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Properties of large scale water lenses for solar concentration were investigated. These lenses were built from readily available materials, normal tap water and hyper-elastic linear low density polyethylene foil. Exposed to sunlight, the focal lengths and light intensities in the focal spot were measured and calculated. Their optical properties were modeled with a raytracing software based on the lens shape. We have achieved a good match of experimental and theoretical data by considering wavelength dependent concentration factor, absorption and focal length. The change in light concentration as a function of water volume was examined via the resulting load on the foil and the corresponding change of shape. The latter was extracted from images and modeled by a finite element simulation.
© 2015 Optical Society of America
1. Introduction
Solar concentrators can increase the system efficiency for solar based energy conversion systems (SECS), e.g. solar photovoltaic (SPV) or solar thermoelectric generators (STEG). A variety of solar concentrators are reported based on different type of lenses, fresnel lenses or parabolic mirrors. Moreover, enhancement of the system efficiency has been accomplished with the help of actuators to operate as a solar tracker with the trade-off of the total system cost. For large scale solar energy conversion systems, the cost for efficiency enhancement increases dramatically with size. So an inexpensive solution for solar concentration would make solar energy conversion systems more economically realizable. Water lenses i.e. water filled in plastic foil constituting a plano-convex lens shape is a promising candidate for the purpose of a cost effective solar concentrator. The main obvious advantages of this kind of lens are:
- Both the water and the plastic foil are economical and readily available
- UV radiation from the sunlight purifies the water by destroying bacteria
- Most of the solar UV radiation, which leads to a long term destruction of the plastic foil, is filtered out by the water
- Their properties can be adjusted
- It also serves as a water reservior to be utilised for cooling purpose of SECS
- It allows the silicon SPV system to function effectively by rendering less heat as infrared (IR) radiation from the sunlight is absorbed by water
One disadvantage of the water lens is sun tracking, i.e. the position of the sun will results in inhomogeneous intensity distribution in the focal spot. This can be easily addressed by employing a secondary optics.
A range of liquid lenses is reported in [1–7] which are mainly confined to small scale. A constant amount of liquid was used in a confined container to form the liquid lens [1, 4, 5]. The shape of the lens as well as the optical properties were modified by applying pressure to the liquid filled chamber in order to change the lens aperture [1], by use of a servo motor without changing the lens aperture [4] and by applying pressure to one side of the container surface [5]. A surface equation of completely filled liquid lens is investigated and characterized in [8]. A fabrication process of small dimensional liquid lenses with homogeneous pressure distribution over a plastic foil is presented in [7]. Some finite element simulation as well as measurement of the liquid is also reported in [2, 6], considering the elastic foil membrane. Moreover, the fluid pressure loads on the plastic foil were extracted from a picture in [6] and calculated and compared in [2]. The applications of liquid lenses in micro-scale are reported in [3] and the lens property were tuned according to the requirement by various methods.
In this work, a large scale water lens was investigated considering the hyper-elastic material property of the plastic foil and the variable load distribution over the lens surface was evaluated. Afterwards, a certain volume of water was charged on the foil and the resulting lens aperture radius and height were evaluated. Moreover, the water lens response as a function of water volume was investigated regarding three points of view: i.e. the mechanical, optical and spectral response. A further comparative study with an aspherical lens was also carried out to evaluate the deviation of the water lens from the ideal lens behavior. From this point onwards in this work, the investigated system is addressed as water lens instead of liquid lens.
Solar energy has been converted to a utilisable form of energy by various techniques like SPV or STEG. These conversion techniques suffer from low efficiency or low power density. The absorber temperature and the solar irradiance can be enhanced by using solar concentrators. The use of state of art solar concentrators is limited due to their fabrication, operation and maintenance costs. A water lens can reduce those costs with a trade-off of concentration factor to some unknown extent. Moreover, it is easily prepared for operations with available cost effective materials.
2. Model of the water lens
When water is poured in a solid container it takes the shape of it. But when it is poured on an impenetrable surface like a plastic foil, the overall shape becomes more complex. The extraction and evaluation of the water lens properties starts with the determination of its shape. The theory and process of the water lens material modeling, mechanical modeling and the optical modeling are presented in this section.
