Abstract

An efficient method to implement the coarse integral holographic (CIH) concept for dynamic CIH displays is to scan the information generated from a spatial light modulator (SLM) of a low space bandwidth product (SBP) but high bandwidth to form the hologram array for the integral optics. Previously, just over half of the SLMs bandwidth was utilized due to the fact that the galvanometer scanner in use could not tile all the holograms that the SLM is capable to produce, resulting in the loss of nearly half of the field of view (FOV). Here, we propose a full bandwidth dynamic CIH display using a large resonant scanner in conjunction with a hybrid raster scanner, which can utilize the full bandwidth of the spatial light modulator and double the horizontal FOV. Experimental results confirm that with the SLM and scanners as used, the FOV can reach 48° when the SLM reaches its full bandwidth. This approach can be used for future scalable and tileable CIH display systems.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Holographic video is considered the holy-grail of three-dimensional (3D) auto-stereo displays because it generates arbitrary wavefronts providing imagery with all the 3D visual cues [1–7]. It has various potential applications such as 3D game, 3D television (TV), 3D advertisement, 3D medical imaging, etc [8–11]. 3D holographic video displays are implemented by computer-generated hologram (CGH), spatial light modulator (SLM) and laser sources [12–16], where the CGH algorithm calculates the diffraction pattern that reconstructs the 3D scene when the laser beam illuminates the SLM presenting the CGH. Unfortunately, the information content of a hologram with a large optical extent, i.e. the product of image size and field of view (FOV), is much greater than the capabilities of current spatial light modulators (SLMs) due to their low space bandwidth product (SBP) (large pixel pitch and small area) [17].

Recently, many 3D hologram display systems are proposed to improve the information content using different scanning mechanisms. Takaki et al. proposed a horizontally scanning holographic display system [18]. An image generated by a high-speed SLM is squeezed in the horizontal direction and enlarged in the vertical direction by an anamorphic imaging system. The anamorphic imaging system, consisting of two orthogonally aligned cylindrical lenses, has different magnifications in the horizontal and vertical directions. MIT proposed the holographic video display system [19], in which the travelling high-resolution one-dimensional holographic fringes generated by an acousto-optic modulator are descanned using a polygonal scanner. The number of pixels and the pixel pitch of the modulator were 1,080 × 1,920 and 8.0μm × 8.0μm, respectively. Xuewu et al developed a full colour full-parallax digital 3D holographic display system by using 24 physically tiled SLMs, an optical scan tiling approach and two sets of RGB lasers, which could display 378-Mpixel holograms at 60 Hz, with a displayed image size of 10 inch in diagonal [20]. Jia et al. developed a scanning 3D colour video display based on rotational tiled gratings and a vertical diffuser [21].

We previously proposed a Coarse Integral Holography (CIH) [22], which uses coarse integral optics to angularly tile several low SBP holograms to form a modest size but wide FOV display (i.e. a larger optical extent). An array of holograms, each with full 3D information and representing a slightly different viewing angle, is arranged behind the coarse integral optics consisting of a matching lenslet array and a large common transform lens. The choice of the array layout allows view information to be flexibly distributed between the horizontal and vertical FOVs, which can be adjusted separately. We have demonstrated static and dynamic CIH displays. The static physical prototype of a CIH display is achieved by recording a static array of holograms in a holographic film and appropriate coarse integral optics [22]. The dynamic holographic video was achieved by scanning a single low SBP but high bandwidth (e.g. moderate resolution, coarse density, and high frame rate) SLM to angularly tile multiple holograms into a large image size and large FOV [23].

However, the previous CIH display was only able to use 50% of the SLM’s bandwidth due to the limited spatial bandwidth of the galvanometer mirror scanner. The scanning system could not tile (without overlap) the total number of sub-holograms which the SLM was capable of producing in one frame period. In this paper, we propose a novel scanning method incorporating a cascaded scanner with an x-y raster scanner fully utilizing the SLM bandwidth for the current CIH display to increase the hologram’s horizontal FOV.

