Three-dimensional imaging based on electronically adaptive liquid crystal lens Hui Li,1,2,3,* Fan Pan,4 Yuntao Wu,2,3 Yanduo Zhang,2,3 and Xiaolin Xie1 1
School of Chemistry and Chemical Engineering, Huazhong University of Science and Technology, Wuhan 430074, China 2
School of Computer Science and Engineering, Wuhan Institute of Technology, Wuhan 430073, China 3 4
Hubei Key Laboratory of Intelligent Robot, Wuhan 40073, China
College of Post and Telecommunication, Wuhan Institute of Technology, Wuhan 430073, China *Corresponding author: [email protected] Received 6 August 2014; revised 24 September 2014; accepted 6 October 2014; posted 15 October 2014 (Doc. ID 211491); published 17 November 2014
In this paper, we present a relatively simple method to acquire a 3D image based on an electrically controlled liquid crystal (LC) lens. Its advantage is that this proposed method does not need any mechanical movements to acquire a 3D image. The tunable-focus LC lens combined with a high-resistance layer (PEDOT) is applied by an overdrive method to become a key optical component for use in a 3D imaging system. Multiple 2D images of slightly different perspectives are recorded, respectively, and 3D images, according to a proposed mapping and projection method, can be reconstructed. This is the first report, to the best of our knowledge, on using an LC lens to reconstruct 3D images. The proposed 3D imaging system is novel for its compact and smart features, so it is attractive for some compact 3D imaging systems. © 2014 Optical Society of America OCIS codes: (110.6880) Three-dimensional image acquisition; (230.3720) Liquid-crystal devices; (170.0110) Imaging systems. http://dx.doi.org/10.1364/AO.53.007916
1. Introduction
The movie Avatar brings people into an amazing 3D virtual world. For that movie, 3D imaging, which has swept the whole world in a short time, becomes an exciting technology and trend. Nowadays, it has been widely applied in many fields, such as 3D shows [1], 3D games [1], 3D TV [1,2], 3D movies [1], and 3D medical image analysis [3–5]. A typical 3D imaging system is mainly composed of an imaging lens and camera [6–8]. Utilizing the above hardware, 2D images of different perspectives can be used to reconstruct the 3D images of a target by different optical methods or complex computer algorithms [9–13]. In those methods, the imaging lens and camera are all key elements of the 3D imaging systems. As those 1559-128X/14/337916-08$15.00/0 © 2014 Optical Society of America 7916
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traditional lenses or arrays all have fixed focal lengths, the 2D images of different perspectives are only recorded via changing positions along an optical axis. The imaging system based on those lenses or array needs frequent mechanical movements for focusing and imaging, which has obvious disadvantages. Thus, those mechanical movements make this kind of imaging system generally bulky, heavy, and expensive. It cannot be slim and simple, so it is not feasible for compact systems. In order to solve this problem, a key optical component without any mechanical movements for use in the 3D imaging system is urgently required. In recent years, liquid crystal (LC) material has been widely utilized to fabricate different kinds of optical devices because of its unique electro-optical characteristics; these devices include an LC lens [14–18], LC spatial light modulator [19–21], LC display [22–24], and LC Fabry–Perot device [25–28].
Among those LC devices, an LC lens has many advantages, such as tunable focal length by electrical control, compactness, and portability, and it is easily integrated with other optical systems [29,30]. In 1979, the first LC lenswas realized by Sato [31]. After that, many researchers have studied the LC lens [31–34]. Therefore, the LC lens has been developed to effectively substitute some traditional optical lenses in many imaging applications [35,36]. In this paper, a relative simple method to acquire a 3D image based on an electrically controlled LC lens is first proposed. The improved structure of the LC lens is to combine it with a high-resistance layer (PEDOT) on the top electrode. An overdrive method also is applied to reduce operating voltages of the LC lens [37–39]. For a specification with a 100 μm LC cell gap and 2 mm lens aperture, the operating voltage can be reduced down to less than 6 Vrms, and the focusing time can be dramatically improved to 0.2 s. Then, the 3D imaging system, with the LC lens as a key imaging element, is completed as a highlight in this paper. Those 2D images of different perspectives are achieved only by changing applied voltages continuously without any mechanical movements. Utilizing all captured 2D images, a relatively simple and fast reconstruction algorithm, containing mapping and projection method, is applied to reconstruct a 3D image of the target. In Section 2, device structure and fabrication of the proposed LC lens are presented in detail. The related theory of a 3D imaging system based on the proposed LC lens is described in Section 3. Some results of optical experiments in regards to the LC lens and 3D imaging system are addressed in Section 4, and some interesting discussions about the most important features of the proposed 3D imaging system are also presented. Finally, some preliminary conclusions are obtained in the last section. 2. Devices and Fabrication
Figure 1 depicts the cross section of the proposed LC lens. It mainly consists of two glass substrates and a LC layer. The improved structure of the LC lens is to combine it with a high resistance layer (PEDOT) on the top pattern electrode, which can create a gradient distribution of the electric field, and the majority of preserved energy can be applied. The reason that the material of high-resistance layer is PEDOT rather than other high-resistance materials is that it has