2.1. The model of water
Water properties with respect to temperature and wavelength have been analysed extensively in literature [12, 13]. For this work, the water material model for a temperature of 25°C given by an optical simulation software was used in the wavelength range of 0.2 μm to 200 μm. The refractive index of water varies in between 1.32 and 1.35 over the whole wavelength range, whereas the extinction coefficient rises with the increase of wavelength, these are shown in the top section of Fig. 1. Due to low dispersion (water −0.0371 μm−1, borosilicate crown glass −0.0503 μm−1 at 550 nm), we expect small chromatic aberations. A high extinction coefficient results in a high absorption loss and a low transmission of the electromagnetic wave. The transmittance and the absorbance within a layer of 10 cm water were calculated and are depicted in Fig. 1.
Fig. 1 Optical properties of water: Refractive index and extinction coefficient as used in the optical simulation. The total transmittance and the absorbance for the thickness of 10 cm are calculated from the refractive index and the extinction coefficient.
2.2. The model of linear low density polyethylene
As the shape of the lens determines its imaging properties, a suitable mechanical description of hyper-elastic foils under spatially variable hydrostatic load has to be established. Linear low density polyethylene (LLDPE) plastic foil with an elastic modulus of 160 MPa [17] and Poisson’s ratio of 0.435 [16] were used. The stress-strain curve of LLDPE presented in [17] exhibits a nonlinear behavior which is generally expressed by the strain energy function. The general form of a stress-strain energy function W is
where I1,I2 are I3 are three stretch invariants which are related to the elongation along the three principal axes i.e., λ1,λ2 and λ3. Mathematically they are presented as where, εi is the strain and i = 1,2,3. Generally for incompressible or rubber like material which leads Eqs. (2)–(4) to the following set of equations and hence the stress-strain energy function in Eq. (1) is reduced to a function of two variables and represented asA variety of material models exist with different forms of W [19]. The general form for the stress-strain energy function is
where Cij and Dk are material constants andIn this work, we use the first order Mooney-Rivlin model [19] because of its simplicity, practical use, feasibility, easiness of the parameter extraction and application complexity. The stress-strain energy function of the Mooney-Rivlin model is represented as
where, C1 and C2 are constants. By employing the tensile stress-strain data of LLDPE presented in [17] to the finite element modeling (FEM) software ANSYS, the constants are easily determined. The results are C1 = 3.11 × 105 and C2 = 2.68×106 respectively. The result presented in [17] and the material parameters approximated by the Mooney-Rivlin model were compared by means of the stress strain curve and are shown in Fig. 2. More detailed investigation of LLDPE can be found in [14, 15, 18]. Allthough the modelled stress-strain relation shows distinct deviations to the experimental values, the calculated shape fits to the experimental shape.Fig. 2 The experimental stress- strain data of LLDPE presented in [17] are used to extract the constants of the first order Mooney-Rivlin model. Although the model shows slight deviation from the original material behavior, this model is chosen for the simplicity and applicability.
2.3. The mechanical water lens model
The inflation of hyper-elastic material under fluid pressure was extensively investigated in [20–24]. The fluid load on a hyper-elastic membrane in various contexts was also studied, e.g. deformation due to the fluid load up to a certain water depth [25], deformation due to the fluid load on a cylindrical pre-stressed membrane [26], the variation of the pre-stretching [28], due to uniform fluid load over the entire surface [27], due to different membrane thickness [28], due to rotation of the fluid filled membrane [29] and due to the fully filled membrane with heavy fluid [30]. In case of the water lens, due to the variation of the water volume, the water height and the water lens radii alters in contrast to [25, 27]. Further assumptions for the 23 μm thick LLDPE membrane are a uniform thickness, no initial stress and stationary equilibrium positions i.e., no movement of water. The governing equations and the boundary conditions for these particularities of the water lens can be found in [22, 24] and [25]. Afterwards, by taking one of the measurement datasets as an input, the calculations were performed considering the membrane stretches, the stress resultants and the lens curvature according to the stated process in [22, 25]. As a result, the load distribution over the plastic foil surface, the maximum lens height and the lens radius were realized as a function of fluid volume i.e., water volume.
Generally rubber like materials undergo a large deformation. We have modelled LLDPE by the Mooney-Rivlin model as mentioned in subsection 2.2. The structures made of these classes of materials are known as hyper-elastic materials and are represented by a particular class of element types in the simulation. For this analysis a two node axisymmetric element was used resulting in three degrees of freedom at each node, i.e., translation in x and z direction and rotation about y direction. Due to the symmetric property, only half of the LLDPE foil was modelled with a radius of 60 cm and a uniform thickness of 23 μm. Then the loads calculated in the previous step were exported to the FEM software and applied to an undeformed model of the plastic foil.
