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We report an ultrathin zoom telescopic objective that can achieve continuous zoom change and has reduced compact volume. The objective consists of an annular folded lens and three electrowetting liquid lenses. The annular folded lens undertakes the main part of the focal power of the lens system. Due to a multiple-fold design, the optical path is folded in a lens with the thickness of ~1.98mm. The electrowetting liquid lenses constitute a zoom part. Based on the proposed objective, an ultrathin zoom telescopic camera is demonstrated. We analyze the properties of the proposed objective. The aperture of the proposed objective is ~15mm. The total length of the system is ~18mm with a tunable focal length ~48mm to ~65mm. Compared with the conventional zoom telescopic objective, the total length has been largely reduced.
© 2016 Optical Society of America
1. Introduction
Compact imaging systems are important features of next generations of imaging product. Among key specifications, maybe overall size and manufacturing cost are most important. Nowadays, many imaging systems are designed to be smaller and smaller. For example, adaptive lenses such as liquid lenses and liquid crystal lenses make zoom imaging system more compact due to their tunable curvature radius or tunable index of refraction [1–9]. Using adaptive lenses, no movement parts are needed to change the focal length, and all the elements are fixed. Therefore, the lens system design and fabrication are relatively easy. During the past decade, many zoom lens systems based on the two types of lenses were proposed [10–16]. These imaging systems can achieve good imaging performances by only applying voltages. Although one of main purposes for using liquid lenses is to reduce the lens system size, the current imaging systems based on liquid lenses show little advantage in system length compared with the conventional zoom lens systems. The main reason is that the numerical aperture of the liquid lens is still small. Therefore, usually several liquid lenses are needed to undertake the optical power which is equal to that of a glass lens. Thus, the total system length increases. Therefore, to realize a more compact zoom lens system using liquid lenses is still urgent.
Folded optics [17, 18] provides one way to reduce the system length. Inspired from Cassegrain telescope [19], a multiple-fold lens is proposed. The lens is designed with a series of concentric zone reflectors to focus the light. Thus, the total lens system length is greatly reduced. However, till now, for a multiple-fold lens, it is difficult to realize a zoom lens system using “classical” lens design method (mechanical movement way), because all the concentric zone reflectors are fixed on a substrate. Therefore, the zoom part has to be added behind the multiple-fold lens, but the back focal length is still too limited to allow the movement part to move in a large range.
In this paper, we report and first experimentally demonstrate an ultrathin zoom telescopic objective which consists of an annular folded lens and three electrowetting liquid lenses. The annular folded lens undertakes main part of the focal power of the lens system and reduces the total system length largely. The electrowetting liquid lenses are the zoom part, which cannot only change the focal length, but also correct the aberrations. All parts are fixed, which makes design and fabrication of the zoom lens system relatively easy. The whole system is very thin.
2. Ultrathin zoom telescopic objective and theoretical analysis
The proposed ultrathin zoom objective consists of an annular folded lens and three electrowetting liquid lenses [20] as shown in Figs. 1(a)-1(b). Three electrowetting liquid lenses are fixed behind an annular folded lens. Light enters the annular folded lens through an outer annular aperture. After 8 times reflections by 4 concentric zone reflectors and a circular reflector, the light enters the liquid lens system. The liquid lens system plays the role as a zoom part. Not only the focal length can be tuned, but also the aberrations can be corrected by the three tunable interfaces. In our system, the annular folded lens is used for two main purposes: it undertakes part of the focal power and it can fold the optical path. So the total system length is largely reduced.
Fig. 1 Schematic cross-sectional structure of the ultrathin zoom telescopic objective. (a) Cross-sectional of the zoom objective. (b) Side view of the objective. (c) Zemax layout of the objective
As shown in Fig. 1(c), there are two types of the reflectors. On the front surface of the folded lens, the reflector is circular shape and has no power. However, on the back surface, the four reflectors are concentric zone. Each concentric zone has an aspherical surface. Therefore, the four reflectors have power. The aspherical surfaces are also designed to reduce aberrations.
