Abstract

3D displays have been developed to provide users with a realistic 3D experience. Although various studies have endeavored to establish design principles for 3D displays, a generalized optimized model does not exist in the literature thus far. These circumstances have led to the manufacture of independently qualified 3D products, but expanding these applications remains a challenge. In this paper, we suggest a measurement model and an optimization method for optimized 3D display design. The proposed optimization can be applied to rotatable 3D displays and various pixel structures. Our experimental results based on manufactured displays and simulations confirm the proposed theory of optimization model.

© 2017 Optical Society of America

1. Introduction

3D displays have been studied and developed for more than decades in research and industrial fields. Consequently, various 3D materials have been developed for different applications. Moreover, 3D optics and 3D quality characteristics are well defined to utilize various 3D materials. In the consumer electronics market, consumers can enjoy a 3D experience through 3D displays.

To manufacture realistic 3D displays, light sources and 3D optics have been developed for the path control of light. A high resolution liquid crystal display (LCD) panel and multi-projection array [1] are used as light sources to realize 3D images with high spatial and angular resolution. Full parallax 3D images have also been achieved using micro-lens [2]. To generate horizontal parallax with improved 3D resolution, the design of parallax barriers [3–5] and lenticular lenses [6–8] has been studied. 3D diffraction gratings have enabled wide angle 3D displays [9], and tensor displays can realize a high resolution [10].

Light ray designs have been studied to enhance the image quality of 3D displays. Alignment designs of 3D optics and the panel have been improved the 3D quality [11, 12]. Designs that yield reduced 3D crosstalk have been introduced in [13–15]. The uniform design [16, 17] can generate realistic 3D images. To reduce optical artifacts induced by the panel and 3D optics, slanted designs for avoiding moiré artifacts have been studied [18–21]. These previous studies have laid down the principles of individual 3D displays. However, they do not provide an optimized measurement model for global design.

3D display characteristics vary according to the intended use. For example, 3D displays for 3D digital signage and personal mobile devices should be different. Moreover, 3D characteristics have trade-off relationships. Increasing the 3D resolution decreases the angular resolution and depth expression. Increasing the viewing angle also decreased depth expression. A generalized model is required for modeling the various use cases of 3D displays. In the generalized model, the 3D characteristics, 3D resolution, viewing angle, and 3D image quality should be described according to different 3D design parameters.

For rotatable 3D displays that can operate in both the portrait and landscape mode, the requirements for 3D quality must be satisfied for both the portrait and landscape mode. Rotatable 3D displays provide reasonable 3D quality with a liquid-crystal lens array [22, 23], square lens [24], crosstalk reduced pentile display [25], and moiré free design [26]. Nanoveu Pte Ltd manufactures rotatable 3D displays with good quality [27]. These studies and products have laid down the principles of rotatable 3D displays; however, they do not provide the principles for rotatable 3D display design with different 3D design parameters.

In this paper, we introduce a measurement model and an optimization method for overall 3D design, which can be applied to rotatable 3D displays and various pixel structures. We propose 3D display design optimization by using the 3D quality measurement model. Further, we define an energy model for 3D light rays according to the 3D display design parameters, which yields light luminance uniformity, red-green-blue pixel color off balance, and 3D moiré artifacts from panel pixels and 3D optical components. We also suggest an lα map to design 3D displays that can operate in both the landscape and portrait mode, where l and α denote the lens pitch and slant angle of 3D optics, respectively.

2. 3D quality energy model

The reproduction of 3D light rays using a flat panel and 3D optics has several limitations. First, the number of light rays is much less than that in the real world. The light rays should be as uniformly distributed as possible in the spatial and angular domain. Second, 3D light rays are composed of primary colors: red, green, and blue. To generate natural color in 3D space, light rays of primary colors should be uniformly balanced. Finally, additional frequencies induced by pixels and 3D optics should be avoided. Figure 1 shows the artifacts caused by the lack of luminance uniformity, lack of color uniformity, and moiré artifacts. The 3D displays of Fig. 1, which contain artifacts, are experimental results of this study.

 

Fig. 1 Various 3D displays that have 3D artifacts caused by the (a) lack of luminance uniformity, (b) lack of color uniformity, and (c) moiré artifacts. Images of 3D displays were captured using a camera.

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To measure the above characteristics, we define a 3D quality energy model with a luminance uniformity term EL, color uniformity term EC, and moiré term EM. The overall 3D quality energy can be calculated by

E=λ1EL+λ2EC+λ3EM,
where λ1, λ2, and λ3 are weight parameters.

We introduce a light field representation and negentropy, which are used to measure luminance uniformity (EL) and color uniformity (EC).

  • Light field representation

    A 4D light field representation is a map that can be defined as

    L:Ω×ΠR(x,y,s,t)L(x,y,s,t).
    By using the above light field representation, a light ray that passes through two parallel planes, Ω and Π, can be represented by four parameters (x, y, s, t) [28,29], as shown in Fig. 2(a). In the 3D display case, the x axis is located on the 3D display, and the s axis is the user position plane. For horizontal parallax 3D displays, y and t can be ignored. In Fig. 2(b), p(x) is the location of a pixel on the x axis, and its s value can be calculated using the following equation:
    p(s)=fdfp(x)Dfu,
    where f is principal point length for the lenticular lens and effective thickness gap for the parallax barrier, D is the viewing distance, and u is the effective focal point of x [30]. The light ray of Fig. 2(b) is plotted by a line, since paraxial approximation is used. In the light field representation spatial and angular information are represented spontaneously since the x axis represents spatial information and the s axis represents angular information. Moreover, interpretation is simple since a lay represents as a dot in the light field representation.

  • Negentropy

    Negentropy (J) is the reverse of entropy and is defined in [31] as

    J=SmaxS,
    where S is entropy and Smax is the maximum value of the entropy. In the uniformity sense, a low negentropy indicates a uniform distribution.

 

Fig. 2 (a) Light field representation (b) light field representation in 3D displays.

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2.1. Luminance uniformity term

Sampled pixels of the panel are projected onto a certain view point through 3D optical components. When the sampled light rays are uniformly distributed, realistic 3D images are obtained. However, non-uniform sampled light rays yield structured artifacts. As shown in Fig. 1(a), light rays are not uniformly distributed; rather, they appear to be agglomerated and structured.

Light rays from one horizontal line have a uniform distribution since 3D optics such as the lenticular lens and parallax barriers are periodic. However, the uniformity of the light rays from several lines depends on the lens pitch and the slant angle of the design. Figure 3 shows light rays from a 3D display; the y value indicates the yth line on the panel and V indicates the viewing area on the x axis. Figure 3(a) and (d), and Fig. 3(b) and (e) show light rays from a horizontal line when y = 1 and y = 2, respectively. On comparing Figs. 3(a)–3(b) with Figs. 3(d)–3(e), it is difficult to distinguish whether they are uniformly distributed or not.

 

Fig. 3 Luminance uniformity: light rays and light field representation of 3D displays. (a), (b), and (c) are representations for a non-uniformly distributed 3D display; (d), (e), and (f) are representations for a uniformly distributed 3D display; (a) and (d) show light rays from one horizontal line when y = 1; (b) and (e) show light rays from one horizontal line when y = 2.

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Figure 3(c) and (f) show light rays both of y = 1 and y = 2 in the light field representation. The uniformity of luminance can be easily measured in the light field representation domain since light rays are represented by dots. If we compare Fig. 3(c) and (f), we can see that the light rays in Fig. 3(f) are more uniformly distributed than those in Fig. 3(c).

To measure luminance uniformity (EL) in the light field representation space, negentropy is used as a measure of distance to uniformity. The negentropy of luminance uniformity means that, if light rays are distributed with the same numbers in the blocks, then EL becomes 0. The large value of EL indicates that the distribution of light rays are far from a uniform distribution. The luminance values of (x, s) in the light field representation can be calculated using Eq. (3).

The negentropy of luminance uniformity can be defined using the concept of Eq. (4).

EL=PRlogPR+1NbPilogPi
PR=NLNb×Nb,
Pi=niNL,
where the first term of Eq. (5) represents Smax since the maximum entropy is attained when all the outcomes are equiprobable.