2. CIH displays

CIH uses coarse integral optics to angularly tile several low SBP holograms to form a modest size wide apparent FOV angle (FOVA). Figure 1 shows the principle of CIH displays. An array of holograms, each with full 3D information and representing a slighting different view angle, is arranged behind the coarse integral optics consisting of a matching physical or virtual lenslet array and a large common transform lens. The choice of the array layout allows view information to be flexibly distributed between the horizontal and vertical FOVA, which can be adjusted separately. The dynamic version of the CIH was established by scanning a single low SPB but high bandwidth SLM to form the virtual hologram array for the integral optics. Moreover, the full colour display (with three primary colours) has also been incorporated using time sequential colour scheme and taking advantage of the SLM’s high bandwidth.

 figure: Fig. 1

Fig. 1 The principle of CIH displays, (a) layer-based algorithm for calculating a 3D hologram, (b) static CIH display, and (c) dynamic CIH display.

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CIH display systems use the CGH algorithms to calculate a 3D hologram, complete with depth and parallax cues, from different view positions. Multiple fast CGH algorithms have been demonstrated [24–28]. In this CIH system, we use a layer-based algorithm to calculate holograms. The algorithm can be summarized into four steps: (i) a 3D object’s depth information and image information is rendered from multiple angular views. The depth information is used to separate the image information into multiple layers images of the 3D object sliced along its depth direction, which can be expressed as:

G(x,y,z)=nGn(x,y)
(ii) Each layer image is Fourier transformed to create a Fourier holographic pattern for that layer. Pn(x,y)=FFT(Gn(x,y)). (iii) Each layer’s Fourier hologram is multiplied by a holographic lens to allow the image plane to be reconstructed at its appropriate depth, which can be expressed as:
Qn(x,y)=Pn(x,y)×exp[jk2(x2znx+y2zny)]
(iv) The summation of layers becomes the final hologram for this view:

Q(x,y)=n=1NQn(x,y)

The calculated holograms can be reconstructed by a static CIH display system with a lens array, or by a dynamic CIH display system with a scanning system. In the scanning system, the frequency of the x-axis scanner is 70Hz with FOVA angle of 24°. The previous CIH display had 30 horizontal sub-holograms and 6 vertical sub-holograms. The video frame frequency was 23.33 Hz. The DMD used as a SLM has a pixel size of 1,024 pixels × 768 pixel. The bandwidth of this CIH system is expressed by 1024 pixels × 768 pixel × 30 H-views × 6 V-views × 3 colours × 1 bit × 23.33 frame/s = 9.0x109 bit/sec. The maximum global array switching rate for the DMD is 22,727 frames per second. Thus, the full SLM bandwidth is calculated by 1,024 pixels × 768 pixel × 22.727 k frames/s = 17.8x109 bit/sec. Therefore, the CIH display was only able to use 50% of the SLMs bandwidth.

To fully utilize the SLM bandwidth of the previous CIH display, the scanner’s mirror size, horizontal deflection angle, and/or scanning frequency must be increased. However, the previous CIH display used the best performing commercial galvanometer available for the aluminum mirror’s size, deflection. We investigated using an auxiliary resonant vertical dither scanner, using the extra bandwidth to create vertical sub-lines for each horizontal scan lines, thereby increasing the number of vertical sub-holograms [29]. The additional scanner however, adds cost, size, and is optically, mechanically and electronically more complicated than the previous CIH system.

To implement full bandwidth displays in this proposed investigation, we used a new hybrid raster scanner (HRS) using a large resonant scanner and a large galvanometer scanner. This HRS has a larger FOVA at the same frequency as the previous CIH system, allowing double the number of horizontal sub-holograms and FOV, and, full utilization of the SLM’s bandwidth. Compared to the vertical dither resonant scanner system, the proposed method would provide a larger horizontal FOV and parallax, as well as vertical FOV. Moreover, the propose method is optically similar to the previous dynamic CIH, while optically, mechanically and electronically simple.

