1. Introduction

Thus far, three-dimensional (3-D) display has been regarded as one of the promising technologies for the human-friendly visual interface providing an intuitive understanding of 3-D images. Therefore, a lot of research works have been done for the development of various 3-D displays, which are capable of visualizing the 3-D images that are as natural and real as things we see and experience in the real world [1–3].

There are several types of 3-D displays, which include stereoscopic, holographic and volumetric displays [1–3]. Among them, the stereoscopic display, where a concept of binocular disparity is employed as the depth cue, has been known as the most popular 3-D display type since it can be simply implemented, compared to other types of 3-D displays. However, in the stereoscopic display, not a real 3-D image, but a pair of two-dimensional (2-D) left and right-eye images is delivered to their respective eyes to produce a binocular disparity. Thus, it has the fundamental human-factor problems such as eye fatigue, headache and dizziness, causing the viewer to feel uncomfortable and the feeling of naturalness to be reduced [4–6].

As an alternative to the stereoscopic display, the holographic display has been actively researched since it has been regarded as one of the real 3-D displays, which is free from the human-factor problems. However, even though the holographic display is one of the real 3-D display techniques, its practical implementation appears to be very difficult at this time due to the unavailability of its key electro-optical devices. That is, full-color holographic camera systems for live capturing of the daylight-illuminated outdoor scenes have not been developed, as well as large-scale spatial light modulators (SLMs) for displaying the high-resolution holographic data have not been commercially available [7,8]. These critical issues of the current holographic 3-D display have prevented it from being widely accepted in the practical application fields.

As another approach for the real 3-D display, the floating display has been also suggested, where object images with real depth are floated into the free space near the viewer simply by using either of a mirror or a lens [9–13]. More recently, advanced floating displays such as the table screen 360° 3-D display using a small array of high-speed projectors [14], 360° floating 3-D display based on light-field regeneration [15] and interactive glasses-free tabletop floating 3-D display with conical screen and modular projector arrays [16] were proposed as well. But, due to the simple optical configuration of the mirror or lens-based floating display system, many types of those displays have been presented [9–13]. Among them, the Fresnel lens-based floating display system has been actively researched since it can be implemented in a large scale with the simple flat-type optical lens, which is called a Fresnel lens [10,11]. Here, the Fresnel lens is an optical component which can be used as a very cost-effective and light-weight alternative to the conventional optical lens. In particular, it would be very effective for the case of the large-scale floating display system since the size and weight of the optical convex lens employed in this large system appears to be too big and heavy to handle and operate [11]. Moreover, in this display system, 2-D or 3-D object images, as well as the real objects can be used as the input signals, and large-scale objects can be directly viewed in the free space as the floating images without needs of any special glasses.

However, the Fresnel lens-based floating display system still has several problems to be overcome for its practical application, which include low image-resolution, small viewing-zone, narrow viewing-angle, image distortion and large volume size [11,17]. Among them, the large-scale volume of the display system has been regarded as the most critical issue in its practical application. This volume issue looks like an inherent problem of this display system resulting from its operational principle. That is, the floating image is normally set to be located in front of the Fresnel lens, and its position is determined by the lens equation related with the focal length of the lens and the position of the input object. In practice, the distance between the input object and the Fresnel lens, which virtually represents the physical depth of the display system must be set to be longer than the focal length of the lens. Thus, the volume size of the conventional Fresnel lens-based floating display system inevitably gets much increased. Furthermore, as the focal length of the Fresnel lens increases, the corresponding volume size of the display system also increases which limits its practical application.

Therefore, in this paper, we propose a new type of slim-structured Fresnel lens-based electro-floating display system by employing a polarization-based optical path controller (P-OPC), which is composed of two quarterwave plates (QWPs), a half mirror and a reflective polarizer [17]. In the proposed system, the optical path between the input plane and Fresnel lens, representing the physical depth of the conventional display system, can be reduced by one third by repetitive transmision and reflection of the input beam through the P-OPC.

