In this paper, we demonstrate a multi-functional liquid-crystal lens (MFLC-lens) based on dual-layer electrode design. Compared with the previous 3D endoscopes, which use double fixed lens capturing, the proposed LC lens is not only switchable between 2D and 3D modes, but also is able to adjust focus in both modes. The diameter of the MFLC-lens is only 1.42mm, which is much smaller than the available 3D endoscopes with double fixed lenses. To achieve the MFLC-lens, a high-resistance layer needs to be coated on the electrode to generate an ideal gradient electric-field distribution, which can induce a lens-like form of LC molecules. The parameters of high-resistive layer are investigated and discussed with an aim to optimize the performance of the MFLC-lens.
© 2016 Optical Society of America
1.1 Tunable liquid crystal lens
Liquid crystal (LC) lenses are active optical elements with electrically tunable focal lengths without any mechanical movements. Because of the large optical anisotropy of this material, the LC director’s orientation can be easily controlled by applying low voltage to a nematic liquid crystal. When an incident plane wave passes through a lens-like phase difference of LC directors, the wave will be converged or diverged depending on the type of voltage applied to the electrodes. The early reports on LC lenses [1–3] used a ratio of the diameter to the cell thickness of about 2~3 for an LC lens optimized to work like a lens.
Extensive research has been conducted on various types of LC lenses. The hole-patterned electrodes [4–7] which have a simple structure with a high optical quality were initially reported. The spherical electrode [8,9] was then proposed to reduce the phase loss which leads to a short focal length. It was followed by hexagonal patterned LC lens  in order to have less inactive area and faster response time. To increase the switching time of tunable focusing imaging system [11–13], dual frequency lenses [14,15] were proposed to speed up both the rise and decay times of an LC device.
To further improve the optical performance of LC lens, high-dielectric layer [16,17] was used to smooth the phase profile across the lens without attenuating much electrical potential. However, high-dielectric layer increases the operating voltage to higher than 30volts. Therefore, high-resistive layer [18–27] was applied to generate linearly varying electrical potential from the center to the edge. The high-resistive layer for LC lens successfully demonstrated low operating voltage, fast response time, and high optical performance.
However, the LC-lenses reviewed above were used for 2D imaging tunable systems, which were utilized for 2D endoscope applications in the prior publications [28–31]. In this paper, we propose a new LC-lens structure for both 2D/3D tunable endoscopic applications.
1.2 Endoscopy imaging system
An endoscope is an important tool for medical diagnosis. In general, three main kinds of endoscopic imaging systems are available: rigid endoscopes, flexible endoscopes and capsule endoscopes. Conventional endoscopic systems consisting of several solid lenses suffer from a fixed lens. For practical applications using conventional endoscopes, the doctor may have to move the endoscope back and forth during the examination in order to see a clear image, which may make the patient uncomfortable. The liquid crystal lens is an essential optical device with tunable focal length to replace bulky and solid lenses with voice coil motor. LC-lens also has been used for three-dimensional (3D) endoscope systems [31–39]. 3D vision offers the advantage of improved depth perception and accuracy in the performance of endoscopic surgery, particularly for complex surgical tasks such as suturing.
A key limitation of previous studies is that they do not address the focus tunability of LC lenses when switched into 2D or 3D mode. For example, in early cases of using LC lenses for 3D endoscopy , when the LC lens was turned off, the LC lens would act just like a piece of glass. The physician had to move the endoscope back and forth to see a clear image because the LC lens was only able to adjust the focal length in 3D mode and not in 2D mode. Additionally, the prior LC lenses used for endoscopy procedures were using single-layer electrode design, which only have the ability to modulate the focal length in a single mode.
