Abstract

We propose a digital micromirror device (DMD) holographic display, where speckleless holograms can be observed in the expanded viewing zone. Structured illumination (SI) is applied to expand the small diffraction angle of the DMD using a laser diode (LD) array. To eliminate diffraction noise from SI, we utilize an active filter array for the Fourier filter and synchronize it with the LD array. The speckle noise is reduced via temporal multiplexing, where the proposed system supports a dynamic video of 60 Hz using the DMD’s fast operation property. The proposed system is verified and evaluated with experimental results.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Holographic displays are considered the ultimate three-dimensional (3D) displays because they can reconstruct scattered wavefronts from virtual objects rather than two-dimensional (2D) images [14]. However, current liquid crystal (LC)-based spatial light modulators (SLMs) cannot support enough viewing conditions for users, such as a wide viewing angle with a large-sized hologram. The multiplication of the viewing angle and the size of the hologram is called the space-bandwidth product (SBP) [5], generally determined by the number of pixels of the SLM. Prior researches proposed spatial [6] or temporal multiplexing (TM) [7] of SLM to increase SBP of the holographic system. However, spatial multiplexing using multiple SLMs makes optical systems bulky and complicated. TM also has a limitation in that the framerate of the display is divided by the number of TM states. Although a wide viewing angle holographic display has been reported using non-periodic pinholes, there is a background noise issue due to the consistent number of pixels [8].

Another major issue of holographic displays is the speckle noise from a coherent light source [911]. Speckle is a random interference pattern from scattered coherent light, which severely degrades the quality of a reconstructed hologram. Also, high intensity from the constructive interference of the speckle can damage the human visual system. Speckle reduction methods have been proposed via a partially coherent light source [11] and temporal superposition [12]. When partially coherent light is used, the speckle is produced less due to the short coherence length. However, low coherence sacrifices spatial resolution and depth of field of the reconstructed hologram. On the other hand, the temporal superposition mitigates the speckle noise by summating multiple holograms having uncorrelated speckle patterns. It can be realized by applying the TM of holograms that are generated from different random phase patterns [13]. However, since the TM decreases the framerate of the display, a high-framerate SLM is required to apply the method.

Recently, the digital micromirror device (DMD) has been adopted for SLM of holographic display with the advantage of its high-speed operation [1417]. A DMD is composed of micromirrors that can represent the binary states. It allows the DMD to be used as a binary amplitude modulator with a high framerate above 10 kHz [18]. In an amplitude hologram, a complex wavefront is represented via the sideband amplitude encoding method, which adds a complex profile of the desired 3D object, its conjugate term, and DC bias. Then, a bandpass filter is placed on the Fourier plane to eliminate unwanted diffraction noise terms such as DC, the conjugate, and high orders. Combined with galvanometer scanners, a horizontally scanning holographic display, which provides a wide horizontal viewing angle, was proposed [14,15]. Although the system outperforms the conventional holographic display using LC-based SLMs in terms of SBP, there exist several issues such as 1D-only scanning and stability of the physical movement.

 

Fig. 1. (a) Schematic diagram of the conventional DMD holographic display. To apply the directional illumination method, LD and bandpass filter are shifted and are depicted as red arrows. (b) Schematic diagram of the proposed DMD holographic display, where LD and filter take an array structure. The viewing angle is expanded by the directional illumination with TM.

