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Holographic multi-projection using the random phase-free method YUKI NAGAHAMA,* TOMOYOSHI SHIMOBABA, TETSUYA KAWASHIMA, TAKASHI KAKUE,
AND
TOMOYOSHI ITO
Graduate School of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan *Corresponding author: acfa3736@chiba‑u.jp Received 18 November 2015; revised 28 December 2015; accepted 11 January 2016; posted 12 January 2016 (Doc. ID 254054); published 10 February 2016
We demonstrated holographic multi-projection using the random phase-free method and the iterative method. Holographic multi-projection is a method of projecting multiple different images focused on different screens at the same time. The random phase-free method succeeded in improving the image quality. By applying the iterative method to the random phase-free method, the image quality was improved further. The results of our numerical reconstruction and optical experiments confirm that the proposed method improves the image quality. The peak signal-to-noise ratios of the reconstructed images using the proposed method and the conventional method are 30.66 and 13.61 dB, respectively. © 2016 Optical Society of America OCIS codes: (090.1760) Computer holography; (090.2870) Holographic display; (090.5694) Real-time holography. http://dx.doi.org/10.1364/AO.55.001118
1. INTRODUCTION A holographic projector [1,2] uses holographic techniques to project images. As holographic projectors are capable of reconstructing and zooming projection images without using a zoom lens, miniaturization is possible [3–5]. Moreover, holographic projectors can project images in unique ways. For example, a holographic projector having only a single spatial light modulator (SLM) can project multiple different images focused on different screens at the same time, which we call “multi-projection” [6–8]. In addition, a holographic projector can project images that are focused onto a curved screen. However, there are several barriers to realizing holographic projection. One of these barriers is speckle noise. The speckle noise arises from two main factors: the random phase and the rough surface of screens, resulting in random light interference. The random phase is required if we want to observe large reconstructed images exceeding the size of computer-generated holograms (CGHs). Methods of eliminating speckle noise have been proposed, e.g., iterative methods [6–8], the time averaging method [9], and pixel separation methods [10–12]. Recently, a random phase-free method [13] (using a virtual converging light instead of the random phase to diffuse the light to project the image) has succeeded in improving the image quality in the case of a single screen, but it has not been performed in multiprojection. In this paper, we demonstrate holographic multi-projection using the random phase-free hologram and the iterative method. The proposed method improved the image quality of multi-projection. Sections 2 and 3 describe the random 1559-128X/16/051118-06$15/0$15.00 © 2016 Optical Society of America
phase-free hologram and the multi-projection, respectively. Section 4 shows the numerical reconstruction and the optical experiment results of the multi-projection using the random phase-free hologram, and Section 5 concludes this work. 2. RANDOM PHASE-FREE HOLOGRAM Holographic projection requires calculating CGHs, which the original images to be projected are recorded on, so that the CGHs can project the original images. Conventional CGH calculation requires the random phase for the original images, but it also generates speckle noise. Instead of the random phase, the random phase-free method [13] uses the virtual converging light for the original images. [14–16] also used virtual converging light to improve the speckle problem, but they used it only with holograms and original images of the same size. The random phase-free method [13] presented the effectiveness to improve the speckle noise problem in differently sized holograms and original images. Figure 1 shows the geometrical relation between the original image, the hologram, and the virtual converging light. The areas of the image and the hologram are S i × S i and S h × S h , respectively. In this method, we multiply the original image ax i ; yi by the converging light given by wx i ; y i . wx i ; y i is expressed as a converging spherical light: wx i ; yi exp−iπx 2i y 2i ∕λf i ;
(1)
where f i z 1 z 2 is the focal length of the converging spherical light. The distance between the object and the hologram is denoted by z 2. The distance between the focal point of the converging light and the hologram is denoted by z 1. Then,
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Fig. 1. Geometrical relation between the input image, hologram, and virtual converging light.
we can derive Eq. (2) using the geometric relation, as shown in Fig. 1: f i : z1 Si : Sh:
(2)
After multiplying ax i ; y i by wx i ; y i , we calculate the diffraction to the hologram plane from the image plane to generate the hologram. Figure 2 is a reconstructed image of the image “Lena” from amplitude CGH generated by the random phase-free method in the numerical reconstruction. The numerical reconstruction conditions are shown in Table 1. In Table 1, “magnification” means the magnification S i ∕S h of the projected images using aliasing reduced scaled and shifted (ARSS) Fresnel diffraction [17]. This reconstructed image is not contaminated by speckle noise, but it is contaminated by ringing artifacts.