In this paper, the operational principle of the proposed system is analyzed by using the Jones matrix. In addition, to confirm the feasibility of the proposed system in the practical application fields, experiments with test prototypes are also carried out, and the results are comparatively discussed with those of the conventional method in terms of the system volume, floating-image position and size, viewing angle and light efficiency.

2. Conventional Fresnel lens-based electro-floating display

Figure 1 shows an optical configuration of the Fresnel lens-based electro-floating display system, which is composed of a FPD and a Fresnel lens. As seen in Fig. 1, a floating image is located in front of the Fresnel lens, and its position is determined by the lens equation of Eq. (1).

 

Fig. 1 Optical configuration of the Fresnel lens-based electro-floating display.

Download Full Size | PDF

Here, the viewing-area and image size are also regarded as the important display parameters in the Fresnel lens-based floating display system. In this system, the floating image can be observed through the Fresnel lens, as a result the viewing-area of the display system is restricted by the aperture of the Fresnel lens. Figure 2 shows a conceptual diagram of the viewing-area of the Fresnel lens-based electro-floating display system [13].

 

Fig. 2 Conceptual diagram of the viewing-area of the Fresnel lens-based electro-floating display system.

Download Full Size | PDF

As seen in Fig. 2, the viewing-angle of the display system (θ) is defined as Eq. (2), which can be derived from the trigonometric relationship between the floating distance and aperture size of the Fresnel lens.

 

Fig. 3 Relationships between the (a) Object distance (d_o) and floating distance (d_f), (b) Object distance (d_o) and floating-image size (s_out), and (c) Object distance (d_o) and viewing-angles (θ and θ_wv).

Download Full Size | PDF

Figure 3(a) shows the floating distance (d_f) dependence on the object distance (d_o). According to Eq. (1), the object image cannot be floated in front of the Fresnel lens if the object distance gets smaller than the focal length of the Fresnel lens (f). Thus, the object distance must be larger than the focal length of the Fresnel lens to form a floating image in the free space. As seen in Fig. 3(a), the floating distance decreases as the object distance increases. In case the object distance is set to be 400mm, which is equal to two times of the focal length of the Fresnel lens, the object image is floated at the same distance of 400mm in front of the Fresnel lens. On the other hand, as the object distance approaches to the focal length of the Fresnel lens, the corresponding floating distance exponentially increases and eventually reaches to ∞ for the case of d_o = d_f.

Moreover, Fig. 3(b) shows the floating-image size (s_out) dependence on the object distance (d_o). As seen in Fig. 3(b), as the object distance increases, the corresponding floating-image size decreases, whereas it exponentially increases as the object distance reduces down to the focal length of the Fresnel lens. Figure 3(c) also shows the viewing-angles (θ, θ_wv) dependence on the object distance (d_o). As seen in Fig. 3(c), if the object distance increases, the corresponding viewing-angles also increase. However, θ_wv turns out to be the minus value for d_o < 290mm, which means there exists no viewing-area for the entire floating 3-D image. Therefore, the object distance must be greater than the focal length of the Fresnel lens for obtaining the reasonable viewing-angle of θ_wv.

In general, a large-size floating-image with the relatively wide viewing-angle at the long floating distance is required in the practical floating display system. As seen in Figs. 3(a) and 3(b), d_o should be decreased for the large floating distance and large image size. On the other hand, it should be increased for the large viewing angle. That is, three kinds of display characteristics of this floating display are in a trade-off relationship. Thus, the optimum value of d_o can be selected for simultaneous fulfillments of those required display characteristics. For instance, Table 1 shows the operational characteristics of a floating display system. Here, the focal length of the Fresnel lens (f), object-image size (s_in) and aperture size of the Fresnel lens (w) are assumed to be 200mm, 180mm and 400mm, respectively.