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In this Letter, we present a wide viewing angle holographic display system with reduced speckle noise, where the viewing zone is 2D expanded. First, we apply the directional illumination to expand the viewing angle, inspired by structured illumination microscopy (SIM) [1921]. The concept of SIM is that directional plane wave illumination leads to a shift of the specimen’s Fourier spectrum. If the DMD is illuminated by the ($ i $, $ j $)th directional plane wave, the Fourier spectrum of the hologram on the DMD is given by

$${\tilde H_\textit{ij}}\left( {\textbf k} \right) = F\left[ {{h_\textit{ij}}({\textbf r}) \times {e^{i{{\textbf k}_\textit{ij}}{\textbf r}}}} \right] = {H_\textit{ij}}\left( {{\textbf k} - {{\textbf k}_\textit{ij}}} \right),$$
where $ {\textbf r} $ and $ {\textbf k} $ are spatial and frequency vectors, respectively. $ {{\textbf k}_\textit{ij}} $ denotes the $ k $-vector of the illumination, and $ F $ is the Fourier transform operator. $ h $ is the binary signal that is sampled by pixelated structures of the DMD. From Eq. (1), it is found that the Fourier spectrum can be shifted by changing the illumination $ {{\textbf k}_\textit{ij}} $ without spatial movement. Figure 1(a) shows a schematic diagram of the conventional DMD holographic display. $ {{\textbf k}_\textit{ij}} $ is determined by the relation between focal length of the collimating lens ($ {f_1} $) and spatial location of the LD. The lateral shift of the LD while maintaining the position of the lens alters $ {{\textbf k}_\textit{ij}} $, depicted as dotted lines with red arrows. However, the position of the bandpass filter also needs to be adjusted because the Fourier spectrum including the signal with diffraction noise is shifted together. It is difficult to implement because the LD and the bandpass filter should move at high speeds corresponding to the level of display framerate with synchronization.

As a more practical approach, we use the light source and filter as an array rather than a single component. The schematic diagram of the proposed array system is shown in Fig. 1(b). Note that Fig. 1(b) shows the TM image, and the LD array and filter array are synchronized with the DMD. Each component of the LD array and filter array can be actively operated by electrical signals. By adopting the array structures, the directional illumination with proper noise filtering is realized by temporal switching of the arrays without spatial movement. In Eq. (1), the Fourier spectrum is multiplied by the filer array, and the inverse Fourier transform is operated through a lens ($ {f_3} $). The TM profile ($ {h_{\rm TM}} $) on the virtual DMD becomes

$${h_{\rm TM}} = \sum\limits_{i,j} {F^{ - 1}}\left[ {{H_\textit{ij}}\left( {{\textbf k} - {{\textbf k}_\textit{ij}}} \right) \cdot {M_\textit{ij}}({\textbf k})} \right],$$
where $ M $ is the mask profile of filter array. By matching $ {{\textbf k}_\textit{ij}} $ with the bandwidth of the DMD, the entire bandwidth can be expanded in proportion to the number of illumination ($ i \times j $). The expanded bandwidth makes the viewing angle of the hologram wider.

Another advantage of the proposed method is that the framerate of DMD is sufficiently high enough to adopt the temporal speckle reduction method while expanding the proposed viewing angle expansion method. The temporal speckle reduction preserves spatial resolution and depth of field of the hologram. We use the factor of speckle contrast ($ C $) to analyze the amount of the speckle noise. The speckle contrast is calculated by dividing the standard deviation of the intensity by the mean value. It is reduced as proportional to the inverse square root of the number of synthesized independent holograms if the holograms are added during a single frame. We generate the holograms with different random phases to avoid correlation of the speckle patterns. Then, the holograms are temporally multiplexed in a frame as long as each LD and corresponding filter are activated. The maximum number of speckle-reducing frames is calculated by dividing the DMD framerate by $ i \times j \times {f_o} $, where $ {f_o} $ is the output framerate of the implemented system. For instance, 36 sub-holograms can be multiplexed on the condition of a 60 Hz display, six times viewing angle expansion, and 12,987 Hz framerate supporting DMD. Then, the speckle contrast can be reduced 1/6 times. Note that since each filter and LD are still activated during the speckle-reducing frames, they require only the framerate of 360 Hz ($ 3 \times 2 \times 60 $).

