Efficient fabrication method of nano-grating for 3D holographic display with full parallax views

Wenqiang Wan; Wen Qiao; Wenbin Huang; Ming Zhu; Zongbao Fang; Donglin Pu; Yan Ye; Yanhua Liu; Linsen Chen

doi:10.1364/OE.24.006203

1. Introduction

The field of three-dimensional display (3D) has made little fundamental breakthrough since the original observations by Sir Charles Wheatstone in 1838 [1]. Holography as a perfect 3D display can reconstitute both the intensity and phase information from a natural 3D object. However, the refreshable holographic displays are too slow to provide real-time perceive for viewers [2, 3 ]. In practice, multiview 3D displays use a finite number of views to approximate the illusion of continuous parallax without the need of any special glasses [4, 5 ]. Because of their compatibility with commercially available liquid-crystal displays (LCDs), this technology showed great potential in the applications of 3D TV and 3D movie. Multiview 3D displays based on pure geometrical optics, such as parallax barrier, lenticular, or a combination of both [6–11 ], have been proposed and studies extensively, but they are criticized for providing only horizontal-parallax, limited number of viewing zones, reduced brightness, limited resolution, and visual fatigue.

Multiview 3D displays based on diffractive optics produces wide-angle holographic 3D images with significantly reduced data refreshing volume, by using a diffractive element to separate the phase information from the refreshable amplitude information [12]. David Fattal et al. used a directional backlight incorporated with the diffractive elements to generate 64-viewing zones with a resolution of 80 pixels per inch [13]. The technique attracted lots of attention, because it may be applied to the great market of mobile device for its compact profile volume. In this technique, the phase plate, as the most critical component in the design, re-directs the collimated incident light to multiple viewing zones. Therefore, the spacing and the orientation of the nano-grating patterns at each pixel on the phase plate need to be carefully designed based on diffractive optics. According to our calculation, the spacing variation needs to be as small as 2 nm so as to separate adjacent viewing zones in 3 degree. The only available nanofabricating technology that can achieve such patterning accuracy is E-beam lithography [14–16 ]. Although E-beam lithography is a flexible tool for small size prototype, the sequential writing process has an extremely low throughput. For instance, a 1mm² diffractive grating with a spatial frequency of 5000 lines/mm will cost 4-8 hours of fabrication using E-beam writing lithography. When the size of the phase plate is increased to 6-inch, the time consumption and cost became unfordable for commercial applications. As a result, the fabrication of phase plate becomes the bottleneck that prevents the diffractive optics based multiview 3D display to be used in large display, such as television application.

In this paper, we develop a flexible method for fabricating nanostructures at a high throughput. Using this nanofabrication method, the spatial frequency, as well as the orientation of the diffractive gratings can be modulated continuously. Furthermore, the nano-gratings can be fabricated pixel by pixel, which significantly shortened the time consumption of the fabrication process. Using the homemade lithography system, we fabricate two diffractive elements with full pixel coverage, on which we overlaid high-resolution binary masking patterns. We present a 9-view 3D scene with horizontal-parallax and a 64-view 3D scene with full-parallax. To evaluate the images quality of the 3D display, we measure the angular divergence for a single viewing zone. The angular divergence in horizontal axis and vertical axis is 1.5 degrees, and 1.25 degrees (FWHM), respectively, slightly larger than the simulated result of 1.2 degrees by FDTD. Furthermore, the fluctuation of the intensity for each viewing zone is within 10%, in consistency with the simulated value. Finally, a series of 3D images observed from various viewpoints are presented. A resolution of 160 pixels per inch per view is achieved and a view angle of 50 degrees is reached for 64-view 3D scene with full-parallax. No ghost images are observed in each viewing zone, because the light rays for each angle can be completely separated by diffractive optics.

2. Multiview 3D displays with nano-grating pixels

In this paper, the proposed multiview 3D display is based on holography. Moreover, the phase information is separated from the amplitude information to significantly reduce the refreshing data volume in video display. As shown in Fig. 1 , a collimated incident beam is modulated by a phase plate, on which nano-gratings with various grating vector re-direct the emergent beam to different viewing zone. To be specific, assume a voxel on the phase plate contains N nano-grating pixels such that the incident beam is modulated to N viewing zones. The amplitude of each emergent beam is further modulated by a corresponding pixel in the amplitude plate. Further assume the phase plate contains M voxel, there will be M × N nano-grating pixel in total, aligned with M × N pixels on the amplitude plate. Finally, the image projected on each view will contain M pixels. In such a way, a multiview 3D scene is formed (Fig. 1).

Fig. 1 Schematic of the proposed multiview 3D holographic display.

