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20 Available online at ScienceDirect Journal of Electrical Systems and Information Technology 1 (2014) D computer generated medical holograms using spatial light modulators Ahmed Sheet a,, Mai El Sayed a, Mai Maged a, Mona Ismail a, Mariam Ali a, Nahed Hussien Solouma b,c, Tarek Abdel-Mottleb b,c a Engineering Applications of Laser, Systems and Biomedical Engineering Department, National Institute of Laser Enhanced Sciences, Faculty of Engineering, Cairo University, Egypt b Engineering Applications of Laser, Biomedical Engineering Department, Cairo University, Egypt c Engineering Applications of Laser, Biomedical Engineering Department, Helwan University, Egypt Available online 11 July 2014 Abstract The aim of this work is to electronically generate the diffraction patterns of medical images and then trying to optically reconstruct the corresponding holographs to be displayed in space. This method is proposed in a trial to find a smart alternative of the expensive and perishable recording plates Production and hosting by Elsevier B.V. on behalf of Electronics Research Institute (ERI). Keywords: Medical; Hologram; Fourier; Recording; Reconstruction; Image 1. Introduction Creating holograms of medical images is a recent topic in visualization. Although the idea has been under research more than twenty years ago, no achievement has been done before the last five years. This is because of the very high computer configuration and optical specification required to do the job. Holography is displaying a three-dimensional image of an object in space. The principle is to save an interference pattern of light coming from that object and a reference beam on special recording plates. This pattern includes the information of amplitude and phase differences required to build a 3-D shape. When the holographic plate is later exposed to a laser beam, the three-dimensional hologram could be displayed and observed from different view. Corresponding author. address: Eng Ahmedsheet@hotmail.com (A. Sheet). Peer review under the responsibility of Electronics Research Institute (ERI) / 2014 Production and hosting by Elsevier B.V. on behalf of Electronics Research Institute (ERI).

21 104 A. Sheet et al. / Journal of Electrical Systems and Information Technology 1 (2014) Fig. 1. Optical construction of the Fourier Hologram. 2. Experimental procedures Creating Computer Generated Hologram (CGH) includes three main steps: (1) Computation of the virtual scattered wave front (Interference Pattern). (2) Encoding the wave front data and preparing it for display. (3) Experimental setup. The following sections present the explanation of these steps Computation of the virtual scattered wave front Numerous numbers of methods can be used for computing the interference pattern for a CGH. We used two of them namely the Fourier Transform Holograph and the Gerchbergand Saxton (GS) algorithm Fourier Transform Holograph Fourier Transform (FT) Holography refers to the creation of holograms that are the Fourier Transform of the subject. The object and the reference light has to lie in the same plane thus the possible objects to be imaged are restricted to planar apertures. For the diffracted electric field to be approximated by the Fourier Transform of the aperture transmission function a(x 0, y 0 ), The observation plane, given by z = z 0, has to be distant from the object plane. Experimentally, a thin spherical lens introduced between the two planes will perform the Fourier Transform at the focal length f as shown in Fig. 1 The electric field for the aperture centered at (x r, y r, 0) is given Eq. (1) E o e ikz e ik 2z (x2 +y 2 ) = Ce ikz e 2z ik (x2 +y 2 ) dx o dy o a(x o x r, y o y r )e ik z (xx o yy o ) i(xx o yy o ) dx o dy o a(x o x r, y o y r )e = Ce ikz e 2z ik (x2 +y 2) A(K x, K y ) (1) The electric field due to the reference point source is given by Eq. (2) ik E p (x, y) = e ikz e 2z ik (x2 +y 2 z ) (xx o+yy o dx o dy o δ (x o, y o )e )C e ikz e 2z ik (x2 +y 2 ) (2) The total electric field is the superposition of E 0 and E p which gives an interference pattern represented by Eq. (3) E(x, y) = E 0 (x, y) + E p (x, y) = C e ikz e ik 2z (x2 +y 2 ) [1 + A(K x + K y )] (3)