The prototype is designed and implemented for demonstration of the presented method. The DLP9000X model from Texas Instruments is used for DMD, whose resolution is WQXGA ($ 1600 \times 2560 $ pixels), and pixel pitch is $ 7.56\; \unicode{x00B5}{\rm m} $. We customize the LD array by mounting six (${i}={1}$, 2, 3 and ${j}={1}$, 2) commercialized LD modules (Thorlabs, CTF635F, wavelength of 635 nm). Focal lengths of the lenses ($ {f_1} $, $ {f_2} $, and $ {f_3} $) are 125 mm, 200 mm, and 100 mm, respectively. The filter array is also customized by attaching commercially available polarization shutters (LC-TEC, PolarSpeed-S-AR), where the periodic pitch between each shutter ($ p $) is 13 mm. Each shutter provides a high framerate of 540 Hz, making it suitable for use with the proposed TM method. This feature allows the viewing angle to be expanded up to nine times with a 60 Hz display.

Figure 2 shows the sideband encoding strategy with the diffraction noise filtering method. In this prototype, the filter array passes bottom sidebands for bottom views (${j}={1}$) and top sidebands for top views (${j}={2}$). Since the opposite side of the Fourier spectrum is conjugated, we pre-conjugate the hologram of top views to compensate for it. When a commercialized SLM is used, the shape of the sideband is a rectangle with a 2:1. To match the shape with the shutter used in this Letter, i.e., square shape, we apply an anamorphic transform to change the ratio of the Fourier spectrum [22]. The anamorphic transform system is composed of a lens ($ f = 100 \; {\rm mm} $), two $ x $-cylindrical lenses ($ f = 150 \; {\rm mm} $), and a $ y $-cylindrical lens ($ f = 75 \; {\rm mm} $), located between the DMD and the lens ($ {f_2} $) in Fig. 1 (omitted for simplicity). The magnifications of the anamorphic system are $ {m_x} = 1.50 $ and $ {m_y} = 0.75 $. Then, we design the pitch between each LD ($ d $) to match the spatial shifts of the Fourier spectrum with the period of the filter array ($ p $). The $ d $ is set as 12.2 mm when $ p $ is 13 mm by the relation of $ d = {f_1}{m_x}p/{f_2} = 2{f_1}{m_y}p/{f_2} $. The spatial size of the single-side band for each illumination is calculated by $ {w_x} = 2{f_2}\tan [ {{{\sin }^{ - 1}}(\lambda /2q{m_x})} ] $ and $ {w_y} = {f_2}\tan [ {{{\sin }^{ - 1}}(\lambda /2q{m_y})} ] $, where $ \lambda $ is wavelength, and $ q $ is the pixel pitch of DMD.

 

Fig. 2. Frequency domain design to utilize the filter array. The sideband encoding and the anamorphic transformation are implemented to match the structure of the filter array. The DC components are blocked using the bezel of the array.

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Although the proposed method expands viewing angles corresponding to directional illumination, the expanded wavefront suffers optical aberrations due to deviation from the optical axis. We pre-compensate for the aberrations arising from the optical system by modulating the phase profile of the hologram. We experimentally obtain the correction phase profiles through the Zernike feedback algorithm [1,4]. The coefficients of several major aberrations (tilt, defocus, and astigmatism) are acquired in the implemented system to make the sharpest point spread function in the intended 3D space. Since the optical aberration functions are spatially variant, it is required to obtain the correction phase functions for every 3D object point. However, to find and apply the correction functions for all points is impractical because over two million pixels of DMD requires too high computational costs. Assuming that the aberration function is smoothly variant and the differences in depth are negligible, we obtain only a total of six global correction functions, each corresponding to the central 3D point of each illumination. Then correction is applied using each global correction phase map for each illumination. The $ 4f $ relay system is implemented using aberration-corrected camera lenses (Canon, F1.8, $ {f_1} $ of 200 mm and Zeiss, F2.0, $ {f_2} $ of 100 mm) to support the assumption of slow-varying variation.

