- Email: [email protected]
Design and fabrication of fluid controlled dynamic optical lens system
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Optics and Lasers in Engineering 43 (2005) 686–703
Design and fabrication of fluid controlled dynamic optical lens system R.A. Gunasekaran, M. Agarwal, A. Singh, P. Dubasi, P. Coane, K. Varahramyan Institute for Micromanufacturing, Louisiana Tech University, Ruston, LA 71272, USA Received 1 February 2004; received in revised form 1 July 2004; accepted 1 September 2004 Available online 26 October 2004
Abstract A novel small fluid controlled optical lens system that is capable of displaying dynamic variation of its focal length and field-of-view (FOV) is designed and fabricated. In this active lens system, appropriate volume of the optical fluid can be pumped into or out of the lens chamber to provide double-convex (DCX) or double-concave (DCV) lens effect. Simple optical imaging experiments were performed using different sets of glass lenses with fixed focal lengths to determine the optimum lens configuration required for designing a dynamic optical lens system. The experimental results obtained from the glass lenses demonstrate that a combination of a single DCX lens with three DCV lenses provides a wider FOV. The flexible membranes for fluid controlled lenses were fabricated using polydimethylsiloxane polymer material, which has good optical transparency and elasticity. A simple fluid injection system is used to vary the radius of curvature of the lenses, and thereby to change the focal length. A dynamic optical lens system with a combination of one DCX and multiple variable focal length DCV lenses as designed here can image an object with a wide range of focal length and FOV. With this fluid controlled optical system, the FOV and focal length could be continuously varied and a maximum FOV of 118.31 could be achieved. The smallest f-number (f/#) for this fluid controlled single lens system was found to be 1.3, which corresponds to the numerical aperture value of 0.35. r 2004 Elsevier Ltd. All rights reserved.
Corresponding author. Tel.: +1 318 257 5115; fax: +1 318 257 5104.
E-mail address: [email protected] (R.A. Gunasekaran). 0143-8166/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2004.09.012
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Keywords: Dynamic optical lens system; Variable focal length lens; Wide field of view; Polymer lens; Fluid actuated lenses; Fluid focus lenses; Variable focus lens
1. Introduction The development of advanced optical devices and focal plane arrays are essential for high performance electro-optical imaging systems [1–4]. These systems require a number of miniature mechanical and optical components, and are useful for a number of domestic and military applications [3,4]. Owing to the ever-increasing demand for functional optical systems for aerial imaging and surveillance, a large number of manufacturers are developing complex and highly compact optical devices that can provide a wide field-of-view (FOV) and variable focal lengths [5–7]. The optical components or assemblies are generally developed to provide specific functions including wide angle of view, variable focal length, foveated images, etc. These lenses could be used in micro-air vehicles (MAVs), bio-medical diagnostic and surgical devices, vertical scanners, and optical holography devices [8–10]. Recently, extensive efforts have been made to mimic the bio-vision systems found in living creatures and to develop artificial bio-inspired optical lens systems [11,12]. Many bio-optical systems found in nature, including the human eye and the eyes of fishes, birds, animals etc. are single lens systems, which display very complex and remarkable visual features [12]. Most of the biological single lens systems tend to show minimal spherical and chromatic aberrations [11,12]. In addition to the singlelens systems, several compound lens systems have been found in nature [11,12]. It has been demonstrated that the complex visionary features in bio-optical systems arise from two main characteristics such as, the existence of a gradient of refractive indices in the lens (graded index (GRIN) lenses) and the ability of the lens to change its shape dynamically [1,11,12]. All these lenses in the biological systems including the GRIN lenses are known to consist of a large number of protein layers, and are capable of offering viewing angles close to 1801. Many bio-vision systems exhibit a variation of the index of refraction in their eye lenses. This characteristic together with the contracting nature of the eye lens may provide the exceptional degree of vision that is required to adjust for near and far focus [11]. GRIN lenses have been fabricated by a number of methods including printing, electrophoresis, and by lithography using gradient masks [13–18]. It should be noted that until now, no successful report on the fabrication of a single lens structure that can mimic the biooptic system has been reported. It is known that the eye of a fish is capable of viewing objects at 1801 [19]. Commercially available fish-eye lens systems that can provide a wide FOV contain multiple lenses [20]. Each of these lenses is manufactured to tight specifications and are assembled as a unit [20]. Several different configurations for the fish-eye lens systems have been reported [21–23]. Optical systems that are controlled by fluidic, electric, and mechanical actuation to provide variable focal lengths have been reported by a number of groups [24–34]. The phenomenon of electrowetting is also
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utilized in the fabrication of a dynamic lens system that can exhibit variable focal lengths [25–28]. Another notable system employs birefringent nematic liquid crystals to dynamically change the refractive index (n) and focal length by the application of an electric field. Some studies have shown that a change in the n values of more than 0.6 as a function of electric field is possible [11,29–32]. The fluid controlled optical systems typically consist of a lens chamber with channels to pump optical fluids in order to change the radius of curvature of the polymer membranes and the focal length of the resulting lens [33–35]. Most of the reported systems appear to have a single lens structure [33–35]. In some designs, a single spherical lens is mounted at the center of the membrane to produce foveated images. These lenses are capable of displaying variable focal lengths, but are not suitable for achieving wide FOV. The objective of this research is to design and develop an optical lens system that could display a dynamic variation of the focal length with a wide range of FOV. In contrast to the reported results, our experiments demonstrate that the use of a single variable focal length lens is inadequate to capture the images with large FOV. In the absence of an artificial single-lens bio-vision system, our experiments revealed that at least a set of multiple concave lenses together with a single convex lens is required to provide a wide FOV. In this paper, we report our attempts to fabricate a dynamically varying optical lens system, which could be successfully used for imaging with a large FOV and variable focal length.