3. Proposed full bandwidth CIH displays based on a hybrid raster scanner

3.1. Full bandwidth CIH displays

To achieve a CIH display that uses the full bandwidth of the SLM, we propose a scanning CIH display system with a hybrid raster scanner. This section will discuss the system architecture, the SLM/scanner synchronization schemes, and the calibrations setup, including derivation of the model of the scans coordinate system through the scanners.Figure 2 shows the scanning principle of full bandwidth CIH display system using HRS. The full bandwidth CIH display system includes a HRS, two 4f-systems, a Fourier transform lens, a DMD and a laser sub-system. The HRS is composed of a one-dimensional (1D) resonant scanner (1D-RS) and a one-dimensional galvanometric scanner (1D-GS), as shown in Fig. 3. The 1D-RS is located at the focal-plane of the first 4f-system. The first 4f-system, consisting of two convex lens (#1 lens and #2 lens), is located the between Fourier transform lens and 1D-RS and enlarges the hologram size from the Fourier transform lens. The 1D-RS is used as the horizontal scanner while the 1D-GS as the vertical scanner. The 1D-RS and 1D-GS are used to raster the sub-holograms into an array, and equivalently scan the horizontal and vertical fields of view. Another 4f-system (#3 lens and #4 lens) is used as the final optical system in scanning system to arrange the sub-holograms and lenslets and angularly tile them into a larger array, or equivalently relay the angularly scanned hologram from the scanner into free space. The maximal scanning angle represents the maximal FOVA of the display system. The 1D-RS scans sub-holograms to form the horizontal FOV. We can lay out different sub-view holograms during the whole scanning range. The galvanometric scanner scans to form the vertical FOV by vertically distributing rows of horizontal sub-holograms. The space bandwidth product (SBP) of the display is expressed by SBP = H × V × C × R × N × F, where H and V is the resolution of the DMD, N is the number of colour lasers, F is the frame rate of the DMD, C is the number of sub-holograms and view zones in horizontal direction, and R is the sub-holograms and view zones in vertical direction. The diffraction equation of a hologram presented on the SLM [18,19] is d(sinφr-sinφi) = , where φr is the diffraction angle, φi is the incidence angle, m is the diffraction order, λ is the beam wavelength, and d is a pixel pitch of the SLM used for displaying the diffraction fringes. Here φr = -φi = φ because the dynamic CIH uses a DMD as the SLM. Thus, the diffraction equation becomes 2dsinφ = . Therefore, the hologram’s horizontal and vertical diffraction view zones are φ = arcsin(mλ/2d). Thus, the view zone extent of each sub-hologram of the dynamic CIH is same because each sub-hologram uses the same wavelength and SLM. To achieve full SBP utilization of the DMD, the proposed system uses the resonant scanner’s improved horizontal scan capabilities to increase the number of horizontal sub-holograms. Keeping the same view zone extent of each sub-hologram, the overall horizontal number of view zones and FOV are doubled in the proposed system. Resonant scanners are electromechanically driven oscillating devices with a sinusoidal motion of a fixed frequency [30–33], which allow a higher working frequency and a larger mirror at same scanning angle or a larger scanning angle and larger mirror size at the same scanning frequency to a galvanometric scanner.

 figure: Fig. 2

Fig. 2 CIH display with Hybrid Resonant Scanner (HRS): horizontal resonant scanner and vertical galvanometer. Lens L1 to L4 are attached lens array (virtual).

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 figure: Fig. 3

Fig. 3 The principle of HRS.

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We use a large SC-21 type resonant scanner provided by Electro-Optical Products Corporation. Different torsion mode scanners [34–36], the scanner is a taut band scanner, of which the spring is fastened to the frame at both ends, making the scanner much less susceptible to wobbling at low frequencies. Figure 3 shows the structure of the 1D-RS. The 1D-RS is composed of a round mirror, a spring, a scanner base, a pair of armatures. The mirror is fixed to the spring, which is anchored to the scanner base. The armatures, made by iron or magnetic materials, are attached to the spring and passes through the magnetic field of a drive coil. The drive coil is modulated to implement the oscillatory motion of the rotor assembly (the spring, armature, and mirror assembly). The 1D-RS also includes a pickup coil, which can determine the mirror’s position and provide feedback to an auto-gain control (AGC) driver. The AGC driver energizes the drive coil at the scanner’s resonant frequency. 1D-GS is a galvanometer scanner, which can be steered to a desired position [37–40], while 1D-RS cannot be frequency modulated. Therefore, we use the signal from the pickup coil to synchronously control the 1D-GS.