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The incident beam illuminated on a nano-grating is assumed to be a plane wave:

U_{i} (r) = A_{i} (r) e x p (- i k_{i} \cdot r)

Analogously, the wave diffracted from the nano-grating will be:

U_{d} (r) = A_{d} (r) e x p (- i k_{d} \cdot r)

where A_i(r) and A_d(r) are the amplitude of the incident and diffractive wave, respectively; k _i and k _d are the effective wave vectors of the incident and diffractive wave, respectively. According to the Raman-Nath regime, for a grating, K, depicted in Fig. 2 , the diffraction relationship between the incident beam and the first order diffraction beam can be written as [17]:

k_{d} = k_{i} - G

where |G| = 2π/Λ is the grating vector, Λ is the period of the nano-grating. By combining Eq. (3), |k _i| = n2π/λ, |k _d | = 2π/λ and G, the nano-grating period can be calculated as:

\frac{1}{Λ_{x}} = \frac{n \cos α_{1} - \cos α_{2}}{λ}

\frac{1}{Λ_{y}} = \frac{n \cos β_{1} - \cos β_{2}}{λ}

where Λ_x and Λ_y are the x and y components of the grating period, respectively; n is the refractive index of the phase plate; α ₁ and β ₁ are the incident angle from x axis and y axis for the incident beam, respectively; α ₂ and β ₂ are the diffraction angle from x axis and y axis for the diffraction beam. By combining Eq. (4) and Eq. (5), the grating period Λ can be written as:

Λ = \sqrt{\frac{λ^{2}}{{(n \cos α_{1} - \cos α_{2})}^{2} + {(n \cos β_{1} - \cos β_{2})}^{2}}}

The orientation angle of the grating vector φ from the y axis can be calculated by:

Fig. 2 The incident beam is modulated by each nano-grating pixel.

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\tan φ = \frac{Λ_{x}}{Λ_{y}} = \frac{n \cos β_{1} - \cos β_{2}}{n \cos α_{1} - \cos α_{2}}

Therefore, the phase plate is the vital optical component, on which the grating vector of each nano-grating pixel determines the propagation direction of the diffracted beam. In other words, the diffraction wave vector can be calculated accordingly by the predefined position of the viewing zone and the pixel in the phase plate. Assuming the wavelength of the illumination beam is 532 nm, and the adjacent viewing zones are separated by 3 degree, the increment for the period of nano-grating needs to be as small as 2 nm.

3. Optical setup for fabricating nano-gratings

From aforementioned analysis, the fabrication of the phase plate is challenging due to the critical requirement on the accuracy of the spatial frequency for nano-gratings. The electron beam lithography is a feasible method for fabricating such nano-grating arrays [18, 19 ]. However, the size of the phase plate is limited due to low efficiency and high cost of the sequential patterning process, which eventually hinders the technology from applying to large display applications. Lithography is an alternative patterning method with much higher throughput and lower cost [20–22 ], but the period of the nano-gratings patterned by these lithography system cannot be changed at a nano-scale step, resulting in incompletely separated viewing zones and unpleasant 3D sensation.

In this paper, we propose a lithography system that can pattern nano-grating arrays with the capability to control the period of nano-gratings at a sub-nanometer level. As shown in Fig. 3 , a plane wave illuminates a phase modulated component, which is composed of two Fourier transform lens and a diffraction grating. The light field at the rear focus plane of the first Fourier transform lens is:

U (x, y) = c' e x p [j k \frac{x^{2} + y^{2}}{2 (f_{1} - d)}] \times \int_{+ \infty}^{+ \infty} \int_{+ \infty}^{+ \infty} t (x_{0}, y_{0}) e x p (- j k \frac{x x_{0} + y y_{0}}{f_{1} - d}) d x_{0} d y_{0}

where x ₀, y ₀ and x, y are the coordinates of diffraction grating profile and the rear focus plane of the first Fourier transform lens, respectively; d is the distance between the first Fourier transform lens and the diffraction grating. The light field at the rear focus plane of the last Fourier transform lens will be:

U (x_{1}, y_{1}) = c'' \int_{+ \infty}^{+ \infty} \int_{+ \infty}^{+ \infty} U (x, y) e x p (- j k \frac{x x_{1} + y y_{1}}{f_{2}}) d x d y

where f ₁ and f ₂ are the focal length of the first and the last Fourier transform lens, respectively.

c'

,

c''

is constant. k is the wave vector of incident beam. x ₁, y ₁ are the coordinates of the rear focus plane of last Fourier transform lens.

Fig. 3 Schematic illustration of the proposed lithography system.

