Inspired by the biomechanics of the human eye, which includes a crystalline lens, ciliary muscles, and zonular fibers, the proposed variable-focus lens system consists of a PDMS lens, winding-type SMA actuator, and load arms. The PDMS lens is encircled and stretched by the load arms joined to an outer ring that is rotated by the winding-type SMA actuator, thereby changing the focal length of the lens. In contrast to other single tunable-focus lenses, the proposed system uses a gel-type PDMS lens, which is insensitive to gravity and external vibration, and can be made into a biconvex or aspheric shape. The design of the proposed system is described in detail, and experimental results demonstrate the validity of the proposed system.
©2009 Optical Society of America
Just as eyes are an indispensible organ for humans, vision systems are a key component in robots, hand-held devices, surveillance units, and industrial systems. Furthermore, a variable-focus function in a vision system is essential to enhance the perception capability. For example, a vision system with an adjustable focal length can allow a robot to obtain accurate and clean images of objects at various distances. While conventional focusing systems are reliable and have a good focusing ability, their use of glass lenses and an electric motor to control the distance between the glass lenses make them difficult to include in a compact lens system. In addition, precise and expensive mechanisms are required to position the lenses along a straight line.
Recently, single variable-focus lens systems have attracted considerable attention as an effective solution to overcome the limitations of conventional systems. The major feature of single lens systems with a tunable focus is that the focal length can be adjusted by changing the refractive index or the physical radius of the curvature of the lens. Most variable-focal lenses can be classified into three types: liquid crystal lenses, electro-wetting lenses, and liquid-filled lenses. The liquid crystal lens can change its refractive index distribution by the applied variable voltages, and it is simple and shock-resistant since the focal length is electrically tunable without any moving elements [1,2]. However, the liquid crystal lens is limited to a small lens and it needs a high AC voltage source. Electro-wetting lenses are composed of a droplet of liquid on the surface and a power system providing high voltage . The surface tension and contact angle of the droplet can be continuously and rapidly changed in proportion to the supplied voltage, yet this also requires a high voltage and it is difficult to fabricate a large aperture. Meanwhile, liquid-filled lens systems using fluidic pressure [4,5] or pneumatic pressure  consist of a membrane made of PDMS (polydimethyl-siloxane), liquid, a chamber containing the liquid, and a fluidic pump or pneumatic pump that applies pressure to the chamber. Although a liquid lens is simple and can produce a relatively large aperture, it requires a bulky pump system. Furthermore, liquid lens systems are sensitive to external vibration and gravity, and their use of liquid makes it intrinsically difficult to make biconvex and aspheric lenses.
Accordingly, to resolve these difficulties, a novel variable-focus lens system inspired by the biomechanics of the human eye is proposed. Unlike other tunable-focus lenses, we use a gel-type lens that is relatively insensitive to external disturbance, and can be made biconvex or aspheric with the appropriate lens mold. Similar to the mechanism of the human eye, in which an elastic crystalline lens is contracted or expanded by the ciliary muscles and zonular fibers, a gel-type lens is contracted or expanded by a muscle-like SMA(shape memory alloy) wire and mechanical parts. In previous research, the current authors developed the first prototype of a biomimetic variable-focus lens system, called KNU(Kyungpook National University) eye-I . Therefore, this paper presents KNU eye-II, a new miniaturized version of KNU eye-I, that is composed of a gel-type PDMS lens, winding-type SMA actuator, and mechanical parts. The focal length of the PDMS lens is changed by the mechanical parts and winding-type SMA actuator. The design concept and key characteristics of KNU eye-II are described in detail and its efficacy demonstrated by experimental results.
2. Accommodation of human eye
An incident ray of light reflected from a specific object passes through the cornea and crystalline lens, and an image is formed on the retina. The photoreceptors on the retina then transmit the image to nerve cells which send signals to the brain. However, the key to the adaptability of the human eye is the crystalline lens, which is biconvex, elastic, transparent, and changes its physical shape to adjust the focal length. The crystalline lens in the human eye is completely encircled by the ciliary muscles of the ciliary body and zonular fibers of the suspensory ligament, which also support the adaptability function, as shown in Fig. 1. Thus, to view a distant object, the ciliary muscles are relaxed first, causing the zonular fibers to become taut. As a result, the crystalline lens becomes flatter and the focal length of the lens longer, as shown Fig. 1(a). Conversely, to view a nearby object, the tension of the zonular fibers is decreased by contracting the ciliary muscles, making the crystalline lens thicker and the focal length of the lens shorter, as shown Fig. 1(b).