As soon as the deformed shapes are obtained, the lens shape was extracted by means of previously calculated water lens radius and maximum height. Subsequently the lens shapes were imported into the optical simulation software for further analysis. The whole FEM simulation were repeated for the different water volumes accounting the lens radius, the maximum lens height and the water load distribution over plastic foil as parameters.
2.4. The optical water lens model
We started the optical modeling by importing the water lens shape for a particular volume obtained in the previous step into the optical simulation software. The shape in the previous step provided a 2D line profile only, therefore the line profile was turned into a closed curve and then rotated around the optical axis of the lens, i.e. the z axis. The material assigned for the lens is water with the material properties mentioned in subsection 2.1. The lens was considered to have a bare surface without any sort of coating to simulate undisturbed reflection and absorbance; the rays were allowed to perform all optical phenomena, e.g. transmission through the volume, reflection and ending due to energy loss. A recorded solar spectrum was taken as input for the optical source which produces a plane wave with the same size as the lens diameter. The incident power for the surface was calculated to be 1000 W/m2. After that an analysis surface was built at an arbitrary position. Then the ray-tracing was performed and the focal length was determined by algorithm. At this point the analysis surface was placed at the focal spot and the intensity profile was obtained. Another algorithm was used to calculate the loss for the incident spectrum as the light propagated through a significant volume of water. From the spectral analysis, the output spectrum was obtained which was used to perform the calculation of the concentration factor. The whole procedure was then repeated for lenses with different volumes. Afterwards, the data extracted from the measurement was also employed to investigate the performance of the measured lens shape. It enables the exclusion of the disturbances present in field tests, e.g. the fluctuating solar incident radiation due to clouds.
3. Experimental approach
The water lens construction requires mainly two things: a plastic foil and the water. We used LLDPE plastic foil with a thickness of 23 μm, which was mounted on a large ring with 1.2 m diameter and supported by three 2 m long stands. The foil was filled with tap water and directly exposed to the sun, are shown in Fig. 3. An absorber plate was used to find the focal length by observing the smallest focal spot and then it was fixed at that point. Then the focal length was documented which is the distance between the water surface subjected to the solar radiation and the absorber plate at the focal spot. Afterwards, a spectrometer protected by a ND filter of 2.4 was employed to record the spectrum of the concentrated sunlight by replacing the absorber plate. Then the unaltered solar spectrum was collected. In both cases the spectrum under dark condition was recorded which then was subtracted from the earlier recorded spectrum. Subsequently, the picture of the water lens was taken, from which the lens shape was extracted later. This procedure was repeated several times while the water load of the foil was increased with each iteration.
Fig. 3 The experimental setup of the water lens of 10 liter water volume. The water radius, water height and the foil deformations are the tree main mechanical parameters which changes due to the change of water volume.
From the water lens images the x and z position values were taken by a data point extraction program. A fourth order equation was employed to extract the lens shape from the measured values using maximum congruency fitting with an average coefficient of determination (R2) of 0.9995. Generally the coefficient of determination is a number which indicates how good data fit to a curve or line. The water lenses build from a smaller water load showed a greater deviation from the average coefficient of determination than the lenses made of a larger water load as shown in Fig. 4. These equations excluded the slight deviation of the measured values. They were imported into the optical simulation software and the lens was simulated with water modeled as described in subsection 2.1. A series of analyses was carried out to determine the important parameters of the system: the absorption loss, the concentration factor and the focal length.
Fig. 4 The lens shapes obtained from the measurement photo are approximated by an equation and their match has been evaluated with coefficient of determination (R2). The perfect match would result in the ideal value, R2 = 1. With the increase of the water volume, the approximation is nearing the ideal value. Also, the average of R2 for all the water volume is close to the ideal value.
4. Results
4.1. The mechanical properties of the lens
In this section, the performance of a lens with a particular volume was investigated from three points of view, i.e. the image measurement data and the equation representing the lens shape derived from the images and the simulation.