In this paper, the proposed multi-functional LC lens (MFLC-lens), is able to switch to and from 2D and 3D modes, and can further change the focus in both modes. The system is investigated by using dual-layer electrodes and a high resistive transparent film. Table 1 shows a brief comparison between conventional 3D endoscopes (with two fixed solid lenses), LC lenses for 3D endoscopes based on hexagonal arrangement , and the proposed endoscopy imaging system using an MFLC lens. The high resistance film is used to minimize the electric field interference of the two electrode layers. To the best of our knowledge, this is the first report describing a “single” LC lens, which can modulate the focal length in both 2D and 3D modes. The proposed LC lens will be mainly used for endoscopic imaging systems.
2. Basic principle
2.1 Liquid crystal lens
To understand the mechanism of liquid crystal lenses, it is necessary to detail the properties of nematic liquid crystals. The nematic phase is one of the most important phases to produce a liquid crystal lens with a gradient refractive index. Birefringence ascribes to the splitting of a light ray into two components (the ordinary ray and the extraordinary ray) when it enters birefringent materials. These two components have orthogonal polarizations. The refractive index of the ordinary ray is independent of the orientation of the incident ray entering the material. In contrast, the refractive index of the extraordinary ray is dependent on the angle between the incident ray and the orientation of the optical axis of the materials, which depends on the liquid crystal director orientation. Therefore, when the liquid crystal director is tilted, supposing the orientation of the incident ray is fixed, a variation in the refractive index of the extraordinary ray is induced. In liquid crystals, the tilting is attained by use of an electric field. The refractive index presented by the liquid crystals varies between the ordinary index () and the extraordinary index () due to the alternations of the director orientation in each area. A mechanical torque is induced due to the elasticity of the nematic liquid. A torque, applied on a particle, influences director deformations in the liquid crystal. Nonzero deformations will result in a nontrivial torque in the director field. The free energy can be minimized using this torque balance, which can be explained by Euler-Lagrange equations. The Poisson equation (or Laplace in regions where the charge density is zero) describes electrostatic potential, which dictates the definition of the electric charge and its density corresponding to the applied electric field. The elastic charges interact via the Coulomb potential which results in a collective macroscopic director reorientation . There is a convergence solution after this interaction, leading us to use the Berreman4x4 matrix method to determine director configuration induced by the interaction. Due to the complexity of this method, Smet’s macro-model for LC cells is preferable. The nematic liquid crystal is a long-range orientational order of rod like polar molecules. In a nematic liquid crystal with positive anisotropy under an applied electric field, directors reorient toward electric field direction. In addition, electric field induces a dipole moment density with two components one in direction of extraordinary axis and another along ordinary axis. The balance of the dielectric, viscous, and elastic torques determines the director dynamics, which can affect the response time and operating voltage. Three types of torques which affects liquid crystal molecules are: Elastic (), Electrical (), and Viscosity (), where K, and C are constants. and try to tilt the molecule in the opposite direction as . The equilibrium of torques can be written in a well-known first-order system form  in which equilibrium equations in a steady state and effective voltage can be easily obtained.
2.2 High-resistive material
The orientation of LC directors is determined by potential differences across the two conductive layers at the top and bottom of the liquid crystal. This can change LC lens properties. To make a lens-like effect in a liquid crystal cell a hole-patterned electrode on the glass is designed as shown in Fig. 1(a). However, high driving voltages are required to make a gradient potential from the edge of the LC lens to the center of the LC lens, due to the shielding of the voltage in the glass substrate. If the electrode’s position is upside-down as in Fig. 1(b), the required driving voltage is lower, but there is no lens-like distribution of the refractive index. The applied voltages can be lowered using a high dielectric (high-k) layer coated on the hole-patterned electrode to smooth the phase profile across the lens, though a lower applied voltage is still desired. Because of the thickness of this layer (~few µm), high-K layer shields a portion of the applied voltage as in Fig. 1(c). This problem can be solved by using a thin film layer with high-resistivity (high-R) as in Fig. 1(d), which also provides more options to fabricate an LC lens according to aperture size. By adjusting to a proper frequency, the aperture becomes larger the driving frequency becomes lower. When the aperture is small, a higher driving frequency is needed. Thus, making LC lenses with various sizes will be possible with a very low driving voltage.