Here, Nb is the number of blocks, NL is the total number of light rays, and ni is the number of light rays in the ith block. In Fig. 3, the total number of light rays NL is 120, and Nb is 36 since the x and s axes are divided into six blocks. The value of EL for Fig. 3(c) is ten times that for Fig. 3(f).

2.2. Color uniformity term

Light rays originating from a panel comprise red, green, and blue light rays, unlike real light. The color representation of a 3D display depends on the design of 3D optics. Without the uniform distribution of red, green, and blue light rays to certain viewpoints, unwanted red, green, and blue color artifacts are induced, as shown in Fig. 1(b).

Figure 4 illustrates red, green, and blue light rays in the space and light field representation. Similar to luminance uniformity, color uniformity is not represented in the light ray plot, but it is clear in the light field representation.

 

Fig. 4 Color uniformity: light rays and light field representation of 3D displays. (a), (b), and (c) are representations for non-uniformly distributed color; (d), (e), and (f) are representations for uniformly distributed color; (a) and (d) show light rays from one horizontal line when y = 1; (b) and (e) show light rays from two horizontal lines when y = 1 and y = 2.

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Similar to the luminance uniformity term, color uniformity can be calculated in the light field representation on the basis of negentropy as follows:

EC=PCRlogPCRPCGlogPCGPCBlogPCB++1Nb(PiRlogPiR+PiGlogPiG+PiBlogPiB),
PCR=NLRNb×Nb,PCG=NLGNb×Nb,PCB=NLBNb×Nb,
PiR=niRnLR,PiG=niGNLG,PiB=niBNLB,
where Nb is the number of blocks, and NLR, NLG, and NLB are the total number of red, green, and blue light rays, respectively. niR, niG, and niB indicate the number of red, green, and blue light rays in the ith block, respectively.

2.3. Moiré term

3D moiré artifacts occurs when the frequencies of pixels and slanted lens generate additional visible frequencies. 3D design containing visible additional frequencies leads to the deterioration of 3D quality, as shown in Fig. 1(c). Moiré artifacts are modeled by a simplified spectral model based on Fourier analysis [32]. First, we define the model function of a 3D optical component (o(x, y)) and a pixel structure (p(x, y)). Then, a spectral model of the 3D optical components (O(u, v)) and the pixel structure (P(u, v)) is constructed by Fourier analysis. Finally, a moiré model (M(u, v)) is derived by the superposition of 3D optics and pixel structure.

To construct a spectral model, a lenticular lens, which is a 3D optical component with slant angle θ and lens pitch L can be approximated using a sinusoid function as

o(x,y)=0.5cos[2πfL(xcosθ+ysinθ)]+0.5,
where fL is Lcosθ and θ′ is (90° − θ). Its frequency response, O(u, v), is given by
O(fLcosθ,fLsinθ)=O(fLcosθ,fLsinθ)=14,O[0,0]=12.

The slit barrier or parallax barrier, which is a 3D optical component having a barrier aperture size of τL cos θ, can be approximated using a periodic rectangular function as

o(x,y)=Πo(τL(xcosθτL+ysinθ))={1,|xcosθ|τL20,|xcosθ|>τL2,L2<xL2
where Πo represents a periodic function with period Lcosθ and pulse width τLcosθ. Its frequency response is expressed as follows:
O(u,v)=τLfLsinc(τL(ucosθ+vsinθ)).

The pixel structure of the display panel with horizontal pixel pitch TH, vertical pixel pitch TV, horizontal pixel pitch without black matrix τH, and vertical pixel pitch without black matrix τV can be modeled by a periodic rectangular function as

p(x,y)=ΠH(xτH)×ΠV(yτV),
where
ΠH(xτH)={1,0,|x|τH2|x|>τH2,TH2<xTH21,0,|x|τV2|x|>τV2,TV2<xTV2.
Its frequency response is expressed as follows:
P(u,v)=τHTHsinc(τHu)τVTCsinc(τVv).
where ★ indicates convolution.

3D moiré can be modeled by

o(x,y)p(x,y)O(u,v)P(u,v)=M(u,v).

Among the frequencies induced by 3D optics and panel pixels, viewers can only conceive visible frequencies. Therefore, we define the cost for moiré with the visible frequency criterion as

CM=v1v2u1u2λ(u,v)M(u,v)dudv,
where λ(u, v) represents the optical modulation transfer function parameters of the human eye.

Figure 5 demonstrates the modeling of 3D optical components and panel pixels as well as their corresponding frequency response. The lenticular lens is modeled by a sinusoidal function and the pixel structure is modeled by a periodic rectangular function. The superposition of the optical component and pixel structure is analyzed by convolution in the frequency space. Owing to the superposition of 3D components and panel pixels, there exist additional frequencies (blue dots). The additional frequencies that can be perceived by viewers are in the visible frequency range, and are indicated by red dots.

 

Fig. 5 Spectral model for 3D display moiré based on Fourier analysis.

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3. 3D design optimization

To obtain an optimized design using a general model, the viewing angle and rays under a lens, which determine the 3D resolution [33], are important in addition to the 3D characteristics described in Sec. 2. The 3D characteristics can be modeled by two variables, lens pitch (L) and slanted angle (θ). Gap can be a constant value since it is usually fixed for a material. To design rotatable 3D displays, we convert the above parameters into l and α, where l is the number of pixels in the lens pitch L and α is tan θ.

If the slanted lens is designed for the landscape mode having lens pitch L and slant angle θ, then the lens pitch for the portrait mode can be expressed as

LP=Ltanθ=Lα.

The viewing angle for the landscape mode VL and portrait mode VP are

VL=2atanL2g,
VP=2atanL2gα,
where g is the gap between a panel and a 3D optical component. In the lα map, as shown in Fig. 6, VL and VP are expressed as a vertical line and slant line, respectively. To design a 3D display with
θ1<VL<θ2,θ3<VP<θ4
the lens pitch and slant angle can be determined in the valid region in Fig. 6.

 

Fig. 6 lα map for design of 3D displays.

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If the 3D quality energy model is represented using the lα map, Eq. (1) becomes

E=EL(l,α)+λ1EC(l,α)+λ2EM(l,α,p¯),
where λ1 and λ2 represent normalized parameters, such as max(EL)max(EC) and max(EL)max(EM), respectively.

In the lα map is a parameter that describes the pixel structure. Figure 7 illustrates an lα map, which is calculated using Eq. (5) for luminance uniformity, Eq. (8) for color uniformity, and Eq. (19) for moiré.

 

Fig. 7 lα map for luminance uniformity, color uniformity and 3D moiré.

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4. Experimental Results

To validate the 3D model optimization, we manufactured four 3D displays and conducted simulations. We also included previously manufactured 3D displays in our lα map. 3D displays of EyeFly3D [27] and Berkel [6] are indicated in Fig. 8. The figure shows that they have good luminance uniformity, color uniformity, and moiré characteristics.

 

Fig. 8 lα map for 3D display design optimization.

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Our desired viewing angles for landscape and portrait modes are

5°<VL<18°,10°<VP<25°.

Figure 8 shows the valid region, which satisfies the criterion in Eq. (25). The colored value of Fig. 8 represents the energy value obtained using Eq. (24), which includes luminance uniformity, color uniformity, and moiré. λ1 and λ2 values of Eq. (24) are 4.47 and 2783, respectively. In the valid region, which is the trapezoid region, we selected four design parameters based on the 3D quality energy value, which were used for three displays with good 3D quality and one display with bad 3D quality. We manufactured four 3D displays with a 31.5 inch 4K (3,840×2,160) LCD panel and parallax barrier. The 3D parameters for the four displays are listed in the Table 1.

Tables Icon

Table 1. 3D display parameters for design 1, 2, 3, and 4.

Figure 9 and 10 represent luminance uniformity and color uniformity in the light field representation, repectively. The number of light rays in a block in Fig. 9 is similar for all four displays but the number of red, green, and blue light rays in a block is not similar in the display with design 4, as shown in Fig. 10. Designs 1, 2, and 3 have color balanced characteristics; however, the color of design 4 is not balanced.

 

Fig. 9 Luminance uniformity in the light field representation of (a) design 1, (b) design 2, (c) design 3, and (d) design 4.