some advantages in fabricating this lens. The highresistance layer of the LC lens is manufactured by PEDOT, which provides good transparency in the visible region and has the advantage of high resistance and relatively high stability. The fabrication lens technological flow of the LC lens in a clean room is presented as follows. A highresistance layer of PEDOT (Sigma-Aldrich), about 30 nm thickness of 4000 rmp∕30 s, was fabricated by spin-coating on the top glass substrate. The major advantage of spin-coating is convenience over sputtering. The surface resistance of the PEDOT layer is about ∼1 MΩ∕□. To maintain the PEDOT layer stability, the layer needs twice heating. The first heating is to dry it; the hot plate was set as 120°C for 1 h. Then the second heating is to prevent damage to the PEDOT, and the hot plate was set as 150°C for 2 h. The layer of indium-tin oxide (ITO) was sputtered on the PEDOT layer with about 20 nm thickness. A single circular hole electrode pattern with 2 mm diameter was fabricated by UV photolithography and wet hydrochloric acid (HCL) etching on the top ITO film. A layer of thin polyimide (PI) forming an alignment film was fabricated by spin-coating on both inner surfaces of the two substrates and by rubbing along the x direction, which let all LC directors to generate at around a 2° pre-tilt angle, as shown in Fig. 1. The so-called LC director is statistically used to describe the orientation of many LC molecules. After the above procedures, the high-resistance layer, the two substrates with the expected electrode pattern, and formed alignment films composed the empty LC cell by sandwiching glass microspheres as the spacer. The commercially available LC, E44 (Merck), was poured into the empty cell by capillary action. The other critical technological parameters were that the thickness of the LC layer was 100 μm and a square wave of proper frequency-voltage pair was applied to the two electrodes. The overdrive method will be discussed in detail in Section 4. The target of the proposed LC lens is to design a kind of LC lens, which has relatively fast focusing, low operation voltages, and simple fabrication for acquiring 3D images in a relatively simple way. 3. Theory of Imaging
In this section, principles of the 3D imaging system based on the LC lens mentioned above will be presented. The basic principle and theory of an LC lens will be first explained. Then the theory of 3D imaging system based on the LC lens will be discussed. A. Theory of LC Lens
Fig. 1. Structure diagram of proposed LC lens.
In order to clearly analyze the electrical features of the LC lens under a voltage, the equipotential line distribution in the LC layer is calculated by a continuous elastic body theory and an electric finite difference method. The physical parameters of E44 used in the calculation are ε∥ 22.0, ε⊥ 5.2, K 11 15.5 × 10−7 , K 22 13.0×10−7 , and K 33 28.0 × 10−7 . According to the previous theory, the director is 20 November 2014 / Vol. 53, No. 33 / APPLIED OPTICS
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expressed as nˆ cos δkˆ sin δˆi, where kˆ and ˆi are, respectively, the unit vector of direction x and direction z, and δ is the tilt angle of the director. ˆ 2 The LC’s free energy density is f 12 fK 11 ∇ · n 1 2 2 ˆ ˆ g − 2 E · D, where K 33 nˆ × ∇ × n K 22 nˆ · ∇ × n Dε·E and εij ε⊥ δij Δεni nj (εxx ε∥ , εyy εzz ε⊥ , Δε ε∥ − ε⊥ ). Electric field strength is E −∇V, and V is the voltage of the top electrode. The minimum free-energy density is obtained by Euler equations, and then the LC reaches a stable state, as follows: ∂f ∂ ∂f ∂ ∂f − 0 − ∂δ ∂x ∂ ∂δ ∂z ∂ ∂δ ∂x
and
∂z
∂f ∂ ∂f ∂ ∂f − 0: − ∂V ∂x ∂ ∂V ∂z ∂ ∂V ∂x ∂z As shown in Fig. 2, the equipotential line distribution in the LC layer is calculated by the finite difference method. The electric field distribution is relatively uniform due to the design of the highresistance layer, which represents a smooth gradient electric field distribution. The simulation result indicated by the top pattern electrode with a high resistance has the ability to achieve a gradient electric field distribution and to simultaneously maintain the energy inside the LC layer. According to the result, it is feasible that, to achieve low operating voltage and improve the focusing time simultaneously, the proposed LC lens utilized high resistance to become the internal continuously distributed electrode. LC is a birefringence material. It has a birefringence property, including ordinary and extraordinary refractive indexes. However, different rotating tilt angles of the LC director correspond to different refractive index values. The effective refractive index can be calculated using the following formula:
Fig. 2. Calculated electric field equipotential lines of the LC lens under applied voltages of 5 Vrms at 1 KHz. 7918
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n2eff θ
n2e
cos2
n2o n2e ; θ n2o sin2 θ
(1)
where ne and no are the extraordinary and ordinary refractive indices, respectively. θ is the included angle between the incident light and the optical axis, as shown in Fig. 3. According to the above fabrication procedure, an LC lens sample can be obtained. When the applied voltage is not loaded, all LC molecular structures are parallel to the two substrates and have a uniform refractive index ne . But, when the applied voltage is turned on, marginal LC molecular structures are rotated about 90° because of the electric field. At the same time, the effective refractive index of the central area is still ne , and the marginal area is changed to no . Then the transition area between the central and marginal areas has neff θ. Thus, a gradient distribution of the refractive index is formed in the LC layer, which exhibits features of a convex lens. Based on the birefringence property of an LC, the effective focal length of the LC lens can be obtained: f
r2 ; 2Δn · dLC
(2)
where the focal length (f ) of the LC lens is related to the circular radius (r), the refractive index difference Δn (the difference between the center and edge of the patterned electrode), and the thickness of the LC layer (dLC ). B. 3D Imaging System based on LC Lens
The proposed 3D imaging system in this paper is mainly composed of an LC lens and a CCD sensor, as shown in Fig. 4. In this system, a target is located in front of the LC lens and away from the optical axis. The CCD sensor is fixed and placed a distance away from the LC lens. During the whole imaging procedure, 2D images of different perspectives can be obtained by CCD with continuously changing applied voltages of the LC lens. In order to reconstruct a 3D image, a mapping function is designed to connect those captured 2D images with a reconstructed 3D image. The mapping function is
Fig. 3. Refractive index ellipsoid.