The designed Multi-functional liquid crystal (MFLC) lens is shown in Fig. 2. Two 550 µm glass substrates (glass substrates 1and 3) are coated with 70 nm ITO, then 20 nm SiO2 and a 170 µm glass (glass substrate 2) which is coated with 200 nm Al. One of ITO substrates (glass substrate 1) is etched with the desired three-hole pattern. A thin layer of high-resistive film (niobium pentoxide-Nb2O5) is deposited on the glass substrate 2 (~31 nm) using a radio frequency (RF) magnetron sputtering system. At an RF power of 30W the Nb2O5 film shows the lowest sheet resistance as reported in . With this result, we set the RF power to 30W, as the voltage would drop close to the electrode if the impedance was too high.
The UV curable resin (NOA68) fills in the space (15µm) between the glass substrate 1 and the glass substrate 2. The polyimide (PI) layer is coated on the glass substrates 2 and 3 as an alignment layer. A UV ozone surface treatment is used to clean and modify the molecular surface of the alignment layer. Anchoring phenomena are responsible for restoring the director orientation in an LC lens when the electric field is switched off. When the electric field is switched on, anchoring prevents the LC molecules from being completely reoriented. The anchoring energy plays an important role in affecting the LC response time. Within the weak anchoring regime, the LC decay time is inversely proportional to the anchoring energy. If we can find a polyimide that has somewhat larger anchoring with the LC material, then the decay time can be improved . The polar anchoring energy of LC molecules on UV-treated PI alignment layers is reported in  to have a faster LC lens; the substrates undergo UV-treatment (at 21.7 mW/cm2) for 20 minutes. Finally, these two PI layers are rubbed anti-parallel in order to form the micro-grooved alignment surface, resulting in a pretilt angle of about 2°. The two glasses are then stacked with a 28um microsphere spacer between them. The cell was filled with E7 at a temperature higher than the isotropic-nematic phase transition to avoid the appearance of gas bubbles and disclination lines to enhance the alignment of the layers. The parameters of the nematic E7 are: , for , and . The quality of alignment layer with different applied voltages is shown in Fig. 3. The alignment layers function the same as different voltages applied to the cell, which yields a good stability of these layers.
4. Experimental results and discussion
Liquid crystals are dielectric materials; however, due to ionic impurities, they usually have nonzero value of conductivity. E7 has a typical conductivity of ~. The dielectric constant is given as a complex quantity, where is the real part of the dielectric constant and is the dielectric loss factor of the medium with . The dielectric dispersion spectrum of a nematic liquid crystal depends on the direction of the applied field with respect to the director (). When , the relaxation frequency decreases to fairly low values (in the range of few kHz to a few MHz). For , the relaxation frequency is in the GHz range. At very low frequencies (≤1kHz), the ionic impurity also contributes to the dielectric properties. The effect of ion impurities grows very large, that is, for the real part and for the imaginary part . The complex dielectric constant of the LC cell can be written as following formulas :18]:Eq. (3), is the resistivity of the resistive film, and are the thicknesses of the resistive film and LC, respectively, ω is the AC frequency, and and are the real and imaginary parts of LC dielectric constants. A general solution for the Eq. (3) is obtained by substituting Eq. (1) and Eq. (2) into Eq. (3), respectively. When solving the differential equation, analytic solution can be difficult. We found the optimized parameters of the high-R layer such as the ratio of resistivity of high-R layer to its thickness (0.03<<0.3) with proper frequency range (10 kHz<f<70 kHz).
