MTF is the most widely used index to quantify imaging resolution of an optical system [29]. To evaluate the optical performance of the AF imaging system with sGD-LC lens. A measure system was set up as Figure 5-1 shows. A 10m-width point source was placed 150mm in front of the system. The CCD sensor was placed at 7.3mm behind the system which is the BFL of the conventional lens-head.
Figure 5-1 Measurement setup for MTF
Since the AF system was in off-state, an unfocused light spot, as shown in Figure
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5-2 (a), was observed by CCD sensor. As the sGD-LC lens was driven for 15cm focal length by corresponding voltage-frequency pairs. The point spread function (PSF) was measured by the CCD sensor, as shown in Figure 5-2 (b), and calculated to MTF by a Fourier Transfer.
In the measurement of MTF, the performance was limited by the width of the point source (10m) and the pixel size (9.3m). Theoretically, the cut-off frequency of the MTF is 50(lp/mm) corresponding to a 10m Point source. However, since the alignment deviation and defects in fabrication and imperfect driving of sGD-LC lens, the cut-off frequency of AF imaging system was damaged down to 30 (lp/mm), as shown in Figure 5-3.
Figure 5-2 Point spread function of the AFsystem in (a) off-state and (b) when sGD-LC lens was driven for 15cm focal length.
Figure 5-3 The calculated MTF of the AF system with sGD-LC lens.
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5.2 LC Zoom Lens
Optical zoom is a very useful design which is widely used in many camera lenses.
Conventional optical zoom lens was a mechanical assembly of lens element. A true zoom lens, also called parfocal lens, is one that maintains focus distance when focal length was changed. A lens loses focus distance when change the focal length was called varifocal lens. The first commercial optical zoom lens--Zoomar 36–82mm f/2.8 was announced by Voigtländer in 1960 [30], while it is a varifocal lens. The major advantage of zoom lens is versatile for many case, a single zoom lens can fit all-rounded. However, conventional optical zoom change focal length by mechanical movement, the structure needs additional space. The demands of mobile devices are slight, small, and thin. Because of these demands, mechanical moveable structure is impractical for mobile use. Liquid Crystal lens is a good answer for mobile zoom system. Since liquid crystal lens is a focal-length tunable lens, additional space is no need for achieve optical zoom. Without any mechanical movement, the volume of the system can be reduced, and optical zoom for mobile devices is achievable.
5.2.1 Basic Theorem of Optical Zoom System
A zoom lens can be separated to three parts as variator, compensator, and erector respectively [3]. As Figure 5-4 shows, Erector was a lens (or lens group) which is erect whole lens, it usually fixed and standing. While variator is the key component of changing focal length, and compensator is a lens group for compensate the image shift and aberration of variator. In general case, variator and compensator are a linked-structures, one of them changing will involve the other one. The movement of
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the Variator is linear since it decides the variance of effective focal length, and because of image shift and aberrations are non-linear changing, so the movement of compensator is non-linear.
Figure 5-4 Three main compositions of zoom lens
5.2.2 Simulation and System Design
For simplifying calculation and reduce the difficulty of design. Paraxial approximation was used for the optical system. Equation (5-1) and Equation (5-2) can be used to obtain the optical power of the zoom system and fix the imaging plane on position of image sensor.
(5-1)
53 lens, D12 is the space between first and second LC lens which was chosen as 10(mm).
Only these three parameters influence zoom ratio. Both of them are proportional to the zoom ratio.
We utilize and as the variator and compensator respectively, as Figure 5-6 shows. In the simulation result, although lens power of the system, K, can be varied, but the lens power of LC lenses were limited within . Therefore, the zoom
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Figure 5-5 Schematic diagram of LC zoom lens
Figure 5-6 Variation of lens power, K, changed by LC lens power, K1 and K2.
5.3 Image Defects of AF Imaging System
Defocus which is the first-order aberration has been well-answered. The aberrations should be analyzed in the next. However, the analyzing and reducing of third or higher order aberrations are requiring waveform of sGD-LC lens. Since the waveform investigation of sGD-LC lens was still need to be improved, the analysis of aberrations cannot be achieved now. Although AF imaging system has been demonstrated an impressive image quality, there are still some defects of captured image. In this section, some defects of AF imaging system will be illustrated.
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5.3.1 Leakage of Ordinary Ray.
Theoretically, ordinary should be blocked by polarizer perfectly and only extra-ordinary ray will incident LC lens. However, because of every sGD-LC was homemade, the alignment is not as precise as FAB, so sGD-LC lens cannot driving as ideal model.