The scan angle of the resonant scanner is inversely proportional to the frequency, and is a function of the mirror size. The resonant frequency can be expressed as [41]:

fR=12πkt4lJ
where k is a constant dependent on the taut band material used, t is the taut band spring thickness, l is the taut band length, J is the inertial momentum of the rotor assembly, l is the taut band length. To ensure that the taut band does not fatigue and eventually fail over time, the thickness of the taut band couldn’t exceed material stress levels during operation. Thus, the taut band spring thickness t satisfies the following equation [41]:
t=lSϕ
where S is the taut band material’s torsional stress coefficient, and ϕ is the maximum rotational scan angle. We design a large resonant scanner with scanning frequency of 70Hz, scanning angle of 48°, and the diameter of 50mm. The large mirror allows us to conveniently adjust the hologram size and scanning angle under the full bandwidth. The relationship between sub-hologram size and sub-view angle can be simply expressed as [42]:
ΔhΔθnλ2
where Δh is the hologram size and Δθ is width of viewing window, λ is the wavelength, and n is number of pixels. Based on Eq. (4), the large mirror allows us to have larger size, smaller FOV holograms angularly tiled together into a correspondingly larger hologram with the same previous combined FOV. On the other hand, the combined hologram can also be optically transformed to the same previous size but with a larger FOV in the horizontal direction. In this proposed system, horizontal scan of the resonant scanner works in conjunction to increase the horizontal FOVA of the display and to fully utilize the SLMs bandwidth. The scan frequency of the horizontal scanner is 70Hz in order to ensure the same frame frequency as the current CIH video displays. The horizontal FOVA becomes 48°, twice of the view range displayed previously with the same sub-view angle, thus utilizing the entire bandwidth of the SLM.

3.2. Synchronization of scanners and SLM

The full bandwidth CIH display system can continuously form colour 3D holographic video with large FOV by combining multiple horizontal and vertical sub-FOVAs. For this propose, the proposed system has three synchronization relationships: 1) 1D-RS and 1D-GS, (2) 1D-RS and DMD, and (3) DMD and three colour lasers. The synchronization between 1D-RS and 1D-GS can consistently display the multiple sub-holograms located the same horizontal line onto the corresponding vertical sub-FOVA. The synchronization between 1D-RS and DMD can consistently display the sub-holograms onto the corresponding horizontal sub-FOVA. The synchronization between DMD and three colour lasers can regularly display the colour holograms on the horizontal line. The 1D-RS scans at one fixed frequency, which means it cannot produce an arbitrary waveform. Based on this consideration, we use the 1D-RS as the maser device of the proposed system, while other devices are used as slave device following the master device. We use the TTL level square wave, provided by the 1D-RS, as the reference signals to control other devices. Figure 4 shows the controlling signal timing of scanners and line scanning pattern. Based on the output of the line sync of the large resonant scanner, a vector waveform is produced to implement an efficient boustrophedonic scan. The vector waveform signal is utilized to control the 1D-GS. Moreover, the original phase difference between the 1D-RS and 1D-GS is set to 90° by adjusting the phase of the reference signals with respect to the position of the mirror of the 1D-RS. The DMD is set to a continuous slave mode and a display trigger signal is produced based on the reference signal of 1D-RS. First, we perform a frequency multiplication of the reference signal of 1D-RS to produce a higher frequency TTL signal, where the multiplication factor is determined by the total horizontal view number. The high frequency TTL signal is used as the trigger signal of the DMD. Finally, we utilized the frame synchronization output signals of the DMD to directly control the three colour lasers.

 figure: Fig. 4

Fig. 4 Scanning pattern, (a) scanning timing and (b) scanning trajectory.

