## Abstract

We report a tunable microdoublet lens capable of creating dual modes of biconvex or meniscus lens. The microdoublet lens consists of a tunable liquid-filled lens and a solid negative lens. It can be tuned either by changing the shape of the liquid-filled lens into bi-convex or meniscus or by changing a filling media with different refractive index. The micro-fabrication is based on photopolymer microdispensing and elastomer micromolding methods. The microdoublet lens can provide a solution for minimizing optical aberrations and maximizing the tunability of focal length or field of view by controlling variable and fixed lens curvatures.

©2004 Optical Society of America

## 1. Introduction

Tunable microlens arrays can play functional roles in medical stereoendoscopy, telecommunication, optical data storage, and photonic imaging, since microlens tunability can offer attractive figure of merits such as high light throughput and extinction for optical switching application, image magnification or field of view (FOV) change for multiple imaging. Tunable microlenses have been recently demonstrated using electrowetting, re-orientation of liquid crystal, or fluidic adaptive lens [1–6]. However, most previous works have been focused on a singlet microlens. Therefore the focal length tunability depends on the control of single lens curvature or the change of refractive index. A novel tunable microdoublet lens proposed here has two lens curvatures and it can create dual modes of biconvex or meniscus tunable lens. Unlike the previous tunable singlet microlenses, the focal length or FOV tunability of the microdoublet lens can be maximized by controlling the ratio of two lens curvatures as well as by selecting two different refractive indices. The suitable combination of two lens curvatures and refractive indices can also minimize optical aberrations through microdoublet lens. This paper presents the design, microfabrication and characterization of tunable microdoublet lens array based on photopolymer microdispensing, elastomer micromolding and bonding fabrication methods.

## 2. Basic configurations of tunable microdoublet lens array

The microdoublet lens consists of a tunable liquid-filled microlens and a solid negative elastomer lens of different refractive indices (n_{elastomer} and n_{liquid}) acting in combination. Each liquid-filled microlens with a variable and fixed lens curvature is connected by microfluidic networks as shown in Fig. 1. The variable lens curvature is dynamically modulated with the deflection of a thin elastomer membrane under the pneumatic control via microfluidic channels. The fixed lens curvature is predetermined from the geometry of lenslet mold. The microdoublet lens can be tuned either by changing the shape of the liquid-filled lens into bi-convex or meniscus, or by changing a filling media with different refractive index. In particular, the selection of two different refractive indices determines the tunable range of focal length. For higher refractive index of the tunable lens than that of the solid lens, under positive pressure is a high power converging lens and under negative pressure is a low power diverging lens, or vice versa.

## 3. Lens curvatures design of microdoublet

The variable lens curvature of the microdoublet mainly depends on the deflection of the distensible circular membrane. The deflection can be approximately estimated with the analytical formula for a uniformly loaded distensible circular plate with large deflections based on the theory of plates [6]. The maximum deflection *w _{0}* is derived by

where *ΔP* is the pressure drop, *a* is the radius, *t* is the thickness and *E* is the elastic modulus of a membrane. The equation shows that the maximum deflection is proportional to the cube root of the pressure and inversely proportional to the cube root of the thickness. Assuming that the profile of a deflected membrane is modeled as a spherical cap, the radius of variable lens curvature *R _{v}* is taken as

where *φ* is the aperture radius of microlens. The effective focal length of the microdoublet *f* can be calculated by applying thin-lens equation for a microdoublet lens consisting of an elastomer solid lens and a liquid-filled tunable lens acting in combination as the below.

where *R _{v}* is the radius of variable curvature,

*R*is the radius of a fixed curvature,

_{f}*n*is the refractive index of elastomer, and

_{E}*n*is the refractive index of a filling media.

_{L}The fixed lens curvature is determined by replicating lenslets on the mold with silicone elastomer. The curvatures of lenslets are controlled with the dispensed volume of photopolymer. More details will be discussed in the next session.