4.1 Optimizingh high-R layer parameters
As discussed above, Eq. (3) becomes a complicated equation to solve analytically after substituting Eq. (1) and Eq. (2) into Eq. (3), especially when looking for proper thickness, resistivity and frequency. Therefore, we prepared ten samples varied by resistivity and thickness to find a proper frequency to operate the LC lens as shown in Table 2. The sheet resistance of the samples was measured by Mitsubishi Hiresta-UP MCP HT450 using a URS standard probe. The Atomic Force Microscope (AFM) images of the deposited Nb2O5 with different conditions [see Table 2] are shown in Fig. 4 to indicate the surface roughness of samples. From the measurement results, all the surfaces are smooth and uniform with root mean square (RMS) roughnesses in the sub-nm range (0.3nm to 0.5nm), and the numbers are shown in Table 2.
We prepared a single hole liquid crystal (LC) lens with a diameter of about 2 mm. To investigate the LC lens performance, interference patterns were measured using two cross polarizers when LC lenses were placed between them. Figure 5 demonstrates the LC lens fringe patterns when they are applied with 1 kHz driving frequency and 6 Vrms. Figure 5 clearly presents that most of the samples show interference patterns only on the edge of lens, which cannot form an ideal lens profile. Furthermore, Sample 4 and Sample 7 did not respond to the applied voltage (6Vrms) when the function generator was set to a 1 kHz output frequency. But when we increased the frequency from 1 kHz to 66 kHz, we found that only Sample 4 and 7 can generate an ideal lens profile, as shown in Fig. 6. It should be noted that there was no lens effect for other samples even at higher frequencies (1 kHz – 66 kHz).
Obviously, when a highly- resistive layer (in this case Nb2O5) is used for LC-lens, the ratio of has to be well controlled. In the experiment, the of sample 4 and 7 are 0.324 and 0.038, respectively. From the results, the samples will be workable when the frequency range is 10 - 15 kHz and 33- 66 kHz, as shown in Fig. 6. Thus, after we determine the frequency according to the device compatibility we can change the applied voltage to change the focal length of the LC lens. Finally, Sample 4 was chosen, because it could work at lower frequency, and can results in lower power consumption. Moreover, most devices are adapted to human audible frequency (20 Hz - 20 kHz); therefore, electronics are made to produce a frequency lower than 20 kHz.
In Fig. 6, we conclude that a suitable driving frequency with a ratio of is required to operate an LC lens at low applied voltage. In the study above on Nb2O5 we found that all these parameters are applicable to lowering the driving voltage and improving performance of multi-functional liquid crystal (MFLC) lenses. All the parameters were optimized in sample 4, therefore, we utilize these parameters such as ratio and its working frequencies for MFLC lens as explained in the following section.
4.2 Optical performance of the MFLC-lens
In this section, the properties of MFLC lenses are investigated using an interference method. The MFLC cell is placed between two crossed polarizers in which the rubbing direction makes an angle of 45° with respect to each polarizer. A beam from a helium-neon (He-Ne) laser operating at 632 nm is expanded and passes through the MFLC-lens placed between two crossed polarizers, as shown in Fig. 7(a). The liquid crystal is birefringent, which means that different polarizations of light travel at different speeds through it, and are refracted differently. The first polarizer contains both types of ordinary and extraordinary waves. When the waves pass through the liquid crystal, the ordinary wave experiences a spatial phase shift but the extraordinary wave experiences a spatially varying phase shift. When these two waves exit the liquid crystal, their phases are different. Finally, when they pass through the second polarizer, interference will occur. The retardation difference of the two adjacent constructive or destructive interference rings indicates a phase change of 2π. Furthermore, the variation in phase retardation induced by the applied voltage shows how the electrical field alters the lens properties.
Figure 8(a) shows the interference patterns present in the 2D mode when the MFLC-lens is used with (1 kHz). In this mode only the large circular lens is activated as increasing the applied voltage, the number of the circular interference fringes changes and the property of the MFLC lens is electrically controllable. When a 3D image is desired and multiple perspective images are needed, the electrodes in the MFLC-lens will switch to the first layer of electrode from the second layer in which there are three lenslets available. As shown in Fig. 8(b), the 3D lenses are obtained by applying (1 kHz).
