Journal of Micromechanics and Microengineering
`
`Diamond turning and soft lithography processes
`for liquid tunable lenses
`
`To cite this article: H M Leung et al 2010 J. Micromech. Microeng. 20 025021
`
`View the article online for updates and enhancements.
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`IOP PUBLISHING
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`J. Micromech. Microeng. 20 (2010) 025021 (11pp)
`
`JOURNAL OF MICROMECHANICS AND MICROENGINEERING
`
`doi:10.1088/0960-1317/20/2/025021
`
`Diamond turning and soft lithography
`processes for liquid tunable lenses
`
`H M Leung1, G Zhou1,3, H Yu1, F S Chau1 and A S Kumar2
`
`1 Micro/Nano System Initiative Laboratory, Department of Mechanical Engineering, National University
`of Singapore, 10 Kent Ridge Crescent, Singapore 119260
`2 Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent,
`Singapore 119260
`
`E-mail: mpezgy@nus.edu.sg
`
`Received 11 October 2009, in final form 9 December 2009
`Published 18 January 2010
`Online at stacks.iop.org/JMM/20/025021
`
`Abstract
`Making use of the capability of high precision diamond turning in producing 3-dimensional
`free form optical surfaces with excellent surface finish, molds for various types of liquid
`tunable microlenses are fabricated. Subsequently, a rapid prototyping process known as soft
`lithography is applied to the fabricated mold to replicate multiple lens structures. This method
`provides an efficient and reliable way of generating rotationally symmetric free form optical
`surfaces that are otherwise difficult to produce with conventional methods such as lithography
`and etching methods. Using atomic force microscopy, white light interferometry and a
`mechanical profiler, it is verified that the surface quality and dimensional accuracy of the
`replicas are preserved. We demonstrate the practical usefulness of the proposed fabrication
`methods by developing and experimentally testing three different liquid tunable lenses, namely
`(1) a diffractive/refractive hybrid lens that reduces chromatic aberration within the visible
`spectrum, (2) a double focusing lens and (3) an aspherical lens that minimizes spherical
`aberration.
`
`(Some figures in this article are in colour only in the electronic version)
`
`1. Introduction
`
`Producing three-dimensional (3D) free form surface relief is
`important in the field of optics, especially when the demand
`for optical quality and versatility continue to increase. At
`the same time, optical systems are continuing to strive for
`compactness, with many working with light sources that can
`range from x-rays to IR [1–5]. This drives the active research
`on microlenses, which increasingly requires design of free
`form surface relief to optimize the optical performance of the
`lens systems targeted for a specific application. Applications
`that have benefited from the use of free form optical surfaces
`include beam shaping [6–8], imaging systems [9, 10], optical
`data storage systems [11, 12] and aberration reduction
`[5, 13–15].
`In many instances, free form optical elements
`can also reduce lens count, thereby enabling the miniaturizing
`of optical systems.
`
`3 Author to whom any correspondence should be addressed.
`
`There are a number of fabrication methods that have
`been developed to fabricate free form micro-optical elements.
`Among them is a method that makes use of selective wet
`etching on a boron-doped silicon substrate [16]. Alternatively,
`lithography and etching techniques can be used to fabricate
`micro-refractive [17] and micro-diffractive lenses such as
`Fresnel lens [3, 18, 19]. If binary optic masks are used, stepped
`profiles will result. Each time the number of phase levels is
`doubled with an additional cycle of photolithography with a
`binary optic mask, there is a mask alignment error introduced
`[20]. Thus, to keep the alignment error within a reasonable
`limit, the number of phase levels fabricated has to be small.
`This in turn limits the efficiencies of the lenses. The use of gray
`scale masks and high-energy-beam-sensitive (HEBS) glass
`has provided alternatives that address some of the fabrication
`issues associated with binary optic masks. In contrast to binary
`optic masks, the use of gray scale masks and HEBS requires
`just a single exposure-etching process to produce multiple
`phase levels that can closely approximate continuous profiles.
`There is also a research team that modified the conventional
`
`0960-1317/10/025021+11$30.00
`
`1
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`© 2010 IOP Publishing Ltd Printed in the UK
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`J. Micromech. Microeng. 20 (2010) 025021
`
`lithography cum etching method to produce various structures
`with sloping walls.