 

Fig. 3. (a) Example of captured image from raw binary hologram. (b) Aberration-corrected result using a correction map. (c) Speckle-noise-reduced result by TM. (d) Pre-measured global correction maps.

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Fig. 4. (a) Speckle contrast ratio versus the number of TM. (b), (c) Experimental results of the 2D uniform hologram without TM and with TM of 30 frames, respectively. (d), (e) Enlarged distributions of (b) and (c), respectively.

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We display the holograms blended from intensities and depth maps of six orthographic views. The holograms are generated by the layers-based method [23], where they are sliced by 32 depths and have a depth range from 0.5 cm to 1.4 cm after the relayed virtual DMD. The size of the hologram is $ 9.1 \times 7.3 \times 0.9 \;{{\rm mm}^3} $. The experimental results are captured using a CCD sensor (FLIR, GS3-U3-91S6C-C) adapted with a C-mount lens (Nikon, AF Micro Nikkor 60 mm F2.8). The shutter speed of the image sensor is set as 1/60 s for all the results in this Letter. Figure 3 is an example of the experimental result showing the process and effect of the aberration correction and the speckle reduction method. Figure 3(b) shows that the aberrations are well corrected using the proposed global method compared with the raw hologram [Fig. 3(a)]. The pre-measured global correction map is used corresponding to each LD, as shown in Fig. 3(d). We multiplex 30 holograms for each frame by changing the random phase profile to reduce speckle noise. In Fig. 3(c), it is confirmed that the quality of the hologram is remarkably enhanced with TM. Next, a 2D hologram of the uniform intensity image is captured to analyze the speckle reduction method quantitatively. Figure 4(a) shows the experimentally obtained speckle contrast ratio with increasing numbers of TM states. Figures 4(b) and 4(c) are the captured images when the number of TM is 1 and 30, and Figs. 4(d) and 4(e) are zoom-in intensity profiles, respectively. The speckle contrast values are calculated as 0.2827 and 0.0581. It shows that the implemented system reduces the speckle contrast as the ratio of 0.2055 when 30 frames are multiplexed. The reduction ratio is well matched with the theoretically expected value of 0.1826, and the overall tendency is also consistent with the theory (inverse square root of the number of TM).

 

Fig. 5. Captured results in changing the image sensor’s observation angles. Each viewing zone covers $ \pm {3.2^ \circ } \times \pm {3.2^ \circ } $ from the center axis, indicated by the inset in the right bottom.

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Fig. 6. (a) Experimental result when the 2D (first) and 3D holograms (second through fourth) are displayed. (b) Four sample frames of the holographic video as focusing on the middle depth. Top columns are experimental photographs, and bottoms are input images (see Visualization 1).

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Figure 5 is a set of experimentally captured images according to the viewing angle. The image sensor focuses on the head of the dragon hologram. In the sub-images, the left bottom insets are the number of illuminations ($ i $, $ j $), and the right bottom insets are the observing angles corresponding to the center of each viewing zone. Considering the bezel of the used filter and efficiency of the hologram’s information, we design each viewing angle as $ \pm {3.2^ \circ } \times \pm {3.2^ \circ } $ rather than the period of the sub-viewing zone of 7.4°, where it is given by $ \tan ^{ - 1} (p/{f_3}) $. It has an advantage in that the size of the hologram increases but brings some non-observable regions to the boundary of the sub-viewing zones. The discrete viewing angle issue would be mitigated as the fill factor of the filter array is enhanced in the future. Using the proposed TM illumination technique, the viewing zone is 2D expanded to $ \pm {9.6^ \circ } \times \pm {6.4^ \circ } $ effectively. We carry out another experiment to show a 3D focus cue with the feasibility of the high-framerate application using a 3D object of the butterfly. Figure 6(a) is a captured image of shifting the focal plane of the image sensor. The first image is obtained when the object is rendered and displayed on the 2D plane (1.4 cm after DMD) for comparison. The object is 3D rendered in identical conditions with the dragon object to capture the second through fourth images. The focus cue is confirmed by the results of changing the focal plane. Finally, holographic videos are recorded sequentially, changing the focal planes from the front to the rear. The videos are recorded as 60 Hz using a high-framerate CMOS sensor (FLIR, FL3-U3-20E4C-C). Four sample frames of the video with input images are illustrated in Fig. 6(b). Entire frames are available from Visualization 1.

