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Abstract
A multi-view 3D display system consisting of modules for capturing three-dimensional objects, image processing (creating 3D image files), and a display screen for displaying 3D images has been developed. Large screens using multiple projectors to improve performance, such as view resolution, have been created. A prototype of the device was built using four projectors equivalent to 4K resolution, and 34-inch 3D images with a viewing angle of 35 degrees and a large depth were demonstrated. The display screens are designed using a vertically aligned lenticular sheet and a scattering layer that evenly diffuses light in both vertical and horizontal directions. We have experimentally demonstrated the ability to “look around” an object on the screen.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
There are different types of the real 3D display systems, including multi-view, holographic and integral imaging methods [1–3]. Although the main ideas of autostereoscopic displays were proposed more than 100 years ago, no one of them without the critical drawbacks which are the obstacles for mass production. Integral imaging 3D display is one of the promising displays that provide different perspectives according to viewing direction and is the most simple and suitable method of creating real 3D image. It has essential advantages in comparison with other methods (absence of the complicated mechanical and optical system, use of inexpensive materials in manufacture, possibility of simultaneous vision by the several viewers and others), which allow producing autostereoscopic 3D display with satisfactory color image. However, there are still some physical limitations. Limitations of current displays are the small view angle, small image depth, low resolution and presence of sharp edges at the transition between adjacent viewing zones.
The resolution and the image size can be increased if the multi-projection system is used. Different types of projection integral imaging systems have been proposed for various applications [4–8]. Autostereoscopic displays having a large screen, for example, more than 100 inches are constructed using multiple projectors. A multi-view display system that combines multiple flat-panel 3D displays through a multi-projection system was proposed in [9] in order to increase the number of views. Multi-view display module using the four projectors was proposed to realize a 14.4-inch large-screen 3D display in [10]. A 100-inch 300-Mpixel multi-projection 3D display using 300 projectors was developed in [11]. Multi-view autostereoscopic projection display, using a pair of micro-electromechanical (MEMS) scanner based projectors, a head-tracking camera, and a rotating retro-reflective diffuser screen is demonstrated in [12]. A resolution enhanced integral imaging display method using two micro-lens arrays (MLA) with different focal lengths for capturing and display respectively is proposed in [13]. A computational multi-projection display is proposed by employing a multi-projection system combining with compressive light field displays in [14]. In [15] preliminary design of the multi-view 3D system based on integral imaging was carried out. The real-time integral imaging scheme was also realized and experimentally demonstrated. Multi-projectors are used for improving the performance, such as viewing resolution, viewing angle, etc. In [16] a method for increasing the number of pixels of an integral 3D image by using multiple liquid crystal display panels and a multi-image combining optical system was presented. A method that enlarges the viewing zone of an integral 3D image using multiple projectors was proposed in [17].
One of the most significant disadvantages of integral imaging method is the compromise between the number of viewpoints and image resolution in each view. An autostereoscopic multi-view 3D display architecture based on the multiplexing and demultiplexing of orbital angular momentum (OAM)-carrying beams was presented in [18]. The concept of encoding of 2D image information using OAM modes, multiplexing of different OAM channels, and then simultaneous separation of different images into various viewing angles was described. This approach breaks the dependence between number of views and image resolution. This might pave the way for the next generation of multiview 3D display technologies. With more views of 2D images encoded with different OAM modes, it is expected that smoother parallax and high resolution can be achieved at the same time. Choosing encoding/decoding LG (Laguerre-Gauss) modes and displacement of off-axis points carefully allow encoding of different OAM modes for multiplexing in a single transmission channel with minimum crosstalk in the reconstructed images [19]. Note that the LG modes are the solutions of the Maxwell equations in graded-index optical fibers [20]. This compatibility between OAM based 3D display and data communication using optical fiber can provide the possibility for all-optical collection, transmission, and rendering of 3D information.
The viewing resolution of the 3D image can also be increased by using spatiotemporally multiplexed projector with a large number of pixels, instead of 2D display panels [21]. In [22] a method for the viewing angle and viewing resolution enhancement of integral imaging based on time-multiplexed lens stitching is demonstrated using the directional time-sequential backlight and compound lens-array.