## 4. Microfabrication procedure

The microfabrication of tunable microdoublet lens array is based on micromolding and photopolymer microdispensing technologies as shown in Fig. 2. A 20 µm thick SU-8 photoresist as a mold of a solid negative elastomer lens array is initially patterned on a glass substrate in order to define the mold for the microfluidic network and the ring confinements of microdroplets (step I). The surface of the patterns is hydrophobically modified with fluorine based plasma to maximize the surface energy of SU-8 ring confinements [7]. Under the precise control of a droplet volume using a glass pipette (30µm in inner diameter) and a pump regulator with timed control unit, nanoliter-scale photopolymer (Norland optical adhesive 68) is dispensed onto the hydrophobic ring confinements prepatterned on a hydrophilic glass substrate. The dispensed lenslets of photopolymer are symmetrically formed into convex shape due to the uniform distribution of surface energy. The lenslets are cross-linked under UV exposure (step II). The critical functions of the ring confinements serve as providing microfluidic networks of all microlenses and spatial confinement of photopolymer droplets as well. In addition, the dispensed droplets are self-aligned in the center of the ring confinements. The fixed lens curvature is controlled with either a droplet volume of a dispensed photopolymer or a diameter of the ring confinement. The lens mold is replicated with polydimethylsiloxane (PDMS) elastomer, which is spincoated on the mold, baked at 120 °C for 15 minutes and peeled off from the mold. If microdroplets on the lens mold are densely arranged, anti-stiction coating such as Teflon^{®}-like polymer or parylene is required on the lens mold prior to PDMS replication. In the device, the anti-stiction layer is coated with Teflon^{®}-like polymer from STS (step III and IV). The elastomer microcavities are formed by bonding the replica of fixed lens curvatures with a thin elastomer film (less than 30µm) for variable lens curvatures. The thin elastomer film is separately prepared on another silicon substrate with an anti-stiction layer of photoresist. The replicated elastomer and thin elastomer film are permanently bonded together with an oxygen plasma surface treatment onto both sides and then directly detached from the substrate without dissolving the photoresist (step V and VI). Note that the thin PDMS less than 30µm in thickness need to be baked in oven at 90°C to avoid forming the bubble in the film due to the temperature difference. Figure 3 shows the SEM images of a microfabricated elastomer microcavity incorporating a fixed curvature and a variable curvature for a liquid-filled microdoublet lens, which can be tuned by an applied pressure through a microfluidic channel.

## 5. Lens characterizations

Two fixed and variable lens curvatures of microdoublet lens were characterized with an optical interferometric profiler (Wyko^{®}). The fixed lens curvature of microdoublet is determined by the curvature of lenslet on the mold, which is controlled by the dispensed volume of a photopolymer. The measured profile is comparable to that of the spherical cap calculated from lens thickness and aperture diameter. It is shown that the maximum deviation, defined by the ratio of the difference between the calculated spherical and measured profiles to the measured profile, is only less than 0.5% at the edges. Therefore, the method for calculating the dispensed volume at nanoliter scale is acceptable. The control of fixed lens curvatures with different dimension of ring confinements have also been characterized according to the dispensed volume as shown in Fig. 5. The dispensed volume of each lenslet ranges from 4nL to 30nL and it was calculated by the same method as previously described. Due to the hydrophobic confinement, the radius of fixed lens curvature decreases with dispensed volume without the expansion of droplet diameter. The change of radius of fixed curvature slows down as dispensed volume increases. The volume variation of 20 lenslets dispensed under the same pressure and dispensing conditions is less than 2.7 %.

The radius of variable lens curvature of microdoublet is dynamically tuned with the applied pressure. Figure 6 depicts the dependence of the maximum deflection of the elastomer membrane with the applied pressure for different membrane thicknesses (6a) and diameters (6b). An elastomer membrane with a diameter of 500 µm and a thickness of 10.88 µm is elastically deflected from -73 µm to 65 µm under the pressure range from -10 kPa to +10 kPa. In cases where the maximum deflection is much larger than the thickness of the membrane plate, the maximum deflection is proportional to the cube of the applied pressure as shown in Eq. (1). However, for small deflection compared to membrane thickness, the maximum deflection is theoretically linearly proportional to the applied pressure and the fourth power of the diameter [7]. The maximum deflection versus applied pressure for different membrane diameters and constant thickness is also shown in Fig. 6(b). In large deflection, the measured result corresponds to the deflection calculated by using Eq. (1) and it is shown that the maximum deflection increases with the cube root of the applied pressure as shown as the broken line in Fig. 6(a). The calculation is carried out with the elastic modulus of 4 MPa. The radius of the variable lens curvature with respect to the applied pressure was calculated by using Eq. (2) with the measured maximum deflection. Figure 7 shows that the variable lens curvature of a 350 µm in diameter and 27 µm thick circular membrane changes according to pressure drop between -10kPa to 10 kPa. The deflected concave or convex shapes of the membrane are symmetric across the circular membrane.