The used liquid lens is an electrowetting-actuated lens with variable focal length. Its focal length is changed due to electrowetting effect. According to Young–Lippmann equation, the relationship of the contact angle θ and the applied voltage U can be described as follows [1]:
where ε is dielectric constant of the insulating layer, d is the thickness of the insulating layer, and 𝛾1, 𝛾2 and 𝛾12 are the interfacial tensions of sidewall/oil, sidewall/water and oil/water, respectively.From Fig. 1(c), the optical power of the zoom lens system is determined by two parts: the fixed part and the zoom part. We assume the power of the fixed part is Φf, and the power of the zoom part is Φz. The effective focal length f of the zoom lens system can be expressed as
where n1 is the refractive index of the oil, while n2 is the refractive index of the conductive liquid, and r1, r2, r3 are the radii of the three electrowetting liquid lenses, respectively.3. Fabrication
For the proposed ultrathin zoom objective, the annular folded lens and electrowetting liquid lenses are the main elements. The annular folded lens is fabricated using diamond turning technology, as shown in Fig. 2(a). The material of the folded lens is calcium fluoride (CAF2). Measured by Taylor Hobson (A profile testing instrument), the form errors of the aspheric surfaces (from the inner zone to the outer zone) are ~340nm, ~280nm, ~330nm and ~280nm, respectively. Average polished roughness of each aspheric zone is within 5nm RMS with peaks to 50nm. After diamond turning, silver reflectors are coated on the four concentric aspheric zones and the planar circular zone, as shown in Figs. 2(b)-2(c). The diameter of the fabricated folded lens is ~15mm, as shown in Fig. 2(c). The electrowetting liquid lenses are a commercialized liquid lens Arctic 39N0 produced by Varioptics [21] as the tunable element. The effective aperture of the liquid lens is ~3.9mm. The materials of the liquid lens are shown in Table 1. The fabricated objective is shown in Fig. 3. The total length of the proposed objective is ~18mm, while the diameter is ~30mm.
Fig. 2 Fabricated annular folded lens. (a) Folded lens without coating. (b) Back view of folded lens coated with silver film. (c) Front view of folded lens coated with silver film.
Table 1. Refractive index and Abbe number of the materials we used
Fig. 3 Fabricated ultrathin zoom telescopic objective. (a) Whole view of the objective. (b) Side view of the objective. (c) Front view of the objective. (c) Back view of the objective.
4. Simulation
In Zemax simulation, the focal length of the proposed zoom telescopic objective can be tuned from ~48mm to ~65mm. In the tuning range, the field of view (FOV) and F number vary with the focal length, as shown in Table 2. We also simulated the PSF (point spread function) and ray aberration shown in Fig. 4 and Fig. 5, respectively. In the tuning range, the performances of the proposed objective in PSFs with different focal length are equally good, and the diameter of the ray traced spots is almost the same as that of the airy disk, which indicates that the three liquid lenses can correct aberrations when zooming. From the ray aberration in Fig. 5, we see that due to central obscuration, the ray aberrations are only shown in the marginal area. Although the spherical aberration, comma, astigmatism and chromatic aberration still exist in our proposed objective, the residual aberrations are small enough to be acceptable for an image system.
Table 2. Detailed parameters of the proposed objective
Fig. 4 FFT (Fast Fourier Transformation) PSF of the proposed objective. (a) f = 48mm. (b) f = 57mm. (c) f = 65mm.
As a comparison, we also simulated a conventional refractive telescope objective. The simulated conventional objective is a cemented doublet lens, which is a very common type of telescope objective. We simulated three objectives with the same parameters (FOV, effective aperture, focal length and so on) as that of our proposed objective for three different focal lengths. The three telescope objectives are optimized with least aberrations. The total lengths of the three optimized telescope objectives are ~54mm, ~59mm and 67mm, respectively. We give the modulation transfer function (MTF) of the proposed zoom telescopic objective and conventional refractive telescope objectives with different focal lengths, as shown in Figs. 6 (a), 6(c), and 6(e). The layout and total length are shown in Figs. 6(b), 6(d), and 6(f). The conventional refractive telescope objective and our proposed objective have the same effective aperture. The effective aperture of our objective is ~7.1mm, which is calculated based on the following equation [17]:
where dout is the outer diameter of the annular aperture, and din is inner diameter of the annular aperture. Compared with a full aperture lens system, the MTF of our objective degrades in the low-spatial and middle-spatial frequency range due to central obscuration, as shown in Figs. 6(a), 6(c) and 6(e). However, our proposed objective has an obvious advantage. That is, our proposed objective is much thinner than the conventional objective, and without mechanically moving parts, as shown in Figs. 6(b), 6(d) and 6(f).Fig. 6 MTF and total length of the proposed objective and conventional telescope objectives. (a) MTF at f = 48mm. (b) Total length for f = 48mm. (c) MTF at f = 57mm. (d) Total length for f = 57mm. (e) MTF at f = 65mm. (f) Total length for f = 65mm.
5. Experiments and result discussions
To evaluate the optical performance of the proposed objective, we use a collimator tube to test the resolution. The setup is shown in Fig. 7. The resolution testing setup consists of a light source, a spectral filter, a resolution target, a collimator tube and a CMOS digital camera. The light source is a white light. When the light passes through the spectral filter, the remained wavelength (λ) is ~550nm. Then, the light enters the collimator tube. The collimated light enters our proposed zoom objective. Finally, the image is captured by the CMOS camera. The focal length of the collimator tube is ~500mm, and the aperture is ~80mm. The diagonal size of CMOS is ~7.18mm. The maximum resolution is 2592 × 1944. The pixel size in the CMOS is 2.2μm × 2.2μm. We use 1280 × 960 mode, because the image circle of our proposed objective is ~3.57mm. The largest and smallest line widths of resolution target are ~80μm and ~20μm, respectively. The back focal length of our proposed lens is ~3mm. The setup of the proposed objective and CMOS camera is shown in Fig. 8(a).