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Fig. 3. Iterative method for amplitude CGH.
A. Improving the Image Quality Using the Iterative Method
In order to remove the ringing artifact and to improve the image quality of the reconstructed images, we apply an iterative method to the random phase-free method [18]. Figure 3 shows the improved method for amplitude CGHs by using the iterative algorithm. The calculation steps of the iterative method are as follows: 1. We multiply the original image ax i ; y i by the converging light given by wx i ; y i . The resulting complex amplitude is defined as ui x i ; y i ax i ; y i × wx i ; y i . 2. We calculate the diffraction to the hologram plane from the image plane. In this paper, we use ARSS Fresnel diffraction [17] as the diffraction algorithm. This diffraction can perform light propagation with different sampling pitches on the hologram and image planes, leading to lensless zoomable holographic projection [3–5]. 3. We extract only the real part of uh x h ; y h on the amplitude CGH (constraint in the hologram plane): (3) gx h ; y h Refuh x h ; y h g: 4. We calculate inverse diffraction to the image plane from the hologram plane. The diffracted results are denoted by ui0 x i ; y i . 5. Weffi update only the amplitude part of ui0 x i ; y i by pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ax i ; y i . pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ui0 x i ; y i : (4) ax i ; y i × 0 jui x i ; y i j This is the constraint in the image plane. Subsequently, we obtain the new image plane ui x i ; y i . We repeat the above iteration of steps 2–5 until the preset iteration number or good image quality is reached. Figure 4 shows the reconstructed images of the image “Lena” from amplitude CGHs. These amplitude CGHs are generated by the iterative method. The ringing artifact is considerably reduced by the iterative method. ui x i ; y i
Fig. 2. Reconstructed image of the image “Lena” from the amplitude CGH generated by the random phase-free method in the numerical reconstruction.
Table 1.
Numerical Reconstruction Conditions
SLM resolution SLM pixel pitch (Sampling pitch in the hologram plane) Laser wavelength Projection distance z 2 Magnification
512 × 512 4.0 [μm]
3. MULTI-PROJECTION
513.8 [nm] 0.7 [m] ×12.0
We propose multi-holographic projection using the random phase-free method and the iteration algorithm in order to improve the image quality of the projected images. Figure 5 shows the setup for the multi-projection. A projector that simply
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Research Article to be projected by the iterative algorithm described in Section 2.1. 2. After the iteration process, we sum all the complex amplitude holograms. 3. Finally, we convert the complex amplitude holograms to the amplitude hologram.
Fig. 4. Reconstructed images from the amplitude CGHs generated by the combination of the random phase-free method and the iterative method in the numerical reconstruction.
Figures 7(a) and 7(b) show the original images on Screen 1 and Screen 2. The numerically reconstructed images of the images “Lena” and “Mandrill” from the amplitude CGHs that are generated by the random phase-free method without the iterative algorithm are shown in Figs. 7(c) and 7(d). Numerically reconstructed images from amplitude CGHs generated by the combination of the random phase-free method and the iterative method are shown in Figs. 7(e) and 7(f ). Figures 8(a) and 8(b) show the numerically reconstructed images from the amplitude CGHs that are generated by the conventional random phase method. Figures 8(c) and 8(d) show the numerically reconstructed images using the conventional random phase method with the iterative method.
Fig. 5. Setup for multi-holographic projection.
consists of a laser and a single-amplitude SLM is capable of projecting multiple images on “Screen 1” and “Screen 2” simultaneously. Figure 6 shows how to calculate the multi-projection hologram. The calculation steps of the multi-projection hologram are as follows: 1. We set the virtual spherical light wx i ; y i as shown in Fig. 6. Then, we generate the hologram for each image
Fig. 6. How to calculate the multi-projection hologram.