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The optical transmittance of the diffraction grating, t(x ₀,y ₀), can be written as:

t (x_{0}, y_{0}) = \cos (2 π a x_{0})

Then the light field of the last Fourier transform lens at the rear focus plane can be written as:

U (x_{1}, y_{1}) = c''' e x p [j π λ a^{2} (f_{1} - d)] \cos [j 2 π \frac{a (f_{1} - d)}{f_{2}} x_{1}]

where

c''' e x p [j π λ a^{2} (f_{1} - d)]

is phase constant, a is the spatial frequency of the diffraction grating. From Eq. (11), the light field at the rear focal plane of the last Fourier transform lens is an interference pattern formed by the ± 1 order of diffracted beams. Moreover, the spatial frequency for the light field can be modulated continuously by changing d (the insert of Fig. 3), the distance between the first Fourier transform lens and the diffraction grating. In addition, the orientation of the interference fringes can be controlled by rotating the diffraction grating via a rotation motor ( ± 0.05°).

Finally, the light field at the rear focal plane of the last Fourier transform lens is focused by an objective lens to form an minified interference pattern (i.e. the nano-grating) on the photoresist. The maximum spatial frequency of the nano-grating is determined by the minimum value of (a _limit, aMf ₁/f ₂), where a _limit is the maximum spatial frequency due to the diffraction limit; M is the demagnification of the objective lens. An aperture is placed at the rear focal plane of the last transform lens to block scattering light. As a result, the size of each nano-grating pixel is determined by the size of the aperture and the magnification of the objective lens. Through each exposure, a nano-grating pixel is formed. Therefore, the nano-grating arrays can be made “pixel-by-pixel” with a speed much faster than the E-beam lithography.

4. Experiments and results

4.1 Fabrication of the phase plate

As shown in Fig. 4 , a compact diode-pumped solid-state laser Awave351-0.5W@1k (Advanced Optowave Corporation. Wavelength: 351 nm. Repetition rate: 1 kHz. Pulse duration: less than 15 ns) was employed as the illuminating light source. The focal length of both Fourier transform lens was 75 mm. The spatial frequency of the diffraction grating was 133 lines per millimeter. For an aperture of 400 μm × 400 μm, and an objective lens with a demagnification of 20X, the period of the nano-grating fabricated by the lithography system can be varied from 380 nm to 2000 nm, and the size of each nano-grating pixel was 20 μm × 20 μm. Controlled by a stepping motor, the accuracy of the longitudinal movement for the diffraction grating was 1 um, resulting in an accuracy within 1 nm for the period of fabricated nano-grating. It only took 5 minutes to fabricate nano-gratings over an area of 100 mm², 500 times faster than the speed of E-beam lithography.

Fig. 4 Photograph of the proposed lithography system.

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We patterned a 2.5 inch 9-view diffractive element with horizontal parallax and a 6 inch 64-view diffractive element with full parallax on the positive photoresist (RJZ-390, RUIHONG Electronics Chemicals), as shown in Fig. 5(c) . The diffractive element was composed of subwavelength grating pixels with varying spacing from 500 nm to 1250 nm. The viewing angle of the diffractive element was 40 degree for 9-view horizontal parallax and 50 degree for 64-view full-parallax. The SEM photo of the nano-grating pixel was shown in Fig. 5(a)-5(b). The total number of the pixels was 2400 × 1800 for 9-view phase plate and 6400 × 4800 for 64-view diffractive element. Several binary masking patterns [Fig. 5(d)] were also fabricated by a hybrid lithography system (IGRAPHY, SVG Optronics) to produce various 3D scenes. The patterns on the amplitude plate were the combination of the parallax images, designed by 3D computer graphic.

Fig. 5 (a) The partial enlarged SEM photo of nano-grating pixels. (b) The SEM photo of the 6 inch phase plate with nano-grating pixels. (c) Photograph of the 6 inch 64-view phase plate with full pixel coverage. (d) Photograph of the binary masking pattern.

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4.2 Angular divergence

The optical properties of the 2.5-inch phase plates were measured under the illumination of a collimated laser beam with a wavelength 532nm. The angular divergence of the views was slightly larger than the diffraction limit, because of the finite spectral and angular distribution of the input light. As shown in Fig. 6(a) , the angular divergence in horizontal direction was measured to be 1.5 degrees (FWHM) by charge coupled device (DH-HV1351UM-M, DAHENG Image Vision Technology), slightly larger than the simulated value of 1.2 degrees by FDTD at the viewing angle of 0 degrees. The angular divergence in vertical direction was measured to be 1.25 degrees (FWHM), as shown in Fig. 6(b), consisting with the simulated value. Therefore, the nano-grating pixels fabricated by the homemade lithography system can be used in 3D holographic displays to modulate collimated illumination into multiple viewing zones.