22 A. Sheet et al. / Journal of Electrical Systems and Information Technology 1 (2014) Fig. 2. Typical GS algorithm (Lehar) Gerchbergand Saxton (GS) algorithm This is a phase only hologram algorithm used by the SLM software. We employ the GS algorithm as a computational algorithm in order to improve the deterioration of the reconstructed image. Fig. 2 is a block diagram made by the author to illustrate typical a GS algorithm. In the GS algorithm for Fourier holograms, Fourier and inverse Fourier transforms correspond to reconstructions from a hologram and hologram generation, respectively. We start the computational algorithm by adding a random phase to an input image, and calculate the diffraction pattern calculation from the latter. We extract only the phase components from the diffracted light to generate a kinoform. The kinoforms are reconstructed by inverse diffraction calculation. We replace the amplitude of the reconstructed light with the original input image. Repeating the above processes, the GS algorithms gradually improve the quality of the reconstructed images Encoding the wave front data and preparing it for display Once you know what the scattered wave front of the object looks like or how it can be computed, it must be sent to a spatial light modulator (SLM). SLM is a device that modulates the coherent light spatially based on its control input. The SLM is used to encode output patterns for aerial mapping. Also, the SLM accepts the pattern information from a computer and converts the input coherent light from laser source into the required output patterns. In our work, we used in our experiments two types of the SLM: 1. PLUTO (Phase Only Spatial Light Modulators)The PLUTO Spatial Light Modulator (SLM) is used to control an LCOS (Liquid Crystal-on-Silicon) active matrix reflective mode phase only LCD with resolution and a 0.7 diagonal. 2. SLM (LC 2002) Phase and amplitude modulation:slm (LC 2002) is used to control an LCOS (Liquid Crystal-on- Silicon) active matrix transitive mode with resolution Fig. 3. Reconstruction of the CGH.

23 106 A. Sheet et al. / Journal of Electrical Systems and Information Technology 1 (2014) Fig. 4. Top view of the experiment using reflective SLM Experimental setup Modulating the input interference pattern with coherent light beam by the SLM and some optical elements to observe the hologram on display. Fig. 3 is a block diagram made by the author to show the elements used to reconstruct the hologram in the experiment which are Laser source. Beam expander. Collimator (Biconvex Lens). SLM. Biconvex lens (Inverse Fourier). Planer concave (magnify the hologram. Fig. 5. Front view of the experiment using reflective SLM.

24 A. Sheet et al. / Journal of Electrical Systems and Information Technology 1 (2014) Fig. 6. Result hologram of a dice. F1 is the focal lens of lens 1 (Collimator). F2 is the focal lens of lens 2 (Inverse Fourier). F3 is the focal les of lens 3 (Magnification) Figs. 4 and 5 show live images of the optical setup used in the experiment taken in the laboratory, front and top shots are taken for the optical table that contains the components of the setup 3. Results (a) A software program that generates the interference pattern of a 2-D image by Fourier algorithm. (b) Experiment generates 2-D hologram using PLUTO reflective SLM (as a new trend in reconstructing the holograms) using its software which is built in the GS algorithm. Figs. 6 8 show images for the output holograms taken in the laboratory. Fig. 7. Result hologram of a skull.

25 108 A. Sheet et al. / Journal of Electrical Systems and Information Technology 1 (2014) Future work Fig. 8. Result hologram of a HoloEye logo. We are working on eliminating the DC term that is shown in the resultant image. We are working on the 3-D hologram and viewing it in space and that can be done using more than one system of this system each one will generate different view of the 3-D object and by specific alignment 3-D hologram can be generated. 5. Conclusions Combining the Sciences of Optical Engineering, Laser Engineering, Mathematics, Computational Techniques and Software Programming. The author could reach a satisfying output of A three dimensional Holographic Image by the use of SLM And software Algorithm, A result that can be a very good seed for a very interesting research area in the career path of the author. Reference slehar/fourier/fourier.html