specific value, and 0 is the initial value) can be computed by those captured 2D images. The computed formula is K −1 1X x y Ix; y; zr E ; ;z ; K i0 i M i×zzr M i×zzr r 0
(5)
0
where M i is the corresponding magnification factor between the selected ith image and the first image (at the shortest focal length), Ei is the magnified ith image, and k is the total number of recorded 2D images. 4. With the above equation, the 2D intensity image at a specific depth finally can be obtained.
Fig. 4. 3D imaging system based on the LC lens diagram, where two polarizers were set at points A and B, respectively.
xi ; yi ; zi ↔ f xi ; yi ;
(3)
where xi ; yi ; zi represents a point at the 3D surface of the target, and f xi ; yi is, correspondingly, the 2D intensity image of the target, as shown in Fig. 4. With above Eq. (3), we can obtain a 3D image of the target based on those captured 2D images. In brief, Eq. (3) is to construct the mapping relationship between the 2D intensity image and the 3D surface of the target. During the mapping process, one important parameter is depth information of the target. If the proposed LC lens is utilized, according to those 2D images, the depth information of the target at specific applied voltages can be obtained directly. In other situations, the depth z and related 2D intensity image information could not be obtained directly. A computational method is needed to be constructed based on those captured 2D images. However, those can be easily realized by a ray backprojection algorithm [40,41]. The algorithm based on the proposed LC lens can be realized by the following steps: 1. First, with changing applied voltages, multiple 2D images of different perspective can be respectively obtained by CCD. 2. Second, the magnification factor, between the image of the shortest focal length and any image of the other focal length, can be computed by the following formula: Mi
f 1 d − f i ; f i d − f 1
With Eqs. (4) and (5), we can obtain the 2D intensity image of any depth. Comprehensively considering the computing time and image quality, the number of those 2D intensity images should be a trade-off. Then, by Eq. (3), the 3D image of the target could be preliminarily reconstructed by all the above 2D intensity image information. 4. Experiment and Results
In order to present features of the LC lens and 3D imaging system, some experiments are described in detail. In this section, the major electro-optical features of the fabricated LC lens are given first; then the relatively simple method for acquiring 3D imaging of a target is presented and discussed. A. LC Lens
An experiment was set up to measure focused spot patterns and focal length of the LC lens, as shown in Fig. 5. The sample was mounted on an optical displacement platform. A white parallel light was used to illuminate the sample. The transmitted light was collected and detected by a CCD (3 megapixel, 1∕2 in:, and 6.4 mm × 4.8 mm in size). The detected data were analyzed by a computer. First, to characterize the optical focusing properties of the fabricated LC lens, a white parallel light was used to obtain its 2D intensity distribution images at different voltages. The distance between the LC lens and CCD, 265 mm, was fixed without any movements in the whole measurement. Three photos at different voltages were respectively captured, as shown in Fig. 6. When the applied voltage is 1.2 Vrms, it is clear that the left image is apparently a nonfocusing state. After the voltage up to 2 Vrms, the middle image presents an obvious focusing state.
(4)
where f 1 is the shortest focal length, f i is the ith focal length, and d is the distance between the LC lens and CCD. 3. Based on the magnification factor M i, the intensity images of the target at zr (r represents a
Fig. 5. Experiment setup. 20 November 2014 / Vol. 53, No. 33 / APPLIED OPTICS
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Fig. 6. Top three images are, respectively, at 1.2 Vrms, 2 Vrms, 6 Vrms; the curve is a PSF of the LC lens at 2 Vrms along the horizontal direction of the cross section.
When the applied voltage is continuously increased, the LC directors in the LC layer slowly reorient. After stabilizing, the directors have a new distribution: a smooth gradient refractive index distribution. At this state, the point spread function (PSF) of the LC lens along the horizontal direction of the cross section is computed by the captured focusing pattern, and the FWHM of the focusing profile is about 100 μm. As the transmittance of an LC lens in electrode areas is different from that in nonelectrode areas, there are different refractive indexes between electrode areas and nonelectrode areas in the LC lens. Thus, the 2 mm diameter circular pattern shown in the middle image has been formed by the different refractive index on the different areas. Given both PSF and the pattern of the focusing light spot, it is clearly shown that the LC lens has quite a good focusing feature. Then the voltage was increased to 6 Vrms; the right image shows an outof-focusing state. From the above three states, we can conclude that the focal length of the LC lens can be tunable by the external applied voltage without any mechanical movements, and that the LC lens is a positive lens. Second, the white parallel light was still used to measure the focal length of the LC lens. As the white light will cause chromatic aberration, a beam profiling camera from DataRay Inc., WinCamD UCD12, was utilized to confirm the focal length of the LC lens at different applied voltages. After more than five measurements at every voltage point, the relationship between focal length and the applied voltage can be obtained, as shown in Fig. 7. The range of the focal length is tunable from 20 to 480 mm, while the applied voltage is changed from 1.1 to 6 Vrms. The result shows that the curve of focal length versus applied voltage is an inverse proportion. The applied voltage gradually increases with decrease of the focal length. Based on the curve in Fig. 7, the focal length of 2 Vrms, which is very close to the real value of 265 mm, is 260 mm. That led to the conclusion that Fig. 7 can exactly present the 7920
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Fig. 7. Relationship between applied voltage and focal length.