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Fig. 10 Color uniformity in the light field representation of (a) design 1, (b) design 2, (c) design 3, and (d) design 4.

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To verify moiré artifacts, we conducted image based simulation. Figure 11 demonstrates the simulation results for moiré artifacts. For this simulation, we generated an image superposing by the pixels and parallax barrier (top). Then, we performed a Fourier transform to obtain the frequency response. The circle indicates the visible frequency range and is located at a low frequency range since we cannot perceive high frequency components. The superposition of pixels and parallax barriers induces additional frequencies; however, the user is aware of additional frequencies in the visible frequency range only. As shown in Fig 11, we can verify that design 1, design 2, and design 3 are free of moiré artifacts; however, design 4 has moiré artifacts.

 

Fig. 11 3D moiré simulation: superposition of pixels and parallax barrier (top) and frequency response (bottom) for (a) design 1, (b) design 2, (c) design 3, and (d) design 4.

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Figure 12 shows the images of the four manufactured displays. The images were obtained using a camera. 3D images obtained using designs 1, 2, and 3 have good 3D quality without luminance uniformity, color uniformity, and moiré artifacts, as verified by the 3D quality energy model. However, the 3D image obtained using design 4 has strong color uniformity and moiré artifacts.

 

Fig. 12 Camera captured images from four manufactured rotatable 3D displays.

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Figure 13 shows the light profile of design 1. The crosstalk is 61.4% and 18.3% for the landscape and portrait mode, respectively. The full-width at half-maximum for the landscape and portrait mode is 2.21° and 3.49°, respectively.

 

Fig. 13 Crosstalk of design 1 for landscape and portrait modes.

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We conducted simulations on 3D quality to verify the lα map modeling. For the simulations, the full-width at half-maximum (WH) of each light ray is assumed to be

WH=Vl,
where V is the viewing angle.

Figure 14 shows simulation results for various l and α values. The simulation results confirm the luminance uniformity and color uniformity measurable model. Figure 15 shows simulation results for various l and α values.

 

Fig. 14 Simulated results for luminance and color uniformity term.

1st line: designs 1, 2, 3, and 4 (from left to right)

2nd line: Good luminance and color uniformity, (l, α) = (1.3,0.2), (1.7,1.9), (2.2,0.9), and (2.7,1.2)

3rd line: Bad luminance uniformity, (l, α) = (1.3,0.3), (1.7,0.7), (2.0,1.7), and (2.9,1.6)

4th line: Bad color uniformity, (l, α) = (1.9,0.9), (2.0,1.0), (2.2,1.1), and (2.9,1.9)

5th line: Bad luminance and color uniformity, (l, α) = (1.0,1.5), (1.3,1.3), (1.5,1.5), and (2.0,0.5)

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Fig. 15 Simulated results for moiré term.

1st line: With 3D moiré artifacts, (l, α) = (1.0,1.0), (1.0,0.1), (1.4,0.5), and (2.0,1.0)

2nd line: Without 3D moiré artifacts, (l, α) = (1.0,1.5), (1.2,0,2) [6], (1.5,1.5), and (1.6,0.3) [27].

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5. Conclusions

We constructed a measurement model for the design optimization of rotatable 3D displays. We defined a 3D quality energy model with luminance uniformity, color uniformity, and moiré terms. Luminance uniformity and color uniformity were measured in the light field representation domain with the negentropy value. 3D moiré was measured using a spectral model based on Fourier analysis. Then, we ascertained the 3D moiré artifacts by using image based simulation. We also plotted luminance uniformity, color uniformity, and moiré energy on the lα map. The viewing angles and 3D resolutions for landscape and portrait modes were represented on the lα map. By using the lα map, the optimized design for a rotatable 3D display could be determined.

In this paper, we did not consider the characteristics of 3D optics such as aberrations of the lenticular lens and aperture size of 3D optical films. Moreover, we did not analyze 3D qualities that have trade-off relationships among each other, such as crosstalk, 3D spatial resolution, and depth expression. Increasing the l value increases the angular resolution and crosstalk but decreases the 3D spatial resolution. In future research work, we will consider the characteristics of 3D optics and construct a model to represent these mutually dependent 3D quality characteristics on the lα map. Moreover, we will consider optimum aperture size of barriers on the lα map to reduce crosstalk.

Acknowledgment

The first author wishes to thank Hyun Sung Chang and Byongmin Kang for useful discussions and comments.

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  1. Y. Takaki and N. Nago, “Multi-projection of lenticular displays to construct a 256-view super multi-view display,” Opt. Express 18(9), 8824–8835 (2010).
    [Crossref] [PubMed]
  2. R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. of the IEEE 97(6), 1067–1077 (2009).
    [Crossref]
  3. S.-K. Kim, K.-H. Yoon, S. K. Yoon, and H. Ju, “Parallax barrier engineering for image quality improvement in an autostereoscopic 3D display,” Opt. Express 23(10), 13230–13244 (2015).
    [Crossref] [PubMed]
  4. H. J. Lee, H. Nam, J. D. Lee, H. W. Jang, M. S. Song, B. S. Kim, J. S. Gu, C. Y. Park, and K. H. Choi, “A high resolution autostereoscopic display employing a time division parallax barrier,” in SID Symposium Digest vol. 37, pp. 81–84 (2006).
  5. W. Mphepo, Y.-P. Huang, and H.-P. D. Shieh, “Enhancing the brightness of parallax barrier based 3D flat panel mobile displays without compromising power consumption,” J. of Displ. Technology 6(2), 60–64 (2010).
    [Crossref]
  6. C. Van Berkel, “Image preparation for 3D LCD,” Proc. SPIE 3639, 84–91 (1999).
    [Crossref]
  7. R. B. Johnson and G. A. Jacobsen, “Advances in lenticular lens arrays for visual display,” Proc. SPIE 5874, 587406 (2005).
    [Crossref]
  8. V. Urruchi Del Pozo, J. Algorri Genaro, J. Sánchez-Pena, M. Geday, X. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electronics Review 20(3), 260–266 (2012).
    [Crossref]
  9. D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
    [Crossref] [PubMed]
  10. G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Transactions Graphics 31, 1–11 (2012).
    [Crossref]
  11. C. Van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE 3012, 179–186 (1997).
    [Crossref]
  12. Q.-H. Wang, X.-F. Li, L. Zhou, A.-H. Wang, and D.-H. Li, “Cross-talk reduction by correcting the subpixel position in a multiview autostereoscopic three-dimensional display based on a lenticular sheet,” Appl. Opt. 50(7), B1–B5 (2011).
    [Crossref] [PubMed]
  13. C. Lee, G. Seo, J. Lee, T.-h. Han, and J. G. Park, “Auto-stereoscopic 3D displays with reduced crosstalk,” Opt. Express 19(24), 24762–24774 (2011).
    [Crossref] [PubMed]
  14. J. Konrad, B. Lacotte, and E. Dubois, “Cancellation of image crosstalk in time-sequential displays of stereoscopic video,” IEEE Trans. Image Process. 9(5), 897–908 (2000).
    [Crossref]
  15. P. J. Seuntiëns, L. M. Meesters, and W. A. IJsselsteijn, “The negentropy principle of informationitle>Perceptual attributes of crosstalk in 3D images,” Displays 26(4), 177–183 (2005).
    [Crossref]
  16. R. Fukushima, K. Taira, T. Saishu, Y. Momonoi, M. Kashiwagi, and Y. Hirayama, “Effect of light ray overlap between neighboring parallax images in autostereoscopic 3D displays,” Proc. SPIE 7237, 72370 (2009).
    [Crossref]
  17. M. Salmimaa and T. Järvenpää, “3-D crosstalk and luminance uniformity from angular luminance profiles of multiview autostereoscopic 3-D displays,” J. Soc. Inf. Disp. 16(10), 1033–1040 (2008).
    [Crossref]
  18. V. Saveljev and S.-K. Kim, “Simulation and measurement of moiré patterns at finite distance,” Opt. Express 20(3), 2163–2177 (2012).
    [Crossref] [PubMed]
  19. K. Oku, Y. Tomizuka, and Y. Tanaka, “Analysis and reduction of moiré in two-layered 3D display,” in SID Symposium Digest vol. 38, pp. 437–440 (2007).
  20. Y. Kim, G. Park, J.-H. Jung, J. Kim, and B. Lee, “Color moiré pattern simulation and analysis in three-dimensional integral imaging for finding the moiré-reduced tilted angle of a lens array,” Appl. Opt. 48(11), 2178–2187 (2009).
    [Crossref] [PubMed]
  21. V. V. Saveljev, J.-Y. Son, B. Javidi, S.-K. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. of Displ. Technology 1(2), 347 (2005).
    [Crossref]
  22. Y.-C. Chang, T.-H. Jen, C.-H. Ting, and Y.-P. Huang, “High-resistance liquid-crystal lens array for rotatable 2D/3D autostereoscopic display,” Opt. Express 22(3), 2714–2724 (2014).
    [Crossref] [PubMed]
  23. K. Shigemura, J. Matsushima, Y. Ibata, K. Masumura, T. Asai, and T. Sato, “a two-way multiview 3D display using liquid crystal lens,” SPIE Newsroom (2016).
  24. C.-T. Chang, W.-L. Chen, C.-H. Shih, and W.-M. Huang, “Landscape/portrait dual mode lens type 3D display using a 2d lens array,” in SID Symposium Digest vol. 43, pp. 308–311 (2012).
  25. J. Kim, C.-K. Lee, Y. Jeong, C. Jang, J.-Y. Hong, W. Lee, Y.-C. Shin, J.-H. Yoon, and B. Lee, “Crosstalk-reduced dual-mode mobile 3D display,” Journal of D. Technology 11(1), 97–103 (2015).
    [Crossref]
  26. K. Choi, Y. J. Jeong, B. Kang, J.-H. Lee, Y. Choi, and D. Nam, “Design and implementation of landscape/portrait mode convertible light-field 3D display,” in SID Symposium Digest vol. 47, pp. 986–989 (2016).
  27. “EyeFly3D – glasses-free 3D,” [Online]. Available: http://www.eyefly3d.com/ .
  28. M. Levoy and P. Hanrahan, “Light field rendering,” in SIGGRAPH (1996), pp. 31–41.
  29. S. Gortler, R. Grzeszczuk, R. Szeliski, and M. Cohen, “The lumigraph,” in SIGGRAPH (1996), pp. 43–54.
  30. Y. J. Jeong, H. S. Chang, D. Nam, and C.-C. J. Kuo, “Direct light field rendering without 2D image generation,” J. Soc. Inf. Disp. 24(11), 686–695 (2017).
    [Crossref]
  31. L. Brillouin, “The negentropy principle of information,” J. Appl. Phys. 24, 1152–1163 (1953).
    [Crossref]
  32. I. Amidror, R. D. Hersch, and V. Ostromoukhov, “Spectral analysis and minimization of moiré patterns in color separation,” J. Electron. Imaging 3(3), 295–317 (1994).
    [Crossref]
  33. L. Hill and A. Jacobs, “3-D liquid crystal displays and their applications,” Proc. of the IEEE 94(3), 575–590 (2006).
    [Crossref]