Table 1. Operational Parameters of a Floating Display System

View Table | View all tables in this article

First, to satisfy the condition of d_f > 300mm, the object distance is set to be smaller than 600mm according to Eq. (1) and Fig. 3(a). Second, to fulfill the condition of s_out > 130mm, the object distance is set to be smaller than 470mm according to Eq. (4) and Fig. 3(b). Third, to satisfy the viewing-angle condition of θ_wv > 40°, the object distance must be larger than 460mm based on Eq. (3) and Fig. 3(c). Thus, in order to fulfill all those required display characteristics of the display system, the object distance (d_o) must be set to be between 460mm and 470mm. That is, the object distance, representing the physical depth of the display system, must be kept to be relatively large to provide the floating image with the reasonable size, viewing angle and depth. As seen in Table 1, the object distance should be more than two times of the focal length of the Fresnel lens and more than one and half times of the floating distance, in order to satisfy the display requirements. Therefore, the conventional Fresnel lens-based floating display system cannot avoid from being increased in its physical volume, which limits its practical application.

3. Proposed system

3.1 Overall system configuration

Figure 4 shows an overall configuration of the proposed slim-structured Fresnel lens-based electro-floating display system, which is largely composed of three parts such as input FPD, polarization-controlled optical path controller (P-OPC) and Fresnel lens. Here, the P-OPC is a new optical device employed in the proposed system to control the optical path of the input beam based on its polarization state. First, an object image to be floated is loaded on the FPD. The object beam coming from the FPD is then input to the P-OPC, which is composed of a set of optical devices such as two quarter-wave plates (QWPs), half mirror (HM) and reflective polarizer (RP), and located between the FPD and Fresnel lens. With this P-OPC, the straight optical path of the conventional floating display system can be folded up three times, and transformed into a sum of three sub-optical paths such as Path-1 (from the FPD to the RP) and Path-2 (from the RP to the HM) and Path-3 (from the HM to the Fresnel lens). Of course, the sum of those three paths is equal to the original optical path of the conventional floating display system. That is, the absolute distance between the FPD and Fresnel lens, representing the physical depth of this display system, can be reduced by approximately one third, which means that the new device of the P-OPC enables the volume of the conventional system to be reduced down to almost 33%.

 

Fig. 4 Optical configuration of the proposed system: (a) Schematic diagram of the P-OPC, (b) Enlarged-view of the P-OPC with recursive optical paths.

Download Full Size | PDF

As seen in Fig. 4(a), the optical components composed of the P-OPC can be assembled as the film-type optical elements. That is, two film-type QWPs are laminated on both sides of the half mirror, and the reflective polarizer is attached to the flat Fresnel lens. As shown in Fig. 4(b), the optical beam coming from the object image displayed on the FPD, which is vertically polarized, is transmitted to the reflective polarizer through the QWP, half mirror and another QWP (‘Path-1’). This optical beam is then reflected from the reflective polarizer and propagated back to the half mirror (‘Path-2’). Furthermore, the optical beam reflected from the half mirror also transmitted to the Fresnel lens through the QWP and reflective polarizer (‘Path-3′). The optical beam coming out from the P-OPC is finally projected into the free space to form a floating image in front of the Fresnel lens according to the lens equation of Eq. (1).

3.2 Operational principle of the P-OPC

As shown in Fig. 5(a), the P-OPC, which is composed of two QWPs, a reflective polarizer and a half mirror, can generate the polarization-controlled recursive optical path between the input FPD and Fresnel lens by repetitive transmissions and reflections of the optical beam, which then enables the physical volume of the proposed system to be much reduced.

 

Fig. 5 Operational principle of the P-OPC: (a) Schematic diagram of the P-OPC and the resultant polarization-controlled optical path, (b) Polarization state variations of the optical beam propagating the P-OPC.

Download Full Size | PDF

Figure 5(b) shows the input and output polarization states of the optical beam at each optical devices. That is, the linearly polarized input beam passing through two QWPs and a half mirror, is reflected back from the reflective polarizer and propagates to the half mirror passing through the QWP. This beam is then reflected back again from the half mirror and propagate to the Fresnle lens passing through the QWP based on its polarization state. In other words, the P-OPC generates a recursive optical beam between the FPD and Fresnel lens, which means it shortens the straight optical path of the conventional display system to be one third by folding it up three-times. Here, the operational principle of the P-OPC can be analyzed by using the Jones matrix for each path [17].