Fig. 7. (a) Original image for Screen 1. (b) Original image for Screen 2. Reconstructed images from amplitude CGHs generated by the random phase-free method without the iterative algorithm for (c) Screen 1 and (d) Screen 2 on numerical reconstruction. Numerically reconstructed images from amplitude CGHs generated by the combination of the random phase-free method and the iterative method for (e) Screen 1 and (f ) Screen 2.
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the original images and the reconstructed images (Figs. 7 and 8). When using the combination of the random phase-free method and the iterative method, these PSNRs are 30.66 and 24.05 dB, respectively. The PSNRs are higher than those of the conventional methods. 4. EXPERIMENTAL SETUP
Fig. 8. Reconstructed images from amplitude CGHs generated by the random phase method for (a) Screen 1 and (b) Screen 2 on numerical reconstruction. Reconstructed images from amplitude CGHs generated by the combination of the random phase method for (c) Screen 1 and (d) Screen 2, and the iterative method on numerical reconstruction.
The numerical reconstruction conditions are shown in Table 2. A comparison of Figs. 7(d) and 7(f ) shows that the ringing artifact by the iterative method is considerably reduced in the case of multi-projection. A comparison of Figs. 7(f ) and 8(d) shows that the speckle noise is reduced by the random phase-free method also in the case of multi-projection. Table 3 shows the peak signal-to-noise ratio (PSNR) between Table 2.
Magnification Iterative number
SLM resolution SLM pixel pitch (Sampling pitch in the hologram plane) Laser wavelength Projection distance of Screen 1 and Screen 2 Magnification Iterative number
2048 × 1080 4.0 [μm] 513.8 [nm] 0.5 [m] and 1.0 [m] ×6.0 10
PSNRs of the Reconstructed Images Random Phase Method
Screen 1 Screen 2
Table 4. Experimental Conditions
Numerical Reconstruction Conditions
SLM resolution SLM pixel pitch (Sampling pitch in the hologram plane) Laser wavelength Projection distance of Screen 1 and Screen 2
Table 3.
The optical experiment conditions are shown in Table 4. The optical system that we constructed is shown in Fig. 9. Figures 10(a) and 10(b) show the optical reconstructed images of the images “Lena” and “Mandrill” from the amplitude CGHs that are generated by the random phase-free method alone. The optical reconstructed images from the amplitude CGHs generated by the combination of the random phase-free method and the iterative method are shown in Figs. 10(c) and 10(d). In Figs. 11(a) and 11(b), we show the optical reconstructed images of the images “Lena” and “Mandrill” using the random phase method alone. In Figs. 11(c) and 11(d), we show the optical reconstructed images using the random phase method and the iterative algorithm. A comparison of Figs. 10(b) and 10(d) reveals that the uneven brightness in Fig. 10(d) is less than that in Fig. 10(b). This is because the ringing artifact was reduced by the iterative method. A comparison of Figs. 10(d) and 11(d) reveals that the speckle noise in Fig. 10(d) is less than that in Fig. 11(d). All of the calculations in this work were performed by our wave optics library: CWO++ [19].
Random Phase-Free Method
No Iteration [dB]
10 Iteration [dB]
No Iteration [dB]
10 Iteration [dB]
8.42 8.93
13.61 14.43
25.64 22.10
30.66 24.05
Fig. 9. Optical system.
1920 × 1080 8.5 [μm] 513.8 [nm] 0.8 [m] and 1.0 [m] ×3.0 10
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5. CONCLUSION We applied a combination of the random phase-free method and the iterative method to multi-projection. The PSNRs of the reconstructed images using the proposed method and conventional method were 30.66 and 13.61 dB, respectively. The PSNRs of the proposed method were higher than those of the conventional methods. The proposed method improved the image quality in the case of multi-projection. Funding. Japan Society for the Promotion of Science (JSPS) KAKENHI (25330125, 25240015); Kayamori Foundation of Information Science Advancement; Yazaki Memorial Foundation for Science and Technology. REFERENCES
Fig. 10. Optical reconstructed images from the amplitude CGHs generated by the random phase-free method for (a) Screen 1 and (b) Screen 2. Optical reconstructed images from the amplitude CGHs generated by a combination of the random phase-free method and the iterative method for (c) Screen 1 and (d) Screen 2.