2017 (1)

Y. J. Jeong, H. S. Chang, D. Nam, and C.-C. J. Kuo, “Direct light field rendering without 2D image generation,” J. Soc. Inf. Disp. 24(11), 686–695 (2017).
[Crossref]

2015 (2)

J. Kim, C.-K. Lee, Y. Jeong, C. Jang, J.-Y. Hong, W. Lee, Y.-C. Shin, J.-H. Yoon, and B. Lee, “Crosstalk-reduced dual-mode mobile 3D display,” Journal of D. Technology 11(1), 97–103 (2015).
[Crossref]

S.-K. Kim, K.-H. Yoon, S. K. Yoon, and H. Ju, “Parallax barrier engineering for image quality improvement in an autostereoscopic 3D display,” Opt. Express 23(10), 13230–13244 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (1)

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

2012 (3)

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Transactions Graphics 31, 1–11 (2012).
[Crossref]

V. Urruchi Del Pozo, J. Algorri Genaro, J. Sánchez-Pena, M. Geday, X. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electronics Review 20(3), 260–266 (2012).
[Crossref]

V. Saveljev and S.-K. Kim, “Simulation and measurement of moiré patterns at finite distance,” Opt. Express 20(3), 2163–2177 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (2)

W. Mphepo, Y.-P. Huang, and H.-P. D. Shieh, “Enhancing the brightness of parallax barrier based 3D flat panel mobile displays without compromising power consumption,” J. of Displ. Technology 6(2), 60–64 (2010).
[Crossref]

Y. Takaki and N. Nago, “Multi-projection of lenticular displays to construct a 256-view super multi-view display,” Opt. Express 18(9), 8824–8835 (2010).
[Crossref] [PubMed]

2009 (3)

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. of the IEEE 97(6), 1067–1077 (2009).
[Crossref]

R. Fukushima, K. Taira, T. Saishu, Y. Momonoi, M. Kashiwagi, and Y. Hirayama, “Effect of light ray overlap between neighboring parallax images in autostereoscopic 3D displays,” Proc. SPIE 7237, 72370 (2009).
[Crossref]

Y. Kim, G. Park, J.-H. Jung, J. Kim, and B. Lee, “Color moiré pattern simulation and analysis in three-dimensional integral imaging for finding the moiré-reduced tilted angle of a lens array,” Appl. Opt. 48(11), 2178–2187 (2009).
[Crossref] [PubMed]

2008 (1)

M. Salmimaa and T. Järvenpää, “3-D crosstalk and luminance uniformity from angular luminance profiles of multiview autostereoscopic 3-D displays,” J. Soc. Inf. Disp. 16(10), 1033–1040 (2008).
[Crossref]

2006 (1)

L. Hill and A. Jacobs, “3-D liquid crystal displays and their applications,” Proc. of the IEEE 94(3), 575–590 (2006).
[Crossref]

2005 (3)

V. V. Saveljev, J.-Y. Son, B. Javidi, S.-K. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. of Displ. Technology 1(2), 347 (2005).
[Crossref]

P. J. Seuntiëns, L. M. Meesters, and W. A. IJsselsteijn, “The negentropy principle of informationitle>Perceptual attributes of crosstalk in 3D images,” Displays 26(4), 177–183 (2005).
[Crossref]

R. B. Johnson and G. A. Jacobsen, “Advances in lenticular lens arrays for visual display,” Proc. SPIE 5874, 587406 (2005).
[Crossref]

2000 (1)

J. Konrad, B. Lacotte, and E. Dubois, “Cancellation of image crosstalk in time-sequential displays of stereoscopic video,” IEEE Trans. Image Process. 9(5), 897–908 (2000).
[Crossref]

1999 (1)

C. Van Berkel, “Image preparation for 3D LCD,” Proc. SPIE 3639, 84–91 (1999).
[Crossref]

1997 (1)

C. Van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE 3012, 179–186 (1997).
[Crossref]

1994 (1)

I. Amidror, R. D. Hersch, and V. Ostromoukhov, “Spectral analysis and minimization of moiré patterns in color separation,” J. Electron. Imaging 3(3), 295–317 (1994).
[Crossref]

1953 (1)

L. Brillouin, “The negentropy principle of information,” J. Appl. Phys. 24, 1152–1163 (1953).
[Crossref]

Algorri Genaro, J.

V. Urruchi Del Pozo, J. Algorri Genaro, J. Sánchez-Pena, M. Geday, X. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electronics Review 20(3), 260–266 (2012).
[Crossref]

Amidror, I.

I. Amidror, R. D. Hersch, and V. Ostromoukhov, “Spectral analysis and minimization of moiré patterns in color separation,” J. Electron. Imaging 3(3), 295–317 (1994).
[Crossref]

Arregui, X.

V. Urruchi Del Pozo, J. Algorri Genaro, J. Sánchez-Pena, M. Geday, X. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electronics Review 20(3), 260–266 (2012).
[Crossref]

Asai, T.

K. Shigemura, J. Matsushima, Y. Ibata, K. Masumura, T. Asai, and T. Sato, “a two-way multiview 3D display using liquid crystal lens,” SPIE Newsroom (2016).