3. Design of KNU EYE-II
3.1 Design requirements and conceptual drawing
Specific design requirements were considered for the three main components, the variable-focus lens, actuator, and mechanical parts, to provide KNU eye-II with a similar adaptability to the human eye. First, the variable-focus lens should be transparent and gel-type to reduce the distortion from external vibration and gravity, its focal length should be adjustable based on changing it physical curvature, like a crystalline lens, and the lens material should allow easy fabrication of various shapes. Second, a single actuator should be adequate to change the focal length, as the asynchronous movement of two or more actuators can cause undesired errors, and the actuator should be compact to make the lens system smaller. Finally, the mechanical parts should be lightweight, as simple as possible, and able to operate simultaneously with one actuator, allowing the variable-focus lens to be encircled and pulled with equal force and equal displacement, similar to zonular fibers. Thus, to realize the above features, each component of KNU eye-II was carefully selected and designed, as detailed in the following sections, and the overall design concept of KNU eye-II is outlined as follows.
Essentially, as illustrated in Figs. 2 and 3, the physical curvature of the elastic lens is changed by pulling and releasing. When the outer ring turns clockwise, the eight load arms connected to the outer ring pull the lens with equal force and equal displacement, thereby adjusting the focal length of the lens. Based on conceptual drawings, KNU eye-II was designed using computer-aided design(CAD) software, CATIA V5. Thus, Fig. 4 shows a CAD drawing of KNU eye-II composed of a PDMS lens, winding-type SMA actuator, and mechanical parts.
3.2 Variable-focus PDMS lens
The variable-focus lens is made of a PDMS polymer, SYLGARD 184 Silicone Elastomer from Dow Corning. PDMS polymers have a lot of attractive material properties, including an outstanding transparency within the visible wavelength range, low surface roughness, high elasticity, excellent temperature stability, a good solvent resistance. Figure 5 shows a schematic of the PDMS lens, where the circumferential part is omitted to calculate the initial focal length. The initial focal length of the PDMS lens in air before any pulling by the load arms is calculated using the following thin lens equation:
where f is the initial focal length of the PDMS lens, nPDMS is the refractive index of the PDMS polymer, R 1 is the radius of the curvature of the lens surface closest to the light source, R 2 is the radius of the curvature of the lens surface farthest from the light source, i.e. the distance along the lens axis between the two surface vertices. Thus, the initial focal length of the PDMS lens is 16.8 mm calculated from the design parameters: nPDMS =1.43, R 1 =14.12 mm, and R 2 =-14.12mm.
The proposed PDMS lens is biconvex and symmetric, as shown in Fig. 6. Unlike other tunable-focus lenses, the PDMS lens is a gel and has elasticity, thereby preventing any deflection by external vibration and gravity. Finally, the PDMS lens has eight special protruding parts to connect with the external parts, so as to protect the PDMS lens against fracturing or tearing when the lens is pulled by the actuator. The specifications of the variable-focus PDMS lens are presented in Table 1.
The fabrication process of the PDMS lens is as follows. The two constituents of the PDMS, i.e. the base and curing agent, are mixed together using a weight ratio of 10:1, and any air included in the mixture removed using vacuum de-airing. The mixture is then poured into molds and subsequently cured for 30 minutes at 403 K in an oven to cross-link the polymer. Various mixing ratios were investigated to obtain the appropriate elasticity and flexibility. The molds are composed of two glass concave lenses and two bodies made from resin, WaterShed 11120, and fabricated using a rapid prototype technique called stereo-lithography.