3.2.1 For the ‘Path-1’

Figure 6(a) shows the polarization state variation of the optical beam after passing through each optical element in the ‘Path-1’. In the proposed method, the polarizer attached on the FPD is set to be vertically polarized. Thus, the polarization state of the optical beam can be written by Eq. (5).

 

Fig. 6 Polarization state variations of the optical beam after passing through each optical element in the (a) ‘Path-1’, (b) ‘Path-2’, and (c) ‘Path-3′

Download Full Size | PDF

The optical beam coming from the FPD, which is vertically polarized, is transmitted to the half mirror through the QWP₁. Here, the azimuth angle of the QWP₁ is set to be 45°. Thus, the vertically-polarized optical beam is converted into the left-hand circularly-polarized optical beam by passing through the QWP₁. Since no change of the polarization state of the optical beam occurs in the half mirror, the output polarization state of the optical beam after passing through the QWP₁ and half mirror can be given by Eq. (6).

The optical beam coming from the half mirror then passes through the QWP₂, whose azimuth angle is set to be −45°, where the left-hand circularly-polarized optical beam is converted into the vertically-polarized optical beam. Therefore, the output polarization state of the optical beam after passing through the QWP₂ can be given by Eq. (7).

Thus, the vertically-polarized optical beam coming from the QWP₂ propagates to the reflective polarizer, where it is reflected back and takes on the second beam path of ‘Path-2’ [18,19].

3.2.2 For the ‘Path-2’

Figure 6(b) shows the polarization state variations of the optical beam after passing through each optical element in the ‘Path-2’. The polarization state of the optical beam reflected back from the reflective polarizer is also vertically polarized because the polarization state is maintained, which is shown in Eq. (8).

The optical beam coming from the reflective polarizer passes through the QWP₂, whose azimuth angle is set to be 45°, where the vertically-polarized optical beam is converted into the left-hand circularly-polarized optical beam. Thus, the output polarization state after passing the QWP₂ can be given by Eq. (9).

Now, this optical beam is reflected back again from the half mirror and propagate to the reflective polarizer by passing through the QWP₂, and then takes on the third beam path of ‘Path-3′ [18,19].

3.2.3 For the ‘Path-3′

Figure 6(c) shows the polarization state variations of the optical beam after passing through each optical element in the Path-3. Here, the polarization state of the optical beam reflected back from the half mirror is maintained. However, its rotation direction is reversely changed because the direction of the optical beam is changed. That is, the left-hand circularly-polarized optical beam is converted into the right-hand circularly-polarized optical beam. Thus, the polarization state of the optical beam after being reflected back from the half mirror can be given by Eq. (10).

Now, the optical beam coming from the half mirror is transmitted again to the QWP₂, whose azimuth angle is set to be −45°. The right-hand circularly-polarized optical beam is converted into the horizontally-polarized optical beam by being passed through the QWP₂. Thus, the output polarization state of the optical beam after passing through the QWP₂ can be given by Eq. (11).

That is, the polarization state of the optical beam input to the reflective polarizer is horizontally polarized. Thus, this horizontally-polarized optical beam propagates to the Fresnel lens after passing through the reflective polarizer. Therefore, the polarization state of the optical beam after passing through the reflective polarizer and Fresnel lens can be given by Eq. (12).

These repetitive transmissions and reflections of the optical beam in the P-OPC can be done just by polarization-based controlling of the optical path. The optical beam coming from the P-OPC, is finally projected into the free space in front of the Fresnel lens.

3.3 Performance analysis of the proposed system

3.3.1 Reduction of the system volume

In the proposed system using the P-OPC, the distance between the FPD and Fresnel lens, representing the physical depth of the display system, can be shortened to be d'_o( = d_o/3) as shown in Fig. 4. Therefore, Eq. (1) can be rewritten into Eq. (13) in the proposed system as follows.