In conclusion, we propose and experimentally demonstrate TM with directional illumination for expanding the viewing angle and reducing speckle noise. Using the DMD’s fast operation time, the high framerate of the holographic video display is realized while adopting both advantages. In this Letter, we focus on the hologram formed directly after the SLM, but this technique can also be applied to the case in which the hologram is formed through the lens, called Fourier holography. Then, the size of the hologram becomes larger. A full-color configuration also can be realized by designing the filter array with R/G/B structured illumination considering the diffraction characteristic of DMD. In this case, the framerate is reduced by a factor of three. Since the present method increases SBP and reduced speckle noise, which is a fundamental limitation of the holographic display, we expect that the proposed technique can be utilized for various applications such as hologram calculation [24] and table-top and near-eye holographic displays.

Funding

Korean National Police Agency (PA-H000001); Samsung Display.

Disclosures

The authors declare no conflicts of interest.

REFERENCES

1. A. Maimone, A. Georgiou, and J. S. Kollin, ACM Trans. Graph. 36, 85 (2017). [CrossRef]  

2. G. Li, D. Lee, Y. Jeong, J. Cho, and B. Lee, Opt. Lett. 41, 2486 (2016). [CrossRef]  

3. H. Yu, K. Lee, J. Park, and Y. Park, Nat. Photonics 11, 186 (2017). [CrossRef]  

4. C. Jang, K. Bang, G. Li, and B. Lee, ACM Trans. Graph. 37, 1 (2018). [CrossRef]  

5. G. Zheng, R. Horstmeyer, and C. Yang, Nat. Photonics 7, 739 (2013). [CrossRef]  

6. J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, Opt. Express 16, 12372 (2008). [CrossRef]  

7. G. Li, J. Jeong, D. Lee, J. Yeom, C. Jang, S. Lee, and B. Lee, Opt. Express 23, 33170 (2015). [CrossRef]  

8. J. Park, K. Lee, and Y. Park, Nat. Commun. 10, 1 (2019). [CrossRef]  

9. Y. Deng and D. Chu, Sci. Rep. 7, 5893 (2017). [CrossRef]  

10. Z. Cui, A.-T. Wang, Z. Wang, S.-L. Wang, C. Gu, H. Ming, and C.-Q. Xu, J. Disp. Technol. 11, 330 (2015). [CrossRef]  

11. D. Lee, C. Jang, K. Bang, S. Moon, G. Li, and B. Lee, IEEE Trans Ind. Informat. 15, 6170 (2019). [CrossRef]  

12. Y. Mori, T. Fukuoka, and T. Nomura, Appl. Opt. 53, 8182 (2014). [CrossRef]  

13. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).