2. Experimental Preliminary experiments were conducted using different sets of double concave (DCV) and double convex (DCX) lenses of different focal lengths in order to understand the relationship between the FOV and focal length of the lenses, and to determine the specific combination of lenses that can provide a wider FOV. These lenses were chosen because it is relatively easy to make the fabricated polymer lens system adapt to one of these configurations. For the construction and characterization of fluid controlled optical systems, it was realized that these simple experiments were critical to optimize the design process. A simple optical characterization setup, which includes the CCD camera, video monitor, optical rail and components, and an object with a scale attached to it, was used for imaging through the lenses. The object is a frame containing a series of letters in the form of ‘‘LOUISIANA TECH UNIVERSITY’’ with a scale attached at its bottom. Two such objects are placed in front of the camera, with one object placed perpendicular to the optical axis, and the other placed at an angle of 301 from the optical axis. The purpose of using these two objects is to determine the variation in the focal length and the FOV simultaneously. All the tested lenses are categorized into two groups: static lenses and dynamic lenses. Static lenses are simple glass lenses, and the dynamic lenses are fluid controlled lenses whose radius of curvature can be changed. Fig. 1 shows the schematic representation of the simple setup used for imaging purposes.
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Fig. 2 illustrates the different combination and configuration of DCX and DCV lenses used for imaging. For all of the different lens arrangements, four different distances are marked. As shown in Fig. 2, ‘a’ is the distance between the camera and the DCX lens; ‘b’ is the distance between the DCX and DCV lens; ‘c’ is the distance between the DCV lens and the object; ‘d’ is the length of the object that is viewed by the camera. The FOV (y) is measured by using the formula given in Eq. (1). The total FOV is twice the angle measured by taking the inverse of tangential angle (tan1) of the ratio of one-half the length of the object viewed to the distance between the lens and the object. ðd=2Þ y ¼ 2 tan1 : (1) c In one set of experiments, combinations of one DCX lens of fixed focal length (f ¼ 10 and 20 cm) and a second DCX glass lens of different focal length (f ¼ 5; 10, 15, 20, 30 cm) were used to image the object and determine the variation in the FOV with the focal length of the second DCX lens (Fig. 2a). In another set of experiments, a combination of one DCX lens of fixed focal length (f ¼ 20 cm) and a second DCV glass lens of different focal length (f ¼ 10; 15, 20 cm) were used to image the object and determine the variation in the FOV with the focal length of the second DCV lens (Fig. 2b). Results from the first and second set of experiments showed that DCV lenses provided wider FOV than DCX lenses of the same focal length and that wider FOV can be achieved by using DCV lenses of lower focal length. As shown in Fig. 2(c,d), various combinations and arrangements of DCX and DCV lenses of different focal lengths were used to determine the variation in the FOV with respect to the configuration and the focal length of these lenses. The focal length (f) of the DCX lenses were 10, 20, or 30 cm, whereas the focal length (f) of the DCV lenses were 10, 15, or 20 cm. The results obtained from simple experiments were found to be useful for designing and fabricating an optical system with similar combinations of lenses as described above using optically transparent flexible materials. The reason behind using the flexible lens material is that, by varying the radius of curvature of these
Optic Axis θ Camera
Field of view
Object
100 cm Fig. 1. Illustration of the arrangement of camera and the object.
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Fig. 2. Illustrations of the optical arrangements consisting of one DCX lens of fixed focal length with additional: (a) one DCX lens; (b) one DCV lens; (c) two DCV lenses; (d) three DCV lenses.
lenses dynamically by pumping fluid into and out of the lens chamber, one can achieve variable focal length and FOV. Since polydimethylsiloxane (PDMS) is the choice of material for optical transparency, durability, flexibility and biocompatibility, several polymer lenses were made in different sizes by casting PDMS material in suitable circular mold. After curing the PDMS membrane inside the mold, two such membrane units were combined by placing a spacer in between, and the whole assembly was sealed and made leak proof. A small hole was made in the spacer unit to fabricate the channel for pumping fluid with a high refractive index fluid (in this case DI water) into and out of the lens chamber. The lenses constructed in this manner were used to simulate the same conditions as used for the static lens
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Fig. 3. Fluid-actuated single variable focal length lens system.
configuration. Fig. 3 shows the assembled single variable focal length lens system of 7.9 mm in radius with 1.5 mm thick spacer in between. Imaging of the object was done with different combinations of dynamic lenses. A syringe pump was used to increase or decrease the volume of fluid in the lens chamber, and the image was captured at different fluid levels. First, a single dynamic lens was actuated as DCX and DCV lens by pumping fluid into or out of the lens chamber (0.02 ml each time) to view the object. A static DCX glass lens (f ¼ 10 cm) was placed between the dynamic lens and the camera (Fig. 2a and b) to image the object. Since the use of two or three double concave lenses in contact results in higher FOV, polymer lenses were made in a similar fashion. In the set of experiments that followed, the object was imaged using integrated two or three dynamic lenses in DCV configuration by pumping fluid out (0.02 ml each time) from all the lenses identically.
3. Results and discussion Initially the object was imaged only by using a CCD camera with no additional lens between the camera and the object, and the total FOV of the camera lens was measured to be 12.21. Fig. 4a shows the series of images captured using the setup shown in Fig. 2a, where the focal length of the first DCX was 10 cm and the focal length of the second DCX lens was either 5, 10, 15, 20 or 30 cm. The variation in the FOV with the change in the focal length of the second DCX lens is shown in Fig. 4b. It was observed that as the focal length of the second DCX lens decreases, FOV increases. Figs. 5a and 5b show the series of images captured using the setup as illustrated in Fig. 2a and 2b, respectively, with a fixed DCX lens (f ¼ 20 cm) in front of the camera along with DCX or DCV lenses of different focal lengths (f ¼ 10; 15,
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(a)
FOV (degree)
30
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0 (b)
0
5
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15
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35
Focal Length (cm)
Fig. 4. (a) Images captured using the setup shown in Fig. 2a with the first DCX lens of f ¼ 10 cm and a second DCX lens of different focal lengths. (b) Focal length vs. FOV for the DCX lenses.