In this paper the multi-view 3D display system which includes the modules of capturing three-dimensional objects, image processing (creation of 3D image files) and display screen for the 3D image displaying was developed. The main objective of this paper is to demonstrate experimentally an autostereoscopic multi-view 3D display system using four projectors and a large screen. Multi-projector system is used for improving the performance, such as viewing resolution. Besides, a large screen maintains a more realistic experience. One of advantages of the method is that the lenticular screen does not have to be matched to a display panel pitch, thus saving considerable expenditure. Different types of low cost lenticular sheets and diffuser layers were tested in order to obtain high quality 3D images. A distinctive feature of our method is the use of a specially selected diffuser scattering light equally in both vertical and horizontal directions. This allowed us to achieve smooth motion parallax and reduce crosstalk. Another advantage of our system of using projectors and a diffuser is the absence of the so-called “picket-fence” effect where the black mask of the liquid crystal display (LCD) panel forms real images in the viewing field when a 3D display is made using an LCD panel and a non-slanted lenticular screen.
The basic design of the system consisting of a projector, diffuser layer and lenticular lens is presented in Fig. 1. As shown in Fig. 1, the light rays from a display element of the projector are incident on a screen, which produces viewpoints for observes.
Fig. 1. Schematic representation of the 3D display system. 1 – projector; 2 – display element; 3 – projection lens; 4 – elemental image; 5 – diffuser layer; 6 – lenticular lens; 7 – viewing zone; 8 – observer; $\varphi$ - viewing angle; D – lens-pitch; f – focal length and R – curvature radius of the elemental lens.
The viewing angle of the integral imaging display is defined by the lens-pitch of the lenticular sheet and the focal length of the elemental lens:
2. Multi-view display system
The design of the 3D system includes several steps: capture of 3D images, creating 3D image files and displaying 3D images.
2.1 Experimental system
An experimental display system was designed and constructed (Fig. 2). Four projectors with a 4K equivalent resolution are arranged in a 2 × 2 array horizontally and vertically. The display screen consists of a diffuser layer scattering uniformly in both vertical and horizontal directions and lenticular sheet. Here we present a simple case of the vertical orientation of the lenticular lenses. In [15] we considered also the case of slanted axes of the lenticular lenses. The specifications of the prototype are presented in Table 1.
Fig. 2. Multi-projector 3D imaging system: (a) front view; (b) rear view of 53-inch screen and 4 HD projectors
Table 1. Parameters of the display prototype.
The projectors and screen are adjusted on the optical table with a simple pitch test method. The multi-projector system (Fig. 2) is constructed to increase the size and resolution of the 3D image. Four full HD digital light processing (DLP) Acer projectors are combined together. The problems of alignment of boundaries, colors, etc. are solved. The boundaries between images and color and brightness variations from different projectors are eliminated by optical and image processing methods (see Section 2.2). A 53-inch size screen (Fig. 2) is designed and 3D images are demonstrated.
Gap distance between the projectors and screen depends on the pitch size of the lenticular lens and number of viewpoints. This distance is equal to 50 cm for the lenticular sheet with the pitch D = 1.27 mm (20 lpi) and number of viewpoints N = 6.
2.2 Combining images from four projectors
Four projectors, the images of which are slightly overlapped as shown in Fig. 3, are used in order to increase the resolution. Several problems arise in this case: precise alignment between the projected images, light brightness, and color matching among all projectors, etc Fig. 4.
It can be seen that the brightness in the overlapping parts is higher than in other parts. Images were corrected by the image processing to compensate for the increased brightness at the intersection of the images of adjacent projectors. The brightness of the entire image can be smoothed by reducing the brightness of the pixels corresponding to the overlapping parts. Along each axis, the brightness of the image changes over a part of the image (set in the MatLab program, Fig. 4) according to the expression ${x^{ - a}}$, where x is the pixels coordinate and a is the power index. The optimal power index depends on the optics of the projectors and it was found experimentally. In our case, it was found, that a = 3/2.
2.3 Alignment of projectors and screen
Precise alignment between the projected images and screen is required in order to obtain high quality 3D image.
2.3.1 Rough adjustment
The distance between the screen and projector is determined by the parameters of the projector, lenticular sheet, and view numbers. The size of the 3D image depends on the number of view N for the given lenticular sheet and display matrix of the projector. The image size in horizontal direction is defined as L = (m/N)D, where m is the resolution (pixel number in horizontal direction) of the projector’s display matrix, N is the view number, and D is the pitch of the lenticular sheet. We obtain that the image size L = 406 mm for the number of views N = 6 and L = 271 mm when N = 9 for the lenticular sheet with 20 lpi and matrix with m = 1920.