14. Y. Takaki and K. Fujii, Opt. Express 22, 24713 (2014). [CrossRef]  

15. Y. Takaki, Y. Matsumoto, and T. Nakajima, Opt. Express 23, 26986 (2015). [CrossRef]  

16. M. Chlipala and T. Kozacki, Opt. Lett. 44, 4255 (2019). [CrossRef]  

17. J.-Y. Son, B.-R. Lee, O. O. Chernyshov, K.-A. Moon, and H. Lee, Opt. Lett. 38, 3173 (2013). [CrossRef]  

18. S. Lee, Y. Jo, D. Yoo, J. Cho, D. Lee, and B. Lee, Nat. Commun. 10, 1 (2019). [CrossRef]  

19. M. G. Gustafsson, J. Microsc. 198, 82 (2000). [CrossRef]  

20. B. Lee, J.-Y. Hong, D. Yoo, J. Cho, Y. Jeong, S. Moon, and B. Lee, Optica 5, 976 (2018). [CrossRef]  

21. B. Lee, C. Jang, D. Kim, and B. Lee, IEEE Trans. Ind. Informat. 15, 6155 (2019). [CrossRef]  

22. H. Kim, C.-Y. Hwang, K.-S. Kim, J. Roh, W. Moon, S. Kim, B.-R. Lee, S. Oh, and J. Hahn, Appl. Opt. 53, G139 (2014). [CrossRef]  

23. H. Zhang, L. Cao, and G. Jin, Appl. Opt. 56, F138 (2017). [CrossRef]  

24. G. Makey, Ö. Yavuz, D. K. Kesim, A. Turnalı, P. Elahi, S. Ilday, O. Tokel, and F. Ö. Ilday, Nat. Photonics 13, 251 (2019). [CrossRef]  

References

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  1. A. Maimone, A. Georgiou, and J. S. Kollin, ACM Trans. Graph. 36, 85 (2017).
    [Crossref]
  2. G. Li, D. Lee, Y. Jeong, J. Cho, and B. Lee, Opt. Lett. 41, 2486 (2016).
    [Crossref]
  3. H. Yu, K. Lee, J. Park, and Y. Park, Nat. Photonics 11, 186 (2017).
    [Crossref]
  4. C. Jang, K. Bang, G. Li, and B. Lee, ACM Trans. Graph. 37, 1 (2018).
    [Crossref]
  5. G. Zheng, R. Horstmeyer, and C. Yang, Nat. Photonics 7, 739 (2013).
    [Crossref]
  6. J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, Opt. Express 16, 12372 (2008).
    [Crossref]
  7. G. Li, J. Jeong, D. Lee, J. Yeom, C. Jang, S. Lee, and B. Lee, Opt. Express 23, 33170 (2015).
    [Crossref]
  8. J. Park, K. Lee, and Y. Park, Nat. Commun. 10, 1 (2019).
    [Crossref]
  9. Y. Deng and D. Chu, Sci. Rep. 7, 5893 (2017).
    [Crossref]
  10. Z. Cui, A.-T. Wang, Z. Wang, S.-L. Wang, C. Gu, H. Ming, and C.-Q. Xu, J. Disp. Technol. 11, 330 (2015).
    [Crossref]
  11. D. Lee, C. Jang, K. Bang, S. Moon, G. Li, and B. Lee, IEEE Trans Ind. Informat. 15, 6170 (2019).
    [Crossref]
  12. Y. Mori, T. Fukuoka, and T. Nomura, Appl. Opt. 53, 8182 (2014).
    [Crossref]
  13. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).
  14. Y. Takaki and K. Fujii, Opt. Express 22, 24713 (2014).
    [Crossref]
  15. Y. Takaki, Y. Matsumoto, and T. Nakajima, Opt. Express 23, 26986 (2015).
    [Crossref]
  16. M. Chlipala and T. Kozacki, Opt. Lett. 44, 4255 (2019).
    [Crossref]
  17. J.-Y. Son, B.-R. Lee, O. O. Chernyshov, K.-A. Moon, and H. Lee, Opt. Lett. 38, 3173 (2013).
    [Crossref]
  18. S. Lee, Y. Jo, D. Yoo, J. Cho, D. Lee, and B. Lee, Nat. Commun. 10, 1 (2019).
    [Crossref]
  19. M. G. Gustafsson, J. Microsc. 198, 82 (2000).
    [Crossref]
  20. B. Lee, J.-Y. Hong, D. Yoo, J. Cho, Y. Jeong, S. Moon, and B. Lee, Optica 5, 976 (2018).
    [Crossref]
  21. B. Lee, C. Jang, D. Kim, and B. Lee, IEEE Trans. Ind. Informat. 15, 6155 (2019).
    [Crossref]
  22. H. Kim, C.-Y. Hwang, K.-S. Kim, J. Roh, W. Moon, S. Kim, B.-R. Lee, S. Oh, and J. Hahn, Appl. Opt. 53, G139 (2014).
    [Crossref]
  23. H. Zhang, L. Cao, and G. Jin, Appl. Opt. 56, F138 (2017).
    [Crossref]
  24. G. Makey, Ö. Yavuz, D. K. Kesim, A. Turnalı, P. Elahi, S. Ilday, O. Tokel, and F. Ö. Ilday, Nat. Photonics 13, 251 (2019).
    [Crossref]

