tunable liquid-filled lens integrated with aspherical surface for spherical aberration compensation

Tunable liquid-filled lens integrated with aspherical surface for spherical aberration

compensation

Hongbin Yu*, Guangya Zhou, Hui Min Leung, and Fook Siong Chau

Micro/Nano Systems Initiative, Department of Mechanical Engineering, National University of Singapore, Singapore 117576

*[email protected]

Abstract: A novel liquid-filled lens design is presented. During fabrication, high precision single point diamond turning (SPDT) is introduced into standard soft lithography process to fabricate an aspherical surface constituting one end of lens. This enables the spherical aberration associated with the operation of the conventional liquid-filled lenses to be compensated for. Through flexibly optimizing this surface contour, it can be designed to work within particular working regions with improved optical quality. At the same time, the deformable elastic membrane is still adopted at the other end of the lens, thus preserving the high focal length tunability. This proof of concept and the performance of the proposed lens have been demonstrated using the lateral shearing interferometry experiment..

©2010 Optical Society of America

OCIS codes: (220.3630) Lenses; (110.1080) Active or adaptive optics; (230.4685) Optical microelectromechanical devices.

References and links

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microfluidic network,” Opt. Express 11(19), 2370–2378 (2003). 4. D. Y. Zhang, N. Justis, V. Lien, Y. Berdichevsky, and Y. H. Lo, “High-performance fluidic adaptive lenses,”

Appl. Opt. 43(4), 783–787 (2004). 5. H. B. Yu, G. Y. Zhou, F. K. Chau, F. W. Lee, S. H. Wang, and H. M. Leung, “A liquid-filled tunable double-

focus microlens,” Opt. Express 17(6), 4782–4790 (2009). 6. L. Pang, U. Levy, K. Campbell, A. Groisman, and Y. Fainman, “Set of two orthogonal adaptive cylindrical

lenses in a monolith elastomer device,” Opt. Express 13(22), 9003–9013 (2005). 7. K. H. Jeong, G. L. Liu, N. Chronis, and L. P. Lee, “Tunable microdoublet lens array,” Opt. Express 12(11),

2494–2500 (2004). 8. J. Chen, W. Wang, J. Fang, and K. Varahramyan, “Variable-focusing microlens with microfluidic chip,” J.

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(2004). 10. W. Qiao, F. S. Tsai, S. H. Cho, H. Yan, and Y. H. Lo, “Fluidic intraocular lens with a large accommodation

range,” IEEE Photon. Technol. Lett. 21(5), 304–306 (2009). 11. F. S. Tsai, S. H. Cho, Y. H. Lo, B. Vasko, and J. Vasko, “Miniaturized universal imaging device using fluidic

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#118669 - $15.00 USD Received 16 Oct 2009; revised 26 Jan 2010; accepted 26 Feb 2010; published 28 Apr 2010(C) 2010 OSA 10 May 2010 / Vol. 18, No. 10 / OPTICS EXPRESS 9945

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photopolymerization and molding,” J. Microelectromech. Syst. 17(5), 1210–1217 (2008).

1. Introduction

As for the most commonly-used solid lens components in current commercial market, the lens structure is usually fabricated into solid substrates, such as glass and polymer, by milling or molding methods [1]. Once made, their optical performance such as focal length is fixed, and as a result, different lenses or some tuning mechanisms are needed in order to meet individual application requirements. By comparison, the recently developed pressure-driven liquid-filled lens, which is inspired from biological lenses found in animal and human eyes, can provide greater flexibility. It commonly consists of a chamber sealed with a deformable elastic membrane with a liquid (the most commonly-used being water), introduced into the chamber through the integrated microchannel network, acting as the lens medium. By simply controlling the liquid pressure, the resulting deformation of the membrane finally determines the lens surface contour, altering its optical properties, such as focal length [2]. A few types of liquid-filled lenses have been successfully developed and their focal lengths have been demonstrated to be tunable over a large range (from infinity to several millimeters for some particular designs) [3–8]. At the same time, some novel optical systems and devices have also been presented based on this technology [9–15]; for example, Zhang DeYing et al reported an adaptive zoom lens by combining two liquid-filled lens components without requiring any tuning mechanism [9], Wen Qiao et al adopted a fluidic lens as an intraocular lens to achieve a large accommodation range [10], Frank S. Tsai et al demonstrated a miniaturized universal imaging device using fluidic lens [11], and the authors’ group developed a tunable Shack-Hartmann wavefront sensor based on a liquid-filled microlens array [12]. It is obvious that the liquid-filled lenses can bring distinct advantages to certain optical application areas. Therefore, it has been receiving much interest in recent times.