Beausoleil, R. G.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Bennis, N.

V. Urruchi Del Pozo, J. Algorri Genaro, J. Sánchez-Pena, M. Geday, X. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electronics Review 20(3), 260–266 (2012).
[Crossref]

Brillouin, L.

L. Brillouin, “The negentropy principle of information,” J. Appl. Phys. 24, 1152–1163 (1953).
[Crossref]

Brug, J.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Chang, C.-T.

C.-T. Chang, W.-L. Chen, C.-H. Shih, and W.-M. Huang, “Landscape/portrait dual mode lens type 3D display using a 2d lens array,” in SID Symposium Digest vol. 43, pp. 308–311 (2012).

Chang, H. S.

Y. J. Jeong, H. S. Chang, D. Nam, and C.-C. J. Kuo, “Direct light field rendering without 2D image generation,” J. Soc. Inf. Disp. 24(11), 686–695 (2017).
[Crossref]

Chang, Y.-C.

Chen, W.-L.

C.-T. Chang, W.-L. Chen, C.-H. Shih, and W.-M. Huang, “Landscape/portrait dual mode lens type 3D display using a 2d lens array,” in SID Symposium Digest vol. 43, pp. 308–311 (2012).

Choi, K.

K. Choi, Y. J. Jeong, B. Kang, J.-H. Lee, Y. Choi, and D. Nam, “Design and implementation of landscape/portrait mode convertible light-field 3D display,” in SID Symposium Digest vol. 47, pp. 986–989 (2016).

Choi, K. H.

H. J. Lee, H. Nam, J. D. Lee, H. W. Jang, M. S. Song, B. S. Kim, J. S. Gu, C. Y. Park, and K. H. Choi, “A high resolution autostereoscopic display employing a time division parallax barrier,” in SID Symposium Digest vol. 37, pp. 81–84 (2006).

Choi, Y.

K. Choi, Y. J. Jeong, B. Kang, J.-H. Lee, Y. Choi, and D. Nam, “Design and implementation of landscape/portrait mode convertible light-field 3D display,” in SID Symposium Digest vol. 47, pp. 986–989 (2016).

Clarke, J. A.

C. Van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE 3012, 179–186 (1997).
[Crossref]

Cohen, M.

S. Gortler, R. Grzeszczuk, R. Szeliski, and M. Cohen, “The lumigraph,” in SIGGRAPH (1996), pp. 43–54.

Dubois, E.

J. Konrad, B. Lacotte, and E. Dubois, “Cancellation of image crosstalk in time-sequential displays of stereoscopic video,” IEEE Trans. Image Process. 9(5), 897–908 (2000).
[Crossref]

Fattal, D.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Fiorentino, M.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Fukushima, R.

R. Fukushima, K. Taira, T. Saishu, Y. Momonoi, M. Kashiwagi, and Y. Hirayama, “Effect of light ray overlap between neighboring parallax images in autostereoscopic 3D displays,” Proc. SPIE 7237, 72370 (2009).
[Crossref]

Geday, M.

V. Urruchi Del Pozo, J. Algorri Genaro, J. Sánchez-Pena, M. Geday, X. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electronics Review 20(3), 260–266 (2012).
[Crossref]

Gortler, S.

S. Gortler, R. Grzeszczuk, R. Szeliski, and M. Cohen, “The lumigraph,” in SIGGRAPH (1996), pp. 43–54.

Grzeszczuk, R.

S. Gortler, R. Grzeszczuk, R. Szeliski, and M. Cohen, “The lumigraph,” in SIGGRAPH (1996), pp. 43–54.

Gu, J. S.

H. J. Lee, H. Nam, J. D. Lee, H. W. Jang, M. S. Song, B. S. Kim, J. S. Gu, C. Y. Park, and K. H. Choi, “A high resolution autostereoscopic display employing a time division parallax barrier,” in SID Symposium Digest vol. 37, pp. 81–84 (2006).

Han, T.-h.

Hanrahan, P.

M. Levoy and P. Hanrahan, “Light field rendering,” in SIGGRAPH (1996), pp. 31–41.

Hersch, R. D.

I. Amidror, R. D. Hersch, and V. Ostromoukhov, “Spectral analysis and minimization of moiré patterns in color separation,” J. Electron. Imaging 3(3), 295–317 (1994).
[Crossref]

Hill, L.

L. Hill and A. Jacobs, “3-D liquid crystal displays and their applications,” Proc. of the IEEE 94(3), 575–590 (2006).
[Crossref]

Hirayama, Y.

R. Fukushima, K. Taira, T. Saishu, Y. Momonoi, M. Kashiwagi, and Y. Hirayama, “Effect of light ray overlap between neighboring parallax images in autostereoscopic 3D displays,” Proc. SPIE 7237, 72370 (2009).
[Crossref]

Hirsch, M.

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Transactions Graphics 31, 1–11 (2012).
[Crossref]

Hong, J.-Y.

J. Kim, C.-K. Lee, Y. Jeong, C. Jang, J.-Y. Hong, W. Lee, Y.-C. Shin, J.-H. Yoon, and B. Lee, “Crosstalk-reduced dual-mode mobile 3D display,” Journal of D. Technology 11(1), 97–103 (2015).
[Crossref]

Huang, W.-M.

C.-T. Chang, W.-L. Chen, C.-H. Shih, and W.-M. Huang, “Landscape/portrait dual mode lens type 3D display using a 2d lens array,” in SID Symposium Digest vol. 43, pp. 308–311 (2012).

Huang, Y.-P.

Y.-C. Chang, T.-H. Jen, C.-H. Ting, and Y.-P. Huang, “High-resistance liquid-crystal lens array for rotatable 2D/3D autostereoscopic display,” Opt. Express 22(3), 2714–2724 (2014).
[Crossref] [PubMed]

W. Mphepo, Y.-P. Huang, and H.-P. D. Shieh, “Enhancing the brightness of parallax barrier based 3D flat panel mobile displays without compromising power consumption,” J. of Displ. Technology 6(2), 60–64 (2010).
[Crossref]

Ibata, Y.

K. Shigemura, J. Matsushima, Y. Ibata, K. Masumura, T. Asai, and T. Sato, “a two-way multiview 3D display using liquid crystal lens,” SPIE Newsroom (2016).

IJsselsteijn, W. A.

P. J. Seuntiëns, L. M. Meesters, and W. A. IJsselsteijn, “The negentropy principle of informationitle>Perceptual attributes of crosstalk in 3D images,” Displays 26(4), 177–183 (2005).
[Crossref]

Jacobs, A.

L. Hill and A. Jacobs, “3-D liquid crystal displays and their applications,” Proc. of the IEEE 94(3), 575–590 (2006).
[Crossref]

Jacobsen, G. A.

R. B. Johnson and G. A. Jacobsen, “Advances in lenticular lens arrays for visual display,” Proc. SPIE 5874, 587406 (2005).
[Crossref]

Jang, C.

J. Kim, C.-K. Lee, Y. Jeong, C. Jang, J.-Y. Hong, W. Lee, Y.-C. Shin, J.-H. Yoon, and B. Lee, “Crosstalk-reduced dual-mode mobile 3D display,” Journal of D. Technology 11(1), 97–103 (2015).
[Crossref]

Jang, H. W.

H. J. Lee, H. Nam, J. D. Lee, H. W. Jang, M. S. Song, B. S. Kim, J. S. Gu, C. Y. Park, and K. H. Choi, “A high resolution autostereoscopic display employing a time division parallax barrier,” in SID Symposium Digest vol. 37, pp. 81–84 (2006).

Järvenpää, T.

M. Salmimaa and T. Järvenpää, “3-D crosstalk and luminance uniformity from angular luminance profiles of multiview autostereoscopic 3-D displays,” J. Soc. Inf. Disp. 16(10), 1033–1040 (2008).
[Crossref]

Javidi, B.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. of the IEEE 97(6), 1067–1077 (2009).
[Crossref]

V. V. Saveljev, J.-Y. Son, B. Javidi, S.-K. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. of Displ. Technology 1(2), 347 (2005).
[Crossref]

Jen, T.-H.

Jeong, Y.