Fig. 11. Optical reconstructed images from the amplitude CGHs generated by the random phase method alone for (a) Screen 1 and (b) Screen 2. Optical reconstructed images from the amplitude CGHs generated by the combination of the random phase method and the iterative method for (c) Screen 1 and (d) Screen 2.
1. E. Buckley, “Holographic laser projection,” J. Display Technol. 99, 1–6 (2010). 2. T. Shimobaba, T. Kakue, and T. Ito, “Real-time and low speckle holographic projection,” in IEEE International Conference on Industrial Informatics INDIN’ 15 (Special Session on Digital Holography for Industrial Applications) (IEEE, 2015), pp. 732–741. 3. T. Shimobaba, M. Makowski, T. Kakue, M. Oikawa, N. Okada, Y. Endo, R. Hirayama, and T. Ito, “Lensless zoomable holographic projection using scaled Fresnel diffraction,” Opt. Express 21, 25285– 25290 (2013). 4. I. Ducin, T. Shimobaba, M. Makowski, K. Kakarenko, A. Kowalczyk, J. Suszek, M. Bieda, A. Kolodziejczyk, and M. Sypek, “Holographic projection of images with step-less zoom and noise suppression by pixel separation,” Opt. Commun. 340, 131–135 (2015). 5. C. Chenliang, X. Jun, L. Qing, and L. Wei, “Speckle suppression in a scaled holographic display from single phase-only computer generated hologram,” SID Symp. Dig. Tech. Pap. 46, 526–529 (2015). 6. M. Makowski, M. Sypek, A. Kolodziejczyk, and G. Mikuła, “Threeplane phase-only computer hologram generated with iterative Fresnel algorithm,” Opt. Eng. 44, 125805 (2005). 7. P. Zhou, Y. Bi, M. Sun, H. Wang, F. Li, and Y. Qi, “Image quality enhancement and computation acceleration of 3D holographic display using a symmetrical 3D GS algorithm,” Appl. Opt. 53, G209–G213 (2014). 8. C. Chang, J. Xia, L. Yang, W. Lei, Z. Yang, and J. Chen, “Specklesuppressed phase-only holographic three-dimensional display based on double-constraint Gerchberg-Saxton algorithm,” Appl. Opt. 54, 6994–7001 (2015). 9. J. Amako, H. Miura, and T. Sonehara, “Speckle-noise reduction on kinoform reconstruction using a phase-only spatial light modulator,” Appl. Opt. 34, 3165–3171 (1995). 10. Y. Takaki and M. Yokouchi, “Speckle-free and grayscale hologram reconstruction using time-multiplexing technique,” Opt. Express 19, 7567–7579 (2011). 11. M. Makowski, “Minimized speckle noise in lens-less holographic projection by pixel separation,” Opt. Express 21, 29205–29216 (2013). 12. Y. Mori, T. Fukuoka, and T. Nomura, “Speckle reduction in holographic projection by random pixel separation with time multiplexing,” Appl. Opt. 53, 8182–8188 (2014). 13. T. Shimobaba and T. Ito, “Random phase-free computer-generated hologram,” Opt. Express 23, 9549–9554 (2015). 14. H. Aagedal, M. Schmid, T. Beth, S. Tiewes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996). 15. M. Pasienski and B. DeMarco, “A high-accuracy algorithm for designing arbitrary holographic atom traps,” Opt. Express 16, 2176–2190 (2008). 16. J. S. Liu, N. Collings, W. A. Crossland, D. P. Chu, A. Waddie, and M. R. Taghizadeh, “Simulation and experiment on generation of an arbitrary array of intense spots by a tiled hologram,” J. Opt. 12, 085402 (2010).
Research Article 17. T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. 15, 075405 (2013). 18. T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic
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projection to multiple tilted planes,” Opt. Commun. 333, 274–280 (2014). 19. T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++:CWO++ library,” Comput. Phys. Commun. 183, 1124–1138 (2012).