`Instead of using a stationary mask, the
`team put the mask in continuous motion during UV exposure
`[21]. By taking into consideration the motion of the mask,
`the light propagation characteristics and variation in refractive
`index across the depth of the photoresist it is possible to
`design various 3D structures with smooth continuous profiles.
`Other alternatives developed include excimer laser ablation
`techniques which can be used to write 3D lens structures on
`polymeric substrates [22]. Photoresist thermal reflow methods
`have also been successfully implemented to produce various
`lens structures that can achieve high fill factors [23, 24].
`Thus far, the fabrication methods discussed all involve
`clean room processes which use non-contact methods such as
`lithography and laser ablation to define the lens structures.
`There is another class of fabrication process that uses
`mechanical methods to produce 3D microstructures. Single-
`point diamond turning (SPDT) and diamond shaping are
`prominent examples. Typically, with the use of either high
`frequency response piezoelectric actuators for a fast tool servo
`[25] or mechanical slides with a feedback response for a
`slow tool servo [26], diamond turning processes can be very
`precisely controlled. With the proper selection of rotational
`speed, feed rate, depth of cut, geometry of the diamond tip on
`the cutting tool and substrate material, microstructures with
`surface quality suitable for optical purposes can be fabricated
`with diamond machining methods [15, 27].
`There has been increasing emphasis on variable focusing
`lenses as many optical systems now require dynamic tuning to
`sense and acquire data. Most of the liquid tunable lenses in the
`literature focus on developing different methods to improve the
`actuation methods and frequency response of tunability. For
`instance, the electrowetting effect has been used to change
`the surface energy and hence the radius curvatures of liquid
`lenses on dielectric surfaces and capillaries [28, 29]. There
`is also a type of liquid lens that makes use of pressure to
`harmonically oscillate a liquid lens to improve the response
`times [30]. Alternatively, liquid pressure can be used to deform
`an elastic membrane of either uniform [31, 32] or radially
`varying thickness [33, 34].
`Here we present a fabrication process that combines
`diamond machining and soft
`lithographic replication to
`produce various liquid tunable lenses.
`Instead of solely
`focusing on the design of the actuation method of liquid
`lenses, there are also special considerations to enhance targeted
`aspects of optical performances of the liquid lenses. We
`demonstrate that it is possible to exploit the main strengths of
`the diamond machining technique, which are its versatility in
`fabricating genuine 3D free form structures and the precision
`in dimensional control, to generate continuous optical surface
`relief in combination with liquid tunability capabilities with
`an elastomeric membrane.
`
`2. General structure of the tunable liquid lenses
`
`Figure 1 shows the overall design of the liquid lens proposed
`in this work.
`It consists of a cylindrical lens cavity which
`has a certain lens profile of interest integrated on its bottom
`
`H M Leung et al
`
`(a)
`
`(b)
`
`(c)
`
`Figure 1. The overall device consists of two parts. (a) The first is a
`thick slab of PDMS consisting of a lens profile of interest, a lens
`cavity and two liquid channels. (b) The second part is a thin film of
`PDMS bonded over it. (c) A cross-sectional view of the device with
`the approximate dimensions of the structural features.
`
`surface. On both sides of the lens cavity are narrow and long
`liquid channels, one acting as an inlet and the other acting as
`an outlet. This structure is hermetically sealed by a thin and
`elastic film of polydimethylsiloxane (PDMS) with only two
`small holes punctured above the ends of the liquid channels to
`allow the delivery of liquid from an external source to the lens
`cavity. When distilled water, the working liquid of choice,
`is pumped into the cavity, the uniform pressure created will
`deform the PDMS film and that constitutes the tunable liquid
`refractive lens.
`The deformation of the PDMS film is subjected to a fixed
`boundary condition due to the permanent bonding of the film
`to the slab. As a result, the deformation does not follow an
`exact spherical shape. Nevertheless, as a rule of thumb, if only
`within 80% of the central region of the lens is considered, it
`can be safely assumed that the deformation is spherical [35].
`Moreover, considering the small thickness–diameter ratio of
`the elastic film used in this work, there is little rigidity at
`the circular boundary. An 80% or smaller aperture is used
`in the experiments carried out in this work to ensure that the
`boundary effects do not affect the experiments.