3.3.2 Display characteristics

Even though the object distance is reduced in the proposed system by using the P-OPC, the display characteristics of the proposed system such as the floating distance (d'_f), viewing angle (θ', θ'_wv) and floating-image size (s'_out), can be kept to be same with those of the conventional system.

As seen in Eqs. (1) and (13), d'_f equals to d_f if d'_o is given by one-third of d_o. That is, the floating-distance of the proposed system is exactly same with that of the conventional system. Equations (2) and (3) for the viewing angles can be also rewritten into Eqs. (14) and (15) in the proposed system based on Eq. (13).

Equations (14) and (15) show that the viewing-angle of the proposed system is same with that of the conventional system as far as the total object distance of the proposed system is kept to be same with that of the conventional system such as 3d'_o = d_o. In addition, Eq. (4) for the floating-image size can be rewritten into Eq. (16) in the proposed system according to Eq. (13).

Equation (16) shows that the floating-image size of the proposed system is equal to that of the conventional system while the total object distance of the proposed system is kept to be same with that of the conventional system such as 3d'_o = d_o. In brief, the display characteristics of the proposed system such as the floating distance, viewing angle and floating-image size, can be kept to be same with those of the conventional system, while the physical volume of the proposed system has been reduced by one third compared to the conventional system.

4. Experiments and the results

4.1 Optical setup for the experiments

Figure 7 shows the experimental setups of the proposed and conventional floating display systems for comparison. That is, Figs. 7(a) and 7(b) show the top and side views of those systems. As seen in Figs. 7(a) and 7(b), the object distance (OD_conv, OD_prop) between the FPD and Fresnel lens of the proposed system visually appears to be shortened by one third compared to that of the conventional system.

 

Fig. 7 Experimental setups of the conventional and proposed systems: (a) Top-view, (b) Side-view.

Download Full Size | PDF

As seen in Fig. 7(b), two kinds of optical components such as the FPD and Fresnel lens are used in the conventional system, while in the proposed system three kinds of optical components such as the FPD, P-OPC and Fresnel lens are used. Here, a smart phone (Samsung Galaxy Note, 5.3” and 1,280 × 800 pixels) whose size and resolution are given by 5.3” and 1,280 × 800 pixels, respectively, is used as the FPD, and a Fresnel lens (Model: FL63-160, Diypro) whose focal length and size are given by 63mm and 160mm, respectively, is used as a floating lens in both of the proposed and conventional systems [20]. Moreover, the P-OPC is fabricated with a set of optical components such as a half mirror, two film-type QWPs (Model: APQW92-004-HT, American Polarizer Inc.) and a film-type reflective polarizer (Model: Wire-grid polarizing film HCN, Asahi Kasei E-materials Corporation), where two film-type QWPs are attached to both side of the half mirror and the film-type reflective polarizer is attached to the back side of the Fresnel lens [21,22].

Table 2 shows the operational characteristics of the display systems used in the experiments. Here, the object-image size (s_in) is assumed to be 42mm. A circular-shape Fresnel lens, whose diameter is 160mm, is also used in the experiments, but due to the limited size of the reflective polarizer, a square-shape mask is inserted in front of the Fresnel lens. Thus, the practical aperture size of the Fresnel lens (w) is set to be 95mm.

Table 2. Operational Parameters of the Conventional and Proposed Experimental Systems

View Table | View all tables in this article

First, to satisfy the condition of d_f > 90mm, the object distance is set to be smaller than 210mm based on Eq. (1). Second, to fulfill the condition of s_out > 20mm, the object distance is set to be smaller than 190mm according to Eq. (4). Third, to satisfy the condition of θ_wv > 40°, the object distance must be larger than 180mm according to Eq. (3). Thus, in order to fulfill all those required characteristics of the display system, the object distance must be set to be between 180mm and 190mm. Base on this analysis, the object distance of the conventional (d_o) and proposed (d'_o) systems are set to be 180mm and 60mm in the experiments. Then, the calculated display characteristics using the given parameters for each of the conventional and proposed systems are shown in Table 3.

