This paper describes a simple method for fabricating a variable-focus lens by
using PDMS (polydimethylsiloxane) and filling with liquid for the
variable-focus lens. The lens diameter of 2-mm was designed in this experiment
and expected to reach the focal length in the range of 3 ~ 12 mm. The
theoretical value between the liquid volume and the lens contact angle at
different focal lengths were simulated and measured. The pumped-in volumes
ranged from 200 to 1400 $\mu$l, the contact angles ranged from 14.25 degrees to
49.02 degrees. Changing the deformation of PDMS film using different
micro-fluidic volume produces the variable focal length from 4 10 mm in this
experiment. The proposed method successfully fabricated a variable-focus lens.
Bonding PDMS only once using no expensive instrument such as oxygen plasma was
accomplished. The final objective is to insert the variable focus lens into
portable optical imagery products.Comment: Submitted on behalf of EDA Publishing Association
  (http://irevues.inist.fr/EDA-Publishing

Yang, Chung-Yao

Yang, Hsiharng

Yeh, Mau-Shiun

English

arXiv

This paper describes a simple method for fabricating a variable-focus lens by using PDMS (polydimethylsiloxane) and filling with liquid for the variable-focus lens. The lens diameter of 2-mm was designed in this experiment and expected to reach the focal length in the range of 3 ~12 mm. The theoretical value between the liquid volume and the lens contact angle at different focal lengths were simulated and measured. The pumped-in volumes ranged from 200 to 1400 µl, the contact angles ranged from 14.25°to 49.02°. Changing the deformation of PDMS film using different micro-fluidic volume produces the variable focal length from 4 ~ 10 mm in this experiment. The proposed method successfully fabricated a variable-focus lens. Bonding PDMS only once using no expensive instrument such as oxygen plasma was accomplished. The final objective is to insert the variable focus lens into portable optical imagery products

I-Revues

 Stresa, Italy, 25-27 April 2007 
 
FABRICATION OF MINIATURIZED VARIABLE-FOCUS LENS USING LIQUID FILLING 
TECHNIQUE  
 
Hsiharng Yang1 , Chung-Yao Yang1, Mau-Shiun Yeh2 
 
1Institute of Precision Engineering, National Chung Hsing University, Taichung, Taiwan 40227 
2Materials & Electro-Optics Research Division, Chung-Shan Institute of Science & Technology, Tao-
Yuan, Taiwan 325 
 
ABSTRACT 
This paper describes a simple method for fabricating a 
variable-focus lens by using PDMS 
(polydimethylsiloxane) and filling with liquid for the 
variable-focus lens. The lens diameter of 2-mm was 
designed in this experiment and expected to reach the 
focal length in the range of 3 ~ 12 mm. The theoretical 
value between the liquid volume and the lens contact 
angle at different focal lengths were simulated and 
measured. The pumped-in volumes ranged from 200 to 
1400 μl, the contact angles ranged from 14.25∘to 
49.02 . C∘ hanging the deformation of PDMS film using 
different micro-fluidic volume produces the variable focal 
length from 4 ~ 10 mm in this experiment. The proposed 
method successfully fabricated a variable-focus lens. 
Bonding PDMS only once using no expensive instrument 
such as oxygen plasma was accomplished. The final 
objective is to insert the variable focus lens into portable 
optical imagery products. 
 
