioptic and Optotune lenses, respectively.As a first comparison, the Corning Varioptic focused spots have much smaller increases in tip/tilt and coma compared with the Optotune ones.The Optotune samples show very pronounced aberrations in higher gravity regimes.
The results for 83.8% encircled energy radius r 0.838 over various lens commands are shown in Fig. 13.Overall, the analysis shows consistent results for both microgravity and Earth gravity with a few key differences.Both lenses show a lower 83.8% encircled energy radius around the focus in 0 g, closer to the diffraction limit, indicating an improved beam quality.Optotune lenses show significant but minor increases in focal power in microgravity compared with Earth gravity.The increased focal length could be due to gravity providing some resistance to the actuation force that gets transferred horizontally due to surface tension on the lenses, whereas the smaller  radius is most likely due to lower aberrations in microgravity causing less smearing of the lens PSF.Lens focusing power increased in microgravity by 0.024 D for the Optotune EL-16-40-TC-VIS lens, with a summary given in Table 2.
The Optotune lens has well-constrained and consistent error bars throughout the lens commands in Fig. 13, but the Corning Varioptic lens shows slightly larger error bars across the extremes of the sweep.This increased error caused the hyperbolic fits to be constrained toward the central section of points.The deviation seems to be due to the defocus pattern that the Corning Varioptic lens forms, which smears and causes the measured encircled energy radius to deviate.The defocus pattern could be due to multiple reflection and interference at the oil and water interface on the inside surface of the lens and has been observed in previous focus sweep experiments in normal gravity environments. 2,6An example of the defocus pattern is shown in Fig. 14.The same defocus pattern is observed in lab measurements, indicating that this is likely to be multiple beam interference and not a gravitational-dependent effect alone.The cause of this smearing is not obvious, but it could be due to vibration of the liquid lens during the flight.There is no significant correlation of this smearing to particular times of the flight or parabola.Some of the vibration also appears to make its way into the image as a result of circular standing waves, visible in the center of Fig. 14.As these lenses are designed for imaging and not coherent optics, it does not affect their target applications but does make them potentially unsuitable for coherent communication systems.
Both lenses show additional low-intensity reflections angled from the main beam.These reflections appear to be separate from the defocus pattern as they are primarily in focused samples and decrease in intensity for defocused samples.The decrease in intensity after defocusing suggests that these reflections are between the lens cover glass and the ND filter used in the experiment.The effects from these reflections were mitigated as described previously using an AOI around the centroid of the focal samples.Small effects on centroid position may be present in the regression analysis, but this is mitigated using all samples in the experiment and Table 2 Summary of changes in the quantitatively determined properties of lenses, with 95% confidence intervals.Positive tilt is in the opposite direction as apparent gravitational field and all changes are referenced from 1 g baseline.A significant (p < 0.05) negative tilt is observed in both lenses, and a significant increase in focal power is observed in the Optotune lens.not just the focal samples in which the reflection is most visible, as well as the reflections being a much lower intensity than the beam.