`
`2
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`J. Micromech. Microeng. 20 (2010) 025021
`
`together with the lens
`The tunable refractive lens,
`integrated at the bottom of the cavity, form an optical lens
`system that can be designed to improve imaging qualities over
`a range of focal lengths. The actuation of the liquid lens
`involves the pumping of just one liquid. Although in the
`experiments of this work a digitally controlled syringe pump
`was used to control the volume of injection, pressure sensors
`could be used to tune the focal length of the liquid lens instead,
`as demonstrated in [36, 37].
`There are a number of advantages of using diamond
`machining techniques to fabricate molds of liquid lens devices
`of such a design as indicated in figure 1(c). Firstly, the
`feature sizes of the lens device range between the orders
`of micrometers and millimeters. The aspect ratios of the
`different features are also vastly varied.
`Devices with
`these characteristics typically cannot be easily fabricated with
`the use of lithography and etching techniques. Moreover,
`these techniques would not be able to efficiently remove the
`large volume of material that is required to create the cavity
`that can be as large as 12 mm in diameter and 800 μm
`in depth. The large depth of the lens cavity is sometimes
`necessary to accommodate an optical surface that has large
`height variation across its diameter.
`In addition, it is also
`likely that the walls of the cavity could not be vertically etched
`for depths in that range. In contrast, the versatility of diamond
`machining enables it to create such features with ease without
`compromising the surface integrity and dimensional accuracy.
`The depth and size of the structure fabricated by diamond
`turning are limited only by the geometry and size of the
`diamond tip on the inset, which is typically in the order of
`a few hundreds of microns to a millimeter.
`The rotationally symmetrical
`lens cavity and the
`integrated lens profile are generated by diamond turning
`while the rectangular liquid channels are produced by the
`shaping process. To ensure affordability and efficiency of
`the fabrication process, a rapid prototyping method known as
`soft lithography is used on the diamond machined mold. It
`is a replication process that utilizes an elastomeric material to
`replicate structures with features as small as in the nano scale
`with high reliability [38]. Because soft lithography preserves
`the main strength of diamond machining, which is the tight
`dimensional control that accompanies the generation of 3D
`surface relief, the two processes complement each other well.
`Apart from being able to achieve rapid replication, there
`are other advantages of combining soft
`lithography with
`PDMS and diamond turning on a rigid PMMA plate. Any
`cutting tool has a limited tool life and toward the end of the
`tool life, there might be geometrical changes on the tool tip
`that affect the dimensional accuracy of the machining and
`surface quality of the work piece produced. Thus, it would be
`advantageous to first fabricate a high-quality lens device on a
`rigid substrate with diamond machining before using the soft
`lithographic process to obtain multiple replicas. This method
`enables a larger number of usable lens devices to be produced
`within the inset’s tool life.
`In addition, hermetic sealing can be easily achieved
`between a PDMS replica and a PDMS membrane with the
`use of oxygen plasma, which gives the proposed fabrication
`flow process an added advantage.
`
`H M Leung et al
`
`Figure 2. The cross-sectional views of the tunable lens device at
`each stage of the fabrication process are shown. Firstly, diamond
`turning of a certain lens profile and cavity on a PMMA substrate
`was carried out. After shaping of liquid channels, the PMMA mold
`was completed. After a cycle of soft lithography, a PDMS inverted
`replica was obtained. The desired PDMS device was obtained after
`a second cycle of soft lithography. A PDMS membrane was bonded
`to the slab of PDMS replica, sealing the cavity. Holes are punctured
`at the ends of the liquid channels to enable the pumping of the
`refractive lens.
`
`3. General fabrication process flow
`
`Here, three different types of liquid lenses will be presented.
`The general structures of the lenses are all similar to those
`shown in figure 1 and so are the fabrication processes. The
`only difference between them is the integrated lens profile
`generated by diamond turning at the bottom of each lens
`cavity. The three different integrated lens profiles explored
`in this work are namely (1) a diffractive Fresnel lens, (2) a
`double focusing lens and (3) an aspherical lens.