1. INTRODUCTION 
 
As imagery CCDs and CMOS detecting devices 
productions has gradually increased in recent years, the 
pixels of the detecting device and fabrication process 
yield rate have also improved. That resulted in promoting 
the development of the whole digital image storage 
industry. The primary lens today is the more complicated 
zoom lens made up of more than ten slices of optical 
glass. A single lens slice is called a lens element. Several 
lens elements make up an entire lens. Presently, the zoom 
lens is made primarily of a spherical convex lens, non-
spherical convex lens, plane mirror or concave lens using 
different lens collocations. The focus of an entire lens is 
changed by the movement of the relative position 
between the lens elements. However, some zoom lenses 
are very large, heavy and difficult to carry. Present 
developments have tended towards thinner and lighter 
lens elements. The key components must be miniaturized 
to attain this goal. The single and independent variable 
focus lens has become the current fashion. Variable focus 
lens research has been carried out for a while.  
Present research on variable focus lens can be 
divided into two driving methods. The first involves 
changing the lens radius of curvature using pressure. The 
second method involves varying with the applied voltage. 
In the pressure method, the PDMS membrane is the main 
parts of the variable focus lens. Chronis et al. fabricated 
the tunable liquid-filled microlens array integrated on top 
of a microfluidic network using soft lithography 
techniques [1]. The focal length of all microlenses is 
controlled using an elastomeric array by regulating the 
pressure in the micro-fluidics network. The structure is 
produced by jointing PDMS to glass using oxygen plasma. 
However, the jointing process is complicated and the 
glass is easily broken. Jeong et al. fabricated a tunable 
microdoublet lens array to form biconvex or meniscus 
lens [2]. It consisted of a tunable liquid-filled lens and a 
solid negative lens. The shortcoming is that the jointing 
process required expensive instruments like oxygen 
plasma. Chen et al. fabricated the tunable microlens 
consisting of a thin film with a 3D convex lens, chamber 
and microchannel made of PDMS [3]. The shortcomings 
were the jointing process being complicated and the 
alignment between the convex lens and microchannel. 
Agarwal et al. fabricated multi-level structures using 
lithography and ICP etching. The chamber was formed 
after jointing the multi-level structures [4]. Pressure is 
used to place tunable lens after lay over PDMS thin film 
on the chamber top and bottom. Pressure from the liquid 
filling in the microchannel is used to obtain variable focus 
in the optical lens system [5, 6].  
Other variable-focus lens driven by the changing 
voltage can be divided into two methods. The first is 
electrowetting [7]. The second is liquid crystal rotation 
[8-12]. Kuipe used two immiscible liquids to form a 
meniscus. The first liquid is electrically conducting and 
the second insulates [7]. When a voltage is input, it will 
cause the contact angle of the interface between the two 
liquids to change, causing the focal length of the 
meniscus to vary. This method requires a high voltage 
input that may cause the liquids to vaporize. Ren et al. 
researched into variable-focus lens using liquid crystal 
molecules [8]. The liquid crystal will rotate when voltage 
is applied causing the refractive index to change. The 
©EDA Publishing/DTIP 2007 ISBN: 978-2-35500-000-3              
Hsiharng Yang, Chung-Yao Yang, Mau-Shiun Yeh 
Fabrication of miniaturized variable-focus lens using liquid filling technique 
 
necessary material is not easily to obtain and the structure 
is more complicated. This method is still research in 
progress [8-12].  
    This paper describes a simple method for fabricating a 
variable-focus lens using PDMS as the principal part for 
the variable-focus lens. PDMS has the advantages of 
elasticity and highly reproductivity. A simple fabrication 
process and common lithography instruments are 
proposed for producing such a variable-focus lens. 
 
2. VARIABLE-FOCUS LENS DESIGN  
 
A variable-focus lens with a diameter of 2-mm was 
designed in this experiment and expected to reach the 
focal length in the range of 3 ~ 12 mm. The theoretical 
value between the liquid volume and lens contact angle at 
different focal lengths was calculated using the lens 
formula. From thin lens equation [13], 
( )
1 2
1 1 1
1n
f R R
= − −⎛ ⎞⎜ ⎟⎝ ⎠
               (1) 
When 2R →∞ , the following equation is obtained. 
1 1R f n
⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
= −                      (2) 
A schematic diagram to sketch the contact angle related 
to the lens profile is shown in Figure 1. All symbols are 
listed in Table 1. 
 
Figure 1. Schematic diagram showing contact angle and 
lens sag height in hemi-sphere. 
 