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3.3. Scanning modeling

The proposed scanning sub-system includes a two-dimensional (2D) scanner, consisting of two one-dimensional scanners, and 4f imaging system. First, a scanning model of two 1D scanners is built to determine the positional relationship between reconstructed holograms. When the mirror of X scanner is rotated by a fixed waveform, the rotated mirror controls the reflection direction of the outgoing rays from X scanner. The horizontal coordinate position of the outgoing beam on the final image plane is controlled by the scanning angle of X mirror. Similarly, Y mirror controls the coordinate along the vertical axis. Hence the coordinates of the outgoing beam are determined by the rotation angles of the X and Y scanners. In such a process, two coordinate systems are defined for the scanning model of two scanners as follows:

  • 1) Dynamic coordinate system OX'Y'Z', which is fixed to the mirror of X scanner. The dynamic coordinate system is rotated with the rotation of the mirror of X scanner. The origin is the center of the mirror of X scanner, positioned at O(0;0;0).
  • 2) Static coordinate system OXYZ, which is coincident with target scanning plane.

The relationship between scanning coordinates is shown in Fig. 5. When the mirrors are originally static, the dynamic coordinate system is overlapped with the static coordinate system. The rotation axis of the X scanner is perpendicular with the rotation axis of the mirror of Y scanner. The distance between two scanning axes is denoted by h. The X-axis of OXYZ is parallel to the rotation axis of the mirror of Y scanner, while Y-axis of OXYZ is perpendicular to the rotation axis of the mirror of Y scanner. Let α denote the rotation angle of X scanner, while β represents the rotation angle of Y scanner. G is the center of the mirror of Y scanner. The scanning plane is located at Z = z0.

 figure: Fig. 5

Fig. 5 The scanning coordinate relationships.

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Based on the scanning geometry, the direction vector of the outgoing ray from the Y scanner can be expressed as:

v=w2(q,w)q
The intersection of the reflected ray by the X mirror with the Y mirror can be expressed as:
A=Q+ηyw
with
ηy=q,GQq,w
where w,q,Qand G are determined by the rotation angle α, β and h. The outgoing rays from Y scanner can be expressed as v and A in Eqs. (7) and (8). In the scanning system, the 4f system can be used to relay and focus the scan onto the image plane. When an image lens is located at Z = z0, the lights converge onto the image plane of the image lens. The components of the outgoing rays in the X direction and Y direction are expressed, respectively, as:
{μx=tanμx=Bxz0+hμy=tanμy=Byz0
where Bxand Byare the intersections of the reflected ray from the X-Y scanning system with the screen. Based on the imaging principle of lenses, the transform matrix of imaging lens is expressed as:
[CxCyμxμy]=[100001001f01001f01][BxByμxμy]
For the transform matrix of an imaging lens, we ignore its physical parameters, such as thickness. The coordinate position of hologram on the image plane of the imaging lens can be expressed as
[DxDyDy]=[Cx+z1×μxCy+z1×μyz0+z1]
based on which, the position of hologram is compensated. Our previous work [22] used a subjective observation instead of a theoretical model to guide the position compensation. The calibration of each view took time and the calibration accuracy was not very high. In this work, we use the above theoretical model to guide the position compensation, which proves to be efficient and highly accurate.

4. Experiments and results

4.1 Experimental setup

Based on the principle of the proposed system shown in Fig. 1, a full bandwidth CIH display with large FOV was prototyped. Figure 6 shows the experimental setup. In this system, the DMD is the same device (ViALUX GmbH V-7000 VIS) as the previous dynamic CIH system. The DMD has 1024 × 768 micro mirrors of 13.7μm pitch, and an active mirror array area of 14 × 10.5 mm2. The maximum global switching rate of the DMD can achieve a frame rate of 22,272 Hz, for a full bandwidth of 17.5 Gbit/s. The usable spectral range covers all wavelengths from 350 nm to 2500 nm.

 figure: Fig. 6

Fig. 6 Experimental setup, (a) entire system overview, (b) the laser and DMD configurations, and (c) the HRS configurations.