Centroid Analysis
Figures 15 and 16 show stacked and averaged images of the spot on the detector taken at each of their focal commands.The dominant aberration present is tip/tilt, with large changes between each gravity regime as summarized in Table 2 and measured using centroiding the PSFs from each lens.The change in tip/tilt is linear with the effect of gravity, with the linear regression shown in Fig. 17 for the Corning Varioptic and Optotune lenses, respectively.Both lenses adhere well to the linear fit, with an R 2 value of 0.98.Both lenses exhibit a downward tip/tilt of 0.80 mrad for the Corning Varioptic lens and 4.20 mrad for the Optotune lens.Estimating a lower bound for the RMS wavefront error in Earth gravity based on tip/tilt alone gives 1.2 waves for the Corning Varioptic lens and 26.5 waves for the Optotune lens.The value derived for the Optotune lens is much closer to 27 waves as listed in previous experimentation of a similarly sized lens 10 and significantly higher than the 2.5 waves quoted by the manufacturer. 4he residuals of the linear regression in tip/tilt have a standard deviation of 0.20 mrad for the Optotune lens and 0.04 mrad for the Corning Varioptic lens.Lab measurements show a standard deviation of 0.02 mrad for both lenses, indicating that vibration or other effects likely affected the results, but significantly more for the Optotune lens, which may be due to its higher fluid mass.We observe no significant correlation with the tip/tilt with acceleration or gyroscopic measurements, indicating that resonance of the test setup with the aircraft's vibration is unlikely to have affected measurements, although this requires careful followup.
Qualitatively, it can also be seen in Figs.11 and 12 that coma and astigmatism are also present, especially in hypergravity regimes.Corning Varioptic lenses exhibit less change in tip/tilt and maintain nearly identical optical performances.Optotune lenses show a larger change in tip/tilt, with significant coma observed in the hypergravity regime, as shown in Fig. 16.
The imaged PSFs for the Corning Varioptic lenses are well contained, with no observable spread in hypergravity compared with microgravity.The spots for the Optotune lenses are more spread out, suggesting that vibration or other environmental factors may have impacted the experiment and contributed to the observed aberrations.However, the imaged spots look visually tighter in microgravity, suggesting that there may be a gravity-dependent effect.The presence of more fluid in Optotune lenses may be a contributing factor to their optical performance being more significantly affected by environmental conditions.An idealized diagram showing how fluid deformation could cause the resultant aberrations is shown in Fig. 18, although in reality there would still be some minor fluid curvature at 0 g conditions due to surface tension.
As mentioned previously, the regression analysis may be affected by low-intensity reflections between the ND filter and lens cover glass, but this effect is unlikely to significantly affect the regression analysis due to their low intensity having a limited effect on the centroid and the reflections dissipating rapidly when defocused.

Temperature Drift
Both liquid lenses used in this experiment have been shown to drift in focal length due to temperature variations.A temperature plot for both lenses, as shown in Fig. 19, indicates that temperature throughout the parabolas was within 4°C for all of the parabolas, with a gradual decrease after the lenses reached the peak temperature, as measured on the Raspberry Pi SenseHat modules.The Optotune temperature was slightly higher than the Corning Varioptic temperature during the flight, which is expected as Optotune lenses generate heat from their voice coil and high current operation.Histograms, as shown in Fig. 20, reveal that a vast majority (75%) of the 0 and 1 g data points are in the same range, effectively controlling for temperature drift during the experiment.Moreover, hypergravity and zero gravity data are comparable because temperature histograms are almost identical, indicating that the temperature is adequately controlled during the experiment.Interestingly, microgravity parabolas can be observed in the temperature plot, perhaps due to hydrostatic forces when transitioning into hypergravity causing redistribution of air inside the aircraft cabin.