Figure 8 shows the characterizations of the microdoublet lens with DI water (n_{water}=1.33<n_{PDMS}=1.41) and oil (n_{oil}=1.52>n_{PDMS}=1.41) under the applied pressures between -10 kPa and 10 kPa. The focal length depending on the refractive index of the filling media is measured with a laser wavelength of 535 nm. Under the negative pressure is a positive meniscus lens which diverges a colliminated light. However, if the refractive index of a liquid-filled lens is higher than that of the elastomer lens (n_{PDMS}=1.41), the light can converge onto the focus under negative pressure. For example, the focal length for the refractive index of 1.51 changes from negative into positive between -1.5 kPa and -2 kPa. Conversely, under positive pressure is a biconvex lens which converges onto focus. If the refractive index of the filling media is lower than that of elastomer, the light can also diverge even though the lens shape is biconvex. For water of n_{water}=1.33, the focal length changes from negative into positive at the positive pressure between 1 kPa and 1.5 kPa. Especially, for higher refractive index than n_{PDMS}=1.41, the microlens can be coarse tuned with negative pressure as well as fine tuned with positive pressure and vice versa for lower refractive index than that of the elastomer. The focal length ranges from several hundreds of microns to infinity in both positive and negative focal length.

## 6. Conclusions

In this work the microdoublet lens array with wide range tunability has been designed, fabricated and characterized. The novel tunable microdoublet lens can create dual modes of biconvex or meniscus tunable lens. The microdoublet lens can provide a solution for minimizing optical aberrations as well as maximizing the tunability of focal length or field of view either by changing two different lens curvatures or by selecting lens materials of different refractive indices. The microdoublet lens array can be useful for numerous photonic applications including medical imaging in minimally invasive surgery as well as optical communication applications.

## Acknowledgments

This work was supported by the DARPA Bio-Optic Synthetic System (BOSS) program.

## Reference and links

**1. **P. J. Smith, C. M. Taylor, E. M. McCabe, D. R. Selviah, S. E. Day, and L. G. Commander, “Switchable fiber coupling using variable-focal-length microlenses,” Rev. Sci. Instrum. **72**, 3132 (2001). [CrossRef]

**2. **J. Jang and B. Javidi, “Improvement of Viewing Angle in Integral Imaging by Use of Moving Lenslet Arrays with Low Fill Factor,” Appl. Opt. **42**, 1996 (2003). [CrossRef] [PubMed]

**3. **T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phy. Lett. **82**, 316 (2003). [CrossRef]

**4. **L. G. Commander, S. E. Day, and D. R. Selviah, “Variable focal length microlenses,” Opt. Commun. **177**, 157 (2000). [CrossRef]

**5. **D. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. Lo, “Fluidic adaptive lens with high focal length tunability,” Appl. Phy. Lett. **82**, 3171 (2003). [CrossRef]

**6. **N. Chronis, G. L. Liu, K. Jeong, and L. P. Lee, “Tunable liquid-filled microlens array integrated with microfluidic network,” Opt. Express **11**, 2370 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-19-2370 [CrossRef] [PubMed]

**7. **S. Timoshenko, *Theory of Plates and Shells*, (McGraw-Hill, 1940).

**8. **J. Seo, E. Ertekin, M. S. Pio, and L. P. Lee, “Self-assembly templates by selective plasma surface modification of micropatterned photoresist,” 15th IEEE International Micro Electro Mechanical Systems Conference, 192 (2002).