2.3.2 Precise adjustment
Precise alignment between the projectors and the screen can be achieved with a pitch test. The pitch test is a very important step in 3D imaging. The need for the pitch test is to avoid misalignment between the lenticules on the lenticular sheet and projected image. To adjust the position of the screen relative to the projector, a special image is used, which is a set of strips of two colors (in most cases black and white). Black and white stripes are visible on the screen (Fig. 5a, b). When aligning, it is necessary to obtain the most uniform image of the same color, which indicates that each lens of the lenticular array contains the exact number of pixels corresponding to the number of views in the 3D image (Fig. 5d). The presence of two color bars in the 3D image shows the difference between the width of the lenticular lens and the part of the image corresponding to one lens. This means that the part of the image that should be under one lens is wider or narrower than the lens itself, so “beats” occur between the structure of the lenticular sheet and the structure of the image. Projection distortions due to the misalignment of the projector and the lenticular screen occur when the projectors are not exactly in the horizontal plane (Fig. 5c). The alignment procedure can be significantly accelerated with a mirror in front of the screen. First, the screen should be installed on the optical table. Then the spatial position of the projector can be smoothly changed according to the change of the pitch test pattern on the mirror.
Fig. 5. Pitch-test images on the screen.(a, b) misalignment due to incorrect distance between the lenticular lens sheet and projector; c) misalignment due to deviation of the screen and projector from the vertical plane; d) correct alignment between the lenticular lenses and projected image.
2.4 3D image capturing
The quality of the 3D image significantly depends on the method of the image capturing [23]. The integral imaging method implies the 3D information acquisition, which is based on the image capturing by an image sensor through a lens array. Here, the capturing an object from different directions was performed using a rotating platform and a conventional camera. The drawback of the integral imaging method for capturing is the small depth. Capturing an object from different angles with the camera allows us to get a higher depth (Fig. 6). 2D images were captured by rotating platform in 1-2 degrees intervals. Note that the capturing method using a camera and a rotating table allowed us to apply simple mathematical model to create 3D image files (Section 2.5) and image synthesis method described in Section 2.2.
2.5 Creation of 3D image files
To create a 3D image, the original 2D images are used, the number of which corresponds to the number of views. We place a portion of each view under each lens of the lenticular sheet to be able to see each view at a strictly defined angle (Fig. 7). In this case, the order of the views in the neighboring lenses is the same. In the first stage, the original views are converted to images with a vertical resolution equal to the vertical resolution of the screen, and with a horizontal resolution equal to the number of cylindrical lenses involved in the formation of a 3D image to fulfill the above conditions for the formation of the image under the lenticular lenses. Then each view is divided into vertical strips with a thickness of one pixel. We place one strip from each view under one vertical cylindrical lens, i.e. the vertical columns of pixels are aligned with the lenticular lenses. A column of pixels is assigned to one view for each of the N columns. Then the image is formed under the next vertical lens and so on until the end of the formation of the entire image. The result is an image with a horizontal resolution of NM, where N is the number of views and M is the resolution of one view, usually equal to the number of lenses in the lenticular involved in the 3D image. A similar procedure is used to create 3D files for four projectors. Codes for integration of images captured at different angles into one common 3D file are created in MatLab.
2D + z (2D + depth) image files from available resources were also used as the basis for creating 3D images. A three-dimensional model of the object was created based on the depth and color data at each point. Peculiar 2D images (views) were formed for each angle of view using the rotation of the object. However, when using 3D files obtained with the help of a rotating platform, the depth and view angle of 3D images were much better.
3. Experimental results
Below, we present view images with our implemented systems using one and four projectors. The size of the 3D images and viewing distance are increased with the number of projectors. Usually the diffuser which is vertically diffusing only is used in projector based displays. Here we used the diffuser which is scattering uniformly in both directions.
3.1 Single-projector 3D imaging
In Fig. 8 the images of 15-inch size from different viewing directions are shown. High quality images can be perceived in the viewing angle of ${40^ \circ }$. Images change clearly when the observation position changes. The position of the sword (red arrow) relative to the fighter’s head (blue arrow) changes clearly when the observer changes his location from right (Fig. 8a) to left (Fig. 8c). Warrior's leg located in the background is visible in the right view and is not visible in the left view and vice versa for his right shoulder.