20 cm). The variation in the FOV with the change in the focal length for both DCX and DCV lenses is shown in Fig. 6. Although the observed FOV with these lenses is significantly lower, it should be noted that when DCV lenses are used to image the object one could achieve higher FOV. The FOV was found to increase with a decrease in the focal length of the DCV lenses. Tables 1 and 2 show the measured FOV when the object was imaged using different configuration and combination of DCX and DCV lenses with different focal length as illustrated in Fig. 2b–d. The variation in the FOV as a function of the focal length of one, two and three DCV lenses in contact and the first DCX lens is shown in Fig. 7. It can be observed that the FOV varies systematically depending on the focal length and the type of lenses used. These results demonstrate that the FOV increases with the decrease in the focal length of the DCV lenses used to image the object. Interestingly, the FOV also increased with the increase in the number of DCV
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Fig. 5. (a) Images captured using the setup shown in Fig. 2a with the first DCX lens of f ¼ 20 cm and a second DCX lens of f ¼ 10; 15, and 20 cm. (b) Images captured using the setup shown in Fig. 2b with the first DCX lens of f ¼ 20 cm and a second DCV lens of f ¼ 10; 15, and 20 cm.
FOV (degree)
12 9 DCX lenses DCV lenses
6 3 0 0
5
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25
Focal Length (cm) Fig. 6. Focal length vs. FOV for DCX and DCV lenses.
lenses. The FOV from three DCV lenses integrated together is much larger than that from a single DCV lens or integrated two DCV lens system. The focal length of the first DCX lens used in front of the camera to image the object also plays an important role in determining the FOV. The higher the focal length of this DCX lens the higher the FOV will be. The optical image, with a minimum and a maximum
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Table 1 FOV measured using single double convex lens of focal length f ¼ 10 cm and the different combinations of double concave lenses of focal lengths f ¼ 10; 15, and 20 cm FOV (deg) (y) d (in) c (in) b (in) a (in) Three DCV lens-f (cm) Two DCV lens-f (cm) Single DCV lens-f (cm) First DCX lens f (cm)
14.5 9.5 37 0.5 2 — — 10 10
29 18 35 1.5 2 — 10 — 10
42 26 34 2.5 2 10 — — 10
NA NA NA NA NA — — 15 10
18 12 37 1.5 2 — 15 — 10
21.5 13 34 1.5 2 15 — — 10
NA NA NA NA NA — — 20 10
NA NA NA NA NA — 20 — 10
19.5 12 35 1.5 2 20 — — 10
NA–no focus was observed for these combinations.
Table 2 FOV measured using single double convex lens of focal length f ¼ 20 cm and the different combinations of double concave lenses of focal lengths f ¼ 10; 15, and 20 cm FOV (deg) (y) d (in) c (in) b (in) a (in) Three DCV lens-f (cm) Two DCV lens-f (cm) Single DCV lens-f (cm) Single DCX lens f (cm)
46 25.5 30 3 2 — — 10 20
54.5 32 31 3.5 2 — 10 — 20
78 52 32 4.5 2 10 — — 20
34 22 36 1 2 — — 15 20
39 24 34 2 2 — 15 — 20
46 28 33 3.5 2 15 — — 20
32.5 21 36 0.5 2 — — 20 20
37 22 33 2.5 2 — 20 — 20
40 23 32 4 2 20 — — 20
90 1 DCX (f = 10 cm) + 3 DCV
FOV (degree)
1 DCX (f = 20 cm) + 1 DCV 1 DCX (f = 20 cm) + 2 DCV
60
1 DCX (f = 20 cm) + 3 DCV
30
0 0
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30
Focal Length (cm) Fig. 7. Focal length of the DCV lenses vs. FOV for different combinations of the DCX and DCV lenses. The focal length of the DCX lens is fixed in each series of imaging experiment.
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FOV achieved from the above-mentioned lens configuration, is illustrated in Fig. 8a and b, respectively. In the case of polymer lenses, the volume (vc ¼ 0:294 ml) of the lens chamber was calculated by measuring the diameter and the thickness of the spacer unit and by assuming that the PDMS membrane is flat. However, in reality, the PDMS membrane does not remain flat. First, the optical fluid (DI water) was pumped into the lens chamber until the chamber was filled and the membrane became flat. At this point, the volume of the fluid (v1 ¼ 0:289 ml) necessary to fill the chamber without causing any out of plane deflection of the membrane was measured. The small difference between the calculated (vc) and measured (v1) values can be attributed to the sealing joints inside the chamber that would reduce the available space. As mentioned earlier, pumping more fluid into the chamber will make it behave like a DCX lens, whereas the extraction of the fluid from the lens chamber will make it behave like a DCV lens. In the case of the DCX lens configuration, the maximum volume of fluid (v2) that can be pumped into the lens chamber without rupturing the lens membrane was
(a)
(b) Fig. 8. Image of the object captured using (a) a DCX lens (f ¼ 10 cm) and a DCV lens (f ¼ 20 cm), (b) a single DCX lens (f ¼ 20 cm) and a set of three DCV lenses in contact (focal length of each lens is 10 cm).
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measured. If v3 is defined as the difference between v2 and v1 (v3 ¼ v2 v1 ), then v3 represents the volume of fluid that was actually used to cause the deflection of the membranes on both sides to form the DCX lens. Similarly, in the case of the DCV lens configuration, the volume of fluid (v4) that can be gradually pumped out from the already fluid filled (v1) lens chamber was monitored. The maximum volume (v4(max)) of the fluid that could be pumped out was also measured. Theoretically, v1 and v4(max) are expected to be equal. The difference (v5) between v1 and v4(max) would represent the amount of fluid trapped in the chamber (v5=v1v4(max)). It should be noted that v4 represents the volume of the fluid that is pumped out to actuate the lens structure as the DCV lens. The geometrical deflection of the membrane as a result of pumping fluid into the lens chamber is shown in Fig. 9, and the associated volume of the lens chamber above the spacer unit is calculated by using the formula for a spherical cap as given in Eq. (3), where h is the membrane deflection height, r1 is base radius; v3/2 is the volume of the spherical cap which represents one side of the DCX lens. v 3 p 2 ¼ (3) ð3r1 þ h2 Þh: 6 2 From Eq. (3), when the volume (v3) and the radius of spacer unit (u1 ) are known, then the maximum deflection at the center of the membrane (h) can be calculated. Once h is known, the radius of curvature of the lens chamber (r2) as shown in Fig. 9 can be calculated using Eq. (4): r2 ¼
ðh2 þ r21 Þ : 2h
(4)
By considering the thin lens approximations, the focal length (f) can be calculated from the radius of curvature of the lens using the formula given in Eq. (5), where n1 is the refractive index of air and n2 is the refractive index of DI water (n2 ¼ 1:33) inside the lens chamber: r2 f ¼ : (5) 2ðn2 n1 Þ Series of images of the object were captured as a function of the volume of fluid pumped into or out of the lens chamber. The change in the volume of the fluid is correlated to the change in the focal length of the lens. Fig. 10 shows the images of the object captured when the dynamic lens was actuated as the DCX lens along with Deflected membrane h r1
Lens base (diameter = 15.8 mm)
r2 Fig. 9. Schematic diagram showing the lens chamber above the spacer chamber.