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Holographic multi-projection using the random phase-free method YUKI NAGAHAMA,* TOMOYOSHI SHIMOBABA, TETSUYA KAWASHIMA, TAKASHI KAKUE,
AND
TOMOYOSHI ITO
Graduate School of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan *Corresponding author: acfa3736@chiba‑u.jp Received 18 November 2015; revised 28 December 2015; accepted 11 January 2016; posted 12 January 2016 (Doc. ID 254054); published 10 February 2016
We demonstrated holographic multi-projection using the random phase-free method and the iterative method. Holographic multi-projection is a method of projecting multiple different images focused on different screens at the same time. The random phase-free method succeeded in improving the image quality. By applying the iterative method to the random phase-free method, the image quality was improved further. The results of our numerical reconstruction and optical experiments confirm that the proposed method improves the image quality. The peak signal-to-noise ratios of the reconstructed images using the proposed method and the conventional method are 30.66 and 13.61 dB, respectively. © 2016 Optical Society of America OCIS codes: (090.1760) Computer holography; (090.2870) Holographic display; (090.5694) Real-time holography. http://dx.doi.org/10.1364/AO.55.001118
1. INTRODUCTION A holographic projector [1,2] uses holographic techniques to project images. As holographic projectors are capable of reconstructing and zooming projection images without using a zoom lens, miniaturization is possible [3–5]. Moreover, holographic projectors can project images in unique ways. For example, a holographic projector having only a single spatial light modulator (SLM) can project multiple different images focused on different screens at the same time, which we call “multi-projection” [6–8]. In addition, a holographic projector can project images that are focused onto a curved screen. However, there are several barriers to realizing holographic projection. One of these barriers is speckle noise. The speckle noise arises from two main factors: the random phase and the rough surface of screens, resulting in random light interference. The random phase is required if we want to observe large reconstructed images exceeding the size of computer-generated holograms (CGHs). Methods of eliminating speckle noise have been proposed, e.g., iterative methods [6–8], the time averaging method [9], and pixel separation methods [10–12]. Recently, a random phase-free method [13] (using a virtual converging light instead of the random phase to diffuse the light to project the image) has succeeded in improving the image quality in the case of a single screen, but it has not been performed in multiprojection. In this paper, we demonstrate holographic multi-projection using the random phase-free hologram and the iterative method. The proposed method improved the image quality of multi-projection. Sections 2 and 3 describe the random 1559-128X/16/051118-06$15/0$15.00 © 2016 Optical Society of America
phase-free hologram and the multi-projection, respectively. Section 4 shows the numerical reconstruction and the optical experiment results of the multi-projection using the random phase-free hologram, and Section 5 concludes this work. 2. RANDOM PHASE-FREE HOLOGRAM Holographic projection requires calculating CGHs, which the original images to be projected are recorded on, so that the CGHs can project the original images. Conventional CGH calculation requires the random phase for the original images, but it also generates speckle noise. Instead of the random phase, the random phase-free method [13] uses the virtual converging light for the original images. [14–16] also used virtual converging light to improve the speckle problem, but they used it only with holograms and original images of the same size. The random phase-free method [13] presented the effectiveness to improve the speckle noise problem in differently sized holograms and original images. Figure 1 shows the geometrical relation between the original image, the hologram, and the virtual converging light. The areas of the image and the hologram are S i × S i and S h × S h , respectively. In this method, we multiply the original image ax i ; yi by the converging light given by wx i ; y i . wx i ; y i is expressed as a converging spherical light: wx i ; yi exp−iπx 2i y 2i ∕λf i ;
(1)
where f i z 1 z 2 is the focal length of the converging spherical light. The distance between the object and the hologram is denoted by z 2. The distance between the focal point of the converging light and the hologram is denoted by z 1. Then,
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Fig. 1. Geometrical relation between the input image, hologram, and virtual converging light.
we can derive Eq. (2) using the geometric relation, as shown in Fig. 1: f i : z1 Si : Sh:
(2)
After multiplying ax i ; y i by wx i ; y i , we calculate the diffraction to the hologram plane from the image plane to generate the hologram. Figure 2 is a reconstructed image of the image “Lena” from amplitude CGH generated by the random phase-free method in the numerical reconstruction. The numerical reconstruction conditions are shown in Table 1. In Table 1, “magnification” means the magnification S i ∕S h of the projected images using aliasing reduced scaled and shifted (ARSS) Fresnel diffraction [17]. This reconstructed image is not contaminated by speckle noise, but it is contaminated by ringing artifacts.