`The proposed general
`fabrication process flow, as
`summarized in figure 2, combines high-precision single-point
`diamond machining on a polymethylmethacrylate (PMMA)
`substrate and the soft lithographic replication process with
`an elastomeric material known as PDMS. Firstly, the required
`mold has to be produced by diamond machining methods. The
`reverse of the mold will be replicated through a cycle of soft
`lithography and that serves as a PDMS mold for the next cycle
`of soft lithography. The second PDMS replica, which takes on
`the exact shape of the PMMA mold, will then be hermetically
`sealed with a PDMS film to complete the fabrication of the
`required lens device. The fabrication process at each stage
`will be described in greater detail in the subsequent sections.
`
`3
`
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`J. Micromech. Microeng. 20 (2010) 025021
`
`H M Leung et al
`
`Table 1. Machining parameters used to fabricate the PMMA mold.
`
`Infeed
`rate
`−1)
`(mm min
`
`Crossfeed
`rate
`−1)
`(mm min
`
`Spindle Depth of
`speed
`cut
`(rpm)
`(μm)
`
`Turning
`
`5
`
`Shaping
`
`150
`
`5 (for rough cut)
`1 (for last cut)
`150
`
`1000
`
`0
`
`5
`
`5
`
`The machining parameters used are summarized in
`table 1.
`Since only the crossfeed rate for the final cut
`determines the surface roughness, a higher crossfeed rate
`is used for the cutting cycles that precede the final cut to
`expedite the machining process. Only during the last cycle
`of diamond turning will the crossfeed rate be lowered to
`−1 to obtain a smooth surface suitable for optical
`0.1 mm min
`purposes. As opposed to the crossfeed rate, the infeed rate
`does not have a significant effect on the surface finish and it is
`arbitrarily chosen to be the same as the crossfeed rate.
`When diamond turning has completed, the vacuum chuck
`that holds the PMMA plate stops rotating and the shaping of
`the non-rotationally symmetrical liquid channels commences
`immediately after. It should be noted that since turning and
`shaping commenced one after the other without releasing
`the workpiece from the vacuum chuck, they share the same
`machining referencing point.
`As opposed to the integrated lens surface, there is no
`requirement for the surface finish of the water channels since
`their sole purpose is to transport fluid in and out of the
`lens cavity. Therefore, even if the high crossfeed rate of
`−1 during the shaping process results in rough
`150 mm min
`surfaces of the water channels, it is an acceptable speed.
`Moreover, the high speed does not cause perceptible damage
`to the diamond tool tip, partly because the depth of cut is
`merely 5 μm. The PMMA workpiece is released from the
`chuck after the fabrication of lens cavity and liquid channels
`on the diamond cutting lathe are both completed.
`Since the opening of the lens cavity defines the boundary
`condition of the tunable lens, the channels that deliver water to
`it must be sufficiently narrow such that the deformation of the
`PDMS film remains spherical. For all the tunable lens devices
`presented, 80 × 80 μm2 liquid channels are used. Similar
`to the turning of the lens cavity, the two liquid channels are
`shaped in steps of 5 μm until the desired depth is reached.
`
`3.2. Soft lithographic replication processes
`
`With the PMMA master mold at hand, two cycles of soft
`lithographic replication processes need to be performed to
`obtain the PDMS lens device with the required structure.
`PDMS (Dow Corning Corp’s Sylgard 184), a silicone
`elastomer, is chosen to be used for the replication process
`due to its high transmittance over a wide spectral range [39]
`and its elasticity (E ≈ 750 kPa) [40].
`Firstly, a PDMS pre-polymer is prepared by mixing a
`dimethylsiloxane monomer base and curing agent in a ratio
`of 10:1.
`In the presence of platinum-based catalyst, silicon
`hydride groups in the curing agent bond with the vinyl groups
`
`◦
`Figure 3. Image of the 0–45
`facet-cut single crystalline
`diamond-tip cutting tool under an optical microscope.
`
`Figure 4. Depth of cut is maintained at 5 μm and the profile is
`progressively cut until the required depth of the feature is reached.