For investigating the leakage of ordinary ray, we compared inferior and superior sGD-LC lenses. These two sGD-LC lens was fabricated in the same process and same parameter, both their focusing time and driving voltage are very similar. The fringing pattern of two sGD-LC lens was shown in Figure 5-7. This figure shows the focusing quality of inferior one is worse than superior one, but the optical power is almost the same since the relative phase difference is the same.
Figure 5-7 Fringing patterns of (a) inferior and (b) superior sGD-LC lenses.
By driving these two samples with the same AF imaging system which has mentioned in Chapter 4.2. Figure 5-8 is the captured images of the inferior one.
Examining the black background of the image carefully, the leakage of o-ray is
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obviously.
Figure 5-8 Comparison of (a) no o-ray leakage at 90cm, (b) o-ray leakage at 6cm. The right-bottom corner of (b) exist a little o-ray (unfocussed ray).
Ideally, rays from object plane should be guiding to image plane. In Figure 5-8 (a), rays from 90cm which is perfectly focus at CCD sensor since sGD-LC lens is in off state and all LC molecular lied flat and the LC layer just like a glass layer. In Figure 5-8 (b), which is image of near object, the rays are not focusing perfectly since the imperfectly of sGD-LC lens. So the leakage of ordinary ray happened.
Figure 5-9 compared these two sGD-LC lens. The o-ray leakage of superior one is much less than inferior one. The contour of superior one is much expressly than inferior one. We may infer that leakage of o-ray is related to the quality of sGD-LC lens intrinsically.
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Figure 5-9 O-ray leakage comparison of (a) inferior (b) superior sGD-LC lens.
The o-ray (unfocussed ray) of (a) is much stronger than (b).
5.3.2 Tilt of Object Plane
In an ideal optical system, object plane is perpendicular to optical axis. Tilt &
shift lens is an exceptional lens which has a tilt object plane. Tilt & shift lens is minority in lenses and will used in some specific case. Since there are seldom users of tilt & shift lens, most of them are expensive and luxury.
We found that a special “defect” accidently of our AF imaging system which is the tilt of object plane. When the AF imaging system focusing at 15cm, ideally object
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plane is perpendicular to optical axis which is 15cm in front of the focus plane.
However, for our sGD-LC lens, the central area of image is perfectly focusing, while the marginal area of image is defocus. This phenomenon was cause by the tilt of object plane, which was shown in Figure 5-10. In our AF imaging system, object plane was rotate clockwise respect to ideal object plane.
To investigate is the issue cause by imperfection or defects of sGD-LC lens. We rotated the sGD-LC lens 180 degree respect to the optical axis, and the object plane rotated counter-clockwise respect to ideal object plane. To analysis this issue more detail, the waveform of sGD-LC lens should be obtained. Since the deriving technique of waveform is still need to be improved, the advanced analyze of tilt object plane are unavailable now. But this “defect” is not really a shortcoming of sGD-LC lens. In fact, since conventional glass/polymer tilt & shift lenses are expensive and luxury, so the market of this lens is minority. If we can control the tilt angle of the object plane by changing the distribution of LC molecular, the threshold expense of tilt & shift lens will be dramatically reduced, and the users of tilt & shift lens will growth a great number.
Figure 5-10 The ideal and real object plane, while the real object plane is tilt respect to optical axis.
59 optical zoom. We prove that LC optical zoom system is achievable and feasible since the required space of LC lens is much smaller than VCM.
Finally, two defects of sGD-LC lens were illustrated. The leakage of o-ray could be well-improved by a superior sGD-LC lens, this defect was cause by the limitation of homemade fabrication process and could be resolve by industrial manufacturing.
The tilt of object plane is not an actual defect. If we can control the tilt angle of the object plane by changing the distribution of LC molecular, a common, general but cheap tilt & shift lens could be obtained.
Chapter 6
Conclusion and Future work
6.1 Conclusion
Liquid Crystal Lens exhibits the ultimate features, such as the focal length is electrically tunable without any mechanical movement or surface shape changing and its tiny volume is suitable for employing in mobile devices. However, the two major
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issues which are slow focusing time and high driving voltage lead to impractical and unfeasible applications of LC lenses.
Spherical Gradient Driven Liquid Crystal Lens (sGD-LC lens), was proposed to intrinsically solve these two issue. Compare to conventional LC lens, we demonstrated a dramatic improvement for reducing the driving voltage from hundred voltages down to less than 5 Volts. The key element of sGD-LC lens is the coated high resistant layer above controlling electrodes. The first benefit of this structure is that the applied energy can be conserved inside the LC layer. The second benefit is that the resistance layer bridging central and marginal controlling electrode and generate gradient voltage distribution for yielding lens profile. Furthermore, Hi-R layer yield sGD-LC lens voltage and frequency controllable. Each focal length can be optimized by this dual-control which has improved the image quality. The most important breakthrough was that the focusing time has been improved from 20 or more seconds down to less than 1sec (~800ms) for focusing from infinity to 7cm closed object, as Figure 6-1 illustrates.