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Fig. 3. Iterative method for amplitude CGH.
A. Improving the Image Quality Using the Iterative Method
In order to remove the ringing artifact and to improve the image quality of the reconstructed images, we apply an iterative method to the random phase-free method [18]. Figure 3 shows the improved method for amplitude CGHs by using the iterative algorithm. The calculation steps of the iterative method are as follows: 1. We multiply the original image ax i ; y i by the converging light given by wx i ; y i . The resulting complex amplitude is defined as ui x i ; y i ax i ; y i × wx i ; y i . 2. We calculate the diffraction to the hologram plane from the image plane. In this paper, we use ARSS Fresnel diffraction [17] as the diffraction algorithm. This diffraction can perform light propagation with different sampling pitches on the hologram and image planes, leading to lensless zoomable holographic projection [3–5]. 3. We extract only the real part of uh x h ; y h on the amplitude CGH (constraint in the hologram plane): (3) gx h ; y h Refuh x h ; y h g: 4. We calculate inverse diffraction to the image plane from the hologram plane. The diffracted results are denoted by ui0 x i ; y i . 5. Weffi update only the amplitude part of ui0 x i ; y i by pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ax i ; y i . pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ui0 x i ; y i : (4) ax i ; y i × 0 jui x i ; y i j This is the constraint in the image plane. Subsequently, we obtain the new image plane ui x i ; y i . We repeat the above iteration of steps 2–5 until the preset iteration number or good image quality is reached. Figure 4 shows the reconstructed images of the image “Lena” from amplitude CGHs. These amplitude CGHs are generated by the iterative method. The ringing artifact is considerably reduced by the iterative method. ui x i ; y i
Fig. 2. Reconstructed image of the image “Lena” from the amplitude CGH generated by the random phase-free method in the numerical reconstruction.
Table 1.
Numerical Reconstruction Conditions
SLM resolution SLM pixel pitch (Sampling pitch in the hologram plane) Laser wavelength Projection distance z 2 Magnification
512 × 512 4.0 [μm]
3. MULTI-PROJECTION
513.8 [nm] 0.7 [m] ×12.0
We propose multi-holographic projection using the random phase-free method and the iteration algorithm in order to improve the image quality of the projected images. Figure 5 shows the setup for the multi-projection. A projector that simply
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Research Article to be projected by the iterative algorithm described in Section 2.1. 2. After the iteration process, we sum all the complex amplitude holograms. 3. Finally, we convert the complex amplitude holograms to the amplitude hologram.
Fig. 4. Reconstructed images from the amplitude CGHs generated by the combination of the random phase-free method and the iterative method in the numerical reconstruction.
Figures 7(a) and 7(b) show the original images on Screen 1 and Screen 2. The numerically reconstructed images of the images “Lena” and “Mandrill” from the amplitude CGHs that are generated by the random phase-free method without the iterative algorithm are shown in Figs. 7(c) and 7(d). Numerically reconstructed images from amplitude CGHs generated by the combination of the random phase-free method and the iterative method are shown in Figs. 7(e) and 7(f ). Figures 8(a) and 8(b) show the numerically reconstructed images from the amplitude CGHs that are generated by the conventional random phase method. Figures 8(c) and 8(d) show the numerically reconstructed images using the conventional random phase method with the iterative method.
Fig. 5. Setup for multi-holographic projection.
consists of a laser and a single-amplitude SLM is capable of projecting multiple images on “Screen 1” and “Screen 2” simultaneously. Figure 6 shows how to calculate the multi-projection hologram. The calculation steps of the multi-projection hologram are as follows: 1. We set the virtual spherical light wx i ; y i as shown in Fig. 6. Then, we generate the hologram for each image
Fig. 6. How to calculate the multi-projection hologram.