Fig. 8. 3D images from different viewing directions. a) view from the right; b) view from the middle; c) view from the left. Arrows show the relative positions of different parts of fighters.
Here we used the BENQ full HD DLP projector (resolution 1920 × 1080 pixels). It can be seen that the 3D-image has a “looking-around” capability. Objects that are hidden from one view angle become visible from another view angle. Note that the image quality and viewing angle are significantly better than using a single projector in [4–7].
3.2 Multi-projector 3D imaging
The multi-projector system is constructed to increase the size and resolution of the 3D image. Four full HD DLP projectors are combined together and the problems of alignment of boundaries, colors, etc. are solved. The boundaries between images and color and brightness variations from different projectors are eliminated by optical and image processing methods. A high quality 3D display in the 35° viewing angle with smooth motion parallax is realized.
In Fig. 9 the images from different viewing directions are shown. The image size is 34-inches: 744 mm (H) × 420 mm (V). Here we used four full HD DLP Acer projectors (resolution 1920 × 1080 pixels). 3D images with 6-12 views were created. Lenticular sheets with 20 lpi were used in the experiments.
Fig. 9. 34-inch images on 53-inch screen. Images at different observation angles: (a) the picture shows a red LED, which is located behind the foot of the warrior (b).
3D-image has the ability to “look around”. Objects (the LED source located behind the fighter's foot) that are hidden for viewing in the bottom image become visible at a different viewing angle (the upper image). It is seen that there are no borders and color differences between the images of neighboring projectors. There is no viewing distance limit: continuous images can be viewed at distances of z > 1 m.
The viewing zone at the center has a viewing angle of 35° and shows 3D images with smooth motion parallax at distances from 1 m to over 5 m. The value of the depth corresponds to the real depth of the captured 3D object. There are three viewing zones (the primary viewing zone and two secondary viewing zones). Discontinuity occurs only at the transition from the primary viewing zone to the secondary viewing zone.
Crosstalk (ghosting) causes a major perceptual problem in the 3D display system and it is a critical factor determining the image quality of autostereoscopic displays [24,25]. However, as has been shown in [26], crosstalk in the multiview 3D images is not an effective parameter of defining the quality of 3D images. In [27] new quantification parameters for crosstalk, including average crosstalk and crosstalk uniformity, are introduced. It is shown that a global quantitative description of crosstalk show good agreement with the practical visual experience. The optical quality and type of the lenticular lens and the accuracy of alignment of the lenticular to the layout of pixels on the display are the important contributors to crosstalk. The ratio of the pitch of the lenticules to the pixels size on the display also affects the crosstalk. Besides, different areas of the screen may exhibit different levels of crosstalk. The acceptable system crosstalk level in mirror type 3D displays ranged from 18% to 23% [28]. However, it was shown in [24] that 5.8% crosstalk is perceptible, but not annoying. We estimate the level of crosstalk in our system to be less than 10%. This value of crosstalk can be considered to be not annoyed for observers by the distortions and thus acceptable. The quality of 3D images in our system is much better than the images obtained using the multi-view display module employing MEMS projector array [10] and 2 × 2 multi-projection system using a convex mirror array [8]. Most published works using the 4K projection system have not previously demonstrated a clear “look around” property. Note that the existing multi-projector 3D displays have much larger sizes due to larger projection distances. For example, in [11] the projection distance was 3.4 m.
4. Discussion and conclusion
In the experiment, a prototype was built, consisting of four projectors with an equivalent resolution of 4K, located in an array of 2×2 horizontally and vertically. Using projectors has a number of advantages: accurate alignment of the screen with the pixels of the image can be performed. In addition, video images can be easily demonstrated. The development of the proposed low-cost system is based on the use of existing technologies for manufacturing components. The optimum ratio between viewing angle and depth is achieved. 3D image with a size of 34 inches and large depth can be viewed within a viewing angle of 35 degrees from 1 m to over 5 m.
The experimental demonstration of the 3D system, including image capturing, creation of 3D file and image displaying has significant importance for elucidation of possibilities of the technologies of digital processing and displaying of 3D images.
It should be noted that there are still issues of low resolution, depth and view angle. It follows from the experiments that the greater the viewing angle, the less the image resolution and depth range. The image resolution can be increased using multiple projectors. The lenticular arrays with aspheric surface profiles should be developed to increase the viewing angle. The synthesis method including wave-optics and ray-tracing for the acceleration of the simulation of microlenses is effective to design microlenses with aspherical surfaces [29]. The holographic diffusers can be used to increase the contrast and brightness of the images in the display screen [30]. It is necessary to design two-dimensional microlens arrays in order to obtain motion parallax in vertical direction.