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a static DCX lens (f ¼ 10 cm) in between camera and dynamic lens. The variations of focal length and FOV with respect to the volume of fluid pumped into the lens chamber are shown in Fig. 11. It can be observed that, as the fluid is pumped into the lens chamber, the focal length of the formed DCX lens decreases as a result of the decrease in the radius of curvature. Further, as the focal length of this dynamic DCX lens decreases, the FOV increases as observed in the case of static lenses.
Fig. 10. Series of images captured at different volume of fluid (v3) pumped into the lens chamber using single dynamic DCX lens system.
75 Focal Length
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50
0 0.02
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Volume of Liquid Pumped-in (v3) (ml) Fig. 11. Variation in the FOV and focal length as a function of the volume of fluid pumped into the lens chamber using a single dynamic DCX lens system.
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The f-number (f/#) and numerical aperture (NA) of the single dynamic DCX lens system with a radius of 7.9 mm are calculated using the formula given in Eqs. (6) and (7), respectively, where f is the focal length and D is the diameter of the lens: f =# ¼
f ; D
(6)
1 2D NA ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : 2 1 2 D þ f 4
(7)
The change in f-number and numerical aperture with respect to the volume of fluid pumped into the lens chamber of the single dynamic DCX lens system is shown in Fig. 12. The smallest f-number achieved from the single dynamic DCX lens system is 1.3, which corresponds to the numerical aperture value of 0.35. The series of images captured when the dynamic lens was actuated as a DCV lens by pumping fluid out of the lens chamber are shown in Fig. 13a. It should be noted that for this particular lens structure, a maximum of 0.18 ml, could be pumped out from the initial point when the dynamic lens was flat. Figs. 13b and 13c show the series of images captured using the two and three dynamic DCV lenses in contact, respectively. Here, the volume v4 represents the volume of fluid pumped-out from each lens chamber. It can be observed from Fig. 13 that as the number of dynamic variable focal length DCV lenses is increased to image the object, wider field of view can be obtained. From the images captured using the three dynamic DCV lens system (Fig. 13c), it is clear that when the FOV is increased, the image size is reduced. So, further increasing the number of concave lenses to increase the FOV will make the image even smaller and blurred, and the fine details in the image could not be seen clearly. 0.4
f-number ( f /# )
30 25
f-number
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Numerical Aperture
0.3 0.25
20 0.2 15 0.15 10
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35
0.05
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0 0.02
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Volume of Fluid Pumped-in (v3) (ml) Fig. 12. The f-number (f/#) and numerical aperture (NA) as a function of the volume of fluid (v3) pumped into a single dynamic DCX lens system.
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Fig. 13. Series of images captured at different volume of fluid (v4) pumped-out of the lens chamber using: (a) single DCV lens, (b) two DCV lenses in contact, (c) three DCV lenses in contact.
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Figs. 14a–c show the variation in the effective focal length and FOV with respect to the volume of fluid pumped out of the lens chamber for a single, two and three dynamic DCV lens system. The maximum FOV achieved with single dynamic DCV lens was 501 (Fig. 14a). It should be noted that the FOV increases when two DCV
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120 100 80
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Volume of Liquid Pumped-out (v4) (ml)
Fig. 14. Variation in the FOV and focal length as a function of the volume of fluid (v4) pumped-out of each lens chamber using dynamic lens system with: (a) single DCV lens, (b) two DCV lens, and (c) three DCV lens.
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lenses are used to image the object rather than one DCV lens or DCX lens as observed for static glass lenses. Using two DCV dynamic lens system, the maximum FOV that can be achieved was 1121 (Fig. 14b). The FOV increases when three DCV lenses in contact are used to image the object than using a single or two DCV lenses. With the three dynamic DCV lens system the maximum achievable FOV was 118.31 (Fig. 14c). Further to validate the observed large FOV with the above-mentioned lens combinations, ray-tracing simulations were performed. Fig. 15 illustrates the raytraces for various lens configurations tested in this work. As evident from Fig. 15, as the number of DCV lenses increases, the image-forming rays enter the DCV lens at a wider angle from the optical axis, and thereby increasing the FOV. In this respect, the experimentally observed results match the results obtained from the ray-tracing method.
4. Conclusions In the present work, a fluid controlled dynamic optical lens system has been designed and fabricated. A fluid pumping mechanism was used for the deflection of
Fig. 15. (a–c) Ray-tracing diagrams for different combination of DCX and DCV lenses.
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flexible membranes to achieve a variable focal length. Comparative imaging experiments were performed to obtain the relationship between the focal length and FOV for different types of lenses and lens configurations using both static glass lenses of fixed focal length and dynamic PDMS lens system of variable focal length. For proper imaging of the object, a primary DCX lens and a secondary lens of either a single DCX lens, or a single DCV lens or a set of DCV lenses are needed. The focal lengths of both primary and secondary lenses determine the FOV. In general, the FOV of the lens system increases with the increase in the focal length of the primary DCX lens and with the decrease in the focal length of secondary DCX or DCV lenses. Higher FOV could be obtained with a DCV lens than with a DCX lens. It was also observed that increasing the number of DCV lenses with smaller focal length leads to an increased FOV. The FOV is increased when three DCV lenses are used to image the object than with a single or two DCV lenses. The maximum FOV achieved by using a fluid controlled optical lens system with three DCV lenses was 118.31. A simple method to form a wide-angle optical system that is suitable for dynamically imaging objects with minimal image distortion has been identified. The optical transmission characteristics and the aberrations of these dynamic lenses need to be investigated in detail. Further experiments are being conducted to miniaturize the lens system and achieve higher FOV.
Acknowledgements The authors acknowledge the financial support provided by Defense Advanced Research Project Agency (DARPA) for this work.