Although the liquid-filled lens possesses interesting characteristics, one thing that needs to be noted is that the lens surface contour as well as its optical performance is determined by the deformation of the elastic membrane. Considering clamped boundary condition and the resultant mechanical deformation characteristic of a circular thin membrane under uniform pressure, nearly 80% of the central area of the deformed membrane can be approximated as spherical contour. This gives rise to spherical aberration during the whole lens operation range, as has been reported in some previously published literatures [16,17]. Undoubtedly, this will bring negative implications on the real-life applications of the liquid-filled lens.

In this paper, we demonstrate a novel liquid-filled lens in which a fixed aspherical surface acting as one lens end is introduced into the lens structure, whilst the other end is made of deformable membrane as before. Through optimizing the aspherical surface contour, the aforementioned spherical aberration normally associated with liquid-filled lens operation can be significantly reduced within a particular range. It is envisaged that the improved optical performance together with the preserved focal length tunability will greatly facilitate the widely reported liquid-filled lens application areas, such as intraocular lens in ophthalmology, cell phone cameras, optical communication, optical data storage, sensors and other vision applications.

2. Design and fabrication

The proposed design is similar to other reported liquid-filled lenses in that its main body is still fabricated into a PDMS substrate and consists of a sealed chamber with its top covering an elastic membrane and its sidewall connected to a microchannel through which liquid is delivered via an external syringe pumping system. The key difference, which represents the idea behind our design, lies in the bottom surface of this chamber as shown in Fig. 1. As opposed to the most commonly-used flat surface, in the current case, an aspherical surface is adopted to compensate for the inherent spherical aberration that appears during lens operation.


The contour of this surface can be flexibly optimized with ZEMAX to achieve improved optical performance of the lens within a desired operation range (focal length tuning range).

Fig. 1. Schematic of liquid-filled lens design. (a) The whole device, (b) The cross-section of device

Table 1. Structural parameters of designed lens

Part Membrane thickness Lens diameter Slab thickness Microchannel width Parameter 50µm 10mm 5mm 50 µm

Table 1 shows the specific structural parameters adopted in our design. In this case, an effective focal length of 20mm is chosen as the optimized target and only 70% lens aperture (namely 7mm aperture size) is used during the simulation by considering the characteristic of the liquid-filled lens. From the ZEMAX simulation (Fig. 2), it can be seen that the spherical aberration at focus is distinctly reduced from 2.03waves (conventional lens) to

−0.00059waves after performing optimization (wavelength = 0.587µm). For more intuitive demonstration, the results of ray tracing and the corresponding wavefront maps at the focus are also shown in Fig. 2. Since the PV and RMS of wavefront error with respect to reference spherical at focus are mainly caused by spherical aberration, the resultant decreases in their original values of 19.54waves and 5.68waves to optimized 1.383waves and 0.4543waves, respectively, can also be observed. At the same time, the spherical aberration of the lens working over other different regions, or different focal lengths, are also studied and given in Fig. 3. It is seen that with respect to the conventional liquid-filled lens (case 2), its spherical aberration will always be positive and decrease with increasing focal length from 18mm to nearly 40mm, whilst that for the optimized case (case 1), the spherical aberration gradually changes from positive in the shorter focal length regions to nearly zero at the optimized focal length and then turns negative with further increases of focal length. The appearance of a negative spherical aberration is caused by the over-compensation effect introduced by the aspherical surface. When comparing the amplitude of spherical aberration, the absolute value of spherical aberration in case 1 is used and the distinct turning point appearing in the graph corresponds to the chosen optimization point. It can be seen that after optimization the spherical aberration can be reduced when the lens is working in the region in which its focal length is less than 24mm.