2019 (6)

J. Park, K. Lee, and Y. Park, Nat. Commun. 10, 1 (2019).
[Crossref]

D. Lee, C. Jang, K. Bang, S. Moon, G. Li, and B. Lee, IEEE Trans Ind. Informat. 15, 6170 (2019).
[Crossref]

M. Chlipala and T. Kozacki, Opt. Lett. 44, 4255 (2019).
[Crossref]

S. Lee, Y. Jo, D. Yoo, J. Cho, D. Lee, and B. Lee, Nat. Commun. 10, 1 (2019).
[Crossref]

B. Lee, C. Jang, D. Kim, and B. Lee, IEEE Trans. Ind. Informat. 15, 6155 (2019).
[Crossref]

G. Makey, Ö. Yavuz, D. K. Kesim, A. Turnalı, P. Elahi, S. Ilday, O. Tokel, and F. Ö. Ilday, Nat. Photonics 13, 251 (2019).
[Crossref]

2018 (2)

2017 (4)

A. Maimone, A. Georgiou, and J. S. Kollin, ACM Trans. Graph. 36, 85 (2017).
[Crossref]

Y. Deng and D. Chu, Sci. Rep. 7, 5893 (2017).
[Crossref]

H. Yu, K. Lee, J. Park, and Y. Park, Nat. Photonics 11, 186 (2017).
[Crossref]

H. Zhang, L. Cao, and G. Jin, Appl. Opt. 56, F138 (2017).
[Crossref]

2016 (1)

2015 (3)

2014 (3)

2013 (2)

2008 (1)

2000 (1)

M. G. Gustafsson, J. Microsc. 198, 82 (2000).
[Crossref]

Bang, K.

D. Lee, C. Jang, K. Bang, S. Moon, G. Li, and B. Lee, IEEE Trans Ind. Informat. 15, 6170 (2019).
[Crossref]

C. Jang, K. Bang, G. Li, and B. Lee, ACM Trans. Graph. 37, 1 (2018).
[Crossref]

Cao, L.

Chernyshov, O. O.

Chlipala, M.

Cho, J.

Chu, D.

Y. Deng and D. Chu, Sci. Rep. 7, 5893 (2017).
[Crossref]

Cui, Z.

Z. Cui, A.-T. Wang, Z. Wang, S.-L. Wang, C. Gu, H. Ming, and C.-Q. Xu, J. Disp. Technol. 11, 330 (2015).
[Crossref]

Deng, Y.

Y. Deng and D. Chu, Sci. Rep. 7, 5893 (2017).
[Crossref]

Elahi, P.

G. Makey, Ö. Yavuz, D. K. Kesim, A. Turnalı, P. Elahi, S. Ilday, O. Tokel, and F. Ö. Ilday, Nat. Photonics 13, 251 (2019).
[Crossref]

Fujii, K.

Fukuoka, T.

Georgiou, A.

A. Maimone, A. Georgiou, and J. S. Kollin, ACM Trans. Graph. 36, 85 (2017).
[Crossref]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).

Gu, C.

Z. Cui, A.-T. Wang, Z. Wang, S.-L. Wang, C. Gu, H. Ming, and C.-Q. Xu, J. Disp. Technol. 11, 330 (2015).
[Crossref]

Gustafsson, M. G.