Fig. 8 Captured image using a resolution target. (a) Setup. (b) f = 65mm. (c) f = 57mm. (d) f = 48mm.
We first optimize the radii of the three liquid lenses to get optimized solutions for three focal lengths in Zemax-EE. Then we got the applied voltages based on the optimized solutions. Then the optimized voltages were applied to the three electrowetting liquid lenses to obtain the required magnified image, as shown in Figs. 8(b)-8(d). We note that the Figs. 8(b)-8(d) were cropped with resolution 550 × 510. The focal length for Fig. 8(b) is ~65mm, and we could recognize the bars of No. 14. The correspond line width in object space is ~37.8μm. The line pair in image space is ~102cycles/mm. When we change the focal length to 57mm, a relatively smaller image is captured clearly, as shown in Fig. 8(c). The smallest target bar we can recognize is No. 12. The correspond line width in object space and line pair in image space are ~42.4μm and 103cycles/mm, respectively. Further changing the focal length (f = 48mm), the captured image becomes smaller, as shown in Fig. 8(d). The smallest target bar we can recognize becomes larger (No. 9). The correspond line width in object space and line pair in image space are ~50.4μm and 103cycles/mm, respectively. From the experiment, we see that the line pairs with maximum resolution in image space for the three focal lengths are almost the same (~103 cycles/mm), which are slightly different from the simulation result. We believe the difference mainly results from fabrication error.
To further test the optical performance of the proposed zoom objective, we built a real scene, as shown in Fig. 9(a). The scene was placed ~15m away from the objective. A prototype of conventional refractive telescope objective was also fabricated as a comparison. The design of the prototype is the one we used in simulation [Fig. 6(a) and 6(b)], which has the same parameters (FOV, effective aperture, focal length and so on) as that of our proposed objective when f = 48 mm. The fabricated prototypes of conventional and proposed objective are shown in Fig. 9(b). The line widths of Target bars 1 and 2 are 16mm and 3.5mm, respectively. The widest line width of Target bar 3 is ~2mm. The width of the built scene is ~780mm. In the experiment, we first captured the scene with the conventional objective shown in Fig. 9(c). The exposure time is ~65ms. Then we captured the scene with different focal lengths using the proposed zoom objective. The captured images are shown in Figs. 9(d)-9(g). The focal lengths for Figs. 9(d)-9(g) are ~65mm, ~60mm, ~53mm and ~48mm, respectively. We see that all the captured pictures are clear and with high resolution. Comparing the four pictures, the magnification of Fig. 9(d) is the largest, and the FOV is smallest with least the luminous flux on the CMOS. Therefore, we see that the object in the image is the largest but the image is darker. When changing the focal length (shorter), the object in the image becomes smaller and the FOV becomes larger. Finally, the “mushroom” and “bottle” can be seen in the image, as shown in Fig. 9(g). The image also becomes brighter. The exposure time for different focal lengths is the same (~65ms). Comparing the image quality of the conventional and proposed objectives [Fig. 9(c) and 9(g)], we see that whole scene captured by the conventional objective seems clearer than that of the proposed one. From the simulation [Fig. 6(a)], we can get the answer. Due to central obscuration, the MTF of our objective degrades in the low-spatial and middle-spatial frequency range. In high-spatial frequency range, both systems can resolve part of the radial resolution target. However, the proposed telescope objective is much thinner than a conventional telescope objective as shown in Fig. 9(b). From the experiment, we can conclude that the proposed zoom objective cannot only change the focal length, but also correct the aberrations. In fact, comparing with the conventional zoom telescopic objective, the total length is reduced largely (~18mm with tuning focal length range from ~48mm to ~65mm).
Fig. 9 Captured images. (a) Whole scene. (b) Total length of the two objectives. (c) Captured by conventional objective with f = 48mm. (d) Captured by the proposed objective with f = 65mm. (e) Captured by the proposed objective with f = 60 mm. (f) Captured by the proposed objective with f = 53 mm. (g) Captured by the proposed objective with f = 48 mm.
Like other zoom systems based on electrowetting liquid lenses, the optical power of the liquid lens is relatively small comparing with the solid lens. Therefore, the zoom ratio of our proposed zoom objective is relatively small. To get large zoom ratio, there are two methods. Firstly, the power of a liquid lens should be improved. For an electrowetting liquid lens, one effective method is that we can choose of an oil and a conductive liquid with the large difference of index of refraction. In this case, the power of an electrowetting liquid lens can be improved, which helps to increase the zoom ratio. Secondly, we can increase the number of the liquid lens in the system. In this case, the zoom ratio and the ability to correct aberration both can be improved. However, the total length of the system will also be increased.