The maximum water height and water lens radius obtained from simulation, measurement and shape equation are shown in Fig. 5. Here, the lens radius is also referred as lens semi-diameter shown in Fig. 3 which is the radius of the water lens plane surface exposing to the sun. The results of these three methods show a very good consistency as a function of water volume. The maximum reachable volume Vmax was 16 liter and at 17 liter the foil was damaged. With the increase of water volume, the maximum lens height increased almost at linear rate whereas the radius increased initially faster and later slower. Due to the foil material property when Vmax amount of water is removed from the foil, it does not retain to its original shape rather it demonstrates a permanent stretching.
Fig. 5 In the upper picture the water lens maximum height as a function of water volume is compared for the simulation, the measurement and the lens shape represented by the shape equation. The picture in the bottom compares the water lens aperture-radius or semi-diameter as a function of water volume for the same processes.
After obtaining the variable fluid pressure load on the plastic foil, with the help of the FEM software the deformed profile of the foil was calculated. From these foil deformation results and the results depicted in Fig. 5 the water lens shapes were obtained for both of the measurements and the calculations with the equation governing a very high determination coefficient. Figure 6 shows the deformed profile of the foil as well as the lens shape for both simulation and measurement. At the lower volumetric load of 1 liter the measured profile matched well to the simulation, but at a higher load a slight deviation in the horizontal direction was observed. With maximum volume, a foil deformation of 0.42x (foil radius) = 26.91 cm and 0.432x (foil radius) = 25.33 cm was observed for measurement and simulation respectively. At the lowest water volume of 1 liter the foil deformation were 0.1294x (foil radius) = 7.76 cm and 0.127x (foil radius) = 7.64 cm for the measurement and the simulation respectively. The lens height as well as the lens radius changed with increasing water volume, which is clearly visible here as well in Fig. 6. The 16 liter water volume exhibited the maximum height of 12.21 cm and 11.69 cm as well as the maximum radius of 27.57 cm and 26.69 cm for the simulation and the measurement respectively. On the other hand the lowest water volume of 1 liter led to a lens with the lowest lens height i.e., 2.10 cm and 2.27 cm and the lowest lens radius of 15.59 cm and 16.17 cm for the simulation and the measurement respectively. Although the lens mechanical model agrees with the measurement values, some deviation is observed due to the deviation of material model with the actual stress-strain data.
Fig. 6 The simulation and the experimental results of the water loading on the LLDPE foil are compared for four different volume. The simulated foil deformations are represented by lines where as the measured deformations are represented by the symbols.
The results presented in this section indicate that the measured lens shape can be approximated with an equation, which gives rise to the freedom of approximating the behavior of the water lens without disturbances like cloudy weather, wind flow, different incident spectra. As the amount of water increases, the water pressure on the LLDPE foil surface increases resulting in greater foil deformation. Again, to accommodate a larger water quantity the lens radius as well as the lens height increase.
4.2. The optical properties of the lens
In this section several properties of the water lens were characterized from the optical point of view.
The focal length of the water lens is the distance between the water lens plane surface exposing to the sun and the focal plane which is determined by the absorber plate. With the increase of the water volume, three sets of data indicate the decrease of the focal length as shown in Fig. 7. The simulation was carried out for the shape obtained from FEM simulation and for the shape obtained from the equation extracted from the water lens image. An increase in the amount of water caused a rise of the water radius and water height resulting in larger aperture and an increased curvature. This enabled the lens to concentrate light in a shorter distance for a larger water volume. With respect to the minimum volume of 1 liter to the maximum volume of 16 liter, the change of the focal lengths are 50.29%, 48.22% and 49.69% for the measurement, the lens from the equation and the simulated lens respectively.
Fig. 7 the focal length of water lens as a function of volume has been compared for the simulation, the measurement and the lens extracted from photo.
The intensity profile at the focal plane of the water lens are also dependent to the poured water volume as shown in Fig. 8. It has been extracted with the ray tracing operation of the optical simulation software by importing the lens shapes. With the increase of water volume on the LLDPE foil the lens diameter increased resulting in larger lens area. The extended diameter was then subjected to a larger amount of solar radiation, i.e., more solar energy as well as higher water volume demonstrated higher concentration capability causing an upward shift in the intensity profile. With respect to maximum volume to minimum volume, a 80.45% and 83.75% downward shift of the maximum intensity for the simulated lens and the lens from the equation were observed.
Fig. 8 The intensity distribution for different volume of water obtained form the ray tracing has been compared. The intensity increases with the increase of the water volume.