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Design and fabrication of fluid controlled dynamic optical lens system R.A. Gunasekaran, M. Agarwal, A. Singh, P. Dubasi, P. Coane, K. Varahramyan Institute for Micromanufacturing, Louisiana Tech University, Ruston, LA 71272, USA Received 1 February 2004; received in revised form 1 July 2004; accepted 1 September 2004 Available online 26 October 2004
Abstract A novel small fluid controlled optical lens system that is capable of displaying dynamic variation of its focal length and field-of-view (FOV) is designed and fabricated. In this active lens system, appropriate volume of the optical fluid can be pumped into or out of the lens chamber to provide double-convex (DCX) or double-concave (DCV) lens effect. Simple optical imaging experiments were performed using different sets of glass lenses with fixed focal lengths to determine the optimum lens configuration required for designing a dynamic optical lens system. The experimental results obtained from the glass lenses demonstrate that a combination of a single DCX lens with three DCV lenses provides a wider FOV. The flexible membranes for fluid controlled lenses were fabricated using polydimethylsiloxane polymer material, which has good optical transparency and elasticity. A simple fluid injection system is used to vary the radius of curvature of the lenses, and thereby to change the focal length. A dynamic optical lens system with a combination of one DCX and multiple variable focal length DCV lenses as designed here can image an object with a wide range of focal length and FOV. With this fluid controlled optical system, the FOV and focal length could be continuously varied and a maximum FOV of 118.31 could be achieved. The smallest f-number (f/#) for this fluid controlled single lens system was found to be 1.3, which corresponds to the numerical aperture value of 0.35. r 2004 Elsevier Ltd. All rights reserved.
Corresponding author. Tel.: +1 318 257 5115; fax: +1 318 257 5104.
E-mail address: [email protected] (R.A. Gunasekaran). 0143-8166/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2004.09.012
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Keywords: Dynamic optical lens system; Variable focal length lens; Wide field of view; Polymer lens; Fluid actuated lenses; Fluid focus lenses; Variable focus lens
1. Introduction The development of advanced optical devices and focal plane arrays are essential for high performance electro-optical imaging systems [1–4]. These systems require a number of miniature mechanical and optical components, and are useful for a number of domestic and military applications [3,4]. Owing to the ever-increasing demand for functional optical systems for aerial imaging and surveillance, a large number of manufacturers are developing complex and highly compact optical devices that can provide a wide field-of-view (FOV) and variable focal lengths [5–7]. The optical components or assemblies are generally developed to provide specific functions including wide angle of view, variable focal length, foveated images, etc. These lenses could be used in micro-air vehicles (MAVs), bio-medical diagnostic and surgical devices, vertical scanners, and optical holography devices [8–10]. Recently, extensive efforts have been made to mimic the bio-vision systems found in living creatures and to develop artificial bio-inspired optical lens systems [11,12]. Many bio-optical systems found in nature, including the human eye and the eyes of fishes, birds, animals etc. are single lens systems, which display very complex and remarkable visual features [12]. Most of the biological single lens systems tend to show minimal spherical and chromatic aberrations [11,12]. In addition to the singlelens systems, several compound lens systems have been found in nature [11,12]. It has been demonstrated that the complex visionary features in bio-optical systems arise from two main characteristics such as, the existence of a gradient of refractive indices in the lens (graded index (GRIN) lenses) and the ability of the lens to change its shape dynamically [1,11,12]. All these lenses in the biological systems including the GRIN lenses are known to consist of a large number of protein layers, and are capable of offering viewing angles close to 1801. Many bio-vision systems exhibit a variation of the index of refraction in their eye lenses. This characteristic together with the contracting nature of the eye lens may provide the exceptional degree of vision that is required to adjust for near and far focus [11]. GRIN lenses have been fabricated by a number of methods including printing, electrophoresis, and by lithography using gradient masks [13–18]. It should be noted that until now, no successful report on the fabrication of a single lens structure that can mimic the biooptic system has been reported. It is known that the eye of a fish is capable of viewing objects at 1801 [19]. Commercially available fish-eye lens systems that can provide a wide FOV contain multiple lenses [20]. Each of these lenses is manufactured to tight specifications and are assembled as a unit [20]. Several different configurations for the fish-eye lens systems have been reported [21–23]. Optical systems that are controlled by fluidic, electric, and mechanical actuation to provide variable focal lengths have been reported by a number of groups [24–34]. The phenomenon of electrowetting is also
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utilized in the fabrication of a dynamic lens system that can exhibit variable focal lengths [25–28]. Another notable system employs birefringent nematic liquid crystals to dynamically change the refractive index (n) and focal length by the application of an electric field. Some studies have shown that a change in the n values of more than 0.6 as a function of electric field is possible [11,29–32]. The fluid controlled optical systems typically consist of a lens chamber with channels to pump optical fluids in order to change the radius of curvature of the polymer membranes and the focal length of the resulting lens [33–35]. Most of the reported systems appear to have a single lens structure [33–35]. In some designs, a single spherical lens is mounted at the center of the membrane to produce foveated images. These lenses are capable of displaying variable focal lengths, but are not suitable for achieving wide FOV. The objective of this research is to design and develop an optical lens system that could display a dynamic variation of the focal length with a wide range of FOV. In contrast to the reported results, our experiments demonstrate that the use of a single variable focal length lens is inadequate to capture the images with large FOV. In the absence of an artificial single-lens bio-vision system, our experiments revealed that at least a set of multiple concave lenses together with a single convex lens is required to provide a wide FOV. In this paper, we report our attempts to fabricate a dynamically varying optical lens system, which could be successfully used for imaging with a large FOV and variable focal length.
2. Experimental Preliminary experiments were conducted using different sets of double concave (DCV) and double convex (DCX) lenses of different focal lengths in order to understand the relationship between the FOV and focal length of the lenses, and to determine the specific combination of lenses that can provide a wider FOV. These lenses were chosen because it is relatively easy to make the fabricated polymer lens system adapt to one of these configurations. For the construction and characterization of fluid controlled optical systems, it was realized that these simple experiments were critical to optimize the design process. A simple optical characterization setup, which includes the CCD camera, video monitor, optical rail and components, and an object with a scale attached to it, was used for imaging through the lenses. The object is a frame containing a series of letters in the form of ‘‘LOUISIANA TECH UNIVERSITY’’ with a scale attached at its bottom. Two such objects are placed in front of the camera, with one object placed perpendicular to the optical axis, and the other placed at an angle of 301 from the optical axis. The purpose of using these two objects is to determine the variation in the focal length and the FOV simultaneously. All the tested lenses are categorized into two groups: static lenses and dynamic lenses. Static lenses are simple glass lenses, and the dynamic lenses are fluid controlled lenses whose radius of curvature can be changed. Fig. 1 shows the schematic representation of the simple setup used for imaging purposes.