26 Optics Communications 326 (2014) 1 5 Contents lists available at ScienceDirect Optics Communications journal homepage: The holographic display of three-dimensional medical objects through the usage of a shiftable cylindrical lens Dongdong Teng, Lilin Liu, Yueli Zhang, Zhiyong Pang, Biao Wang n School of Physics and Engineering, Sun Yat-Sen University, 135 Xingang West Road, Haizhu District, Guangzhou, Guangdong , PR China article info Article history: Received 2 January 2014 Received in revised form 12 February 2014 Accepted 25 February 2014 Available online 14 March 2014 Keywords: CGH 3D display Time-multiplexing Medical object abstract Through the creative usage of a shiftable cylindrical lens, a wide-view-angle holographic display system is developed for medical object display in real three-dimensional (3D) space based on a time-multiplexing method. The two-dimensional (2D) source images for all computer generated holograms (CGHs) needed by the display system are only one group of computerized tomography (CT) or magnetic resonance imaging (MRI) slices from the scanning device. Complicated 3D message reconstruction on the computer is not necessary. A pelvis is taken as the target medical object to demonstrate this method and the obtained horizontal viewing angle reaches 281. & 2014 Published by Elsevier B.V. 1. Introduction Three-dimensional (3D) medical imaging has proven to be beneficial for medical diagnoses. Tomographic medical imaging, such as magnetic resonance imaging (MRI) and computerized tomography (CT), has been widely used to reconstruct and display 3D medical objects on a 2D screen [1]. But a 2D screen cannot effectively express depth cues of 3D objects [2]. The absence of high-dimensional data presentation may make doctors encounter confusion while doing accurate diagnosis. So, 3D medical objects' display with depth cues in true 3D space is needed urgently. Binocular parallax technology has been developed to display 3D medical objects [3]. But motion parallax cannot be reproduced without wearing a tracking device. In addition, due to the distance conflict between accommodation and convergence, visual fatigue keeps being a problem for the binocular parallax technology. Integral photography (IP) was also used for displaying 3D medical objects [4] with the help of a microlens array. Although the displayed object has full parallax, problems on depth, resolution and viewing angle hinder IP's further extension in the medical field. Computer generated hologram (CGH) was thought as an ideal 3D display technique which provides a natural spatial effect. However, limited by the space bandwidth product characteristics of the spatial light modulator (SLM), the viewing angle of the display is too small for actual applications [5]. n Corresponding author. Tel.: þ address: liullin@mail.sysu.edu.cn (B. Wang). In this paper, for employing a shiftable cylindrical lens, we implement holographic 3D medical objects' displayed with a wide viewing angle based on time-multiplexing. The merit of this developed system is that only a group of 2D slices along one direction are used as source images. 2. Schematic diagram and principle of the developed holographic display system Fig. 1 shows the schematic optical diagram of the developed system in the horizontal x z plane. A phase SLM is placed at the front focal plane of the Fourier lens. One couple of parallel sides of the SLM is set along the x-direction. Through the Fourier lens, CGH fed to the SLM (with a side length of D along the x-direction) generates a 3D image around the focal plane (FP plane) of the Fourier lens (f 1 ). Along the x-direction, the projected 3D image is located between points O 1 and O 2 of the FP plane. Through two lenses L 1 and L 2, the reversed image of the projected 3D image appears around the object plane (OP plane). FP and OP planes are at focal planes of L 1 and L 2, respectively. The distance between two lenses is 2d and their focal lengths are identicalto f 3. The Fourier lens is coaxial with L 1 and L 2 and this common axis is taken as the optical axis of the system. A shiftable cylindrical lens (f 2 ) is introduced into the system at the FP plane to refract the 3D images projected from the SLM, which is called Direction Lens (DL) in the paper. The DL can move along the x-direction and its axial direction is perpendicular to the x z plane. The x-direction message of the SLM is first imaged onto the imaging plane IP 1 through Fourier Lens and DL with a magnification of f 2 /f 1, and then /& 2014 Published by Elsevier B.V.