3.3 Mechanical parts
All the mechanical parts in KNU eye-II, except for the PDMS lens, are as follows: eight grippers, eight load arms, the outer ring, upper part, and lower part, as shown in Fig. 7. The assembled KNU eye-II is shown in Fig. 8 and the specifications are presented in Table 2. To be lightweight, the mechanical components are also fabricated using the stereo-lithography technique.
The gripper design allows the PDMS lens to be evenly stretched in all directions by the eight load arms. If the PDMS lens is directly connected to the load arms without grippers, the PDMS lens could be diagonally pulled when the load arms revolve on the shaft fixed to the body. In addition, the eight grippers connect the PDMS lens to the eight load arms by holding the protruding parts of the PDMS lens. As such, the load arms are designed to encircle the PDMS lens, similar to the zonular fibers encircling the crystalline lens in the human eye, and connect the PDMS lens with the outer ring. To distribute the force generated by the winding-type SMA actuator to the load arms equally, the outer ring is placed between the winding-type SMA actuator and the eight load arms.
3.4 Winding-type SMA actuator
The use of a compact actuator is necessary to miniaturize the lens system, and the popular compact actuators currently in use include stepping motors, micro-fluidic actuators, voice coil motors, piezo actuators, and SMA actuators. However, an SMA actuator was chosen for the proposed system, as it is more suitable for small-sized mechanisms and medical devices, due to its light weight, compact size, and high-power density . An SMA is an alloy that remembers and returns to its original shape after being deformed by applying critical heat to the alloy, plus it has numerous applications in the medical and aerospace industries. Thus, SMA actuators utilize the restoring force of a SMA wire to return to a predetermined state. In general, SMA actuators can be classified into two types according to the driving method: antagonistic type and bias spring type . Bias spring-type SMA actuators consist of one SMA wire and a bias spring to return to a predetermined shape. In contrast, antagonistic-type SMA actuators are composed of two SMA wires placed on both sides of a center point. Thus, antagonistic-type actuators can provide bidirectional movement.
The actuator used in KNU eye-II is an antagonistic and winding-type SMA actuator composed of two SMA wires, thin copper pipes, and one friction pad, as shown in Fig. 8(c). The specifications of the winding-type SMA actuator are presented in Table 3. An antagonistic-type actuator was chosen to improve the response time, while a winding type was chosen to obtain the desired displacement. The SMA wires are wound around the outer ring for efficient use of space and to minimize the bending of the SMA wires. In addition, thin copper pipes are placed between the SMA wires and the outer ring to isolate the outer ring from the high temperature when the SMA wires are heated up. Finally, a friction pad is placed between the upper part and the outer ring to maintain the current focal length after turning off the power of the SMA actuator.
4. Experimental results
4.1 Operation of KNU eye-II
Figure 11 shows the operation process of KNU eye-II. The focal length of the PDMS is at the minimum before any pulling by the load arms, as shown in Fig. 9(a). The PDMS lens is then pulled by the eight load arms with equal displacement and equal force when the outer ring is rotated by the winding-type SMA actuator. Finally, the focal length of the PDMS lens is at the maximum after pulling, as shown in Fig. 9(b). The relationship between the displacement of the load arms and the winding-type SMA actuator is given by
where ΔLSMA , ΔLarm, La, Lb, Rring, and RSMA are the displacement of the winding-type SMA actuator, displacement of the load arm, length from the fulcrum to the outside (9 mm), length from the fulcrum to the inside (8.45 mm), radius of the outer ring (23 mm), and radius of the winding-type SMA actuator (25 mm), respectively. Figure 10 shows the results of the simulated and measured displacement of the load arm with respect to the displacement of the winding-type SMA actuator. The simulated and experimental results matched well, although there was a slight discrepancy due to the tolerance of each mechanical part.