The contact angle equation is calculated as follows: 
2 24
8
D h
R
h
+=                           (3) 
1tan
2
R h
D
α − −=
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
                    (4) 
1tan
2
h
D
β −=
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
.                       (5) 
Then take Eq. (4) and (5) into the following equation  
90γ α β= ° − − 1 12 2 290 tan tanR h h
D D
− −−= ° − −⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ,    
(6) 
and contact angle θ can be expressed as follows: 
θ γ β= + 1 2 290 tan R h
D
− −= −o  
2 2
1
42 2
8
9 0 tan
D h h
h
D
−
⎡ ⎤⎛ ⎞+ −⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥= ° − ⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
 
2
1
1
90 tan
4
h
D
h
D
−
−
= −
⎡ ⎤⎛ ⎞⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
o .                (7) 
From the following equation [14] the theoretical diagrams 
for V-f and V-θ as are obtained shown in Figure 2 and 
3,  
( ) ( )3 22 cos 1 cos
3
RV π θ θ= + −       (8) 
 
Table 1 List of symbols. 
 
Symbol Description 
n Refractive index of medium 
f Focal length 
R Radius of curvature 
D Lens diameter 
h Lens sag height 
θ Contact angle 
V Pumped-in volume 
 
 
Figure 2. Relationship between the input volume and 
focal length (3 ~ 12 mm). 
 
©EDA Publishing/DTIP 2007 ISBN: 978-2-35500-000-3              
Hsiharng Yang, Chung-Yao Yang, Mau-Shiun Yeh 
Fabrication of miniaturized variable-focus lens using liquid filling technique 
 
 
Figure 3. Relationship between the input volume and 
contact angle in different focal length (3 ~ 12 mm). 
 
3. EXPERIMENTAL PROCESS 
 
This study utilized PDMS elastomer as the main part of 
the variable-focus lens. The first mask is patterned with 
round and rectangular cavities (Figure 4) for the lens and 
fluidic channel. The second mask was designed to 
fabricate the cavity that stored the liquid and as the 
barricade to precisely control PDMS membrane. The 
process are shown in Figure 4 and described as follow. 
First, JSR (THB-120N) negative acting photoresist 
is spin-coated onto a PMMA substrate at two-step speeds 
for about ten seconds at 150 rpm and 400 rpm, 
respectively. The device is then soft baked at a 
temperature of about 100 oC for 6 minutes to dry the 
photoresist. The photoresist is then patterned through the 
mask and exposed to ultraviolet light using the 
conventional photolithography technique. The exposure 
dose was about 2000 mJ. After development, the first 
level structure is accomplished.  
The above steps are repeated to form the second 
level circular chamber on top of the first layer after 
alignment with the second mask. After development, the 
substrate with a photoresist structure is heated at a 
temperature of about 120 oC for 5 minutes. The two-layer 
fabrication process was developed to decouple the lens 
from the microchannel and thus minimize the distortion in 
the lens. The PDMS prepolymer mixture is spin cast over 
the mold at 400 rpm for 20 seconds. The PDMS mixture 
is subsequently cured in oven for 20 minutes at 140 oC. 
The cured PDMS is carefully peeled off from the mold. 
The PDMS was then poured into the barricade, a piece of 
PDMS substrate to produce a thickness of about 1 ~ 2 
mm after baking at temperature 140 oC for 20 minutes in 
an oven.  
The PDMS curing agent is spun coating on the 
PDMS substrate at 3000 rpm for 30 seconds resulting in a 
thickness of approximately 3 microns. The final structure 
is completed after the PDMS structure irreversibly 
bonded onto the PDMS substrate at 90 oC for 20 minutes 
in oven. After proper trimming, the principal part of this 
variable-focus lens is accomplished. After that, the liquid 
input volumes are controlled using a micro pump or 
micro actuator. To change the deformation of the PDMS 
film by different microfluidic volume can achieve the 
desired variable focal length (Figure 5). 
 
Coating JSR-120N on 
PMMA
Photolithography(mask 
1)-Microfluidics formation
Coating JSR-120N as 
second layer
Photolithography(mask 
2)-Circular chamber 
formation
PDMS spin cast and cure
PDMS structure bonding to 
PDMS substrate
mask 1
mask 2
PMMA JSR-120N PDMS PDMS Sub.
 
Figure 4. Main fabrication steps and the mask diagrams. 
©EDA Publishing/DTIP 2007 ISBN: 978-2-35500-000-3              
Hsiharng Yang, Chung-Yao Yang, Mau-Shiun Yeh 
Fabrication of miniaturized variable-focus lens using liquid filling technique 
 
Inlet
Outlet
PDMS PDMS Sub. Liquid
 
Figure 5. The acting diagram of the liquid filling variable-focus lens. 
 