property of the LC lens. The shortest focal length of the LC lens will appear when the LC has the maximum birefringence. E44 has around 0.255 of the maximum birefringence in the visible range (ne 1.778 and no 1.523). Based on Eq. (2), the focal length of the LC lens is 19.6 mm under conditions of Δn 0.255, d 100 μm, and r 1 mm. The calculated focal length is almost close to the measured value, 20 mm, which indicates that the LC lens has convergent features. As the inside top electrode configuration is combined with a high-resistance layer efficiently conserved electrical energy inside the LC layer, the smooth gradient electric field distribution is maintained by the high-resistance layer. Compared with a conventional LC lens, which is typically fabricated by two flat substrates clipping a homogeneous LC layer (100 μm thick) and has a circular patterned (2 mm diameter) and internal electrode to yield the desired phase retardation on a uniform LC layer, this proposed LC lens decreases the operating voltage from greater than 20 Vrms to only 6 Vrms. Third, an overdrive method is wildly utilized for accelerating the response time of LC devices [35–38]. With optimized over-driving voltages and the switch of target operation, response time of LC lens can be reduced substantially compared to the conventional one mentioned above without the overdrive method. As known, a thicker LC layer can yield a larger optical power, but the thicker layer generally results in a longer response time. To minimize the response time, we utilize the overdrive method. A large pulse is applied to the electrodes for accelerating response at the beginning. Then the input signal is switched from large pulse to a desired operating voltage to stabilize the focusing effect [37–39]. A circuit board was used to control the duration time of overdrive pulse. Generally, applying a larger pulse at the beginning of the overdrive method can yield a shorter response time, but too high electric energy could break the LC lens; thus, a pulse of less than 20 Vrms is chosen here, as shown in Fig. 8. Under only less than 20 Vrms overdrive voltage,
Fig. 8. Real waveform of overdrive method was detected by an oscilloscope. The magnitude of overdrive pulse was chosen as 10 Vrms since overflow will happen when voltage is more than 18 Vrms. In this measurement, the overdrive time was chosen as 800 ms.
the response time is instantaneous focusing within 0.2 s by 4 Vrms stable operating voltage. Table 1 shows the comparison between the fabricated and conventional LC lens mentioned above. Overall, the proposed LC lens dramatically improves about 99% focusing time and reduces about 70% operating voltage. Above measurements of response time are utilized by EOT-01, which is produced by the Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences. Finally, the module transfer function (MTF) is introduced to evaluate the focusing quality of the proposed LC lens. Those MTF values of the LC lens (square wave of 1 KHz at 5 Vrms) were measured by a knife-edge method [42]. The MTF value of the proposed lens decreases as spatial frequency increases, and it drops to almost zero when the spatial frequency is higher than 80 lp∕mm, as shown in Fig. 9. Compared with the ideal MTF value, the MTF value of the proposed LC lens is normal. Some methods can effectively improve the MTF value, such as adjusting the operating frequency. The method to improve the focusing quality will be studied in the future. B.
3D Imaging System
Fig. 9. Blue line represents the MTF value of proposed LC lens. Red line represents the ideal MTF value. Aperture size is 2 mm. CCD resolution is 50 lp∕mm.
illustrated in Fig. 5. We made the target a Boeing 777 toy, which has a size of 120 mm × 115 mm × 35 mm (L × W × H), to substitute the light source located at approximately 100 cm in front of the LC lens. For the whole capturing process, the distance between the LC lens and the target was fixed without any movements, and the driving voltage of the LC lens was consequently tunable from 1.1 to 6 Vrms at 0.5 Vrms∕Step. Hence, the total k 11 2D images can be recorded sequentially. The size of those captured 2D images is about 3.5 mm × 4.0 mm. Considering that the space of the paper is limited, only six images are selected, as shown in Fig. 10. To the target object, the focusing spot is from far to near along the depth direction with the increase of the applied voltages. From those results, a slight difference (magnification of the object) between the two images can be distinguished. Image quality is closely related to the structure of the LC lens (the high-resistance layer is the most important part of the LC lens). How to control the high resistance in an appropriate value is the key point. In this study, PEDOT, which is an organic material, was chosen as the highresistance layer. Since it is a kind of solution, a spincoating method was utilized to coat this material. However, it still has some issues, such as being a nondurable and inferior quality thin film. Although twice
The experiment was set up to evaluate the major feature of the proposed 3D imaging system, as Table 1.