27 2 D. Teng et al. / Optics Communications 326 (2014) 1 5 Fig. 1. Schematic optical diagram of the display system with a shiftable cylindrical lens (DL). imaged onto the imaging plane IP 2 through L 1 and L 2. It shall be minded that the y-direction message of the SLM cannot be imaged onto these two planes due to DL's constant phase modulation along the y-direction. When the DL arrives at different positions, the x-direction images of the SLM are directed to different locations on IP 1 and IP 2 planes. As shown in Fig. 1, with the DL at Position 1, the x-direction images are directed to P 0 1 Q 0 1 and P 1Q 1 on the IP 1 and IP 2 planes, respectively. But when the DL moves to Position 2, the x-direction images are directed to P 0 2 Q 0 2 and P 2Q 2 accordingly. Differently, the distribution spaces of reversed images of the refracted 3D images do not translate with the shifting of the DL. They overlap with each other around the OP plane and stay between points O 0 1 and O0 2 of the x z plane along the x-direction. This overlapping space is the display space of the target medical object. The shadow region in Fig. 1 shows the horizontal section of the display space. For any displayed point M in the display space, its viewing angle region changes from Q 1 MP 1 to Q 2 MP 2 with the DL shifting from Position 1 to Position 2. According to geometric optics, when the space interval between the two positions is set as (f 2 /f 1 )D, the x-direction images of the SLM are able to link up spatially along the x-direction. As shown in Fig. 1, the Positions 1 and 2 being set as 0.5Df 2 /f 1 and 1.5Df 2 /f 1 away from the optical axis respectively, the point P 0 1 will coincide with Q 0 2 in the IP 1 plane and P 00 1 will coincide with Q 2 in the IP 2 plane. When the DL is shifted to the two positions alternatively and the corresponding CGHs of the point M are encoded onto the SLM synchronously, the adjacent viewing regions Q 1 MP 1 and Q 2 MP 2 will appear alternatively. If the refresh rate of the SLM and the moving speed of the DL are high enough, the receptors in the human eye will have a temporal persistence due to mental processing delay and the point M will be observable in an enlarged viewing angle of Q 1 MP 1 þ Q 2 MP 2 ¼ Q 1 MQ 2 þ Q 2 MP 2 ¼ Q 1 MP 2 along the x-direction en route the after image effect. Through this time-multiplexing method, more available DL positions will further enlarge the viewing angle. Assuming a target medical object being placed in the display space virtually, iteration algorithms is used for holographic encoding which involves an iterative loop of optical field propagation between the 2D slices of the virtual object and the SLM plane [6]. One group of 2D slices of the virtual object are cut along the z-axis, which are source images used for holographic encoding in our proposed system. Although the virtual object is the same, the CGHs will change with DL s movement, because the phase distribution between points O 1 and O 2 in the FP plane changes with 0 0 DL's positions and the FP plane is just in the light field propagation path of the iterative loop. In a word, different CGHs are needed to be encoded onto the SLM and corresponding 3D images are projected from the SLM when the DL translates to different positions in the proposed system. These 3D images are refracted by the DL at corresponding positions, and then through L 1 and L 2 the refracted 3D images are imaged into the same virtual target object but with different viewing regions. As discussed above, if the space intervals between adjacent positions are all set as (f 2 /f 1 ) D, the adjacent viewing regions will connect end by end. Thus, the viewing angle of the displayed object can be enlarged along the x-direction based on the time-multiplexing method. In the area of holographic 3D display, viewing angle's enlargement was usually implemented by projecting multiple CGHs along different viewing directions. For example, a viewing angle of was reached in Ref [7] through a curved array of SLMs which projected CGHs along different viewing directions synchronously. In our previous work, multiple CGHs projected from one SLM were directed to different directions successively by a spinning mirror, then 3601-viewable holographic display was realized per after image effect [8]. A common feature of above technologies is that each CGH requires a specific group of 2D source images along corresponding viewing direction. A wide viewing angle will need many groups of 2D source images for generating multiple CGHs for different viewing directions. As a result, complicated 3D message reconstruction of the target object must be carried out in the computer for obtaining multiple groups of 2D source images. However, in our proposed system, within the provided viewing angle (i.e. 281 in this paper as demonstrated below), the source images for all the CGHs are the same group of 2D slices of the virtual object that is cut along the z-axis. Such a characteristic makes the proposed technique more suitable for the 3D medical display. CT or MRI slices from the scanning device can be used directly and complicated 3D message reconstruction is not necessary when viewing is limited wthin the provided viewing angle. Although for actual medical usage, viewing from different perspectives beyond the currently provided viewing angles is required, the proposed system needs fewer groups (i.e. 3601=281 13) of 2D slices for 3601 message display. So, the quantity of the needed 2D source images is greatly reduced. 3. Analysis of the numerical aperture The resolution in x-direction of a point M depends on its distance away from the IP 2 plane, as shown in Fig. 1. Therefore, points on a displayed 3D object will have gradient x-direction resolution along the z-direction. The inhomogeneous distribution of resolutions will deteriorate the display quality. Only when the IP 2 plane is away from the display space infinitely, a constant

