1. Introduction

In the past more than three decades, electrically tunable liquid crystal (LC) lenses have been paid increasing attention [1], and have been proven to have potential applications in tunable glasses and autofocus systems of mobile devices [2–4]. Many structures, such as non-planar [5], concentric ring [2,3], and hole-patterned [6–8], of LC lens have been proposed. The LC lenses having hole-patterned electrodes are simple in structure, and that driven by two voltages has been proven to have low optical aberrations [9], and optical systems using it can form high quality images [4].

One of the main disadvantages of LC lenses is their polarizer dependency. The polarizer drastically reduces the light amount, enough of which being essential for forming high quality images. There are two approaches to solve the problem of polarizer using. One is to fabricate LC lens with, instead of nematic LC, blue phase LC [10–12]. The small birefringence, narrow stable temperature range, and high driving voltage of blue phase LC, however, make it still difficult for practical use. Another one is replacing the LC layer with stacked layers of LC with orthogonal rubbing directions [2,13,14], but the multi-layer structure usually leads to great increase in the cost and the thickness of LC lens.

In this paper we propose a polarizer-free imaging (PFI) method for an imaging system with an LC lens of single nematic LC layer as a focusing element. A final clear image is obtained by eliminating the image formed by ordinary wave (o-wave) from the mixed images formed by a natural light containing both extraordinary wave (e-wave) and o-wave. The proposal is successfully demonstrated by experiments.

2. Image processing

The setup of the imaging system is shown in Fig. 1. The LC lens is placed in front of a camera module, tuning the focus of the system, to form the image of an ISO 12233 chart on a CMOS sensor in the module. The CMOS camera module is KS5A00 from VIMICRO [2592*1944 resolution, 1/2.5 inch sensor size, and 1.4 μm pixel size]. The lens and non-lens states correspond to the two LC lens states when the applied voltages are on and off, respectively.

 

Fig. 1 Experimental setup of the imaging system.

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Let $I^l$ and $I^{nl}$ be images captured by the image sensor of the camera module when the LC lens is in the lens and non-lens states, respectively. The images formed on the image sensor could be considered to be composed of overlapped images $I_e$ and $I_o$ from e-wave and o-wave, respectively, that is,

If there were a polarizer in the system, $I_o^l$ would be filtered out by the polarizer, and $I^l=I_e^l$ could be tuned by the LC lens, and finally a focused image of the object can be obtained. In this work, $I_o^l$ formed from the non-focused o-wave degrades the image quality. A clear image $I$could be obtained if $I_o^l$were removed, that is,

As $I_o$ does not change with lens state, $I_o^l=I_o^{nl}$ if the object remains static in the time interval between the on and off of the lens state. Then $I_o^l$ in Eq. (3) can be replaced by $I_o^{nl}$, and

In non-lens state, let $\alpha$ (0<$\alpha$<1) represents the fraction of the amount of the o-wave in the incident light wave, then $I_o^{nl}=\alpha I_{}^{nl}$ and $I_e^{nl}=(1-\alpha )I_{}^{nl}$. In the natural light environment discussed in this work, $\alpha =0.5$, and $I_o^{nl}=I_e^{nl}=0.5I_{}^{nl}$. Equation (4) becomes

A clear image $I$is then generated from images $I^l$ and $I^{nl}$. We note that in contrast to the LC lens imaging system using a polarizer where only less than half of light is used, full light is made use of by image sensor in our method.

To keep the brightness of $I$ to the same level of that of $I^l$ and $I^{nl}$, and to restrict the pixel values of $I$within the range of [0, 255], $I$is rescaled and truncated as follows,

Regarding the time for image processing, it takes approximately 4 ms using a PC with CPU of i7-4700 2.4G and memory of 8G without parallel calculations to process two grayscale images of 1280 × 1024 resolution. The time is much shorter than the response time of a current LC lens.

3. Experiment

3.1 Structure of LC lens

The structure of the LC lens [7] used in the work is given in Fig. 2. Indium tin oxide (ITO) transparent electrodes 1 and 3 are coated on glass substrates 1 and 3, respectively. A hole-patterned Chrome (Cr) electrode 2 is coated on glass substrate 2 of 0.7 mm thickness. The diameter of the round hole is 2 mm. The upper electrode is composed of electrodes 1 and 2, which stick to each other by UV curable resin. The thickness of the resin layer is 20 μm controlled by spacers.

 

Fig. 2 Structure of LC lens. The LC lens of 2.0 mm aperture is driven by two voltages V₁ and V₂.

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The LC layer (KW0-048 from Slichem. Δn = 0.30 at 589 nm) of approximate 20 μm thickness is sandwiched between glass substrate 2 and ITO electrode 3. The lower surface of glass substrate 2, facing the LC layer, is spin-coated with polyimide (PI) and rubbed. PI is also coated on electrode 3 which is in contact with LC layer, and rubbed in the antiparallel direction of that on glass substrate 2. AC voltage V₁ is applied across ITO electrodes 2 and 3, and V₂ is applied across ITO electrodes 1 and 3.