The fringe patterns are recorded by means of a CCD sensor and the image intensity is enhanced. Figure 9 shows the phase difference distribution of the MFLC-lens in the direction of rubbing calculated for both 2D and 3D modes based on counting the interference fringes at their position from the center to edge of the MFLC lens. In Fig. 10, the voltages applied to the electrodes are the same as the applied voltages in Fig. 8(a) and (b). It should be noted that the estimated phase distribution parallel to the rubbing direction is the same as the phase distribution in other directions. Because of its perfect circular interference rings, no aberrations are expected.
In Fig. 10(a) the focal length of the measured phase profiles are shown as a result of the phase shift from 0 to 10π radians for voltages from to when the 2D mode is activated. The focal length of the MFLC-lens in 3D mode that results from the phase shift from 0 to 6π radians for voltages from to is shown in Fig. 10(b). It is noted that the niobium pentoxide (Nb2O5) has a high dielectric constant (~41) and has having high resistivity. Therefore, we expect this layer to smooth the phase profile even when the MFLC-lens is not applied with a proper frequency, which can make the high-R layer active. Therefore, if we change the driving frequency from 1 kHz to 12 kHz for this cell, we can achieve the same phase profile with 2.5X times lower applied voltage for the same cell gap. A proper frequency can decrease the applied voltage. For the sample in Fig. 1(a), for 2 mm aperture diameter and a glass substrate of 550 µm with cell gap of 28 µm, the voltage is from 55 to 6.0 when the frequency is 16 kHz. The measured response time of the MFLC lens for 2D and 3D mode was 600ms and 740ms, respectively. Switching time from 2D/3D modes is about 1.5 seconds. The response time could be faster if a liquid crystal material with higher birefringence was used.
Figure 11 shows six images of the ISO 3334 test chart when the position of the chart is located at different distances from the MFLC-lens and when the MFLC-lens is on or off. In Fig. 11(a), the test chart location is 80 mm from the lens with a driving voltage of 12.5. In Fig. 11(b), the test chart location is 125 mm from the lens with driving voltage of 8.5. In Fig. 11(c), the location is in 180 mm with driving voltage of 6.8. The optical power adjustment of the MFLC-lens brings the object into focus, which leads to a sharp and clear image. Figure 7(b) illustrates the experimental setup we used to capture the images using a side viewing endoscope, for captured images shown in Fig. 11(d). Each MFLC-lens can focus on the different depths of an object as the applied voltage varies without any movement for the image sensor or the CCD. The sectional 2D images can be achieved at arbitrary depth positions by altering the focal length of the MFLC-lens. The depth information data was obtained by capturing several 2D images of the 3D object. When the MFLC-lens is switched to 3D mode, each lens can capture a 2D image of the 3D object from different angles at varying tunable depths. Therefore, the system can record the depth information of the image by properly synchronizing the 2D images. A rudimentary 3D image reconstructed from a set of 2D images after object segmentation, image alignment and depth map generation is shows in Fig. 11(e).
A three-dimensional (3D) imaging system is an important technology for objects in close proximity sensing, such as endoscopy. In this paper, a multi-functional liquid-crystal lens (MFLC-lens) is demonstrated for 2D and 3D switchable function. Importantly, this MFLC-lens can further modulate the focal length without mechanical movement in both 2D and 3D modes. To achieve multiple focal length lens functions, a novel structure with dual-layer electrode coated by a high resistive transparent film was developed. The resistivity and thickness of high-R layer and proper operating frequency were optimized for the MFLC-lens. The diameter of the proposed MFLC-lens is only 1.42mm with tunable focal length from infinity to 80mm. It can be easily applied to micro-imaging systems, and objects in close proximity sensing for both 2D and 3D image capturing. Applications may include medical imaging, endoscopy, robotics, and cell phones.
Bahram Javidi acknowledges support from the National Science Foundation (NSF) under the contract no. NSF/IIS-1422179.
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