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Fig. 2 illustrates the different combination and configuration of DCX and DCV lenses used for imaging. For all of the different lens arrangements, four different distances are marked. As shown in Fig. 2, ‘a’ is the distance between the camera and the DCX lens; ‘b’ is the distance between the DCX and DCV lens; ‘c’ is the distance between the DCV lens and the object; ‘d’ is the length of the object that is viewed by the camera. The FOV (y) is measured by using the formula given in Eq. (1). The total FOV is twice the angle measured by taking the inverse of tangential angle (tan1) of the ratio of one-half the length of the object viewed to the distance between the lens and the object. ðd=2Þ y ¼ 2 tan1 : (1) c In one set of experiments, combinations of one DCX lens of fixed focal length (f ¼ 10 and 20 cm) and a second DCX glass lens of different focal length (f ¼ 5; 10, 15, 20, 30 cm) were used to image the object and determine the variation in the FOV with the focal length of the second DCX lens (Fig. 2a). In another set of experiments, a combination of one DCX lens of fixed focal length (f ¼ 20 cm) and a second DCV glass lens of different focal length (f ¼ 10; 15, 20 cm) were used to image the object and determine the variation in the FOV with the focal length of the second DCV lens (Fig. 2b). Results from the first and second set of experiments showed that DCV lenses provided wider FOV than DCX lenses of the same focal length and that wider FOV can be achieved by using DCV lenses of lower focal length. As shown in Fig. 2(c,d), various combinations and arrangements of DCX and DCV lenses of different focal lengths were used to determine the variation in the FOV with respect to the configuration and the focal length of these lenses. The focal length (f) of the DCX lenses were 10, 20, or 30 cm, whereas the focal length (f) of the DCV lenses were 10, 15, or 20 cm. The results obtained from simple experiments were found to be useful for designing and fabricating an optical system with similar combinations of lenses as described above using optically transparent flexible materials. The reason behind using the flexible lens material is that, by varying the radius of curvature of these
Optic Axis θ Camera
Field of view
Object
100 cm Fig. 1. Illustration of the arrangement of camera and the object.
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DCX
DCX d
Camera
(a)
a
c
b DCV
DCX
d Camera
a
b
(b)
c DCV
DCX
d Camera
(c)
a
b
c
DCX DCV d Camera
(d)
a
b
c
Fig. 2. Illustrations of the optical arrangements consisting of one DCX lens of fixed focal length with additional: (a) one DCX lens; (b) one DCV lens; (c) two DCV lenses; (d) three DCV lenses.
lenses dynamically by pumping fluid into and out of the lens chamber, one can achieve variable focal length and FOV. Since polydimethylsiloxane (PDMS) is the choice of material for optical transparency, durability, flexibility and biocompatibility, several polymer lenses were made in different sizes by casting PDMS material in suitable circular mold. After curing the PDMS membrane inside the mold, two such membrane units were combined by placing a spacer in between, and the whole assembly was sealed and made leak proof. A small hole was made in the spacer unit to fabricate the channel for pumping fluid with a high refractive index fluid (in this case DI water) into and out of the lens chamber. The lenses constructed in this manner were used to simulate the same conditions as used for the static lens
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Fig. 3. Fluid-actuated single variable focal length lens system.
configuration. Fig. 3 shows the assembled single variable focal length lens system of 7.9 mm in radius with 1.5 mm thick spacer in between. Imaging of the object was done with different combinations of dynamic lenses. A syringe pump was used to increase or decrease the volume of fluid in the lens chamber, and the image was captured at different fluid levels. First, a single dynamic lens was actuated as DCX and DCV lens by pumping fluid into or out of the lens chamber (0.02 ml each time) to view the object. A static DCX glass lens (f ¼ 10 cm) was placed between the dynamic lens and the camera (Fig. 2a and b) to image the object. Since the use of two or three double concave lenses in contact results in higher FOV, polymer lenses were made in a similar fashion. In the set of experiments that followed, the object was imaged using integrated two or three dynamic lenses in DCV configuration by pumping fluid out (0.02 ml each time) from all the lenses identically.
3. Results and discussion Initially the object was imaged only by using a CCD camera with no additional lens between the camera and the object, and the total FOV of the camera lens was measured to be 12.21. Fig. 4a shows the series of images captured using the setup shown in Fig. 2a, where the focal length of the first DCX was 10 cm and the focal length of the second DCX lens was either 5, 10, 15, 20 or 30 cm. The variation in the FOV with the change in the focal length of the second DCX lens is shown in Fig. 4b. It was observed that as the focal length of the second DCX lens decreases, FOV increases. Figs. 5a and 5b show the series of images captured using the setup as illustrated in Fig. 2a and 2b, respectively, with a fixed DCX lens (f ¼ 20 cm) in front of the camera along with DCX or DCV lenses of different focal lengths (f ¼ 10; 15,
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(a)
FOV (degree)
30
20
10
0 (b)
0
5
10
15
20
25
30
35
Focal Length (cm)
Fig. 4. (a) Images captured using the setup shown in Fig. 2a with the first DCX lens of f ¼ 10 cm and a second DCX lens of different focal lengths. (b) Focal length vs. FOV for the DCX lenses.