Table 3. Calculated Display Characteristics of the Conventional and Proposed Systems

View Table | View all tables in this article

As seen in Table 3, the floating distance, floating-image size and viewing angle of the proposes system are all same with those of the conventional system, which are calculated to be 96.9mm, 22.6mm and 40.9°, respectively. Their object distances are, however, different as mentioned above. That is, the object distance of the proposed system has been reduced down to 60mm from 180mm of the conventional system.

4.2 Test image on the input display panel

Experiments are carried out by using the optical setups for the conventional and proposed systems of Figs. 7(a) and 7(b), and their performances are comparatively discussed in terms of the volume size, floating distance, floating-image size, viewing angle and light efficiency. Figure 8(a) show a test image of ‘Flower’ used in the experiments, and Fig. 8(b) shows the input image displayed on the OLED panel of a Samsung smart phone whose size and resolution are set to be 42mm and 1,280 × 800 pixels, respectively.

 

Fig. 8 A test input image: (a) A test image of ‘Flower’, (b) Input image displayed on the OLED Samsung panel.

Download Full Size | PDF

With the test image of Fig. 8, several display parameters of the conventional and proposed systems including the floating distance, floating-image size, viewing angle and light efficiency are measured and the results are comparatively discussed.

4.2.1 Volume size of the display system

As mentioned above, the volume size of the Fresnel lens-based floating display system directly depends on the distance between the FPD panel and Fresnel lens. Thus, it can be determined by the absolute optical path between the FPD panel and Fresnel lens. As seen in the optical setups of Fig. 7(a), the optical paths between the OLED panel of a Samsung smart phone and Fresnel lens of the conventional and proposed systems are initially set to be 180mm and 60mm, respectively, under the conditions that these systems satisfy all required display characteristics. Accordingly, the physical volume of the proposed system employing a new optical device of the P-OPC has been reduced by one third of that of the conventional system.

4.2.2 Floating distance and floating-image size

As seen in Table 3, the floating distances of the conventional and proposed systems are equally calculated to be 96.9mm by using Eqs. (1) and (13) because their object distances d_o and d'_o are initially set to be 180mm and 60mm, respectively. Figure 9 shows two kinds of the floating images captured from the conventional and proposed experimental systems of Fig. 7. One of them is the focused image right on the Fresnel-lens plane and the other is focused on the projected-image plane with a floating distance. For the visual convinience, the ‘Marker I’ and ‘Marker II’ are located on the Fresnel lens plane, which is assume to be 0mm from the Fresnel lens, and on the projected-image plane, which is assumed to be 96.9mm from the Fresnel lens, respectively. Here, if a CCD camera is focused on the Fresnel-lens plane, as seen in Figs. 9(a) and 9(c), only the ‘Marker I’ and Fresnel lens, which were located on the Fresnel lens plane, are focused, whereas the ‘Flower’ image and ‘Marker II’ are blurred becasue the ‘Flower’ image was floated into the air from the Fresnel lens and the ‘Marker II was located at the distance of 96.9mm from the Fresnel lens. On the other hand, if the CCD camera is focused on the projected-image plane, the floating ‘Flower’ image and ‘Marker II’ are focused, whereas the ‘Marker I’ and Fresnel lens are out of focused in both systems as seen in Figs. 9(b) and 9(d).

 

Fig. 9 Captured floating images from the conventional and proposed systems when (a) & (c) Focused on the Fresnel lens plane (0mm), and (b) & (d) Focused on the projected image plane (97mm), respectively.

Download Full Size | PDF

In the experiments, the floating distances of the ‘Flower’ images from the Fresnel lens are measured to be 97mm in both conventional and proposed experimental systems. According to Table 3, their calculated values are given by 96.9mm, so these differences between the calculated and measured values of the floating distances can be considered to be too tiny to be neglected. Thus, these experimental results confirm the feasibility of the proposed system in the practical application fields.