28 D. Teng et al. / Optics Communications 326 (2014) resolution can be achieved. Under this condition, the geometrical relationships can be expressed as 9 u 1 ¼ f 3 f 2 1 u 1 þ 1 v 1 ¼ 1 >= f 3 ) 2d ¼ 2f 2dv 1 ¼ u 3 f 2 3 =f 2 ð1þ 2 u 2 ¼ f >; 3 where f 3 o2f 2. LaLa 0 denote the marginal rays in Fig. 1. The point La 0 determines the boundary of the light field, which shall be within the effective aperture of L 2. Geometrically, there exist 2ðf 2 =f 1 ÞD þð1=2þo 1O 2 x La þð1=2þo 1O 2 ¼ f 2 f 3 9 = x La 0 ¼ x La þð1=2þo 1 O 2 2d=f 2 ; Combining with Eq. (1), the minimum numerical aperture of L 2 required by the display system is obtained as 2x La 0 f 3 ¼ 4D f 1 þ O 1O 2 f 3 Obviously, the necessary numerical apertures of other lenses are smaller than this value. Actually, the optical system is symmetric. Positions for DL shall include the other two symmetrical positions: 0.5Df 2 /f 3 and 1.5Df 2 /f 3. Based on the same principle, if the DL can be shifted to 2N (N42) positions, 2N adjacent x-direction images of the SLM will be generated and Eq. (3) changes to 2x La 0 f 3 ¼ 2ND f 1 þ O 1O 2 f 3 and the viewing angle will be enlarged by about 2N times along x-direction in the horizontal plane. 4. Experiment implementation A system is set up to implement the idea described above, as shown in Fig. 2. The incident beam is provided by a laser with a wavelength of 532 nm. It is converted into an elliptically polarized light through a 1/4 wave plate. Combining with the followed polarizing beam splitter, proper light intensity is directed to the SLM. A 1/2 wave plate is placed in front of the SLM to adjust the polarization direction of SLM's incident beams. HEO-1080 SLM from Holoeye Photonics AG with a refresh frequency of 60 Hz is used. The SLM is a pure phase modulator with a resolution of and pixel spacing of 8 8 μm 2. Fig. 2. Schematic drawing of the experimental setup. ð2þ ð3þ ð4þ In order to avoid obvious image flicker, displaying frequency of the medical object is set as 15 Hz in our experiment. With a SLM of 60 Hz, four positions are available for the DL and the viewing angle is enlarged around four times. In order to further enlarge the viewing angle through the proposed technology, two horizontally arranged SLMs (SLM1 and SLM2) are aligned in a plane with an inclination angle of α¼41 to the incident beam. The distance between two SLMs is equal to the SLM's side-length: D¼ mm. Under this condition, four positions of the DL are71.5df 2 /f 1 and 72.5Df 2 /f 1 away from the optical axis, respectively. Adjacent eight x-direction images of two SLMs were present on the IP 1 plane. Correspondingly, eight CGHs are needed and about eight-fold enlargement of the viewing angle along x-direction can be realized. Since the shuttle frequency of a translation stage is hard to reach 15 Hz for a large traveling span, a rotating platform is used for the DL's addressing. Four kinds of square parts are cut off from the mother DL, with one side along the axial direction of the mother DL. Their geometrical centers are 1.5Df 2 /f 1,2.5Df 2 /f 1, 1.5Df 2 /f 1 and 2.5Df 2 /f 1 away from the axis of the mother DL along x-direction, respectively. These four kinds of partial cylindrical lens are named as 1.5PL, 2.5PL. 1.5PL and 2.5PL accordingly. Their side lengths are all a¼13 mm. Two for each kind of the partial cylindrical lens are fabricated. In total, eight partial lens are attached to the rotating platform with a sequence of 2.5 PL, 1.5PL. 1.5PL, 2.5PL, 2.5PL, 1.5PL. 1.5PL and 2.5PL, as shown in Fig. 2. Theirgeometricalcentersarelocatedonacirclewitha diameter d¼50 mm surrounding the rotating axis and are separated by equal angular space. The rotating axis is parallel to the optical axis on the horizontal x z plane. The axial direction of each partial cylindrical lens keeps being along the tangential direction of the circle. With this mechanism, addressing of the DL is implemented through rotating the partial cylindrical lenses. For example, when the geometrical center of the partial lens 1.5PL rotates along the optical axis, it is equivalent to the situation that the DL reaches the position which is 1.5Df 2 /f 1 away from the optical axis along the x-direction in Fig. 1. Let the platform rotate at the speed of 7.5 rps. When a partial cylindrical lens soon arrives at the optical axis, corresponding CGHs are fed onto SLM1 and SLM2. The shutter in the light path remains closed until the geometrical center