J. Kim, C.-K. Lee, Y. Jeong, C. Jang, J.-Y. Hong, W. Lee, Y.-C. Shin, J.-H. Yoon, and B. Lee, “Crosstalk-reduced dual-mode mobile 3D display,” Journal of D. Technology 11(1), 97–103 (2015).
[Crossref]

Jeong, Y. J.

Y. J. Jeong, H. S. Chang, D. Nam, and C.-C. J. Kuo, “Direct light field rendering without 2D image generation,” J. Soc. Inf. Disp. 24(11), 686–695 (2017).
[Crossref]

K. Choi, Y. J. Jeong, B. Kang, J.-H. Lee, Y. Choi, and D. Nam, “Design and implementation of landscape/portrait mode convertible light-field 3D display,” in SID Symposium Digest vol. 47, pp. 986–989 (2016).

Johnson, R. B.

R. B. Johnson and G. A. Jacobsen, “Advances in lenticular lens arrays for visual display,” Proc. SPIE 5874, 587406 (2005).
[Crossref]

Ju, H.

Jung, J.-H.

Kang, B.

K. Choi, Y. J. Jeong, B. Kang, J.-H. Lee, Y. Choi, and D. Nam, “Design and implementation of landscape/portrait mode convertible light-field 3D display,” in SID Symposium Digest vol. 47, pp. 986–989 (2016).

Kashiwagi, M.

R. Fukushima, K. Taira, T. Saishu, Y. Momonoi, M. Kashiwagi, and Y. Hirayama, “Effect of light ray overlap between neighboring parallax images in autostereoscopic 3D displays,” Proc. SPIE 7237, 72370 (2009).
[Crossref]

Kim, B. S.

H. J. Lee, H. Nam, J. D. Lee, H. W. Jang, M. S. Song, B. S. Kim, J. S. Gu, C. Y. Park, and K. H. Choi, “A high resolution autostereoscopic display employing a time division parallax barrier,” in SID Symposium Digest vol. 37, pp. 81–84 (2006).

Kim, D.-S.

V. V. Saveljev, J.-Y. Son, B. Javidi, S.-K. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. of Displ. Technology 1(2), 347 (2005).
[Crossref]

Kim, J.

J. Kim, C.-K. Lee, Y. Jeong, C. Jang, J.-Y. Hong, W. Lee, Y.-C. Shin, J.-H. Yoon, and B. Lee, “Crosstalk-reduced dual-mode mobile 3D display,” Journal of D. Technology 11(1), 97–103 (2015).
[Crossref]

Y. Kim, G. Park, J.-H. Jung, J. Kim, and B. Lee, “Color moiré pattern simulation and analysis in three-dimensional integral imaging for finding the moiré-reduced tilted angle of a lens array,” Appl. Opt. 48(11), 2178–2187 (2009).
[Crossref] [PubMed]

Kim, S.-K.

Kim, Y.

Konrad, J.

J. Konrad, B. Lacotte, and E. Dubois, “Cancellation of image crosstalk in time-sequential displays of stereoscopic video,” IEEE Trans. Image Process. 9(5), 897–908 (2000).
[Crossref]

Kuo, C.-C. J.

Y. J. Jeong, H. S. Chang, D. Nam, and C.-C. J. Kuo, “Direct light field rendering without 2D image generation,” J. Soc. Inf. Disp. 24(11), 686–695 (2017).
[Crossref]

Lacotte, B.

J. Konrad, B. Lacotte, and E. Dubois, “Cancellation of image crosstalk in time-sequential displays of stereoscopic video,” IEEE Trans. Image Process. 9(5), 897–908 (2000).
[Crossref]

Lanman, D.

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Transactions Graphics 31, 1–11 (2012).
[Crossref]

Lee, B.

J. Kim, C.-K. Lee, Y. Jeong, C. Jang, J.-Y. Hong, W. Lee, Y.-C. Shin, J.-H. Yoon, and B. Lee, “Crosstalk-reduced dual-mode mobile 3D display,” Journal of D. Technology 11(1), 97–103 (2015).
[Crossref]

Y. Kim, G. Park, J.-H. Jung, J. Kim, and B. Lee, “Color moiré pattern simulation and analysis in three-dimensional integral imaging for finding the moiré-reduced tilted angle of a lens array,” Appl. Opt. 48(11), 2178–2187 (2009).
[Crossref] [PubMed]

Lee, C.

Lee, C.-K.

J. Kim, C.-K. Lee, Y. Jeong, C. Jang, J.-Y. Hong, W. Lee, Y.-C. Shin, J.-H. Yoon, and B. Lee, “Crosstalk-reduced dual-mode mobile 3D display,” Journal of D. Technology 11(1), 97–103 (2015).
[Crossref]

Lee, H. J.

H. J. Lee, H. Nam, J. D. Lee, H. W. Jang, M. S. Song, B. S. Kim, J. S. Gu, C. Y. Park, and K. H. Choi, “A high resolution autostereoscopic display employing a time division parallax barrier,” in SID Symposium Digest vol. 37, pp. 81–84 (2006).

Lee, J.

Lee, J. D.

H. J. Lee, H. Nam, J. D. Lee, H. W. Jang, M. S. Song, B. S. Kim, J. S. Gu, C. Y. Park, and K. H. Choi, “A high resolution autostereoscopic display employing a time division parallax barrier,” in SID Symposium Digest vol. 37, pp. 81–84 (2006).

Lee, J.-H.

K. Choi, Y. J. Jeong, B. Kang, J.-H. Lee, Y. Choi, and D. Nam, “Design and implementation of landscape/portrait mode convertible light-field 3D display,” in SID Symposium Digest vol. 47, pp. 986–989 (2016).

Lee, W.

J. Kim, C.-K. Lee, Y. Jeong, C. Jang, J.-Y. Hong, W. Lee, Y.-C. Shin, J.-H. Yoon, and B. Lee, “Crosstalk-reduced dual-mode mobile 3D display,” Journal of D. Technology 11(1), 97–103 (2015).
[Crossref]

Levoy, M.

M. Levoy and P. Hanrahan, “Light field rendering,” in SIGGRAPH (1996), pp. 31–41.

Li, D.-H.

Li, X.-F.

Martinez-Corral, M.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. of the IEEE 97(6), 1067–1077 (2009).
[Crossref]

Martinez-Cuenca, R.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. of the IEEE 97(6), 1067–1077 (2009).
[Crossref]

Masumura, K.

K. Shigemura, J. Matsushima, Y. Ibata, K. Masumura, T. Asai, and T. Sato, “a two-way multiview 3D display using liquid crystal lens,” SPIE Newsroom (2016).

Matsushima, J.

K. Shigemura, J. Matsushima, Y. Ibata, K. Masumura, T. Asai, and T. Sato, “a two-way multiview 3D display using liquid crystal lens,” SPIE Newsroom (2016).

Meesters, L. M.

P. J. Seuntiëns, L. M. Meesters, and W. A. IJsselsteijn, “The negentropy principle of informationitle>Perceptual attributes of crosstalk in 3D images,” Displays 26(4), 177–183 (2005).
[Crossref]

Momonoi, Y.

R. Fukushima, K. Taira, T. Saishu, Y. Momonoi, M. Kashiwagi, and Y. Hirayama, “Effect of light ray overlap between neighboring parallax images in autostereoscopic 3D displays,” Proc. SPIE 7237, 72370 (2009).
[Crossref]

Mphepo, W.

W. Mphepo, Y.-P. Huang, and H.-P. D. Shieh, “Enhancing the brightness of parallax barrier based 3D flat panel mobile displays without compromising power consumption,” J. of Displ. Technology 6(2), 60–64 (2010).
[Crossref]

Nago, N.

Nam, D.

Y. J. Jeong, H. S. Chang, D. Nam, and C.-C. J. Kuo, “Direct light field rendering without 2D image generation,” J. Soc. Inf. Disp. 24(11), 686–695 (2017).
[Crossref]

K. Choi, Y. J. Jeong, B. Kang, J.-H. Lee, Y. Choi, and D. Nam, “Design and implementation of landscape/portrait mode convertible light-field 3D display,” in SID Symposium Digest vol. 47, pp. 986–989 (2016).

Nam, H.