Furthermore, as seen in Table 3, in both conventional and proposed systems, the floating-image size is calculated to be 22.6mm for the input image whose size is 42mm. Thus, its magnification factor is calculated to be 0.538 according to Eq. (4) in both systems. In the experiments, however, the floating-image sizes of the conventional and proposed systems are measured to be 22.9mm and 23.0mm, respectively, as shown in Figs. 9(b) and 9(d). Thus, the magnification factors of those systems are estimated to be 0.545 and 0.548, respectively, which means that about 1.5% difference between the calculated and measured values of the magnification factors, on the average, has been occured. But, this difference seems to be too small to be neglected, thus these results also confim the feasibility of the proposed system in the practical application fields.

4.2.3 Image quality of the display system

Since the image quality is one of the important display characteristics, image qualities of those conventional and proposed systems are also tested and evaluated. Figure 10(a) shows four kinds of resolution testing patterns for analyzing the image qualities of the conventional and proposed display systems. Each test pattern consists of black and white stripe lines with different spatial frequencies. In the experiments, the stripe widths for each test pattern of Fig. 10(a-1)-10(a-4) are set to be 10, 8, 6 and 4 pixels, respectively. Figures 10(b) and 10(c) show the captured floating images from the conventional and proposed systems, respectively when the test patterns of Fig. 10(a) are used as the input images. As seen in Fig. 10(b-1)-10(b-3) and Fig. 10(c-1)-10(c-3), those stripe patterns look well-recognized in all regions of the floating images. However, for the cases of Fig. 10(b-4) and 10(c-4), small amounts of image distortions have been observed on the outside areas of the stripe patterns in both systems.

 

Fig. 10 (a) Resolution testing patterns with four different spatial frequencies, (b) Captured floating image patterns from the (b) Conventional system, and (c) Proposed system.

Download Full Size | PDF

In fact, as the spatial frequency of the test stripe pattern increases, image distortion happens to occur in its floating image due to the optical imperfection of the Fresnel lens. As seen in Fig. 10, however, a degree of image degradation in the floating image of the proposed system has been found to be almost same as that of the conventional system, which means the proposed system can project the input image into the free space just like the conventional system, while keeping almost the same image quality as of the conventional system even though the light efficiency of the proposed system has been much reduced, compared to that of the conventional system.

4.2.4 Viewing angle of the display system

According to Table 3, the viewing angle for the whole view (θ_wv) is calculated to be 40.9° based on Eq. (3). Figure 11 shows the ‘Flower’ images floated on the conventional and proposed systems and viewed at the different viewing angles of −20°, −10°, 0°, + 10° and + 20°. As seen in Fig. 11, the floating images can be seen in the calculated full-range of θ_wv in both systems. Furthemore, the relative positions of the floating images depending on the viewing angles have been changed in both methods. As seen in Fig. 11, yellow lines are added to each center of the images for visual convenience. On the viewing-angle direction of 0°, floating images are located at the centers in both systems. That is, yellow lines pass through each center of the floating images. Moreover, on the viewing-angle directions of + 10° and + 20°, the floating images start to move to the left from the center lines in proportion to the viewing-angle in both systems. On the other hand, on the viewing-angle directions of −20° and −10°, the floating images start to move to the right from the center lines depending on the viewing-angle in both systems.

 

Fig. 11 Floating ‘Flower’ images viewed at the different viewing angles in each of the (a) Conventional (Visualization 1) and (b) Proposed systems (Visualization 2).

Download Full Size | PDF

These experimental results confirm that the proposed system can project the input image into the free space just like the conventional system, and it also has the same viewing angle as of the conventional system. However, as seen in Fig. 11, some distortions in floating-images have been occurred due to the optical aberration of the Fresnel lens in both systems.