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Figure 6-1 The dramatically improvement of driving voltage and focusing time with GD-LC lens combined with Over-Drive method.
Comparing with the other leading groups in the world, as shown in Table 5, not only the driving voltage was reduced to a practical range that the normal IC could drive but also the focusing time was improved to less than 1sec (800ms). However, the maximum life time of sGD-LC lens is only 2 months. Lengthening the short lifetime is a big topic, which will be discussed in future work.
Comparing to other auto-focusing technologies mentioned in Chapter 1.3, as shown in Table 6. Since the issues of LC lens which are driving and focusing time have almost been solved, the competitiveness of LC lens is much stronger now. Although the image quality still cannot compete with conventional glass/polymer lens-head, but
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this study shows that LC lens is feasible and practical for mobile devices. We consider that as long as improving the image quality in the future, LC lens could be generally utilized on mobile devices.
Table 5 Comparisons of single tunable lenses.
Table 6 Comparison of the AF solutions after the improvements of GD-LC lens.
(For mobile appliacation)
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6.2 Future Work
6.2.1 Resistance Controlling of Hi-R Layer
High resistance layer is the most important part of sGD-LC lens. How to control the Hi-R layer in an appropriate value is the key point. In this study, Clevios-P which is an organic material was chosen as the Hi-R layer. Since Clevios-P is a kind of solution, spin-coated method was utilized to coating this material. However, this Hi-R layer has two issues which are non-durable and inferior quality of thin film. The First one is short lifetime, we have fabricated hundreds of sGD-LC lenses, only one of them still workable after 2 month, while majority of them died in a month. By investigate fringing pattern of the samples, we infer that heat of the current induce deteriorate of Clevios-P. The Second one is inferior quality of thin film which cause by re-dissolved of Hi-R layer which has mentioned in Chapter 3.2.3. The proposed method of re-dissolved of Hi-R layer is 20 minutes ozone sputtering. However, the precision of drop and raise of resistance is hard to control. So resistance cannot be controlled in an precise value.
Utilizing other inorganic materials with sputter may be a good answer.
Comparing sputter inorganic materials and spin-coating Clevios-P, we found that not only the quality of thin film but also lifetime of the thin film, sputter is generally better than spin coating, as shown in Table 7 and Table 8. The major advantage of spin coating is convenience, while the tradeoff is inferior thin film quality, and sputtering is vice versa.
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Table 7 Comparison of organic material and inorganic material
Table 8 Comparison of spin coating and sputtering
6.2.2 Improvement of Zoom Ratio
The simulation result indicates that zoom ratio of LC zoom optical system is approximate 2X. However, the minimum zoom ratio of commercial product must be at least 3X. So, improve the zoom ratio should be the next step. In this LC zoom system, K1, K2 and D12 are three factors which effect EFL of the system. Since K1 and K2 which are the optical power of sGD-LC lens are intrinsically influence by LC cell, so the controllable part is D12. If we want to obtain 3X zoom ratio, D12 should be 2cm, as shown in Figure 6-2. While 2cm is obviously too thick and impractical for mobile devices, periscope lens as shown in Figure 6-3 may be a solution of striving additional space. Since the diameter of LC lens is merely 2mm which is much lesser than the thickness of mobiles, we consider that 3X zoom ratio could be achieved by periscope
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lens.
Figure 6-2 The variation of lens power, K, when D12= 2cm.
Figure 6-3 Schematic diagram of periscope lens.
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6.2.3 Optical design for LC optical system
We have proposed a fast focusing time and low driving voltage LC lens. The MTF of LC imaging system is cutoff at 30 (lp/mm). The first reason is alignment deviation of the optical system, which can be solved by mechanical alignment. The second reason is the defect of LC imaging system intrinsically. That is because, the conventional lens head has been already optimized. Although the additional LC lens is well designed in paraxial optics, but the off-axis beam will cause aberrations.
To improve this issue, the optical design of conventional lens for LC lens can be take into consideration. In the first step, the focusing performance of LC lens should be optimized, and then utilize solid lens to correct the image quality, image aberrations, and enhance MTF. The role of the solid lens is to obtain a balance solution for focusing at infinity and close objects. For a long term target, a well-designed optical system is needed. This design is not only for establish a whole optical system but also for the advanced optical design. For example, Aspherical lens has been widely utilized in modern optical system, and LC lens is able to achieve different form of aspherical lens by controlling the electric field. By integrating LC lens and conventional lens, the quality of LC optical system will be much improved.
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