Conclusions and Future Work
This work shows that liquid lenses perform well in microgravity, with reduced overall aberrations; a downward tip/tilt of 4.20 and 0.80 mrad for the Optotune lens and Corning Varioptic lens, respectively; and a slight increase in focal power of 0.02 diopters for the Optotune lenses, with all quantities going from 1 to 0 g.Based on the tip/tilt measured during this experiment alone, we observe a decrease in the RMS wavefront error of 30.6 waves and 1.4 waves for the Optotune and Corning Varioptic lens, respectively, as a lower bound.The estimate in wavefront error for the Optotune lens is significantly higher than the 2.5 waves quoted by the manufacturer, 4 but it is in line with 27 waves for a liquid lens of a similar size flown on a different parabolic flight. 10A summary of the quantitative results is shown in Table 2.A more pronounced disparity in operation is evident for Optotune lenses compared with Corning Varioptic lenses, which is likely due to their larger aperture size holding more fluid volume.
The defocus patterns observed for the Corning Varioptic lens, which could be caused by multiple beam interference, make them potentially unsuitable for applications in which a long coherence length is required or other lasercom applications in which divergence control could be used, such as integrated beaconing.No similar defocus patterns were observed for the Optotune lens.
During the microgravity flight, changes in temperature were small and limited to ∼10°C in the worst case.Prior studies have also shown that such fluctuations do not have a significant influence on the results. 2,3n combination with previous work on space environment evaluation, 2,3,6 these results show that liquid lenses are well suited for space-based optical systems.Their low SWaP-C and improved performance in microgravity in addition to previously studied operation in TVAC and ionizing radiation effects make them a suitable option for use in a variety of space-related applications. 6uture work includes evaluating different control schemes to compensate for the change in tip/tilt in different gravity conditions and for closed-loop pointing and tracking.
Further study of vibrations is needed, utilizing a vibrometer or faster inertial measurement unit readout due to effects in smeared data points.With the data taken in this experiment, vibration could potentially be quantified using some of the resultant standing waves observed on the sample images.Additionally, vibrometer data could be used to definitely rule out resonance effects.
Future work should also consider repeating the experiment with multiple lenses to estimate the amount of lens-to-lens variation to ensure that the effects observed are not a feature of the lenses used during the experiment.
A numerical simulation of liquid lenses, varying the Bond number, could offer an insightful method for assessing the proportionate influence of gravitational force to surface tension.This approach would provide a theoretical perspective on the potential formation of aberrations and could easily be compared with laboratory measurements and contrasted with experimental microgravity measurements.
In addition, wavefront error is not rigorously evaluated in this study as a wavefront sensor was not used during the microgravity flight.Instead, only lower bounds of the RMS wavefront error are estimated based on changes in tip/tilt.Evaluating the wavefront error using phase retrieval algorithms such as the Gerchberg-Saxton 32 algorithm, Misell's algorithm, 33 and other nonlinear phase retrieval methods was attempted, but this process resulted in too much error and difficulty in convergence to obtain usable results.

Fig. 3
Fig. 3 (a) and (b) Diagram showing the pressure-based principle of operation for Optotune lenses. 4 Fig. 3 (a) and (b) Diagram showing the pressure-based principle of operation for Optotune lenses. 4

Fig. 2
Fig. 2 (a) and (b) Diagram showing the electrowetting principle of operation for Corning Varioptic lenses.16

Fig. 5
Fig.5Diagram of the single optical train in the experimental setup, with components and dimensions labeled.Coordinate frame in blue is centered at the liquid lens, with axes chosen to match with image space axes at the detector.The direction of gravity during the experiment is shown in red.

Fig. 7
Fig. 7 Flowchart of the experiment flight software that runs continuously and records samples

Fig. 6
Fig. 6 Experimental setup affixed to the floor of the zero gravity aircraft.

Fig. 8
Fig. 8 Comparison of Gaussian fit and encircled energy on a highly aberrated sample image from the experiment.

Fig. 10 Fig. 9
Fig.10Histogram of total samples with g-force of each sample.

Fig. 11 Fig. 12 Fig. 13
Fig. 11 Normalized images of focused individual Corning Varioptic samples from (a) 0 g, (b) 1 g, and (c) 1.5+ g gravity regimes with accompanying diffraction limit and 83.8% encircled energies highlighted.Increasing gravity shows minor increases in tip/tilt and coma.

Fig. 14
Fig. 14 Example image of defocused Corning Varioptic sample at 53.5 V lens voltage, with defocus pattern potentially caused by multiple beam interference at the oil/water interface.Centroid and 83.4% encircled energy also highlighted.Tick labels are relative to centroid.

Fig. 17
Fig. 17 Linear regression of tip/tilt of focused samples against sample gravity conditions for (a) Corning Varioptic and (b) Optotune lenses.

Fig. 18 Fig. 19 Fig. 20
Fig.18Potential physical mechanism explaining observed aberrations.Optical fluid sags to the bottom of the enclosure, causing slants in the side, which causes tip/tilt like a prism.Additionally, fluid curvature on the optical membrane creates higher order aberrations, such as coma and astigmatism.

Table 1
List of hardware used in the experiment.