Comparison of Focusing Time and Corresponding Operating Voltagea
Comparison Conventional LC lens mentioned above Our proposed LC lens
Thickness of LC Cell (μm)
Applied Voltage (Vrms)
Focusing Time (s)
100 (E44)
∼20
∼30
100 (E44)
School of Chemistry and Chemical Engineering, Huazhong University of Science and Technology, Wuhan 430074, China 2
School of Computer Science and Engineering, Wuhan Institute of Technology, Wuhan 430073, China 3 4
Hubei Key Laboratory of Intelligent Robot, Wuhan 40073, China
College of Post and Telecommunication, Wuhan Institute of Technology, Wuhan 430073, China *Corresponding author: [email protected] Received 6 August 2014; revised 24 September 2014; accepted 6 October 2014; posted 15 October 2014 (Doc. ID 211491); published 17 November 2014
In this paper, we present a relatively simple method to acquire a 3D image based on an electrically controlled liquid crystal (LC) lens. Its advantage is that this proposed method does not need any mechanical movements to acquire a 3D image. The tunable-focus LC lens combined with a high-resistance layer (PEDOT) is applied by an overdrive method to become a key optical component for use in a 3D imaging system. Multiple 2D images of slightly different perspectives are recorded, respectively, and 3D images, according to a proposed mapping and projection method, can be reconstructed. This is the first report, to the best of our knowledge, on using an LC lens to reconstruct 3D images. The proposed 3D imaging system is novel for its compact and smart features, so it is attractive for some compact 3D imaging systems. © 2014 Optical Society of America OCIS codes: (110.6880) Three-dimensional image acquisition; (230.3720) Liquid-crystal devices; (170.0110) Imaging systems. http://dx.doi.org/10.1364/AO.53.007916
1. Introduction
The movie Avatar brings people into an amazing 3D virtual world. For that movie, 3D imaging, which has swept the whole world in a short time, becomes an exciting technology and trend. Nowadays, it has been widely applied in many fields, such as 3D shows [1], 3D games [1], 3D TV [1,2], 3D movies [1], and 3D medical image analysis [3–5]. A typical 3D imaging system is mainly composed of an imaging lens and camera [6–8]. Utilizing the above hardware, 2D images of different perspectives can be used to reconstruct the 3D images of a target by different optical methods or complex computer algorithms [9–13]. In those methods, the imaging lens and camera are all key elements of the 3D imaging systems. As those 1559-128X/14/337916-08$15.00/0 © 2014 Optical Society of America 7916
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traditional lenses or arrays all have fixed focal lengths, the 2D images of different perspectives are only recorded via changing positions along an optical axis. The imaging system based on those lenses or array needs frequent mechanical movements for focusing and imaging, which has obvious disadvantages. Thus, those mechanical movements make this kind of imaging system generally bulky, heavy, and expensive. It cannot be slim and simple, so it is not feasible for compact systems. In order to solve this problem, a key optical component without any mechanical movements for use in the 3D imaging system is urgently required. In recent years, liquid crystal (LC) material has been widely utilized to fabricate different kinds of optical devices because of its unique electro-optical characteristics; these devices include an LC lens [14–18], LC spatial light modulator [19–21], LC display [22–24], and LC Fabry–Perot device [25–28].
Among those LC devices, an LC lens has many advantages, such as tunable focal length by electrical control, compactness, and portability, and it is easily integrated with other optical systems [29,30]. In 1979, the first LC lenswas realized by Sato [31]. After that, many researchers have studied the LC lens [31–34]. Therefore, the LC lens has been developed to effectively substitute some traditional optical lenses in many imaging applications [35,36]. In this paper, a relative simple method to acquire a 3D image based on an electrically controlled LC lens is first proposed. The improved structure of the LC lens is to combine it with a high-resistance layer (PEDOT) on the top electrode. An overdrive method also is applied to reduce operating voltages of the LC lens [37–39]. For a specification with a 100 μm LC cell gap and 2 mm lens aperture, the operating voltage can be reduced down to less than 6 Vrms, and the focusing time can be dramatically improved to 0.2 s. Then, the 3D imaging system, with the LC lens as a key imaging element, is completed as a highlight in this paper. Those 2D images of different perspectives are achieved only by changing applied voltages continuously without any mechanical movements. Utilizing all captured 2D images, a relatively simple and fast reconstruction algorithm, containing mapping and projection method, is applied to reconstruct a 3D image of the target. In Section 2, device structure and fabrication of the proposed LC lens are presented in detail. The related theory of a 3D imaging system based on the proposed LC lens is described in Section 3. Some results of optical experiments in regards to the LC lens and 3D imaging system are addressed in Section 4, and some interesting discussions about the most important features of the proposed 3D imaging system are also presented. Finally, some preliminary conclusions are obtained in the last section. 2. Devices and Fabrication
Figure 1 depicts the cross section of the proposed LC lens. It mainly consists of two glass substrates and a LC layer. The improved structure of the LC lens is to combine it with a high resistance layer (PEDOT) on the top pattern electrode, which can create a gradient distribution of the electric field, and the majority of preserved energy can be applied. The reason that the material of high-resistance layer is PEDOT rather than other high-resistance materials is that it has