6. Conclusion
In conclusion, we proposed an ultrathin zoom telescopic objective which can achieve continuous zoom change and has reduced compact size. The objective consists of an annular folded lens and three electrowetting liquid lenses. Due to multiple-fold design, the optical path is folded in a lens with the thickness of ~1.98mm. The electrowetting liquid lenses constitute zoom part, which cannot only change the focal length, but also correct the aberrations. An ultrathin zoom telescopic camera is demonstrated. The proposed zoom objective can tune the focal length from ~48mm to ~65mm with high resolution image. Comparing with the conventional zoom telescopic objective, the total length is reduced largely (~18mm with ~15mm aperture).
Funding
“973” Program (2013CB328802), National Natural Science Foundation of China (NSFC) ( 61535007 and 61505127).
References and links
1. B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000). [CrossRef]
2. S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85(7), 1128–1130 (2004). [CrossRef]
3. C. C. Cheng and J. A. Yeh, “Dielectrically actuated liquid lens,” Opt. Express 15(12), 7140–7145 (2007). [CrossRef] [PubMed]
4. H. Ren and S. T. Wu, “Variable-focus liquid lens by changing aperture,” Appl. Phys. Lett. 86(21), 211107 (2005). [CrossRef]
5. L. Li, C. Liu, H. Ren, H. Deng, and Q. H. Wang, “Annular folded electrowetting liquid lens,” Opt. Lett. 40(9), 1968–1971 (2015). [CrossRef] [PubMed]
6. C. W. Chiu, Y. C. Lin, P. C. P. Chao, and A. Y. G. Fuh, “Achieving high focusing power for a large-aperture liquid crystal lens with novel hole-and-ring electrodes,” Opt. Express 16(23), 19277–19284 (2008). [CrossRef] [PubMed]
7. H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, “Tunable-focus flat liquid crystal spherical lens,” Appl. Phys. Lett. 84(23), 4789 (2004). [CrossRef]
8. M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43(35), 6407–6412 (2004). [CrossRef] [PubMed]
9. G. E. Nevskaya and M. G. Tomilin, “Adaptive lenses based on liquid crystals,” J. Opt. Technol. 75(9), 563–573 (2008). [CrossRef]
10. S. Reichelt and H. Zappe, “Design of spherically corrected, achromatic variable-focus liquid lenses,” Opt. Express 15(21), 14146–14154 (2007). [CrossRef] [PubMed]
11. R. Peng, J. Chen, C. Zhu, and S. Zhuang, “Design of a zoom lens without motorized optical elements,” Opt. Express 15(11), 6664–6669 (2007). [CrossRef] [PubMed]
12. S. Lee, M. Choi, E. Lee, K. D. Jung, J. H. Chang, and W. Kim, “Zoom lens design using liquid lens for laparoscope,” Opt. Express 21(2), 1751–1761 (2013). [CrossRef] [PubMed]
13. A. Miks and J. Novak, “Analysis of three-element zoom lens based on refractive variable-focus lenses,” Opt. Express 19(24), 23989–23996 (2011). [CrossRef] [PubMed]
14. Y. H. Lin and H. S. Chen, “Electrically tunable-focusing and polarizer-free liquid crystal lenses for ophthalmic applications,” Opt. Express 21(8), 9428–9436 (2013). [CrossRef] [PubMed]
15. Y. H. Lin, M. S. Chen, and H. C. Lin, “An electrically tunable optical zoom system using two composite liquid crystal lenses with a large zoom ratio,” Opt. Express 19(5), 4714–4721 (2011). [CrossRef] [PubMed]
16. L. Li, D. Wang, C. Liu, and Q. H. Wang, “Zoom microscope objective using electrowetting lenses,” Opt. Express 24(3), 2931–2940 (2016). [CrossRef] [PubMed]
17. E. J. Tremblay, R. A. Stack, R. L. Morrison, and J. E. Ford, “Ultrathin cameras using annular folded optics,” Appl. Opt. 46(4), 463–471 (2007). [CrossRef] [PubMed]
18. E. J. Tremblay, R. A. Stack, R. L. Morrison, J. H. Karp, and J. E. Ford, “Ultrathin four-reflection imager,” Appl. Opt. 48(2), 343–354 (2009). [CrossRef] [PubMed]
19. M. Laikin, “Lens Design,” Chap. 15 (2001).
20. L. Li, C. Liu, and Q. H. Wang, “Ultrathin zoom lens system based on liquid lenses,” Proc. SPIE 9524, 95241B (2015). [CrossRef]
21. www.varioptic.com.