Fig. 6 (a) The angular divergence in horizontal direction at the viewing angle of 0 degrees. (b) The angular divergence in vertical direction at the viewing angle of 0 degrees.

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4.3 9-view 3D display with horizontal parallax

As aforementioned, to produce a 3D scene, each nano-grating pixel was well aligned with the corresponding binary pixel in the amplitude mask. A digital camera was used to capture the displayed images in different viewing zones. As shown in Fig. 7(a), 3D images can be focused to 9 well separated light spot. The fluctuation of the transmitted intensity at each viewpoint was less than 10%. Furthermore, we achieved 9-view 3D images of SVG letters by shifting the digital camera horizontally [Fig. 7(b)]. The 3D images presented well with what has been expected in the calculation [Fig. 7(c)]. The range of the viewing angle was from −20°to 20°with an angle separation of 5 degrees. The depth of field was 50 mm at a viewing distance of 200 mm. No ghost effect was observed in the 3D display system, providing a comfortable binocular observation manner. The resolution for each view was 800 pixel × 600 pixel.

Fig. 7 (a) The 3D images can be focused to 9 well separated light spot and the transmitted intensity at each viewpoint.. (b) The 9-view 3D experimental images of SVG letters (see Visualization 1). (c) The 9-view 3D simulated images of SVG letters.

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4.4 64-view 3D display with full parallax

We also fabricated a 6-inch 64-view phase plate with full parallax to provide true 3D sensation. The 64-view 3D images were focused to a viewing plane at 200 mm from the amplitude plate [Fig. 8(a) ]. The angular distribution of each viewpoint suggested a well separation between adjacent viewing zone. Six photos with various viewing angles were taken using a digital camera as shown in Fig. 8(b). Again, the multiview 3D images produced by diffractive optics fit well with the simulation results [Fig. 8(c)]. The resolution for each view was 800 pixel × 600 pixel.

Fig. 8 (a) The 3D images can be focused to 64 well separated light spot. (b) Six photos with various viewing angles were taken using a digital camera. (c) Six Simulated images with various viewing angles by 3D computer graphic

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5. Discussion and conclusions

In this paper, we proposed a lithography system to fabricate nano-gratings efficiently for the multiview 3D displays. The spatial frequency of the nano-gratings can be controlled by the longitudinal movement of the phase modulating component in the lithography system. Based on the homemade lithography system, several phase plate prototypes with full coverage of nano-grating pixels have been fabricated at a speed of 20 mm²/mins. The optical modulation properties of the phase plate have been tested under the illumination of a collimated laser beam. The angular divergence in horizontal direction and vertical direction were measured to be 1.5 degrees and 1.25 degrees (FWHM), respectively, slightly larger than the simulation result of 1.2 degrees by FDTD. Furthermore, the lightfield of each viewpoint was well separated, providing true 3D sensation without crosstalk or ghost effect. The fluctuation of the light intensity in each viewpoint was less than 10%. Finally, aligned with a binary mask, we achieved 9-view 3D images with horizontal-parallax and 64-view 3D images with full-parallax. The field of view was 40 degrees and the resolution for each viewing zone was 400 pixels per inch for 9-view 3D images, while the viewing angle was 50 degrees and the resolution was 160 pixels/inch per view for 64-view 3D images with full-parallax. The presented prototypes suggested that the homemade lithography system can provide the key technology for fabricating the phase plate efficiently in diffractive 3D display.

The proposed multiview 3D displays can provide real-time 3D video by replacing the binary mask with a high resolution LCD. Theoretically, up to 150 views with a resolution of 200 ppi per view can be achieved by using a 4k LCD display. Furthermore, chromatic 3D images can be realized by the integration of RGB color filter.

Acknowledgments

The present study was supported by the Natural Science Foundation of China (NSFC) (Grant No. 91323303, 61401292, 61505131, 61575135), Jiangsu Provincial Natural Science Foundation of China (Grant No. BK20140350 and BK20150309), the China Postdoctoral Science Foundation (Grant No. 2015M571816), and the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions.

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Efficient fabrication method of nano-grating for 3D holographic display with full parallax views

Abstract

1. Introduction

2. Multiview 3D displays with nano-grating pixels

3. Optical setup for fabricating nano-gratings

4. Experiments and results

4.1 Fabrication of the phase plate

4.2 Angular divergence

4.3 9-view 3D display with horizontal parallax

4.4 64-view 3D display with full parallax

5. Discussion and conclusions

Acknowledgments

References and links

Supplementary Material (1)

Cited By

Figures (8)

Equations (11)

Optics Express