Liquid-filled tunable lenticular lens

To design a naked-eye 3D display, the focal length and thickness of lenticular lenses are key factors. Figure 2(a) shows the construction of lenticular systems using a liquid-filled tunable lenticular lens. We designed a lens pitch (W_pitch), a lens width (W_width), and a lens length of 491 µm, 430 µm and 15 mm, respectively, by fitting to the width of a pair of pixels (W_pair) of a smartphone display (Galaxy S II LTE SC-03D, Samsung Electronics Co., Ltd, Korea). Note that we designed the lens pitches to contain two display pixels, which are a pair of pixels for the right eye and left eye. The whole area of the lenticular lens array is approximately 15  ×  15 mm containing 32 thin rectangular lenses. When we fix the viewing distance as L, the focal length of the lenses (f) is calculated by

$$\begin{eqnarray}&&f=\frac{{{W}_{\text{pair}}}\times L}{2{{w}_{\text{e}}}},\end{eqnarray} \tag{ 1 }$$

because the width of the pair of pixels for the right and left eye should be magnified to twice the distance between the eyes (w_e, 65 mm) when the images reach the viewer's eyes. Using equation (1), we calculated f as 1.13 mm by fixing L as 300 mm. By using f = 1.13 mm, the distance between centers of lenses and surfaces of pixels (C) should be designed to be 1.6 mm according to the equation

$$\begin{eqnarray}&&C={{N}_{\text{L}}}\times f,\end{eqnarray} \tag{ 2 }$$

where the refractive index N_L = 1.4 (refractive indexes of PDMS, water, and glasses are approximately 1.4, 1.3, and 1.5, respectively). Note that we ignore the effect of the thickness of the PDMS membrane for simplifying the calculation. Practically speaking, the thickness of the devices is 0.6 mm because there is a 1.0 mm-thick protective layer on the display pixels. The required radius of curvature of the lenses (R) is calculated as 450 µm using

$$\begin{eqnarray}&&R=f\times \left({{N}_{\text{L}}}-1\right).\end{eqnarray} \tag{ 3 }$$

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In this system, we designed the thickness of the glass substrate as 0.5 mm, the thickness of the PDMS membrane as 100 µm, and the height of the microfluidics as 50 µm.

We fabricated the liquid-filled tunable lenticular lens with simple soft lithography [22]. Figure 2(b) shows the fabrication process of the liquid-filled tunable lenticular lens. We spin-coated PDMS (Sylgard 184 Silicone Elastomer, Dow Corning) on a SU-8 mold (SU-8 Series; MicroChem Corp., MA) at 500 rpm for 10 sec and 1200 rpm for 30 sec to produce a PDMS membrane having microchannels. After heating the SU-8 mold at 100 °C for 30 min on the hot plate, we peeled-off the membrane and put onto a polyethylene terephthalate (PET) film. The membrane and a glass substrate (Matsunami glass Co. Ltd, Japan) were treated with O₂ plasma. Subsequently, the membrane bonded to the substrate. Similarly, inlets for tubing were connected to the membrane. Note that we used PDMS at 10 : 1 ratio of the PDMS base and curing agent (Young's modules of PDMS is about 1.5 MPa) [23]. The stiffness of the PDMS membrane was appropriate to form the lens shape; when the PDMS was too stiff, the PDMS membrane did not deform, but when too soft, it was technically difficult to fabricate the device. Finally, deionized water was introduced to fill the PDMS microchannel. Air bubbles that were sometimes trapped in the microchannel completely disappeared when we applied pressure at approximately 30 kPa. Figure 2(c) shows the fabricated lenticular lens. We used a pressure-driven flow controller (MFCSTM, Fluigent S.A., France) to induce solution into microchannels and to control applied pressure.

In order to determine whether the lens shape is sufficiently cylindrical or not, we measured profiles of the deformed membrane and examined the relationship between the applied pressure and the radius of curvature of the membrane. We used a laser interferometer (VK-X 200, Keyence Co., Ltd, Japan) and its analysis software (VK-X 200 Analysis Application, Keyence Co., Ltd) to measure the profiles of the membrane and the radius of curvature of the membrane. Figure 3(a) shows the height profiles of the membrane while varying the applied pressure from 0 to 30 kPa. The lens shape changed continuously depending on the applied pressure from 0 to 30 kPa. The delamination between the PDMS membrane and the glass layer occurred when we applied pressure more than 50 kPa. Note that air bubble did not occur by applying positive pressure or negative pressure. Figure 3(b) shows the relationship between the applied pressure and the radius of curvature of the membrane. These results indicate that when the applied pressure is 30 kPa, the radius of curvature reaches approximately the 450 µm that is required for 3D imaging.