of a partial lens arrives at the optical axis and keeps opening for 5 μs. Four different partial lenses rotate to the optical axis cyclically in time sequence. Based on the after image effect, wide-view-angle 3D display in the horizontal plane is implemented with the proposed system. The refresh rate of the display system is 15 Hz and no obvious image flicker is observed. Encoding CGHs on a pixelated phase-only SLM will generate a zero-order beam at the Fourier plane as unnecessary noise. In our experiments, a phase of ð2π=λþðx 2 þy 2 Þ=ð2rÞ is added to precalculated phase codes of the CGH [9]. The projected 3D image is then shifted away from the FP plane with a distance of Δd ¼ rf 1 =ðr f 1 Þ and the zero-order noise remains unchanged. Placing a high-pass filter at the FP plane, the zero-order noise is blocked. The shifting along the optical axis does not change the beam propagation directions of the refracted images. So, the introduction of the extra phase do not change all the equations discussed above, except for the distance between Fourier Lens and DL, which changes from f 1 in Fig. 1 to f 1 þδd in Fig. 2. A pelvis of 12:0 12:0 12:0 mm 3 is displayed to demonstrate the developed technology and system. The source images are a group of CT slices from the scanning device with a pitch of 0.2 mm. The resolution of the 2D slice is f 1 ¼250 mm and f 2 ¼ f 3 ¼150 mm are adopted. The diameter of L 2 is 100 mm, which satisfies Eq. (4). The value of r in the added spherical phase is 600 mm. Experimentally, the viewing angle of the displayed 3D pelvis reaches 281 along x-direction in the horizontal plane. With a camera replacing the viewer, captured images for the camera being at different angular positions around the display system are shown in Fig. 3.

29 4 D. Teng et al. / Optics Communications 326 (2014) 1 5 Fig. 3. Captured images when the display system works at (a) 3D image of the pelvis reconstructed on the computer with the used CT slices from the scanning machine. (b) Right " (c) Right " 111. (d) Right " 91. (e) Right " 51. (f) Center (along the optical axis). (g) Left 51. (h) Left 91. (i) Left 111. (j) Left Fig. 4. Captured images with the cursor pointing to one displayed definitive point when the display system works at (a) Right " 111, (b) Right " 51, (c) Left 51, (d) Left 111. A merit of the holographic display is that the display point is definitive and its spatial position does not change with the movement of the viewer. Such spatially definitive displays allow the insertion of medical instruments into the image space for planning and simulating medical procedures like surgery, as indicated by Markon et al. and Maekawa et al. [10 12], who obtained interaction 3D medical displays with floating image visualization systems. The interaction ability of the present holographic display system is demonstrated by introducing a fiber tip into the display space to indicate the display contents as a pointing cursor [8]. Fig. 4 shows the captured image of the displayed pelvis with a red divergent light spot emitting from the fiber as the cursor. Compared with the images in Fig. 3, here the intensity of the SLM's incident light is a little weakened to make the cursor more eye-catching. 5. Conclusion In conclusion, through the creative usage of a shiftable cylindrical lens, a wide-view-angle holographic display system is developed for medical object display in real 3D space. The 2D source images for all the CGHs needed by the display system are one group of CT slices from the scanning device. Complicated 3D message reconstruction on the computer is not necessary. A pelvis is taken as the target medical object to demonstrate this method and the obtained horizontal viewing angle reaches 281. The rotating of DL results in the displayed object point shifting in the slicing plane during the exposure time of 5 ms. Another problem is an assumption of paraxial approximation in this paper, which cannot be met in practice. But the blur induced by shifting of displayed object points and the calculated error from the assumption of paraxial approximation added together are about 44 um along the x-direction, which is less than the resolution (about 100 μm) of human eyes with a pupil diameter 4 mm at the distance of distinct vision. Thus, the display quality of the 3D pelvis is not affected obviously. Although a larger viewing angle is implemented in this paper, the display size and resolution of the developed system are small due to the limited space bandwidth product and frame rate of commercial SLMs. 3D displays with a horizontal viewing angle (4201), a display size (102! 102! 102 mm3) and a transverse resolution (104! 104) are expected to be realized through the developed system if high-performance phase SLMs (with 108 pixel and a frame rate4360 Hz) can be commercialzed. Acknowledgment This work was supported by the Natural Science Foundation of China under Grant no , the National High Technology Research and Development Program of China (No. 2013AA03A106), the National High Technology Research and Development Program of China (No. 2011BAE01B14) and reserve fund from the Natural

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