some advantages in fabricating this lens. The highresistance layer of the LC lens is manufactured by PEDOT, which provides good transparency in the visible region and has the advantage of high resistance and relatively high stability. The fabrication lens technological flow of the LC lens in a clean room is presented as follows. A highresistance layer of PEDOT (Sigma-Aldrich), about 30 nm thickness of 4000 rmp∕30 s, was fabricated by spin-coating on the top glass substrate. The major advantage of spin-coating is convenience over sputtering. The surface resistance of the PEDOT layer is about ∼1 MΩ∕□. To maintain the PEDOT layer stability, the layer needs twice heating. The first heating is to dry it; the hot plate was set as 120°C for 1 h. Then the second heating is to prevent damage to the PEDOT, and the hot plate was set as 150°C for 2 h. The layer of indium-tin oxide (ITO) was sputtered on the PEDOT layer with about 20 nm thickness. A single circular hole electrode pattern with 2 mm diameter was fabricated by UV photolithography and wet hydrochloric acid (HCL) etching on the top ITO film. A layer of thin polyimide (PI) forming an alignment film was fabricated by spin-coating on both inner surfaces of the two substrates and by rubbing along the x direction, which let all LC directors to generate at around a 2° pre-tilt angle, as shown in Fig. 1. The so-called LC director is statistically used to describe the orientation of many LC molecules. After the above procedures, the high-resistance layer, the two substrates with the expected electrode pattern, and formed alignment films composed the empty LC cell by sandwiching glass microspheres as the spacer. The commercially available LC, E44 (Merck), was poured into the empty cell by capillary action. The other critical technological parameters were that the thickness of the LC layer was 100 μm and a square wave of proper frequency-voltage pair was applied to the two electrodes. The overdrive method will be discussed in detail in Section 4. The target of the proposed LC lens is to design a kind of LC lens, which has relatively fast focusing, low operation voltages, and simple fabrication for acquiring 3D images in a relatively simple way. 3. Theory of Imaging
In this section, principles of the 3D imaging system based on the LC lens mentioned above will be presented. The basic principle and theory of an LC lens will be first explained. Then the theory of 3D imaging system based on the LC lens will be discussed. A. Theory of LC Lens
Fig. 1. Structure diagram of proposed LC lens.
In order to clearly analyze the electrical features of the LC lens under a voltage, the equipotential line distribution in the LC layer is calculated by a continuous elastic body theory and an electric finite difference method. The physical parameters of E44 used in the calculation are ε∥ 22.0, ε⊥ 5.2, K 11 15.5 × 10−7 , K 22 13.0×10−7 , and K 33 28.0 × 10−7 . According to the previous theory, the director is 20 November 2014 / Vol. 53, No. 33 / APPLIED OPTICS
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expressed as nˆ cos δkˆ sin δˆi, where kˆ and ˆi are, respectively, the unit vector of direction x and direction z, and δ is the tilt angle of the director. ˆ 2 The LC’s free energy density is f 12 fK 11 ∇ · n 1 2 2 ˆ ˆ g − 2 E · D, where K 33 nˆ × ∇ × n K 22 nˆ · ∇ × n Dε·E and εij ε⊥ δij Δεni nj (εxx ε∥ , εyy εzz ε⊥ , Δε ε∥ − ε⊥ ). Electric field strength is E −∇V, and V is the voltage of the top electrode. The minimum free-energy density is obtained by Euler equations, and then the LC reaches a stable state, as follows: ∂f ∂ ∂f ∂ ∂f − 0 − ∂δ ∂x ∂ ∂δ ∂z ∂ ∂δ ∂x
and
∂z
∂f ∂ ∂f ∂ ∂f − 0: − ∂V ∂x ∂ ∂V ∂z ∂ ∂V ∂x ∂z As shown in Fig. 2, the equipotential line distribution in the LC layer is calculated by the finite difference method. The electric field distribution is relatively uniform due to the design of the highresistance layer, which represents a smooth gradient electric field distribution. The simulation result indicated by the top pattern electrode with a high resistance has the ability to achieve a gradient electric field distribution and to simultaneously maintain the energy inside the LC layer. According to the result, it is feasible that, to achieve low operating voltage and improve the focusing time simultaneously, the proposed LC lens utilized high resistance to become the internal continuously distributed electrode. LC is a birefringence material. It has a birefringence property, including ordinary and extraordinary refractive indexes. However, different rotating tilt angles of the LC director correspond to different refractive index values. The effective refractive index can be calculated using the following formula:
Fig. 2. Calculated electric field equipotential lines of the LC lens under applied voltages of 5 Vrms at 1 KHz. 7918
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n2eff θ
n2e
cos2
n2o n2e ; θ n2o sin2 θ
(1)
where ne and no are the extraordinary and ordinary refractive indices, respectively. θ is the included angle between the incident light and the optical axis, as shown in Fig. 3. According to the above fabrication procedure, an LC lens sample can be obtained. When the applied voltage is not loaded, all LC molecular structures are parallel to the two substrates and have a uniform refractive index ne . But, when the applied voltage is turned on, marginal LC molecular structures are rotated about 90° because of the electric field. At the same time, the effective refractive index of the central area is still ne , and the marginal area is changed to no . Then the transition area between the central and marginal areas has neff θ. Thus, a gradient distribution of the refractive index is formed in the LC layer, which exhibits features of a convex lens. Based on the birefringence property of an LC, the effective focal length of the LC lens can be obtained: f
r2 ; 2Δn · dLC
(2)
where the focal length (f ) of the LC lens is related to the circular radius (r), the refractive index difference Δn (the difference between the center and edge of the patterned electrode), and the thickness of the LC layer (dLC ). B. 3D Imaging System based on LC Lens
The proposed 3D imaging system in this paper is mainly composed of an LC lens and a CCD sensor, as shown in Fig. 4. In this system, a target is located in front of the LC lens and away from the optical axis. The CCD sensor is fixed and placed a distance away from the LC lens. During the whole imaging procedure, 2D images of different perspectives can be obtained by CCD with continuously changing applied voltages of the LC lens. In order to reconstruct a 3D image, a mapping function is designed to connect those captured 2D images with a reconstructed 3D image. The mapping function is
Fig. 3. Refractive index ellipsoid.