H. J. Lee, H. Nam, J. D. Lee, H. W. Jang, M. S. Song, B. S. Kim, J. S. Gu, C. Y. Park, and K. H. Choi, “A high resolution autostereoscopic display employing a time division parallax barrier,” in SID Symposium Digest vol. 37, pp. 81–84 (2006).

Oku, K.

K. Oku, Y. Tomizuka, and Y. Tanaka, “Analysis and reduction of moiré in two-layered 3D display,” in SID Symposium Digest vol. 38, pp. 437–440 (2007).

Ostromoukhov, V.

I. Amidror, R. D. Hersch, and V. Ostromoukhov, “Spectral analysis and minimization of moiré patterns in color separation,” J. Electron. Imaging 3(3), 295–317 (1994).
[Crossref]

Park, C. Y.

H. J. Lee, H. Nam, J. D. Lee, H. W. Jang, M. S. Song, B. S. Kim, J. S. Gu, C. Y. Park, and K. H. Choi, “A high resolution autostereoscopic display employing a time division parallax barrier,” in SID Symposium Digest vol. 37, pp. 81–84 (2006).

Park, G.

Park, J. G.

Peng, Z.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Raskar, R.

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Transactions Graphics 31, 1–11 (2012).
[Crossref]

Saavedra, G.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. of the IEEE 97(6), 1067–1077 (2009).
[Crossref]

Saishu, T.

R. Fukushima, K. Taira, T. Saishu, Y. Momonoi, M. Kashiwagi, and Y. Hirayama, “Effect of light ray overlap between neighboring parallax images in autostereoscopic 3D displays,” Proc. SPIE 7237, 72370 (2009).
[Crossref]

Salmimaa, M.

M. Salmimaa and T. Järvenpää, “3-D crosstalk and luminance uniformity from angular luminance profiles of multiview autostereoscopic 3-D displays,” J. Soc. Inf. Disp. 16(10), 1033–1040 (2008).
[Crossref]

Sánchez-Pena, J.

V. Urruchi Del Pozo, J. Algorri Genaro, J. Sánchez-Pena, M. Geday, X. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electronics Review 20(3), 260–266 (2012).
[Crossref]

Sato, T.

K. Shigemura, J. Matsushima, Y. Ibata, K. Masumura, T. Asai, and T. Sato, “a two-way multiview 3D display using liquid crystal lens,” SPIE Newsroom (2016).

Saveljev, V.

Saveljev, V. V.

V. V. Saveljev, J.-Y. Son, B. Javidi, S.-K. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. of Displ. Technology 1(2), 347 (2005).
[Crossref]

Seo, G.

Seuntiëns, P. J.

P. J. Seuntiëns, L. M. Meesters, and W. A. IJsselsteijn, “The negentropy principle of informationitle>Perceptual attributes of crosstalk in 3D images,” Displays 26(4), 177–183 (2005).
[Crossref]

Shieh, H.-P. D.

W. Mphepo, Y.-P. Huang, and H.-P. D. Shieh, “Enhancing the brightness of parallax barrier based 3D flat panel mobile displays without compromising power consumption,” J. of Displ. Technology 6(2), 60–64 (2010).
[Crossref]

Shigemura, K.

K. Shigemura, J. Matsushima, Y. Ibata, K. Masumura, T. Asai, and T. Sato, “a two-way multiview 3D display using liquid crystal lens,” SPIE Newsroom (2016).

Shih, C.-H.

C.-T. Chang, W.-L. Chen, C.-H. Shih, and W.-M. Huang, “Landscape/portrait dual mode lens type 3D display using a 2d lens array,” in SID Symposium Digest vol. 43, pp. 308–311 (2012).

Shin, Y.-C.

J. Kim, C.-K. Lee, Y. Jeong, C. Jang, J.-Y. Hong, W. Lee, Y.-C. Shin, J.-H. Yoon, and B. Lee, “Crosstalk-reduced dual-mode mobile 3D display,” Journal of D. Technology 11(1), 97–103 (2015).
[Crossref]

Son, J.-Y.

V. V. Saveljev, J.-Y. Son, B. Javidi, S.-K. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. of Displ. Technology 1(2), 347 (2005).
[Crossref]

Song, M. S.

H. J. Lee, H. Nam, J. D. Lee, H. W. Jang, M. S. Song, B. S. Kim, J. S. Gu, C. Y. Park, and K. H. Choi, “A high resolution autostereoscopic display employing a time division parallax barrier,” in SID Symposium Digest vol. 37, pp. 81–84 (2006).

Szeliski, R.

S. Gortler, R. Grzeszczuk, R. Szeliski, and M. Cohen, “The lumigraph,” in SIGGRAPH (1996), pp. 43–54.

Taira, K.

R. Fukushima, K. Taira, T. Saishu, Y. Momonoi, M. Kashiwagi, and Y. Hirayama, “Effect of light ray overlap between neighboring parallax images in autostereoscopic 3D displays,” Proc. SPIE 7237, 72370 (2009).
[Crossref]

Takaki, Y.

Tanaka, Y.

K. Oku, Y. Tomizuka, and Y. Tanaka, “Analysis and reduction of moiré in two-layered 3D display,” in SID Symposium Digest vol. 38, pp. 437–440 (2007).

Ting, C.-H.

Tomizuka, Y.

K. Oku, Y. Tomizuka, and Y. Tanaka, “Analysis and reduction of moiré in two-layered 3D display,” in SID Symposium Digest vol. 38, pp. 437–440 (2007).

Tran, T.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Urruchi Del Pozo, V.

V. Urruchi Del Pozo, J. Algorri Genaro, J. Sánchez-Pena, M. Geday, X. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electronics Review 20(3), 260–266 (2012).
[Crossref]

Van Berkel, C.

C. Van Berkel, “Image preparation for 3D LCD,” Proc. SPIE 3639, 84–91 (1999).
[Crossref]

C. Van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE 3012, 179–186 (1997).
[Crossref]

Vo, S.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Wang, A.-H.

Wang, Q.-H.

Wetzstein, G.

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Transactions Graphics 31, 1–11 (2012).
[Crossref]

Yoon, J.-H.

J. Kim, C.-K. Lee, Y. Jeong, C. Jang, J.-Y. Hong, W. Lee, Y.-C. Shin, J.-H. Yoon, and B. Lee, “Crosstalk-reduced dual-mode mobile 3D display,” Journal of D. Technology 11(1), 97–103 (2015).
[Crossref]

Yoon, K.-H.

Yoon, S. K.

Zhou, L.

ACM Transactions Graphics (1)

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Transactions Graphics 31, 1–11 (2012).
[Crossref]

Appl. Opt. (2)

Displays (1)

P. J. Seuntiëns, L. M. Meesters, and W. A. IJsselsteijn, “The negentropy principle of informationitle>Perceptual attributes of crosstalk in 3D images,” Displays 26(4), 177–183 (2005).
[Crossref]

IEEE Trans. Image Process. (1)

J. Konrad, B. Lacotte, and E. Dubois, “Cancellation of image crosstalk in time-sequential displays of stereoscopic video,” IEEE Trans. Image Process. 9(5), 897–908 (2000).
[Crossref]

J. Appl. Phys. (1)

L. Brillouin, “The negentropy principle of information,” J. Appl. Phys. 24, 1152–1163 (1953).
[Crossref]

J. Electron. Imaging (1)

I. Amidror, R. D. Hersch, and V. Ostromoukhov, “Spectral analysis and minimization of moiré patterns in color separation,” J. Electron. Imaging 3(3), 295–317 (1994).
[Crossref]

J. of Displ. Technology (2)

V. V. Saveljev, J.-Y. Son, B. Javidi, S.-K. Kim, and D.-S. Kim, “Moiré minimization condition in three-dimensional image displays,” J. of Displ. Technology 1(2), 347 (2005).
[Crossref]

W. Mphepo, Y.-P. Huang, and H.-P. D. Shieh, “Enhancing the brightness of parallax barrier based 3D flat panel mobile displays without compromising power consumption,” J. of Displ. Technology 6(2), 60–64 (2010).
[Crossref]