3.2 Properties of LC lens

A lens-like distribution of the effective refractive index n_e(θ) is formed in the LC layer by appropriate voltages V₁ and V₂, where θ is the tilt angle of the LC director. n_e and n_o represent the refractive indices of the e-wave and o-wave, respectively. The frequency of applied voltage is 1 kHz.

The properties of the LC lens are investigated using a Mach-Zehnder interferometer. The aberrations and the optical powers of LC lens are obtained by analyzing the interference fringes, which are captured by Sony XC-ST50 white and black video camera. It is found that with V₁ of 65 V_rms, the LC lens has a relatively wider focusing range with low optical aberrations. As shown in Fig. 3, with V₁ = 65 V_rms, V₂ changes from 20 to 65 V_rms to tune the optical power of the LC lens from approximately 5 to 0.5 m⁻¹ for incident light of 532 nm wavelength. The optical power decreases with increasing V₂, that is, with decreasing V₁-V₂. The aberration also decreases with increasing V₂, and the aberrations in the focusing range (V₂ > 20 V_rms) are lower than the tolerance condition of 0.07 wave [15].

 

Fig. 3 Properties of LC lens. The optical power and RMS aberration change with V₂.

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In the lens state with V₁ of 65 V_rms and various values of V₂, the images of the ISO 12233 chart placed at a distance of 18 cm from the LC lens are analyzed. The modulation transfer function (MTF) obtained from the slanted edge in the image of the ISO 12233 chart is used to evaluate the image quality. MTF50, the spatial frequencies where MTF is 50% of its low frequency value, is used to represent the resolving power of the system. As shown in Fig. 4, MTF50 changes with V₂, and the maximum MTF50 appears at V₂ = 26 V_rms. The chart is then considered as in focus when V₁ = 65 V_rms and V₂ = 26 V_rms. The image processing is performed at these voltages.

 

Fig. 4 MTF50 changing with V₂.

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4. Results

The image of the chart and the areas for the measurements are shown in Fig. 5(a). Figures 5(b) and 5(c) show the images of the slanted bar and the wedge pattern, used to measure the MTF and the contrast, respectively. Each figure contains images captured in the non-lens and lens states of the LC lens, and that are processed with the PFI technology described in Sec. 2. The perceived image sharpness of $I\text{'}$ is higher than that of $I^l$, which is higher than that of $I^{nl}$.

 

Fig. 5 Images captured by the LC lens imaging system. (a) ISO 12233 chart image and the areas for MTF and contrast measurements; (b) slanted bar images; (c) wedge pattern images.

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Figure 6 shows the MTF curves calculated from the slanted edges in images $I^{nl}$, $I^l$ and $I\text{'}$. The spatial frequency of 0.5 cycle/pixel represents the Nyquist frequency of approximately 357 lp/mm of the image sensor.

 

Fig. 6 MTF comparison of the imaging system in the non-lens state, lens state and after image processing.

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As is expected, the blurred image $I^{nl}$captured before the focus tuning by the LC lens exhibits a very low MTF response in the whole frequency range from 0 to the Nyquist frequency. In lens state, the LC lens tunes the e-wave and forms a more focused image on the sensor, and we can see a remarkable increase in the MTF data. A further improvement in MTF is observed in the processed image $I\text{'}$ that is obtained by removing the o-wave image from $I^l$. Throughout all the spatial frequencies, image $I\text{'}$ exhibits rather high contrast.

Similar conclusion on contrast can be drawn from the observation of the wedge patterns in images $I^{nl}$, $I^l$ and $I\text{'}$ shown in Fig. 5(c). Figure 7 gives the gray value distributions measured along the dashed lines in Fig. 5(c). The contrast rises from nearly zero to 0.5 after focus tuning, and finally becomes close to 1 after image processing. The contrast of each image is represented by the ratio of the difference of the max and the min pixel value to the sum of both.

 

Fig. 7 Resolving ability comparison of the imaging system in the non-lens state, lens state and after image processing.

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The proposed method is also tested to capture a more real scene, as shown in Fig. 8. LC lens tuning turns the blurred doll image ($I^{nl}$) to a sharper one ($I^l$), and an even sharper one ($I\text{'}$) is successfully obtained by applying our PFI technology.

 

Fig. 8 Images in non-lens (a) and lens (b) states, and processed image (c).

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To apply the PFI technology, the scene is assumed to be static between the two image captures. It is necessary to acquire the two images in a time interval as short as possible, that is, a fast response LC lens is desired. Various methods have been proposed to realize fast response of LC [16–18], but these methods in turn increase the system complexity. We are working on the high speed PFI and the results will be reported elsewhere.

5. Conclusion

An image processing method is proposed to solve the problem of polarizer dependency of LC lens. Two images, $I^l$ and $I^{nl}$ are first captured when the LC lens are in the lens state and non-lens states, respectively, and a final image $I\text{'}$ is then deduced based on $I^l$ and $I^{nl}$. The proposal is successfully demonstrated by experiments. As no polarizer is used, all available light is made use of in image formation.