4.3. The spectral behavior of the lens
The Intensity spectrum provides some useful information regarding concentration, absorption loss and efficiency. The intensity spectra of the simulated and equation based lens are shown in Fig. 9(a) whereas the corresponding measured spectra are shown in Fig. 9(c). The spectra were taken in the focal plane of the lens. From those results it is also evident that the higher water volume provides higher intensity.
Fig. 9 Intensity and concentration factor as a function of the wavelength has been plotted. Here in (a), the simulated intensity for the calculated lens and the equation based lens are shown, whereas in (c) the corresponding spectrometer measurements are depicted. The concentration factor obtained by employing the input spectrum with the spectrum in (a) and (c) are presented in (b) and (d) respectively.
The concentration factor of a lens is the ratio of the input aperture (A1) i.e., the lens surface area to the detector aperture (A2) i.e., the focal spot area. It can be extracted from the spectral data as follows,
where, I1 and I2 are the total intensity over the lens surface area A1 and the detector area A2 respectively. Considering negligible loss, the second part of Eq. 14 indicates the intensity per unit area can also be used for the concentration factor calculation, which is plotted in the bottom part of the Fig. 9. So with this formula the concentration factor of the lenses for different volumes for the simulation and the equation based lens is plotted in Fig. 9(b). A spectrometer with an input aperture size of 4.155 cm2 were employed to the corresponding concentration factors per wavelength and are shown in Fig. 9(d). It is evident that the concentration factors was constant in the whole spectral range rather decreased at higher wavelengths starting at 700 nm which is related to absorption loss within the water.The average concentration factor over the whole spectral range for the simulation, equation based lens and the measurement are plotted in Fig. 10. As the volume of water increased, the increased intensity led to a higher average concentration factor.
Fig. 10 The average concentration factor over the whole spectral range has been compared for the simulated lens, the equation based lens and the measurement as a function of water volume.
In case of 16 liters, the water lens measurement data is shown in Fig. 9, both the solar spectrum and the concentration factor are lower than expected values which have been developed previously. Again in Fig. 10 the measured average concentration factor deviates from the simulated one and the one of the equation based values. This unexpected behavior was due to irradiation conditions in a field test deviating from idealized conditions. A possible solution to this problem bears the use of a large area solar simulator. The non-uniform incident of solar radiation, scattering of the solar radiation and some waves on the surface of the water caused additional deviations. Figure 10 therefore also represents the sensitivity against environmental perturbations. The solar incident spectra for different volumes of water were recorded and are presented in Fig. 11.
Fig. 11 The incident solar radiation for different water volume as a function of the wavelength are shown. It was recorded after each of the focal plane measurement.
The energy loss in a particular wavelength was calculated for different water volumes by the ray tracing software. From the concentrated rays at the focal spot, the incident rays of 1000 W/m2 for a particular frequency were subtracted. The whole process is repeated over the entire solar spectrum resulting the loss characteristic of particular volumetric water lens over the whole spectral range as shown in the Fig. 12. These calculations were carried out for both of the simulated lens and the equation based lens.
Fig. 12 The loss of water lenses for different water volumes as a function of wavelength are compared for the simulated lenses and the equation based lenses.
Although a higher amount of water provided a higher concentration factor, the lens volume caused greater absorption loss resembling the behavior shown in Fig. 1. The energy loss in the visible spectral range is small, in the UV- range is moderate and in the near infrared region is greater. These properties of a water lens can enhance the efficiency of devices which operate in the visible spectral range. The average loss at 301 nm and 1000 nm was 11.95% and 79.43% more than the loss at a wavelength of 501 nm.
4.4. Comparison of the methods
Figure 13 shows the comparison of the optical properties of the 10 liter water lens for three methods, i.e. the simulated lens shape, the extracted lens shape from photo and the spectral measurement. For the intensity vs. wavelength graph, the upper one in Fig. 13, all three methods show a similar behavior e.g., a spectral dip at 540 nm, 589 nm, 729 nm and 759 nm. Moreover the maximum intensity was observed at 566 nm for spectral measurement with 782 W/m2, at 559 nm for simulation with 761 W/m2 and 559 nm for the equation based lens with 870 W/m2. The concentration factor of these three methods also shows similar shapes with slight deviations, depicted in the middle graph of Fig. 13. The average concentration factor for the simulation, lens shape from images and spectral measurement is 21.79, 23.78, and 18.67 respectively. The lower graph of Fig. 13 shows the normalized spectral loss for the simulation and the spectral measurement. In the spectral range over 500 nm, the normalized loss curves of both methods match whereas below 500 nm a slight deviation is observed.