`
`3.1. Fabrication of the PMMA mold
`
`All diamond machining processes are carried out on a three-
`axes diamond machining lathe, Toshiba-ULG-100A(HY),
`which requires a 10 nm least input increment in the x-, y-
`◦
`and z-axes. To obtain the vertical walls, a 0–45
`facet-cut
`single crystalline diamond-tip cutting tool (Osaka Diamond
`Industrial Co., Ltd) was selected, as shown in figure 3. The
`substrate material is a 3 mm thick and 10 cm wide PMMA
`plate. Since the diamond tip on the inset is a facet-cut tool,
`it is brittle and can be easily chipped if the depth of cut is
`large. Therefore, the profile is machined out progressively in
`numerous cycles, with the depth of cut maintained at 5 μm
`each time. This is illustrated in figure 4.
`The rotationally symmetrical
`lens cavity and the
`integrated lens profile at the bottom surface are both generated
`by SPDT in a single, continuous step.
`This has an
`important implication of ensuring the optical centers of the
`lens integrated on the bottom surface of the lens cavity and
`that of the tunable refractive lens as defined by the deformable
`membrane are automatically aligned. This is because the
`optical center of the tunable refractive lens is defined by
`the circular opening of the lens cavity. As opposed to
`traditional manual alignment of individual adjacent lenses, this
`fabrication method could significantly minimize the human
`error that could arise during manual alignment of the adjacent
`lenses. Much time and effort could also be saved during optical
`testing because of the auto-alignment of the lenses.
`
`4
`
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`J. Micromech. Microeng. 20 (2010) 025021
`
`H M Leung et al
`
`Table 2. Roughness values of the diamond-turned PMMA mold and the replicated PDMS structures.
`
`Object
`
`Diamond-turned
`PMMA
`
`Inverted PDMS mold
`after the 1st cycle
`of soft lithography
`
`PDMS lens device
`after the 2nd cycle
`of soft lithography
`
`Average roughness, Ra (nm)
`RMS roughness, Rrms (nm)
`Mean peak–valley, Rpv (nm)
`
`37
`48
`137
`
`6
`9
`27
`
`17
`22
`49
`
`in the base. As this 3D cross-linking process progresses for
`a sufficiently long period of time, which is determined by the
`mixing ratio and curing temperature, the polymerization effect
`will result in solid PDMS.
`in a
`After degassing the well-mixed pre-polymer
`desiccator, it is poured onto the PMMA master mold and
`◦
`C over
`brought to complete curing at a temperature of 65
`a period of 24 h. Subsequently, the inverted PDMS structure
`is released from the PMMA. This inverted PDMS structure
`has a minimum thickness of 5 mm to ensure sufficient rigidity
`as a mold for the second cycle of soft lithography. Another
`small volume of pre-polymer is prepared in the same manner
`as the first cycle and poured onto the inverted PDMS mold.
`The only difference between the first and second cycles of soft
`lithography is the amount of time that the pre-polymer was
`placed in the oven to cure before release. In the second cycle
`of soft lithography, the pre-polymer is poured on a PDMS
`mold. Because they are of the same material, the two could
`bond permanently if the pre-polymer is left to be completely
`cured, making release of the replica impossible. Thus, instead
`of the usual 2 h, the replica is released after 30 min of curing
`◦
`at 65
`C, when the pre-polymer had solidified sufficiently but
`has yet to be completely cured. Careful release of the two
`was aided with isopropyl alcohol (IPA). The released replica
`◦
`is again left at 65
`C to allow completion of the curing process
`for the next 22 h. The thin PDMS film that is required to seal
`the replicated structure is prepared by spin coating PDMS on
`a silicon wafer. The spin coating process takes place at 1000
`rpm for 60 s at ambient temperature, resulting in an average
`film thickness of 70 μm after curing.
`On the surfaces of PDMS structures are hydrophobic
`methyl groups. To promote hermetic sealing between the
`PDMS film and the PDMS replica, the surfaces are oxidized
`through exposure to a 200 W oxygen plasma for 30 s. After
`◦
`C
`that,
`they are brought
`into contact and left
`in a 65
`oven for over 3 h allowing hermetic bonding between the
`two. Puncturing holes above the ends of the liquid channels
`completes the fabrication process of the tunable hybrid lens
`devices.