Fig. 7. (a) Original image for Screen 1. (b) Original image for Screen 2. Reconstructed images from amplitude CGHs generated by the random phase-free method without the iterative algorithm for (c) Screen 1 and (d) Screen 2 on numerical reconstruction. Numerically reconstructed images from amplitude CGHs generated by the combination of the random phase-free method and the iterative method for (e) Screen 1 and (f ) Screen 2.
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the original images and the reconstructed images (Figs. 7 and 8). When using the combination of the random phase-free method and the iterative method, these PSNRs are 30.66 and 24.05 dB, respectively. The PSNRs are higher than those of the conventional methods. 4. EXPERIMENTAL SETUP
Fig. 8. Reconstructed images from amplitude CGHs generated by the random phase method for (a) Screen 1 and (b) Screen 2 on numerical reconstruction. Reconstructed images from amplitude CGHs generated by the combination of the random phase method for (c) Screen 1 and (d) Screen 2, and the iterative method on numerical reconstruction.
The numerical reconstruction conditions are shown in Table 2. A comparison of Figs. 7(d) and 7(f ) shows that the ringing artifact by the iterative method is considerably reduced in the case of multi-projection. A comparison of Figs. 7(f ) and 8(d) shows that the speckle noise is reduced by the random phase-free method also in the case of multi-projection. Table 3 shows the peak signal-to-noise ratio (PSNR) between Table 2.
Magnification Iterative number
SLM resolution SLM pixel pitch (Sampling pitch in the hologram plane) Laser wavelength Projection distance of Screen 1 and Screen 2 Magnification Iterative number
2048 × 1080 4.0 [μm] 513.8 [nm] 0.5 [m] and 1.0 [m] ×6.0 10
PSNRs of the Reconstructed Images Random Phase Method
Screen 1 Screen 2
Table 4. Experimental Conditions
Numerical Reconstruction Conditions
SLM resolution SLM pixel pitch (Sampling pitch in the hologram plane) Laser wavelength Projection distance of Screen 1 and Screen 2
Table 3.
The optical experiment conditions are shown in Table 4. The optical system that we constructed is shown in Fig. 9. Figures 10(a) and 10(b) show the optical reconstructed images of the images “Lena” and “Mandrill” from the amplitude CGHs that are generated by the random phase-free method alone. The optical reconstructed images from the amplitude CGHs generated by the combination of the random phase-free method and the iterative method are shown in Figs. 10(c) and 10(d). In Figs. 11(a) and 11(b), we show the optical reconstructed images of the images “Lena” and “Mandrill” using the random phase method alone. In Figs. 11(c) and 11(d), we show the optical reconstructed images using the random phase method and the iterative algorithm. A comparison of Figs. 10(b) and 10(d) reveals that the uneven brightness in Fig. 10(d) is less than that in Fig. 10(b). This is because the ringing artifact was reduced by the iterative method. A comparison of Figs. 10(d) and 11(d) reveals that the speckle noise in Fig. 10(d) is less than that in Fig. 11(d). All of the calculations in this work were performed by our wave optics library: CWO++ [19].
Random Phase-Free Method
No Iteration [dB]
10 Iteration [dB]
No Iteration [dB]
10 Iteration [dB]
8.42 8.93
13.61 14.43
25.64 22.10
30.66 24.05
Fig. 9. Optical system.
1920 × 1080 8.5 [μm] 513.8 [nm] 0.8 [m] and 1.0 [m] ×3.0 10
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5. CONCLUSION We applied a combination of the random phase-free method and the iterative method to multi-projection. The PSNRs of the reconstructed images using the proposed method and conventional method were 30.66 and 13.61 dB, respectively. The PSNRs of the proposed method were higher than those of the conventional methods. The proposed method improved the image quality in the case of multi-projection. Funding. Japan Society for the Promotion of Science (JSPS) KAKENHI (25330125, 25240015); Kayamori Foundation of Information Science Advancement; Yazaki Memorial Foundation for Science and Technology. REFERENCES
Fig. 10. Optical reconstructed images from the amplitude CGHs generated by the random phase-free method for (a) Screen 1 and (b) Screen 2. Optical reconstructed images from the amplitude CGHs generated by a combination of the random phase-free method and the iterative method for (c) Screen 1 and (d) Screen 2.