4.2.5 Light efficiency

As seen in Fig. 9, Fig. 10 and Fig. 11, the floating images of the conventional system look much brighter than those of the proposed system. In fact, the P-OPC employed in the proposed system allows one third reduction of the physical volume of the conventional system, but it simultaneously makes an additional light loss in the proposed system. As seen in Fig. 5, only 50% of the optical beam can pass through the half mirror in the ‘Path-1’. In addition, 50% of the optical beam can be also reflected by the half mirror in the ‘Path-3′. Thus, only 25% of the input beam can propagate to the Fresnel lens passing through the P-OPC. Therefore, the light efficiency of the proposed system employing the P-OPC would be reduced down to 25% compared to the conventional system. In practice, light absorptions in each optical element in the P-OPC may occur, so the light efficiency of the proposed system expects to be a little bit lower than 25% [21].

In the experiments, the luminances of the optical beams at each output of the conventional and proposd systems are measured to be 4.72cd/m² and 0.96cd/m², respectively, by using a luminance colorimeter (Model: BM-7A, Westar Display Technologies, Inc.) [23]. Thus, the light efficiency of the proposed system has been experimentally reduced down to 20.3%. compared to the conventional system. This discrepancy of 4.7% between the estimated and measured values of the light efficiency may result from the surface reflections, optical absorptions, and imperpections of the employed optical devices.

4.3 Fabricated display systems

Figures 12(a) and 12(b) show the fabricated prototypes of the conventional and proposed display systems. Figures 12(c) and 12(d) also shows the floating images displayed with these prototypes. As seen in Figs. 12(a) and 12(b), the physical depth lengths of the conventional and proposed systems (SD_conv and SD_prop) are measured to be 200mm and 85mm, respectively. In the experiments, the object distance (d_a) of the proposed system is estimated to be one third of the conventional system. However, for the prototype fabrication, they needs additional spaces for mounting the optical devices within the cases. That is, the conventional system requires more spaces for between the display panel and system case, the display panel and Fresnel lens, and the Fresnel lens and the system case, as well as for the thickness of the display panel, Fresnel lens and system case themselves. Likewise, the proposed system also requires more spaces for between the display panel and system case, the display panel and half mirror, the half mirror and reflective polarizer, the rflective polarizer and Fresnel lens, and the Fresnel lens and system case, as well as for the thickness of the display panel, half mirror, reflective polarizer, Fresnel lens and system case themselves. Thus, the physical depths of the fabricated prototypes of the conventional and proposed systems have been found to be increased to 200mm and 85mm from 180mm and 60mm of their experimental systems, respectively. It means that the prototype size of the proposed system has been reduced to 57.5% compared to the conventional prototype.

 

Fig. 12 Fabricated prototypes of the conventional and proposed systems: (a) Side view, (b) Front view, and (c) & (d) Floated images in each prototype.

Download Full Size | PDF

4.4 Discussions

Table 4 summarizes the experimental results for the conventional and proposed systems. As seen in Table 4, the object distance, representing the depth of the proposed system has been reduced to 33.3% and 42.5% on the optical setups and prototypes, respectively, compared to the conventional ones. On the other hand, the floating distance, magnification factor and viewing angle of the proposed system have been found to be almost same with those of the conventional systems, which can confirm the feasibility of the proposed system.

Table 4. Summarized Experimental Results

View Table | View all tables in this article

However, the light efficiency of the proposed method has been found to be reduced by 20.3% compared to the conventional system since a new optical device of the P-OPC has been employed in the proposed system. In the proposed system, most optical loss occur in the half mirror used in the P-OPC. Thus, for soving this low light-efficiency problem, a new type of the half mirror to function to transmit the left-circular polarized beam while reflecting the right-circular polarized beam, requires to be deveolped. With this optical device, the light efficiency of the proposed system expects to approach to almost 100%.

5. Conclusions

In this paper, we have proposed a new slim-type Fresnel lens-based electro-floating display system by using a polarization-based optical path controller (P-OPC), and its performances have been comparatively discussed with those of the conventional system. From the ray-optical analysis and optical experiments, it is shown that the depth of the proposed system can be shortened up to one third of the conventional system, which enables the same rate of reduction of the volume size of the proposed system. Successful experimental results with optical setups and fabricated prototypes confirm the feasibility of the proposed system in the practical application fields.