4. RESULTS AND DISCUSSION 
4.1 Device fabrication 
Figures 6(a) and 6(b) are SEM photographs of the lens 
structure in photoresist and the replication in PDMS 
structure, respectively. The 3D Confocal Microscopy was 
used to measure the height and 3D surface profile of the 
lens. The PDMS lens chamber is filled with deionized 
water with the refractive index 1.33. Each contact angle 
for a different pumped liquid volume is measured using a 
contact angle and surface tension instrument (FTA200). 
The pumped-in volume is controlled by a micro pump 
instrument in this experiment. Figure 9 shows the variant 
conditions of the contact angle for different pumped 
volumes. When the pumped-in volumes are 200, 400, 700, 
1000, 1200 and 1400 μl, the contact angles are 14.25∘, 
22.63∘, 28.56∘, 38.07∘, 43.22∘ and 49.02∘ in 
Figure 7(a) to Figure 7(f), respectively. And then take 
pumped-in volumes and contact angles into Equation (8) 
that can calculate the radius of curvature. Taking R into 
Equation (2) can get the focal length. The focal length 
ranged from 3.95 mm to 9.69 mm was calculated in this 
experiment. Figure 7(g) is the relationship of the pumped-
in volume and the contact angle. The pump-in volume and 
the contact angle is approximately linear relationship as 
indicated in Figure 7(g). Figure 8 shows the relationship 
between the pumped-in volume and the focal length. Red 
dots in Figure 9 are the experimental data; then take curve 
fitting with the experimental data. Figure 9 shows the 
comparison between the theoretical and experimental 
values of the contact angle and the pumped volume. 
Figure 10 is the comparison between the theoretical and 
experimental values of the pumped volume and the focal 
length. The difference between two curves might be the 
loss of liquids due to possible leaking. The other reason 
may be air trapped in the chamber at the beginning, when 
the air is pressed out of the chamber after pumping. When 
liquids are filled up with the chamber, the pumped-in 
volume will lose a little. Therefore, the error may be 
improved by using some vacuum devices in the future. 
 
(a) 
 
(b) 
Figure 6. SEM photographs; (a) the photoresist structure, 
(b) PDMS structure. 
 
 
(a) 
 
(b) 
©EDA Publishing/DTIP 2007 ISBN: 978-2-35500-000-3              
Hsiharng Yang, Chung-Yao Yang, Mau-Shiun Yeh 
Fabrication of miniaturized variable-focus lens using liquid filling technique 
 
 
(c) 
 
(d) 
 
(e) 
 
(f) 
 
(g) 
Figure 7. Photographs of the contact angle for different 
pumped-in volume measured using a contact angle and 
surface tension instrument (FTA200); (a) 200 μl, (b) 400 
μl, (c) 700 μl, (d) 1000 μl, (e) 1200 μl, (f) 1400 μl, (g) 
relationship between the pumped-in volume and the 
contact angle. 
 
 
Figure 8. Relationship of the pumped-in volume and the 
focal length. 
 
Figure 9. Comparison between theoretical and 
experimental values of the contact angle. 
 
 
Figure 10. Comparison between theoretical and 
experimental values of the focal length. 
 
4.2 Optical performance     
Lens aberrations were simulated by using the 
commercial software, ZEMAX, which can build a model 
to analyze and assist in optical system design. Substitute 
the lens dimension and optical conditions to analyze focal 
length and circle of the least confusion (the envelope of 
convergent light can make up caustic, at the smallest 
radius of caustic is called circle of the least confusion) 
[13]. This area is regard as the best focus point or imaging 
point of the system with the aberration. The Image Space 
(F/#) is 2.8 which usually used in cell phone and the 
pumped-in liquid with refractive index 1.33 in this 
simulation. The simulated focal length is 10.83 mm when 
filling liquid at 200 μl. The simulated focal length is 3.43 
mm when filling liquid at 1400 μl. Therefore, the 
variable-focus lens ranged 3.4 to 10.8 mm focal length 
was achieved in this simulation. The range is closed to 
that calculated by Equation (2) about 4 ~ 10 mm. The 
circles of the least confusion are 51.1 μm and 6.733 μm 
when pumped-in volumes at 200 μl and 1400 μl, 
respectively. From the results, the large pumped-in liquid 
generates the smaller circle of the least confusion. The 
smaller circle of the least confusion can provide the 
clearer imagery quality in the optical system. Figure 11 
shows the variable focus lens in different pumped-in 
©EDA Publishing/DTIP 2007 ISBN: 978-2-35500-000-3              
Hsiharng Yang, Chung-Yao Yang, Mau-Shiun Yeh 
Fabrication of miniaturized variable-focus lens using liquid filling technique 
 