20 cm). The variation in the FOV with the change in the focal length for both DCX and DCV lenses is shown in Fig. 6. Although the observed FOV with these lenses is significantly lower, it should be noted that when DCV lenses are used to image the object one could achieve higher FOV. The FOV was found to increase with a decrease in the focal length of the DCV lenses. Tables 1 and 2 show the measured FOV when the object was imaged using different configuration and combination of DCX and DCV lenses with different focal length as illustrated in Fig. 2b–d. The variation in the FOV as a function of the focal length of one, two and three DCV lenses in contact and the first DCX lens is shown in Fig. 7. It can be observed that the FOV varies systematically depending on the focal length and the type of lenses used. These results demonstrate that the FOV increases with the decrease in the focal length of the DCV lenses used to image the object. Interestingly, the FOV also increased with the increase in the number of DCV
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Fig. 5. (a) Images captured using the setup shown in Fig. 2a with the first DCX lens of f ¼ 20 cm and a second DCX lens of f ¼ 10; 15, and 20 cm. (b) Images captured using the setup shown in Fig. 2b with the first DCX lens of f ¼ 20 cm and a second DCV lens of f ¼ 10; 15, and 20 cm.
FOV (degree)
12 9 DCX lenses DCV lenses
6 3 0 0
5
10
15
20
25
Focal Length (cm) Fig. 6. Focal length vs. FOV for DCX and DCV lenses.
lenses. The FOV from three DCV lenses integrated together is much larger than that from a single DCV lens or integrated two DCV lens system. The focal length of the first DCX lens used in front of the camera to image the object also plays an important role in determining the FOV. The higher the focal length of this DCX lens the higher the FOV will be. The optical image, with a minimum and a maximum
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Table 1 FOV measured using single double convex lens of focal length f ¼ 10 cm and the different combinations of double concave lenses of focal lengths f ¼ 10; 15, and 20 cm FOV (deg) (y) d (in) c (in) b (in) a (in) Three DCV lens-f (cm) Two DCV lens-f (cm) Single DCV lens-f (cm) First DCX lens f (cm)
14.5 9.5 37 0.5 2 — — 10 10
29 18 35 1.5 2 — 10 — 10
42 26 34 2.5 2 10 — — 10
NA NA NA NA NA — — 15 10
18 12 37 1.5 2 — 15 — 10
21.5 13 34 1.5 2 15 — — 10
NA NA NA NA NA — — 20 10
NA NA NA NA NA — 20 — 10
19.5 12 35 1.5 2 20 — — 10
NA–no focus was observed for these combinations.
Table 2 FOV measured using single double convex lens of focal length f ¼ 20 cm and the different combinations of double concave lenses of focal lengths f ¼ 10; 15, and 20 cm FOV (deg) (y) d (in) c (in) b (in) a (in) Three DCV lens-f (cm) Two DCV lens-f (cm) Single DCV lens-f (cm) Single DCX lens f (cm)
46 25.5 30 3 2 — — 10 20
54.5 32 31 3.5 2 — 10 — 20
78 52 32 4.5 2 10 — — 20
34 22 36 1 2 — — 15 20
39 24 34 2 2 — 15 — 20
46 28 33 3.5 2 15 — — 20
32.5 21 36 0.5 2 — — 20 20
37 22 33 2.5 2 — 20 — 20
40 23 32 4 2 20 — — 20
90 1 DCX (f = 10 cm) + 3 DCV
FOV (degree)
1 DCX (f = 20 cm) + 1 DCV 1 DCX (f = 20 cm) + 2 DCV
60
1 DCX (f = 20 cm) + 3 DCV
30
0 0
10
20
30
Focal Length (cm) Fig. 7. Focal length of the DCV lenses vs. FOV for different combinations of the DCX and DCV lenses. The focal length of the DCX lens is fixed in each series of imaging experiment.
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FOV achieved from the above-mentioned lens configuration, is illustrated in Fig. 8a and b, respectively. In the case of polymer lenses, the volume (vc ¼ 0:294 ml) of the lens chamber was calculated by measuring the diameter and the thickness of the spacer unit and by assuming that the PDMS membrane is flat. However, in reality, the PDMS membrane does not remain flat. First, the optical fluid (DI water) was pumped into the lens chamber until the chamber was filled and the membrane became flat. At this point, the volume of the fluid (v1 ¼ 0:289 ml) necessary to fill the chamber without causing any out of plane deflection of the membrane was measured. The small difference between the calculated (vc) and measured (v1) values can be attributed to the sealing joints inside the chamber that would reduce the available space. As mentioned earlier, pumping more fluid into the chamber will make it behave like a DCX lens, whereas the extraction of the fluid from the lens chamber will make it behave like a DCV lens. In the case of the DCX lens configuration, the maximum volume of fluid (v2) that can be pumped into the lens chamber without rupturing the lens membrane was
(a)
(b) Fig. 8. Image of the object captured using (a) a DCX lens (f ¼ 10 cm) and a DCV lens (f ¼ 20 cm), (b) a single DCX lens (f ¼ 20 cm) and a set of three DCV lenses in contact (focal length of each lens is 10 cm).
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measured. If v3 is defined as the difference between v2 and v1 (v3 ¼ v2 v1 ), then v3 represents the volume of fluid that was actually used to cause the deflection of the membranes on both sides to form the DCX lens. Similarly, in the case of the DCV lens configuration, the volume of fluid (v4) that can be gradually pumped out from the already fluid filled (v1) lens chamber was monitored. The maximum volume (v4(max)) of the fluid that could be pumped out was also measured. Theoretically, v1 and v4(max) are expected to be equal. The difference (v5) between v1 and v4(max) would represent the amount of fluid trapped in the chamber (v5=v1v4(max)). It should be noted that v4 represents the volume of the fluid that is pumped out to actuate the lens structure as the DCV lens. The geometrical deflection of the membrane as a result of pumping fluid into the lens chamber is shown in Fig. 9, and the associated volume of the lens chamber above the spacer unit is calculated by using the formula for a spherical cap as given in Eq. (3), where h is the membrane deflection height, r1 is base radius; v3/2 is the volume of the spherical cap which represents one side of the DCX lens. v 3 p 2 ¼ (3) ð3r1 þ h2 Þh: 6 2 From Eq. (3), when the volume (v3) and the radius of spacer unit (u1 ) are known, then the maximum deflection at the center of the membrane (h) can be calculated. Once h is known, the radius of curvature of the lens chamber (r2) as shown in Fig. 9 can be calculated using Eq. (4): r2 ¼
ðh2 þ r21 Þ : 2h
(4)
By considering the thin lens approximations, the focal length (f) can be calculated from the radius of curvature of the lens using the formula given in Eq. (5), where n1 is the refractive index of air and n2 is the refractive index of DI water (n2 ¼ 1:33) inside the lens chamber: r2 f ¼ : (5) 2ðn2 n1 Þ Series of images of the object were captured as a function of the volume of fluid pumped into or out of the lens chamber. The change in the volume of the fluid is correlated to the change in the focal length of the lens. Fig. 10 shows the images of the object captured when the dynamic lens was actuated as the DCX lens along with Deflected membrane h r1
Lens base (diameter = 15.8 mm)
r2 Fig. 9. Schematic diagram showing the lens chamber above the spacer chamber.