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We also measured the focal length of the lens to confirm the focal length's variable range. The measurement method is shown in figure 4(a). A collimated light passed through the lens was focused into linear shapes at the focal point. We moved the camera position to measure the focal length. Figure 4(b) shows the relationship between the applied pressure and the focal length. The theoretical focal length was also calculated from the radius of curvature using equation (3). We confirmed that the device could change its focal length extensively (from 17 to 6 mm) by pressure-driven deformation. While we could not measure the focal length under 6 mm due to constraints of the experimental system, the measured values almost matched calculated values when the applied pressure was within the range 3–6 kPa. Hypothesizing that the focal length of the lenticular lenses matches theoretical calculation over the entire range of the applied pressure, we could estimate that the focal length can be reduced to 1 mm which is required for 3D imaging when the applied pressure is approximately 30 kPa.

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Next, we measured the optical characteristics' dependence on viewing angle. Figure 5(a) shows the method of measuring the view angle dependency of lenticular lenses. We placed the lens on the interlaced image composed of green line for a right eye and black line for a left eye, then observed the green light intensity from various angles (from −20° to 20°) to measure the angle-dependent light intensity for the right eye. After that, we swapped the position of the green lines and the black lines and observed light intensity in the same way to measure changes in light intensity for the left eye. In both cases, we performed this experiment when the membrane was flat and when it was deformed (applied pressure: 0 kPa and 30 kPa, respectively). Figures 5(b) and (c) show the relationship between the view angles and the normalized green light intensity when the membrane was flat and deformed, respectively. When the membrane was flat, the intensity from various angles was almost the same level, indicating that the light went through the membrane without reflection. When the membrane was deformed, peaks of green light intensity for the right eye and left eye were observed around 4°, indicating that the light was focused to those specific directions by the lens effect. These results show that this device has characteristics of lenticular lenses and enables on/off switching of its lens effect by controlling the applied pressure.

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By applying our tunable lenticular lens to existing a smartphone display, our system achieves a 2D/3D switchable naked-eye 3D display. First we confirmed whether we could obtain 3D images through the lens. The interlaced image, which was composed of two different images for the right eye and the left eye, was displayed on a smartphone display. After putting the lens on an interlaced image, the membrane was deformed by applying pressure. When the applied pressure was 10 and 20 kPa, we could not obtain 3D images because the lens deformation was not enough. By applying pressure of 30 kPa, we deformed the membrane to successfully project two different images for the right eye and left eye depending on viewing angles at 4° (figures 6(a) and (b)). This means that our system can display parallax images which are processed as a 3D image in the human brain. Next, we determined whether we could display 2D images with their original resolutions through the device when the membrane was flat. The device was put on the smartphone display, which shows a 2D image with its original pixel resolution. While we obtained the distorted 2D image due to lens effects when the membrane was deformed, we could also observe the clear 2D image when the membrane was flat (figures 6(c) and (d)). This means that our system can display 2D image with original pixel resolution of the smartphone display.

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Finally, we evaluated the luminance retention of the 3D display using our lens by comparing it to a parallax barrier system [4]. We calculated the luminance retention of displays by measuring the luminance of images of screens taken from the viewer's position using image processing software (ImageJ, Wayne Rasband) (figure 6(e)). First, we measured the luminance of the display without attaching our lens. We defined this luminance as the original luminance of the display (Lo). Then, we put our lens on the display and measured the luminance of the two images taken from the viewer's right eye and left eye positions. We defined the luminance of our 3D display (L_3D) as the mean of these values of luminance. After that, we calculated the luminance retention by dividing L_3D by Lo. Figure 6(f) shows the luminance retention of the display through our lenses. Although the maximum theoretical value of the luminance retention is 50% in parallax barrier systems [4], we succeeded in maintaining over 90% of luminance of the display.