We consider the creation of two-dimensional arrays with aspherical surface profiles of microlenses and increasing the number of pixels as further developments. This will allow us to increase significantly the view angle, depth range, and resolution.
Different optical elements can be used to control the rays of light from pixels in the display. Usually, a lenticular array of lenses and parallax or slit barriers are used. Diffraction gratings and microstructures can also be used to control the direction of light rays in 3D displays [31]. A beam of light passing through the grating is scattered at a certain angle. In this case, there is a directional scattering of light due to diffraction. This property of the diffraction grating can be used to increase the number of views in 3D displays. High efficiency subwavelength gratings can be also used for this purpose [32]. Recently, a diffraction-grating based 3D display has been designed using a multiview concept [33]. An optimum design was proposed for diffraction-grating 3D displays [34].
Thus, the multi-view display system employing a DLP projector array with a resolution equivalent to 4K was proposed to realize large-screen 3D display. The experimental system was constructed using four DLP full HD projectors. However, this method is not limited to 2 × 2 projectors array. The system involves capturing three-dimensional objects, creation of 3D image files, and 3D image displaying based on integral imaging technology. The distortions in the projection image were precisely corrected. The 3D images with optimal viewing angle and depth were successfully demonstrated. The additional viewpoints, i.e. smooth motion parallax, give the necessary perception set of the 3D-scenes perspectives and have the property of “looking around” an object.
Proposed displays have a wide range of potential applications including 3D TVs and projection systems, mobile phones, as well as the systems for videoconference and medical applications.
Funding
Russian Science Foundation (17-19-01461).
References
1. J. Geng, “Three-dimensional display technologies,” Adv. Opt. Photonics 5(4), 456–535 (2013). [CrossRef]
2. J. Hong, Y. Kim, H. J. Choi, J. Hahn, J. H. Park, H. Kim, S. W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues,” Appl. Opt. 50(34), H87–H115 (2011). [CrossRef]
3. E. Lueder, 3D Displays (John Wiley & Sons, UK, 2012).
4. J. S. Jang and B. Javidi, “Real-time all-optical three-dimensional integral imaging projector,” Appl. Opt. 41(23), 4866–4869 (2002). [CrossRef]
5. H. Liao, M. Iwahara, N. Hata, and T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Express 12(6), 1067–1076 (2004). [CrossRef]
6. J. S. Jang and B. Javidi, “Three-dimensional projection integral imaging using micro-convex-mirror arrays,” Opt. Express 12(6), 1077–1083 (2004). [CrossRef]
7. Y. Kim, S. G. Park, S. W. Min, and B. Lee, “Projection-type integral imaging system using multiple elemental image layers,” Appl. Opt. 50(7), B18–B24 (2011). [CrossRef]
8. J. Y. Jang, D. Shin, B. G. Lee, and E. S. Kim, “Multi-projection integral imaging by use of a convex mirror array,” Opt. Lett. 39(10), 2853–2856 (2014). [CrossRef]
9. 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]
10. Y. Takaki, H. Takenaka, Y. Morimoto, O. Konuma, and K. Hirabayashi, “Multi-view display module employing MEMS projector array,” Opt. Express 20(27), 28257–28266 (2012). [CrossRef]
11. J. H. Lee, J. Park, D. Nam, S. Y. Choi, D. S. Park, and C. Y. Kim, “Optimal projector configuration design for 300-Mpixel multi-projection 3D display,” Opt. Express 21(22), 26820–26835 (2013). [CrossRef]
12. O. Eldes, K. Aksit, and H. Urey, “Multi-view autostereoscopic projection display using rotatory screen,” Opt. Express 21(23), 29043–29054 (2013). [CrossRef]
13. Z. Wang, A. Wang, S. Wang, X. Ma, and H. Ming, “Resolution-enhanced integral imaging using two micro-lens arrays with different focal lengths for capturing and display,” Opt. Express 23(22), 28970–28977 (2015). [CrossRef]
14. S. Moon, S.G. Park, C.K. Lee, J. Cho, S. Lee, and B. Lee, “Computational multi-projection display,” Opt. Express 24(8), 9025–9037 (2016). [CrossRef]
15. N.I. Petrov, Y.M. Sokolov, M.N. Khromov, and A.L. Storozheva, “Integral imaging multi-view 3D display,” Frontiers in Optics/Laser Science Conference (FiO/LS), Washington, USA, 2017, Paper JTu2A.107.