J. Soc. Inf. Disp. (2)

M. Salmimaa and T. Järvenpää, “3-D crosstalk and luminance uniformity from angular luminance profiles of multiview autostereoscopic 3-D displays,” J. Soc. Inf. Disp. 16(10), 1033–1040 (2008).
[Crossref]

Y. J. Jeong, H. S. Chang, D. Nam, and C.-C. J. Kuo, “Direct light field rendering without 2D image generation,” J. Soc. Inf. Disp. 24(11), 686–695 (2017).
[Crossref]

Journal of D. Technology (1)

J. Kim, C.-K. Lee, Y. Jeong, C. Jang, J.-Y. Hong, W. Lee, Y.-C. Shin, J.-H. Yoon, and B. Lee, “Crosstalk-reduced dual-mode mobile 3D display,” Journal of D. Technology 11(1), 97–103 (2015).
[Crossref]

Nature (1)

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Opt. Express (5)

Opto-Electronics Review (1)

V. Urruchi Del Pozo, J. Algorri Genaro, J. Sánchez-Pena, M. Geday, X. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electronics Review 20(3), 260–266 (2012).
[Crossref]

Proc. of the IEEE (2)

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. of the IEEE 97(6), 1067–1077 (2009).
[Crossref]

L. Hill and A. Jacobs, “3-D liquid crystal displays and their applications,” Proc. of the IEEE 94(3), 575–590 (2006).
[Crossref]

Proc. SPIE (4)

C. Van Berkel, “Image preparation for 3D LCD,” Proc. SPIE 3639, 84–91 (1999).
[Crossref]

R. B. Johnson and G. A. Jacobsen, “Advances in lenticular lens arrays for visual display,” Proc. SPIE 5874, 587406 (2005).
[Crossref]

C. Van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE 3012, 179–186 (1997).
[Crossref]

R. Fukushima, K. Taira, T. Saishu, Y. Momonoi, M. Kashiwagi, and Y. Hirayama, “Effect of light ray overlap between neighboring parallax images in autostereoscopic 3D displays,” Proc. SPIE 7237, 72370 (2009).
[Crossref]

Other (8)

K. Oku, Y. Tomizuka, and Y. Tanaka, “Analysis and reduction of moiré in two-layered 3D display,” in SID Symposium Digest vol. 38, pp. 437–440 (2007).

H. J. Lee, H. Nam, J. D. Lee, H. W. Jang, M. S. Song, B. S. Kim, J. S. Gu, C. Y. Park, and K. H. Choi, “A high resolution autostereoscopic display employing a time division parallax barrier,” in SID Symposium Digest vol. 37, pp. 81–84 (2006).

K. Shigemura, J. Matsushima, Y. Ibata, K. Masumura, T. Asai, and T. Sato, “a two-way multiview 3D display using liquid crystal lens,” SPIE Newsroom (2016).

C.-T. Chang, W.-L. Chen, C.-H. Shih, and W.-M. Huang, “Landscape/portrait dual mode lens type 3D display using a 2d lens array,” in SID Symposium Digest vol. 43, pp. 308–311 (2012).

K. Choi, Y. J. Jeong, B. Kang, J.-H. Lee, Y. Choi, and D. Nam, “Design and implementation of landscape/portrait mode convertible light-field 3D display,” in SID Symposium Digest vol. 47, pp. 986–989 (2016).

“EyeFly3D – glasses-free 3D,” [Online]. Available: http://www.eyefly3d.com/ .

M. Levoy and P. Hanrahan, “Light field rendering,” in SIGGRAPH (1996), pp. 31–41.

S. Gortler, R. Grzeszczuk, R. Szeliski, and M. Cohen, “The lumigraph,” in SIGGRAPH (1996), pp. 43–54.

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Figures (15)

Fig. 1
Fig. 1 Various 3D displays that have 3D artifacts caused by the (a) lack of luminance uniformity, (b) lack of color uniformity, and (c) moiré artifacts. Images of 3D displays were captured using a camera.
Fig. 2
Fig. 2 (a) Light field representation (b) light field representation in 3D displays.
Fig. 3
Fig. 3 Luminance uniformity: light rays and light field representation of 3D displays. (a), (b), and (c) are representations for a non-uniformly distributed 3D display; (d), (e), and (f) are representations for a uniformly distributed 3D display; (a) and (d) show light rays from one horizontal line when y = 1; (b) and (e) show light rays from one horizontal line when y = 2.
Fig. 4
Fig. 4 Color uniformity: light rays and light field representation of 3D displays. (a), (b), and (c) are representations for non-uniformly distributed color; (d), (e), and (f) are representations for uniformly distributed color; (a) and (d) show light rays from one horizontal line when y = 1; (b) and (e) show light rays from two horizontal lines when y = 1 and y = 2.
Fig. 5
Fig. 5 Spectral model for 3D display moiré based on Fourier analysis.
Fig. 6
Fig. 6 lα map for design of 3D displays.
Fig. 7
Fig. 7 lα map for luminance uniformity, color uniformity and 3D moiré.
Fig. 8
Fig. 8 lα map for 3D display design optimization.
Fig. 9
Fig. 9 Luminance uniformity in the light field representation of (a) design 1, (b) design 2, (c) design 3, and (d) design 4.
Fig. 10
Fig. 10 Color uniformity in the light field representation of (a) design 1, (b) design 2, (c) design 3, and (d) design 4.
Fig. 11
Fig. 11 3D moiré simulation: superposition of pixels and parallax barrier (top) and frequency response (bottom) for (a) design 1, (b) design 2, (c) design 3, and (d) design 4.
Fig. 12
Fig. 12 Camera captured images from four manufactured rotatable 3D displays.
Fig. 13
Fig. 13 Crosstalk of design 1 for landscape and portrait modes.
Fig. 14
Fig. 14 Simulated results for luminance and color uniformity term.
Fig. 15
Fig. 15 Simulated results for moiré term.

Tables (1)

Tables Icon

Table 1 3D display parameters for design 1, 2, 3, and 4.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

E = λ 1 E L + λ 2 E C + λ 3 E M ,
L : Ω × Π R ( x , y , s , t ) L ( x , y , s , t ) .
p ( s ) = f d f p ( x ) D f u ,
J = S max S ,
E L = P R log P R + 1 N b P i log P i
P R = N L N b × N b ,
P i = n i N L ,
E C = P C R log P C R P C G log P C G P C B log P C B + + 1 N b ( P i R log P i R + P i G log P i G + P i B log P i B ) ,
P C R = N L R N b × N b , P C G = N L G N b × N b , P C B = N L B N b × N b ,
P i R = n i R n L R , P i G = n i G N L G , P i B = n i B N L B ,
o ( x , y ) = 0.5 cos [ 2 π f L ( x cos θ + y sin θ ) ] + 0.5 ,
O ( f L cos θ , f L sin θ ) = O ( f L cos θ , f L sin θ ) = 1 4 , O [ 0 , 0 ] = 1 2 .
o ( x , y ) = Π o ( τ L ( x cos θ τ L + y sin θ ) ) = { 1 , | x cos θ | τ L 2 0 , | x cos θ | > τ L 2 , L 2 < x L 2
O ( u , v ) = τ L f L sinc ( τ L ( u cos θ + v sin θ ) ) .
p ( x , y ) = Π H ( x τ H ) × Π V ( y τ V ) ,
Π H ( x τ H ) = { 1 , 0 , | x | τ H 2 | x | > τ H 2 , T H 2 < x T H 2 1 , 0 , | x | τ V 2 | x | > τ V 2 , T V 2 < x T V 2 .
P ( u , v ) = τ H T H sinc ( τ H u ) τ V T C sinc ( τ V v ) .
o ( x , y ) p ( x , y ) O ( u , v ) P ( u , v ) = M ( u , v ) .
C M = v 1 v 2 u 1 u 2 λ ( u , v ) M ( u , v ) d u d v ,
L P = L tan θ = L α .
V L = 2 atan L 2 g ,
V P = 2 atan L 2 g α ,
θ 1 < V L < θ 2 , θ 3 < V P < θ 4
E = E L ( l , α ) + λ 1 E C ( l , α ) + λ 2 E M ( l , α , p ¯ ) ,
5 ° < V L < 18 ° , 10 ° < V P < 25 ° .
W H = V l ,

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