`
`4. Experimental results on the reliability of the
`fabrication process
`
`4.1. Surface roughness
`
`Surface roughness is an important consideration in the
`fabrication of optical
`lenses and thus,
`the atomic force
`microscope (AFM) is used to evaluate the surface roughness
`
`of the diamond-turned mold and the PDMS replicas generated
`from the first and second cycles of soft lithography. Because
`the same set of fabrication process parameters is used for
`all the lens devices to be discussed in this work, the surface
`characteristics of the structures obtained at each stage of
`the fabrication process would be similar for all the devices.
`One of the three devices fabricated in this work is a liquid
`tunable diffractive/refractive hybrid lens (refer to section 5
`for more details on this lens) and it is used as an example to
`evaluate the surface quality of the structures produced by the
`proposed fabrication process.
`The 3D and 2D representation of the AFM results on
`the diamond-turned PMMA mold, the inverted PDMS replica
`and the final PDMS replica are shown in figures 5(a)–(c)
`respectively.
`The tabulated values of the average (Ra),
`root mean square (Prms) and mean peak–valley (Rpv) surface
`roughness are given in table 2. Firstly, it can be observed
`that the surface roughness of the diamond-turned PMMA
`is significantly higher than both of the replicated PDMS
`structures and this could be because of the minute surface
`reflow that is present on the released mold. Secondly, the
`average and root mean square roughness of the final PDMS
`replica are 17 nm and 22 nm respectively. Because these
`values are smaller than one-tenth of the smallest wavelength
`in the visible spectrum, the surface roughness will not have any
`adverse effect on the optical performance of the lenses.
`
`4.2. Reliability of diamond turning and soft lithography
`
`It is commonly known that PDMS shrinks upon curing.
`This could lead to distortion of the surface profile which is
`detrimental to the performance of the end product. Although
`the actual dynamics of it
`is not
`thoroughly understood,
`there are a number of research works done to obtain the
`empirical relationship between PDMS shrinkage and a number
`of process parameters during curing of PDMS, such as the
`aspect ratio of the PDMS structures, mixing ratio of base and
`curing agent, baking temperature and baking time [41–44].
`Generally, a lower baking temperature and mixing ratio would
`result in minimal shrinkage [41]. Because of this, the baking
`◦
`temperature is set to be 65
`C such that it can be fully cured
`in a reasonably short period of 2 h while limiting the extent of
`shrinkage within acceptable levels. Furthermore, considering
`that the aspect ratios of the devices developed in this work
`are between 0.02 and 0.07, the shrinkage is expected to be
`minimal.
`To verify that, as well as to substantiate the statement
`that diamond turning is a high-precision process with tight
`
`5
`
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`

`J. Micromech. Microeng. 20 (2010) 025021
`
`H M Leung et al
`
`(a)
`
`(b)
`
`(c)
`
`Figure 5. AFM images of the surface condition of (a) a diamond-turned PMMA plate, (b) a PDMS structure after first cycle of soft
`lithography and (c) a PDMS structure after the second cycle of soft lithography are shown together with a table of mean surface roughness
`of the respective structures.
`
`dimensional control, the surface profiles of the diamond-turned
`PMMA mold and the PDMS replica after two cycles of soft
`lithography of the double focusing lens are studied (refer to
`section 5 for more details on this lens). They are measured
`◦
`tip angle)
`with the use of a conical tip (5 μm tip radius, 40
`on a mechanical profiler (Mitutoyo FormTracer CS5000). The
`narrow liquid channels on opposite sides of the opening of the
`lens cavity are used as markers to ensure that the profiler runs
`across the center of the integrated lens profile on the mold and
`the replica.
`the precision of the diamond turning process
`Firstly,
`is investigated by comparing the intended diamond-turned
`profile that is generated according to ray tracing calculations
`with the measured profile of the diamond-turned PMMA mold.
`From figure 6(a), it is apparent that the surface profile of
`the PMMA mold follows the intended profile extremely well.
`Next, the fidelity of the soft lithographic replication process
`
`is studied by comparing the measured profile of the PDMS
`replica with that of the PMMA mold. With reference to
`figure 6(b), the surface profile of the final replica closely
`resembles that of the PMMA mold very well from x = −5 to
`x = 5 while the regions near the edges deviate slightly from the
`expected profile. This observation is aligned with a simulation
`result reported in [44].
`It demonstrated that distortion
`tends to be near the edges and with increasing aspect ratio,
`distortion will affect areas increasingly closer to the central
`region.