Plastic tube

Microchannel

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Fig. 2. ZEMAX simulation results. (a) Conventional design; (b) Optimized design

Fig. 3. Simulation result of spherical aberration as a function of focal length. (Optimization point is chosen at 20mm focal length)

Since the surface design is currently focused on spherical aberration, its effect on other lens performance criteria, such as astigmatism and coma, should also be studied. Similarly, 5° and 10° incident angles in y filed have also been used in ZEMAX simulation. From the simulation result of astigmatism shown in Fig. 4(a), it can be seen that these is no distinct difference between original and optimized lens. Whilst with respect to the coma, the

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optimized lens demonstrates distinct performance improvement compared to original lens [Fig. 4(b)]. As a result, it can be seen that although the proposed method is mainly focused on spherical aberration compensation, it does not work at the expense of decreased lens performance in other aspects and even it will also do good for some of them.

Fig. 4. Simulation result of (a) astigmatism with y axis and (b) coma along y axis as a function of focal length.

In order to show the design flexibility of our proposed method, we also chose another value, 24mm focal length, as the optimized target; the corresponding results are shown in Fig. 5. As observed, the turning point is now moved to 24mm focal length and the improvement region for spherical aberration is extended to nearly 30mm focal length, but this is achieved at the expense of a reduced compensation effect over the shorter focal length region. Therefore, in real applications, in order to meet the individual requirements, the aspherical surface should be designed based on the trade-off between operation range and compensation effect as well as its effect on the optical performance.

Fig. 5. Simulation result of spherical aberration as a function of focal length. (Optimization point is chosen at 24mm focal length)

The lens is fabricated via the standard soft lithography process [18,19], including the fabrication of the mother mold and the followed molding processes. With respect to the aspherical surface contour, the commonly-used photolithography method (SU-8 based) to fabricate the mother mold is not appropriate for this case. Instead, the single-point diamond

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turning (SPDT) is used due to its high resolution (1nm) and powerful fabrication capability for curved surface. Figure 6 shows the liquid-filled lens fabrication process. Considering the characteristics of SPDT, one mold with its structure the same as that of the final device is first fabricated into a relatively hard PMMA substrate as shown in Fig. 6(a). During this step, two different working modes of SPDT are used to fabricate the aspherical surface as well as the chamber and the integrated microchannel, respectively. In one mode, the PMMA substrate is rotated, whilst the diamond tip is actuated to move along the radial direction, changing its vertical position accordingly. By combining the tip movements along these two directions, structures with rotational symmetry characteristics (such as chambers with aspherical bottom surface) can be obtained. Subsequently, the SPDT is switched to the second mode, in which the PMMA substrate is fixed and the height of the machining tip with respect to the substrate is also kept unchanged. The tip is driven to move back and forth along the radial direction just like scratching to achieve the microchannel structure. Once the mold is available, the liquid PDMS prepolymer is directly poured onto it using a barrel-like container. After complete curing in 65°C for 2 hours, the PDMS substrate with the inverse structure having been transferred is peeled off from the PMMA substrate, acting as the real mother mold for the subsequent replication process [Fig. 6(b)]. The same molding step is repeated except that in this case, since all the used materials are PDMS (including cross-linked PDMS mold and uncured liquid PDMS prepolymer), partial curing under the same temperature for 30 minutes is adopted in order to avoid any fusion between them. With this treatment, not only can the final structure pattern be successfully transferred to the device substrate, but the two parts can be easily detached. After separating these two PDMS parts, the device substrate as shown in Fig. 6(c) is further cured for 1hr 30mins for complete solidification. This device substrate is then bonded using oxygen plasma activation onto a PDMS membrane that has been spin-coated onto a silicon substrate, to form the desired lens structure. Finally, holes are manually drilled to make the inlet and outlet to the external environment [Fig. 6(d)].

Fig. 6. Fabrication process of the presented lens

3. Experimental results

Since the surface quality of a lens directly affects its optical performance, we first characterized this item using atomic force microscopy (AFM) and the corresponding results are shown in Fig. 7 (measured area is 30µm × 30µm).

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Fig. 7. AFM measurement results of surface quality. (a) PMMA mold; (b) PDMS mother mold; (c) PDMS device

It can be seen that after SPDT, the mean roughness and RMS of the surface on the PMMA mold are measured as 22.148nm and 27.389nm, respectively. After performing the first molding step, the surface mean roughness of the PDMS mother mold is reduced to 13.281nm and its RMS decreased to16.911nm. Through the second molding process using this mother mold, 7.721nm mean roughness and 10.059nm RMS can be achieved on the final device surface, sufficient to ensure a good optical surface. The improved surface quality after each molding process is mainly due to the surface tension effect of the liquid PDMS prepolymer, which partially smoothes the rough surface especially at the micro-scale.