4.2 Measurement of focal length
To measure the focal length, the experimental setup was as shown in Fig. 11 in accordance with Korean industrial standards, KS B 5408. A quartz-halogen illuminator (bulb output power = 150 W) was used as the light source, and the light generated from the illuminator was passed through a narrow band-pass interference filter (central wavelength = 546 nm, FWHM = 10 nm). The filtered light beam was then passed through a precision pinhole (diameter = 1 mm), collimating lens (focal length of achromatic lens = 250 mm) to collimate the light beam emitted from the pinhole, and finally the PDMS lens. Thereafter, the light beam was focused on a CCD camera, HVR-2300C  with a 1/2 inch CMOS. One pixel size was 3.2 × 3.2 μm and an effective pixel was 2048(H) × 1536(V). The images were then transferred to a host PC for further image processing. The focal length of the PDMS lens was calculated using Eq. (3).
where f is the focal length of the PDMS lens, fo is the focal length of the collimating lens, y is the size of the subject, and y′ is the size of the image formed on the CCD camera.
The variation of the focal length by the displacement of the winding-type SMA actuator was obtained as shown in Fig. 12, and the results demonstrated that the focal length of the variable-focus PDMS lens could be successfully tuned. In this case, the focal length of the PDMS lens was varied from 16.8 mm to 18.0 mm after contracting the winding-type SMA actuator from 0 mm to 1.2 mm.
For the two given reference displacements, 0.8 mm and 1.2 mm (maximum displacement), the step responses of the SMA actuator are shown in Fig. 13 when that the voltage applied to the SMA wire was 3 V and the current applied was 2A.
4.3 Measurement of focusing ability
To demonstrate the focusing ability of the variable-focus PDMS lens, a simple auto-focusing system was implemented using a contrast detection method based on the following fundamental principle: an accurately focused image has the highest contrast among all images of the same scene. Figure 14 shows the experimental setup used to measure the focusing ability, which was roughly divided into two parts: hardware and software, where a, the distance of the image behind KNU eye-II, was 18.0mm and b, the distance of the resolution target in front of KNU eye-II, was 380mm.
The hardware consisted of a CCD camera, KNU eye-II, and controllers. The main control system consisted of the SMA actuator controller that controlled the winding-type SMA actuator and a microcontroller board using a DSP (TMS320F2812), as shown in Fig. 15. To heat up the SMA wire, which is a resistor from an electrical point of view, the amount of electrical current was controlled by a PWM (Pulse Width Modulation) of the applied voltage. A potentiometer was attached to the lower part to measure the displacement of the winding-type SMA actuator and wired to an ADC (Analog-to-Digital Converter) embedded in the DSP. Meanwhile, the software consisted of an auto-focusing program based on contrast detection. The incident rays of light reflected from the resolution target passed through KNU eye-II and an image was formed on the sensor of the CCD camera. The software then analyzed the contrast information of the image transmitted from the CCD camera, and sent a control command to the controllers. Finally, the controllers activated the winding-type SMA actuator to change the focal length of the PDMS lens based on the control command received from the software. This process was repeated until the subject was accurately focused.
Figure 16 shows the variation in the images during focusing. Fig. 16(a) shows the initial defocused image before any accommodation of the PDMS lens. To focus on the resolution target, the PDMS lens was pulled by the eight load arms, and the focal point moved closer to the resolution target to make the image clearer. Finally, a focused image was obtained, as shown in Fig. 16(b). Consequently, the results demonstrated that the proposed biomimetic lens system can be an effective device for replacing conventional lens systems.
This paper presented a biomimetic variable-focus lens system controlled by a winding-type SMA actuator. Inspired by the biomechanics of the human eye, KNU eye-II includes a single gel-type PDMS lens, muscle-like SMA actuator, and a simple and reliable mechanism to adjust the focal length. The PDMS lens is encircled and pulled by load arms to change the focal length. In experiments, the initial focal length of 16.8 mm is adjusted up to 18.0 mm according to the displacement of the winding-type SMA actuator from 0 mm to 1.2 mm. When compared with other single variable-focus lenses, the proposed PDMS lens is relatively insensitive to external disturbance, plus it is fairly easy to make a lens with a large aperture and biconvex or aspheric shape when using the appropriate lens mold. Further studies will focus on the development of simpler mechanisms and new PDMS lenses with a better performance.
This work was supported by a Korea Science and Engineering Foundation(KOSEF) grant funded by the Korean Government(MEST) (No. R01-2007-000-20630-0)
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