specific value, and 0 is the initial value) can be computed by those captured 2D images. The computed formula is K −1 1X x y Ix; y; zr E ; ;z ; K i0 i M i×zzr M i×zzr r 0
(5)
0
where M i is the corresponding magnification factor between the selected ith image and the first image (at the shortest focal length), Ei is the magnified ith image, and k is the total number of recorded 2D images. 4. With the above equation, the 2D intensity image at a specific depth finally can be obtained.
Fig. 4. 3D imaging system based on the LC lens diagram, where two polarizers were set at points A and B, respectively.
xi ; yi ; zi ↔ f xi ; yi ;
(3)
where xi ; yi ; zi represents a point at the 3D surface of the target, and f xi ; yi is, correspondingly, the 2D intensity image of the target, as shown in Fig. 4. With above Eq. (3), we can obtain a 3D image of the target based on those captured 2D images. In brief, Eq. (3) is to construct the mapping relationship between the 2D intensity image and the 3D surface of the target. During the mapping process, one important parameter is depth information of the target. If the proposed LC lens is utilized, according to those 2D images, the depth information of the target at specific applied voltages can be obtained directly. In other situations, the depth z and related 2D intensity image information could not be obtained directly. A computational method is needed to be constructed based on those captured 2D images. However, those can be easily realized by a ray backprojection algorithm [40,41]. The algorithm based on the proposed LC lens can be realized by the following steps: 1. First, with changing applied voltages, multiple 2D images of different perspective can be respectively obtained by CCD. 2. Second, the magnification factor, between the image of the shortest focal length and any image of the other focal length, can be computed by the following formula: Mi
f 1 d − f i ; f i d − f 1
With Eqs. (4) and (5), we can obtain the 2D intensity image of any depth. Comprehensively considering the computing time and image quality, the number of those 2D intensity images should be a trade-off. Then, by Eq. (3), the 3D image of the target could be preliminarily reconstructed by all the above 2D intensity image information. 4. Experiment and Results
In order to present features of the LC lens and 3D imaging system, some experiments are described in detail. In this section, the major electro-optical features of the fabricated LC lens are given first; then the relatively simple method for acquiring 3D imaging of a target is presented and discussed. A. LC Lens
An experiment was set up to measure focused spot patterns and focal length of the LC lens, as shown in Fig. 5. The sample was mounted on an optical displacement platform. A white parallel light was used to illuminate the sample. The transmitted light was collected and detected by a CCD (3 megapixel, 1∕2 in:, and 6.4 mm × 4.8 mm in size). The detected data were analyzed by a computer. First, to characterize the optical focusing properties of the fabricated LC lens, a white parallel light was used to obtain its 2D intensity distribution images at different voltages. The distance between the LC lens and CCD, 265 mm, was fixed without any movements in the whole measurement. Three photos at different voltages were respectively captured, as shown in Fig. 6. When the applied voltage is 1.2 Vrms, it is clear that the left image is apparently a nonfocusing state. After the voltage up to 2 Vrms, the middle image presents an obvious focusing state.
(4)
where f 1 is the shortest focal length, f i is the ith focal length, and d is the distance between the LC lens and CCD. 3. Based on the magnification factor M i, the intensity images of the target at zr (r represents a
Fig. 5. Experiment setup. 20 November 2014 / Vol. 53, No. 33 / APPLIED OPTICS
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Fig. 6. Top three images are, respectively, at 1.2 Vrms, 2 Vrms, 6 Vrms; the curve is a PSF of the LC lens at 2 Vrms along the horizontal direction of the cross section.
When the applied voltage is continuously increased, the LC directors in the LC layer slowly reorient. After stabilizing, the directors have a new distribution: a smooth gradient refractive index distribution. At this state, the point spread function (PSF) of the LC lens along the horizontal direction of the cross section is computed by the captured focusing pattern, and the FWHM of the focusing profile is about 100 μm. As the transmittance of an LC lens in electrode areas is different from that in nonelectrode areas, there are different refractive indexes between electrode areas and nonelectrode areas in the LC lens. Thus, the 2 mm diameter circular pattern shown in the middle image has been formed by the different refractive index on the different areas. Given both PSF and the pattern of the focusing light spot, it is clearly shown that the LC lens has quite a good focusing feature. Then the voltage was increased to 6 Vrms; the right image shows an outof-focusing state. From the above three states, we can conclude that the focal length of the LC lens can be tunable by the external applied voltage without any mechanical movements, and that the LC lens is a positive lens. Second, the white parallel light was still used to measure the focal length of the LC lens. As the white light will cause chromatic aberration, a beam profiling camera from DataRay Inc., WinCamD UCD12, was utilized to confirm the focal length of the LC lens at different applied voltages. After more than five measurements at every voltage point, the relationship between focal length and the applied voltage can be obtained, as shown in Fig. 7. The range of the focal length is tunable from 20 to 480 mm, while the applied voltage is changed from 1.1 to 6 Vrms. The result shows that the curve of focal length versus applied voltage is an inverse proportion. The applied voltage gradually increases with decrease of the focal length. Based on the curve in Fig. 7, the focal length of 2 Vrms, which is very close to the real value of 265 mm, is 260 mm. That led to the conclusion that Fig. 7 can exactly present the 7920
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Fig. 7. Relationship between applied voltage and focal length.