Figure 8 shows the measured aspherical surface contour in the fabricated lens using the Mitutoyo Form Tracer CS5000. Owing to the high fabrication precision afforded by the SPDT process, the RMS difference between the actual and designed surface contours is calculated to be 32.5nm. Considering the 2nm measurement resolution of this tracer machine, this difference is considered negligible.

Like most liquid-filled lenses, focal length tunability is the most important characteristic. Using the method reported in Ref [20], the variation of focal length as a function of the applied liquid pressure is obtained and shown in Fig. 9 (fluid adopted in current experiment is distilled water). It is clear that with the pressure gradually increased to 10kPa, the focal length can reach values as short as 17mm.

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Fig. 8. Measured aspherical surface contour

Fig. 9. Tunable focal length as a function of applied pressure (*Inset is the fabricated lens)

Although currently we have no capability to quantitatively characterize the improved optical performance, a cyclic lateral shearing interferometer as shown in Fig. 10(a) was built, to qualitatively demonstrate the lens’ optical performance through observation of the interferogram of the transmitted light. In the experiment, a green laser emitted from a single mode (SM) fiber is first collimated by an achromatic lens L1 and directly incident onto the liquid-filled lens under test after passing through an iris. The transmitted light beam is then collimated by a second achromatic lens L2, which is mounted on a precision translation stage. The output beam is then directed to the cyclic lateral shearing interferometer, in which the beam is split into two parts traveling in opposite directions. When they recombine together at the exit of the interferometer, the interference pattern is obtained. The amount of lateral shearing can be controlled by the shift of mirror M3. Figure 10(b) shows the captured interferograms at two different positions (namely different amounts of defocus) with the effective focal length of the liquid-filled lens falling at the optimization point (20mm focal length). It is seen that the interferogram patterns are composed almost entirely of nearly straight lines despite the amount of defocus. From a theoretical analysis, this can only happen when no or negligible spherical aberration is present, thus demonstrating the effectiveness of the compensation provided by the aspherical surface design. When the focal length is tuned shorter (to 18.5mm), a ring-type interferogram can be observed at position A, while at

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position B, the pattern is changed to that of curved lines as shown in Fig. 10(c). This is a distinct characteristic in the presence of spherical aberration, which agrees well with the simulation result – in the region with focal lengths shorter than the optimized point, only partial spherical aberration can be compensated for, therefore leaving positive spherical aberration. Figure 10(d) presents the corresponding interferograms captured at a longer focal length (of 21.5mm). It can be seen that the curved lines pattern appears at position A, while that of the ring-type is observed at position B, which is nearly opposite to the case shown in Fig. 10(c). This is mainly caused by the over-compensation effect that is producing negative spherical aberration as shown in the simulation. All of these phenomena agree well with the analysis based on simulation results, and as a result, the lens performance of our design can be said to be qualitatively verified.

Fig. 10. Qualitative test of lens quality using lateral shearing interferometer. (a) Schematic of optical setup; Inteferograms captured at focal length (b) Equal to; (c) Shorter; (d) Longer than optimized point.

4. Conclusions

A novel liquid-filled lens design has been presented in this paper. In the design, one end of the lens is made of an aspherical surface fabricated by SPDT rather than the commonly-used flat surface. With the design, the spherical aberration associated with conventional designs can be compensated for. As a result, the corresponding optical performance of lens can be significantly improved within particular operation regions, which has been qualitatively verified with observations from a lateral shearing interferometer. At the same time, the deformable elastic membrane is still adopted at the other end, thus preserving the useful feature of high focal length tunability. AFM and tracer machine measurements demonstrate that good surface quality and high-fidelity surface contour are achieved with the fabrication method presented. To the best of our knowledge, this is the first time that high focal length tunability together with enhanced optical quality can be simultaneously realized on one lens without increasing the fabrication complexity.

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Acknowledgements

Financial support by the Ministry of Education Singapore AcRF Tier 1 funding under grant R-265-000-306-112 is gratefully acknowledged.


tunable liquid-filled lens integrated with aspherical surface for spherical aberration compensation

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