`From the profile measurement results, it can be concluded
`that in general that diamond turning is capable of generating
`PMMA molds in strict accordance with the designed values. In
`addition, soft lithography preserves the dimensional integrity
`of the replica, apart from a small region near the edges. By
`using an 80% aperture, it is ensured that the slightly distorted
`regions do not affect subsequent optical experiments.
`
`6
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`APPL-1038 / IPR2020-00897 / Page 7 of 12
`APPLE INC v. COREPHOTONICS LTD.
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`

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`J. Micromech. Microeng. 20 (2010) 025021
`
`H M Leung et al
`
`(a)
`
`(b)
`
`Figure 6. (a) The surface profile of the diamond-turned PMMA
`mold fits the intended profile extremely well. (b) Apart from a small
`portion near the edges, the surface profile of the final PDMS replica
`closely resembles that of the PMMA mold.
`
`5. Various devices fabricated
`
`By tailoring the lens profile to be integrated on the bottom
`surface of the lens cavity, different lenses with different
`functionalities can be obtained with the fabrication flow
`process described in section 2.
`In the following sections,
`the realization of a number of devices based on the fabrication
`process will be described. Their optical performance and
`physical characteristics will also be presented.
`
`5.1. Liquid tunable diffractive/refractive hybrid lens
`
`Chromatic aberration is a phenomenon that arises because
`different wavelengths are focused to different focal lengths.
`This is determined by the dispersion properties of the optical
`elements that the light passed through. The Abbe number of
`an optical element is a measure of its dispersion properties
`and to achieve achromatism, the reciprocal of the product of
`each optical element’s focal length and Abbe number must
`sum up to zero. A diffractive lens has a negative Abbe
`number while a refractive lens has a positive Abbe number.
`Therefore, by combining a diffractive and a refractive lens
`that are appropriately designed, it is possible to minimize
`chromatic aberration within a certain focal range.
`Diffractive surfaces are commonly fabricated with
`lithography and etching techniques [45]. One of the main
`shortcomings of this fabrication method is that it can only
`produce stepped features. In the presence of mask alignment
`errors, the diffractive elements typically have lower efficiency
`as compared to blazed surfaces. Alternative fabrication
`methods that include electron beam writing and gray scale
`masks have improved on these concerns, mostly on silicon-
`based substrates [46, 47]. Since those processes are usually
`lengthy and costly, those methods would be prohibitive if
`large areas or depths need to be processed. SPDT and soft
`
`7
`
`lithography provide a relatively affordable alternative while
`offering greater control over the surface quality and topology
`required.
`The tunable diffractive/refractive hybrid lens developed
`here aims to minimize chromatic aberration within the
`visible spectrum with the optical performance designed to
`be optimized at Fraunhofer D line (λ = 589.2 nm) and
`15 mm focal
`length.
`Distilled water
`is used as the
`working liquid for this and other tunable lenses presented
`in this work and its dispersion properties can be found
`[54]. As a result, the Fresnel lens has 21 annular rings of
`7.365 μm height fitted into a 5 mm diameter lens cavity.
`Figure 7(a) shows the completed PDMS lens device during
`operation. Figure 7(b) shows a 2D cross-sectional view of the
`Fresnel lens captured using a white light interferometer while
`figures 5(c) and (d) show 3D views of the entire Fresnel
`lens surface using an optical microscope and a white light
`interferometer respectively.
`To demonstrate the device functionality of the device,
`experiments were carried out
`to measure the tunability
`and chromatic aberration.
`Initially,
`the lens device was
`pumped with distilled water to fill the lens cavity without
`deforming the PDMS film. With the outlet closed, additional
`liquid was injected through the inlet. The graph shown in
`figure 8 is a summary of how the focal length of the lens device
`changed as increasing amount of water was injected into the
`device. The greater the volume of water injected, the smaller
`the radius of curvature of the deformable membrane and the
`shorter the overall focal length of the hybrid lens device. The
`hybrid lens was measured to have a focal length tunability of
`approximately 17 mm.
`In addition, the magnitude of the chromatic aberration
`of the diffractive/refractive hybrid lens is measured to be
`consistently smaller than that of a conventional single-
`refractive liquid tunable lens for the entire visible spectrum.
`The measured di