M. G. Gustafsson, J. Microsc. 198, 82 (2000).
[Crossref]

Hahn, J.

Hong, J.-Y.

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, Nat. Photonics 7, 739 (2013).
[Crossref]

Hwang, C.-Y.

Ilday, F. Ö.

G. Makey, Ö. Yavuz, D. K. Kesim, A. Turnalı, P. Elahi, S. Ilday, O. Tokel, and F. Ö. Ilday, Nat. Photonics 13, 251 (2019).
[Crossref]

Ilday, S.

G. Makey, Ö. Yavuz, D. K. Kesim, A. Turnalı, P. Elahi, S. Ilday, O. Tokel, and F. Ö. Ilday, Nat. Photonics 13, 251 (2019).
[Crossref]

Jang, C.

B. Lee, C. Jang, D. Kim, and B. Lee, IEEE Trans. Ind. Informat. 15, 6155 (2019).
[Crossref]

D. Lee, C. Jang, K. Bang, S. Moon, G. Li, and B. Lee, IEEE Trans Ind. Informat. 15, 6170 (2019).
[Crossref]

C. Jang, K. Bang, G. Li, and B. Lee, ACM Trans. Graph. 37, 1 (2018).
[Crossref]

G. Li, J. Jeong, D. Lee, J. Yeom, C. Jang, S. Lee, and B. Lee, Opt. Express 23, 33170 (2015).
[Crossref]

Jeong, J.

Jeong, Y.

Jin, G.

Jo, Y.

S. Lee, Y. Jo, D. Yoo, J. Cho, D. Lee, and B. Lee, Nat. Commun. 10, 1 (2019).
[Crossref]

Kesim, D. K.

G. Makey, Ö. Yavuz, D. K. Kesim, A. Turnalı, P. Elahi, S. Ilday, O. Tokel, and F. Ö. Ilday, Nat. Photonics 13, 251 (2019).
[Crossref]

Kim, D.

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Supplementary Material (1)

NameDescription
» Visualization 1       Holographic 3D video. The camera sequentially changes the focal plane from the front to the rear.

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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic diagram of the conventional DMD holographic display. To apply the directional illumination method, LD and bandpass filter are shifted and are depicted as red arrows. (b) Schematic diagram of the proposed DMD holographic display, where LD and filter take an array structure. The viewing angle is expanded by the directional illumination with TM.
Fig. 2.
Fig. 2. Frequency domain design to utilize the filter array. The sideband encoding and the anamorphic transformation are implemented to match the structure of the filter array. The DC components are blocked using the bezel of the array.
Fig. 3.
Fig. 3. (a) Example of captured image from raw binary hologram. (b) Aberration-corrected result using a correction map. (c) Speckle-noise-reduced result by TM. (d) Pre-measured global correction maps.
Fig. 4.
Fig. 4. (a) Speckle contrast ratio versus the number of TM. (b), (c) Experimental results of the 2D uniform hologram without TM and with TM of 30 frames, respectively. (d), (e) Enlarged distributions of (b) and (c), respectively.
Fig. 5.
Fig. 5. Captured results in changing the image sensor’s observation angles. Each viewing zone covers $ \pm {3.2^ \circ } \times \pm {3.2^ \circ } $ from the center axis, indicated by the inset in the right bottom.
Fig. 6.
Fig. 6. (a) Experimental result when the 2D (first) and 3D holograms (second through fourth) are displayed. (b) Four sample frames of the holographic video as focusing on the middle depth. Top columns are experimental photographs, and bottoms are input images (see Visualization 1).

Equations (2)

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H ~ ij ( k ) = F [ h ij ( r ) × e i k ij r ] = H ij ( k k ij ) ,
h T M = i , j F 1 [ H ij ( k k ij ) M ij ( k ) ] ,

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