property of the LC lens. The shortest focal length of the LC lens will appear when the LC has the maximum birefringence. E44 has around 0.255 of the maximum birefringence in the visible range (ne 1.778 and no 1.523). Based on Eq. (2), the focal length of the LC lens is 19.6 mm under conditions of Δn 0.255, d 100 μm, and r 1 mm. The calculated focal length is almost close to the measured value, 20 mm, which indicates that the LC lens has convergent features. As the inside top electrode configuration is combined with a high-resistance layer efficiently conserved electrical energy inside the LC layer, the smooth gradient electric field distribution is maintained by the high-resistance layer. Compared with a conventional LC lens, which is typically fabricated by two flat substrates clipping a homogeneous LC layer (100 μm thick) and has a circular patterned (2 mm diameter) and internal electrode to yield the desired phase retardation on a uniform LC layer, this proposed LC lens decreases the operating voltage from greater than 20 Vrms to only 6 Vrms. Third, an overdrive method is wildly utilized for accelerating the response time of LC devices [35–38]. With optimized over-driving voltages and the switch of target operation, response time of LC lens can be reduced substantially compared to the conventional one mentioned above without the overdrive method. As known, a thicker LC layer can yield a larger optical power, but the thicker layer generally results in a longer response time. To minimize the response time, we utilize the overdrive method. A large pulse is applied to the electrodes for accelerating response at the beginning. Then the input signal is switched from large pulse to a desired operating voltage to stabilize the focusing effect [37–39]. A circuit board was used to control the duration time of overdrive pulse. Generally, applying a larger pulse at the beginning of the overdrive method can yield a shorter response time, but too high electric energy could break the LC lens; thus, a pulse of less than 20 Vrms is chosen here, as shown in Fig. 8. Under only less than 20 Vrms overdrive voltage,
Fig. 8. Real waveform of overdrive method was detected by an oscilloscope. The magnitude of overdrive pulse was chosen as 10 Vrms since overflow will happen when voltage is more than 18 Vrms. In this measurement, the overdrive time was chosen as 800 ms.
the response time is instantaneous focusing within 0.2 s by 4 Vrms stable operating voltage. Table 1 shows the comparison between the fabricated and conventional LC lens mentioned above. Overall, the proposed LC lens dramatically improves about 99% focusing time and reduces about 70% operating voltage. Above measurements of response time are utilized by EOT-01, which is produced by the Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences. Finally, the module transfer function (MTF) is introduced to evaluate the focusing quality of the proposed LC lens. Those MTF values of the LC lens (square wave of 1 KHz at 5 Vrms) were measured by a knife-edge method [42]. The MTF value of the proposed lens decreases as spatial frequency increases, and it drops to almost zero when the spatial frequency is higher than 80 lp∕mm, as shown in Fig. 9. Compared with the ideal MTF value, the MTF value of the proposed LC lens is normal. Some methods can effectively improve the MTF value, such as adjusting the operating frequency. The method to improve the focusing quality will be studied in the future. B.
3D Imaging System
Fig. 9. Blue line represents the MTF value of proposed LC lens. Red line represents the ideal MTF value. Aperture size is 2 mm. CCD resolution is 50 lp∕mm.
illustrated in Fig. 5. We made the target a Boeing 777 toy, which has a size of 120 mm × 115 mm × 35 mm (L × W × H), to substitute the light source located at approximately 100 cm in front of the LC lens. For the whole capturing process, the distance between the LC lens and the target was fixed without any movements, and the driving voltage of the LC lens was consequently tunable from 1.1 to 6 Vrms at 0.5 Vrms∕Step. Hence, the total k 11 2D images can be recorded sequentially. The size of those captured 2D images is about 3.5 mm × 4.0 mm. Considering that the space of the paper is limited, only six images are selected, as shown in Fig. 10. To the target object, the focusing spot is from far to near along the depth direction with the increase of the applied voltages. From those results, a slight difference (magnification of the object) between the two images can be distinguished. Image quality is closely related to the structure of the LC lens (the high-resistance layer is the most important part of the LC lens). How to control the high resistance in an appropriate value is the key point. In this study, PEDOT, which is an organic material, was chosen as the highresistance layer. Since it is a kind of solution, a spincoating method was utilized to coat this material. However, it still has some issues, such as being a nondurable and inferior quality thin film. Although twice
The experiment was set up to evaluate the major feature of the proposed 3D imaging system, as Table 1.
Comparison of Focusing Time and Corresponding Operating Voltagea
Comparison Conventional LC lens mentioned above Our proposed LC lens
Thickness of LC Cell (μm)
Applied Voltage (Vrms)
Focusing Time (s)
100 (E44)
∼20
∼30
100 (E44)