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a static DCX lens (f ¼ 10 cm) in between camera and dynamic lens. The variations of focal length and FOV with respect to the volume of fluid pumped into the lens chamber are shown in Fig. 11. It can be observed that, as the fluid is pumped into the lens chamber, the focal length of the formed DCX lens decreases as a result of the decrease in the radius of curvature. Further, as the focal length of this dynamic DCX lens decreases, the FOV increases as observed in the case of static lenses.
Fig. 10. Series of images captured at different volume of fluid (v3) pumped into the lens chamber using single dynamic DCX lens system.
75 Focal Length
40
60
FOV 30
45
20
30
10
15
0
FOV (degree)
Focal Length (cm)
50
0 0.02
0.08
0.14
0.2
0.26
0.32
0.38
0.44
0.5
Volume of Liquid Pumped-in (v3) (ml) Fig. 11. Variation in the FOV and focal length as a function of the volume of fluid pumped into the lens chamber using a single dynamic DCX lens system.
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The f-number (f/#) and numerical aperture (NA) of the single dynamic DCX lens system with a radius of 7.9 mm are calculated using the formula given in Eqs. (6) and (7), respectively, where f is the focal length and D is the diameter of the lens: f =# ¼
f ; D
(6)
1 2D NA ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : 2 1 2 D þ f 4
(7)
The change in f-number and numerical aperture with respect to the volume of fluid pumped into the lens chamber of the single dynamic DCX lens system is shown in Fig. 12. The smallest f-number achieved from the single dynamic DCX lens system is 1.3, which corresponds to the numerical aperture value of 0.35. The series of images captured when the dynamic lens was actuated as a DCV lens by pumping fluid out of the lens chamber are shown in Fig. 13a. It should be noted that for this particular lens structure, a maximum of 0.18 ml, could be pumped out from the initial point when the dynamic lens was flat. Figs. 13b and 13c show the series of images captured using the two and three dynamic DCV lenses in contact, respectively. Here, the volume v4 represents the volume of fluid pumped-out from each lens chamber. It can be observed from Fig. 13 that as the number of dynamic variable focal length DCV lenses is increased to image the object, wider field of view can be obtained. From the images captured using the three dynamic DCV lens system (Fig. 13c), it is clear that when the FOV is increased, the image size is reduced. So, further increasing the number of concave lenses to increase the FOV will make the image even smaller and blurred, and the fine details in the image could not be seen clearly. 0.4
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Volume of Fluid Pumped-in (v3) (ml) Fig. 12. The f-number (f/#) and numerical aperture (NA) as a function of the volume of fluid (v3) pumped into a single dynamic DCX lens system.
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Fig. 13. Series of images captured at different volume of fluid (v4) pumped-out of the lens chamber using: (a) single DCV lens, (b) two DCV lenses in contact, (c) three DCV lenses in contact.
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Figs. 14a–c show the variation in the effective focal length and FOV with respect to the volume of fluid pumped out of the lens chamber for a single, two and three dynamic DCV lens system. The maximum FOV achieved with single dynamic DCV lens was 501 (Fig. 14a). It should be noted that the FOV increases when two DCV
40
45
30 Focal Length 20
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10 0
0 0.02 0.04 0.06 0.08
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Fig. 14. Variation in the FOV and focal length as a function of the volume of fluid (v4) pumped-out of each lens chamber using dynamic lens system with: (a) single DCV lens, (b) two DCV lens, and (c) three DCV lens.
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lenses are used to image the object rather than one DCV lens or DCX lens as observed for static glass lenses. Using two DCV dynamic lens system, the maximum FOV that can be achieved was 1121 (Fig. 14b). The FOV increases when three DCV lenses in contact are used to image the object than using a single or two DCV lenses. With the three dynamic DCV lens system the maximum achievable FOV was 118.31 (Fig. 14c). Further to validate the observed large FOV with the above-mentioned lens combinations, ray-tracing simulations were performed. Fig. 15 illustrates the raytraces for various lens configurations tested in this work. As evident from Fig. 15, as the number of DCV lenses increases, the image-forming rays enter the DCV lens at a wider angle from the optical axis, and thereby increasing the FOV. In this respect, the experimentally observed results match the results obtained from the ray-tracing method.
4. Conclusions In the present work, a fluid controlled dynamic optical lens system has been designed and fabricated. A fluid pumping mechanism was used for the deflection of
Fig. 15. (a–c) Ray-tracing diagrams for different combination of DCX and DCV lenses.
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flexible membranes to achieve a variable focal length. Comparative imaging experiments were performed to obtain the relationship between the focal length and FOV for different types of lenses and lens configurations using both static glass lenses of fixed focal length and dynamic PDMS lens system of variable focal length. For proper imaging of the object, a primary DCX lens and a secondary lens of either a single DCX lens, or a single DCV lens or a set of DCV lenses are needed. The focal lengths of both primary and secondary lenses determine the FOV. In general, the FOV of the lens system increases with the increase in the focal length of the primary DCX lens and with the decrease in the focal length of secondary DCX or DCV lenses. Higher FOV could be obtained with a DCV lens than with a DCX lens. It was also observed that increasing the number of DCV lenses with smaller focal length leads to an increased FOV. The FOV is increased when three DCV lenses are used to image the object than with a single or two DCV lenses. The maximum FOV achieved by using a fluid controlled optical lens system with three DCV lenses was 118.31. A simple method to form a wide-angle optical system that is suitable for dynamically imaging objects with minimal image distortion has been identified. The optical transmission characteristics and the aberrations of these dynamic lenses need to be investigated in detail. Further experiments are being conducted to miniaturize the lens system and achieve higher FOV.
Acknowledgements The authors acknowledge the financial support provided by Defense Advanced Research Project Agency (DARPA) for this work.
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