Fig. 11. Optical reconstructed images from the amplitude CGHs generated by the random phase method alone for (a) Screen 1 and (b) Screen 2. Optical reconstructed images from the amplitude CGHs generated by the combination of the random phase method and the iterative method for (c) Screen 1 and (d) Screen 2.
1. E. Buckley, “Holographic laser projection,” J. Display Technol. 99, 1–6 (2010). 2. T. Shimobaba, T. Kakue, and T. Ito, “Real-time and low speckle holographic projection,” in IEEE International Conference on Industrial Informatics INDIN’ 15 (Special Session on Digital Holography for Industrial Applications) (IEEE, 2015), pp. 732–741. 3. T. Shimobaba, M. Makowski, T. Kakue, M. Oikawa, N. Okada, Y. Endo, R. Hirayama, and T. Ito, “Lensless zoomable holographic projection using scaled Fresnel diffraction,” Opt. Express 21, 25285– 25290 (2013). 4. I. Ducin, T. Shimobaba, M. Makowski, K. Kakarenko, A. Kowalczyk, J. Suszek, M. Bieda, A. Kolodziejczyk, and M. Sypek, “Holographic projection of images with step-less zoom and noise suppression by pixel separation,” Opt. Commun. 340, 131–135 (2015). 5. C. Chenliang, X. Jun, L. Qing, and L. Wei, “Speckle suppression in a scaled holographic display from single phase-only computer generated hologram,” SID Symp. Dig. Tech. Pap. 46, 526–529 (2015). 6. M. Makowski, M. Sypek, A. Kolodziejczyk, and G. Mikuła, “Threeplane phase-only computer hologram generated with iterative Fresnel algorithm,” Opt. Eng. 44, 125805 (2005). 7. P. Zhou, Y. Bi, M. Sun, H. Wang, F. Li, and Y. Qi, “Image quality enhancement and computation acceleration of 3D holographic display using a symmetrical 3D GS algorithm,” Appl. Opt. 53, G209–G213 (2014). 8. C. Chang, J. Xia, L. Yang, W. Lei, Z. Yang, and J. Chen, “Specklesuppressed phase-only holographic three-dimensional display based on double-constraint Gerchberg-Saxton algorithm,” Appl. Opt. 54, 6994–7001 (2015). 9. J. Amako, H. Miura, and T. Sonehara, “Speckle-noise reduction on kinoform reconstruction using a phase-only spatial light modulator,” Appl. Opt. 34, 3165–3171 (1995). 10. Y. Takaki and M. Yokouchi, “Speckle-free and grayscale hologram reconstruction using time-multiplexing technique,” Opt. Express 19, 7567–7579 (2011). 11. M. Makowski, “Minimized speckle noise in lens-less holographic projection by pixel separation,” Opt. Express 21, 29205–29216 (2013). 12. Y. Mori, T. Fukuoka, and T. Nomura, “Speckle reduction in holographic projection by random pixel separation with time multiplexing,” Appl. Opt. 53, 8182–8188 (2014). 13. T. Shimobaba and T. Ito, “Random phase-free computer-generated hologram,” Opt. Express 23, 9549–9554 (2015). 14. H. Aagedal, M. Schmid, T. Beth, S. Tiewes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996). 15. M. Pasienski and B. DeMarco, “A high-accuracy algorithm for designing arbitrary holographic atom traps,” Opt. Express 16, 2176–2190 (2008). 16. J. S. Liu, N. Collings, W. A. Crossland, D. P. Chu, A. Waddie, and M. R. Taghizadeh, “Simulation and experiment on generation of an arbitrary array of intense spots by a tiled hologram,” J. Opt. 12, 085402 (2010).
Research Article 17. T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. 15, 075405 (2013). 18. T. Shimobaba, M. Makowski, T. Kakue, N. Okada, Y. Endo, R. Hirayama, D. Hiyama, S. Hasegawa, Y. Nagahama, and T. Ito, “Numerical investigation of lensless zoomable holographic
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projection to multiple tilted planes,” Opt. Commun. 333, 274–280 (2014). 19. T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++:CWO++ library,” Comput. Phys. Commun. 183, 1124–1138 (2012).