Fig. 13 Intensity, concentration factor and loss of 10 liter water lens as a function of the wavelength have been compared for the simulation, the lens based on equation and the measurement.
4.5. Comparison of Water lens with aspheric shape
It is important to consider the maximum concentration which could possibly be achieved by the water lens. One limitation is given by deviations of the shape with respect to the idealized aspheric shape. The aspheric lens height z is a function of the distance from the optical axis r and can be represented by the following equation [10]
where, κ is the conic constant, Ai is the higher order term constants and is the radius of lens curvature at the lens vertex.Using the measured focal length of the 10 liter water lens i.e., 114 cm, the optimum corresponding aspheric lens shape has been designed. The design procedure started with producing a simple plano-convex lens having focal length of 114 cm and water as lens material. Thereon the curved lens surface of the plano-convex lens was converted to an aspheric surface. Then the lens was optimized to achieve maximum concentration factor as well as maximum intensity at focal spot by varying the parameters R0, κ, and Ai in Eq. (15). All these design and optimization process were performed by the optical simulation software.
Afterwards the optimization, the 10 liter water lens obtained for photo extraction was compared with the optimized aspheric lens. The upper picture of Fig. 14 compares both of the lens shapes and their focusing capability. The lens thickness or the lens height for the water lens and the aspheric lens are 8.07 cm and 8.55 cm respectively. It is clearly evident that the aberration is less dominant in the aspheric design. Due to low aberration, the maximum intensity in the focal spot of aspheric lens is 1.8 times more than the water lens as depicted in the lower left picture of Fig. 14. Moreover, the spectral performances of the two lenses have been carried out and compared in the lower right picture of Fig. 14. The aspheric lens provides significant elevation of the intensity as well as the concentration factor at every frequency due to the better focusing capability. The average concentration factor over the considered frequency range for the aspheric lens is 99.5 which is 4.2 times greater than the water lens.
Fig. 14 Comparison of the aspheric lens and the photo extracted water lens of 10 liter water volume. The upper picture compares the focusing capability as well as lens shape mismatch. The lower left graph compares the intensity profile in the focal spot. The lower right graph shows the intensity and concentration factor comparison as a function of wavelength.
In terms of optical performance, the water lens is little behind of the idealized aspheric lens. But considering the manufacturing cost and complexity it triumph over the aspheric lens with a slight sacrifice of the focusing capability, the focal spot size and the concentration factor.
5. Conclusion
The water lens exhibited a change of the focal length almost up to 50% which gives one more degrees of freedom for the control. The refractive index of the lens can be changed as well as tuned finely with other transparent liquids and the optical behavior can be tailored accordingly. The lenses presented in this study were investigated in the large scale which was not performed before. The intensity could be increased around up to 400% with the change of water volume. The water lens also demonstrated a moderate average concentration factor over the whole spectral range of up to 25. Although, it has a higher loss at higher wavelengths, it filters out the near infrared spectrum. This can be useful to prevent overheating or can work as a filter for some solar energy conversion devices. The cost for the manufacture is low compared to other state of the art solar concentrators with a trade-off of the concentration factor. Moreover, the cost reduction can be manifolded by the number of existing lenses employing water lens array. The maximum water volume Vmax which is 16 liter in this case shows the best performance for the investigated water lens systems because it demonstrates maximum intensity, smallest focal length and in absence other disturbances maximum concentration factor. Additionally it mimics the ideal aspheric lens shape closely which is a benefit for good optical properties.
Water lenses can be useful for solar thermal application by means of cost reduction and good performance with more flexibility of lens control. In future water lenses shall be investigated for use for different solar energy conversion devices, e.g. solar cell, thermoelectrics, thermo photovoltaic, stirling engine and more. The behavior of the lenses at higher temperatures needs also to be studied as well as the lens behavior with different kind of liquid shall be done.
Acknowledgments
The authors would like to thank Prof. Henning Schütte and Prof. Alexander Struck for their advice regarding the FEM simulations and the mechanical modeling of the foil deformations. Also the authors would like to thank Tashneem Ara Islam and Dakshaw Rohit for the experimental support.
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