16. N. Okaichi, M. Miura, J. Arai, M. Kawakita, and T. Mishina, “Integral 3D display using multiple LCD panels and multi-image combining optical system,” Opt. Express 25(3), 2805–2817 (2017). [CrossRef]
17. N. Okaichi, M. Miura, H. Sasaki, H. Watanabe, J. Arai, M. Kawakita, and T. Mishina, “Continuous combination of viewing zones in integral three-dimensional display using multiple projectors,” Opt. Eng. 57(06), 1 (2018). [CrossRef]
18. X. Li, J. Chu, Q. Smithwick, and D. Chu, “Automultiscopic displays based on orbital angular momentum of light,” J. Opt. 18(8), 085608 (2016). [CrossRef]
19. J. Chu, D. Chu, and Q. Smithwick, “Off-axis points encoding/decoding with orbital angular momentum spectrum,” Sci. Rep. 7(1), 43757 (2017). [CrossRef]
20. N. I. Petrov, “Vector Laguerre–Gauss beams with polarization-orbital angular momentum entanglement in a graded-index medium,” J. Opt. Soc. Am. A 33(7), 1363–1369 (2016). [CrossRef]
21. J.-S. Jang, Y.-S. Oh, and B. Javidi, “Spatiotemporally multiplexed integral imaging projector for large-scale high-resolution three-dimensional display,” Opt. Express 12(4), 557–563 (2004). [CrossRef]
22. L. Yang, X. Sang, X. Yu, B. Yan, K. Wang, and C. Yu, “Viewing-angle and viewing-resolution enhanced integral imaging based on time multiplexed lens stitching,” Opt. Express 27(11), 15679–15692 (2019). [CrossRef]
23. J. Y. Son and B. Javidi, “Three-dimensional imaging methods based on multiview images,” J. Disp. Technol. 1(1), 125–140 (2005). [CrossRef]
24. A. J. Woods, “Crosstalk in stereoscopic displays: a review,” J. Electron. Imaging 21(4), 040902 (2012). [CrossRef]
25. A. J. Woods, C. R. Harris, D. B. Leggo, and T. M. Rourke, “Characterizing and reducing crosstalk in printed anaglyph stereoscopic 3D images,” Opt. Eng. 52(4), 043203 (2013). [CrossRef]
26. J.Y. Son, B.R. Lee, M.C. Park, and T. Leportier, “Crosstalk in multiview 3-D images,” Proc. SPIE 9495, 94950P (2015). [CrossRef]
27. H. Fan, X. Wang, S. Liang, K. Li, R. Jian, Y. Zhou, J. Wang, and J. Zhou, “Quantitative measurement of global crosstalk for 3D display,” J. Soc. Inf. Disp. 24(5), 323–329 (2016). [CrossRef]
28. P. C. Wang, S. L. Hwang, H. Y. Huang, and C. F. Chuang, “System cross-talk and three-dimensional cue issues in autostereoscopic displays,” J. Electron. Imaging 22(1), 013032 (2013). [CrossRef]
29. N. I. Petrov and G. N. Petrova, “Diffraction of partially-coherent light beams by microlens arrays,” Opt. Express 25(19), 22545–22564 (2017). [CrossRef]
30. N. I. Petrov, “Holographic diffuser with controlled scattering indicatrix,” Comp. Opt. 41(6), 831–836 (2017). [CrossRef]
31. J. H. Kulick, G. P. Nordin, A. Parker, S. T. Kowel, R. G. Lindquist, M. Jones, and P. Nasiatka, “Partial pixels: a three-dimensional diffractive display architecture,” J. Opt. Soc. Am. 12(1), 73–83 (1995). [CrossRef]
32. N. I. Petrov, V. G. Nikitin, V. A. Danilov, V. V. Popov, and B. A. Usievich, “Subwavelength diffractive color beam combiner,” Appl. Opt. 53(25), 5740–5744 (2014). [CrossRef]
33. 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]
34. Y. J. Jeong, “Diffraction grating 3D display optimization,” Appl. Opt. 58(5), A21–A25 (2019). [CrossRef]