volumes. The magnified lens imaging photographs at 
different volumes were snapped by 3D optical 
microscopy. The high magnification was generated from 
the high pumped-in volume such as 1400 μl in Figure 
11(c). 
 
(a) 
 
(b) 
 
(c) 
Figure 11. Imaging photographs of 2 mm lens at volume 
(a) 0μl, (b) 400μl, and (c) 1400. 
 
5. CONCLUSION 
 
This paper successfully demonstrated an easier method to 
fabricate a variable-focus lens. PDMS bonding was used 
only once and no expensive instruments such as oxygen 
plasma were used. The structure was fabricated with 
PDMS entirely to decrease the incompatibility between 
different materials. The structure does not easily burst 
because of its elasticity. The further objective is to insert 
the variable focus lens into portable optical imagery 
products. It also can be combined with CMOS or CCD for 
mobile phones, digital cameras, video cameras and 
medical microscopy. Each digital imaging storage media 
and cell phone communication can benefit from this 
technology. It also helps to advance micro 
optoelectromechanical system devices for the lower price 
trend in consuming electronic products. 
 
6. ACKNOWLEDGEMENT 
This work was supported by the National Science Council 
(series no. 94-2218-E-005-014) and Chung-Shan Institute 
of Science & Technology in Taiwan. 
 
7. REFERENCES 
 
[1] Chronis, N., Liu, G. L., Jeong, K. H. and Lee, L. P., 
“Tunable liquid-filled microlens array integrated with 
microfluidic network,” Optics Express, 11(19), pp. 2370-
2378, 2003. 
[2] Jeong, K. H., Liu, G. L., Chronis, N. and Lee, L. P., 
“Tunable microdoublet lens array,” Optics Express, 12(11), 
pp. 2494-2500, 2004. 
[3] Chen, J., Wang, W., Fang, J. and Varahramyan, K., 
“Variable-focusing microlens with microfluidic chip,” 
Journal of Micromechanics and Microengineering, 14, pp. 
675-680, 2004. 
[4] Agarwal, M., Gunasekaran, R. A., Coane, P. and 
Varahramyan, K., “Polymer-based variable focal length 
microlens system,” Journal of Micromechanics and 
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[5] Zhang, D. Y., Justis, N. and Lo, Y. H., “Integrated fluidic 
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[6] Gunasekaran, R. A., Agarwal, M., Singh, A., Dubsi, P., 
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[7] Kuiper, S. and Hendriks, B. H. W., “Variable-focus liquid 
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[8] Ren, H., Fan, Y. H. and Wu, S. T., “Polymer network liquid 
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[9] Ren, H., Fan, Y. H., Gauza, S. and Wu, S. T., “Tunable 
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[10] Ren, H. Fan, Y. H., Lin, Y. H. and Wu, S. T., 
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[11] Fan, Y. H., Ren, H., Liang, X. and Wu, S. T., 
“Tunable-focus liquid crystal microlens arrays for display 
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[12] Ren, H., Fan, Y. H., Lin, Y. H. and Wu, S. T., 
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[13] E. Hecht, Optics, Addison Wesley, CA: University 
Adelphi, pp.262- 268, 2002.   
[14] Jeong, K. H. and Lee, L. P., “A New Method of 
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Medicine ＆ Biology, pp. 380-383, 2002. 
 
 
 
©EDA Publishing/DTIP 2007 ISBN: 978-2-35500-000-3              


Fabrication of Miniaturized Variable-focus Lens Using Liquid Filling Technique

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