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Three lasers (red, green, and blue) are used sequentially illuminate the DMD. The center of the red spectral band is 450 nm, green band is 532 nm, and blue band is 635 nm. The optical configurations are divided into two parts: laser optical configuration and HRS optical configuration. The laser optical configuration uses a collimating and beam-expanding lenses of focal length fl = 15 mm (L1092A) and fl = 150 mm (l1374A). Moreover, longpass dichroic mirrors of 490 nm cutoff (DMLP490L, Thorlabs) and 550 nm cutoff (DMLP550L, Thorlabs) as well as a reflective mirror are used to implement the beam combiner. The HRS optical configuration includes two 4f-systems, which are labeled in Fig. 3. In the first 4f-system, the lens L1 has the focal length of fl = 150 mm and lens L2 has fl = 400 mm. In the second 4f-system, the lens L3 has fl = 100 mm and lens L4 has fl = 200 mm. Moreover, the f/# of the lens L3 and lens L4 should be less than f/# = 1.123 to accept the 48° scanning angle.

The resonant scanner (SC-21, Electro-Optical Products Corporation) is customized with a 50mm diameter mirror. The scanner operates at fixed 70 Hz frequency. The AGC driver (AGC-220-BNC), a feedback amplifier driver using the scanner as a frequency sources, is used to sustain the scanner operation at resonant frequency. The AGC driver can provide a high stability (0.01%) and a position output signal (POS). The standard operating temperature is 0 °C to + 65 °C. We use the POS to synchronously control the DMD and Y scanner. The maximal scanning angle is 70° and the scanning angle can be set by AGC amplitude adjustment in the range of 10% to 100% of the full amplitude. In the proposed system, the scanning angle is set to 48° and thus the double of horizontal fields of view scanned by the resonant scanner. The galvanometric scanner (6260HM44A) is integrated by a 50mm mirror (6M2650X44B050S4) with beam rotation of +/−22°. The mirror is a beryllium substrate, flatness of λ/2, multilayer hard dielectric over silver, R>98% over 550 nm-15 μm. The MicroMax single axis scanner driver is integrated with a high power servo driver amplifier.

The synchronization and controlling of all devices is implemented in a Labview platform in combination with a multi-function DAQ card, using a repeatable trigger to produce the control signals required in Fig. 4. The DMD works at slave mode in an infinite loop for continuous hologram sequence video display.

4.2 System calibration results

To obtain a high quality display, we perform system calibrations for Y scanning, colour intensity, and conjugation images. First, we use ZEMAX software’s highly accurate ray tracing to simulate the scanning subsystem. The simulated optical configuration of the HRS is shown in Fig. 7(a), where the mirror of X-scanner is located on the focal plane of the FT lens, while Y-scanner is located behind it. The X and Y scanners are rotated at + 10° and −10°, respectively. The final images are taken at the image plane of the 4f-system. In the simulation a wavelength of 550 nm is used. As the simulation shows in Figs. 7(a) and 7(c), the image position of the X scanner is not changed with the scan angle, while that of Y scanner does change. In Figs. 7(b) and 7(c), the red, green, and blue rays represent the rays tracing at different scanning angles. In Fig. 7(c), the shifts at + 10° and −10° are + 7.33 mm and −7.33 mm, respectively. So, the error in the image position of the Y scanner needs to be compensated for, in order for obtaining a high-quality 3D holographic display for different views. In this proposed method, the shift position due to the Y scanner can be calculated using Eq. (12). The calculated shifts are used in the layer based hologram generation to compensate the position shift. Subsequently, we perform the numerical simulation to verify this scanning model.

 figure: Fig. 7

Fig. 7 Scanning simulation by using ZEMAX, (a) 3D optical path of the HRS scanner, (b) 1D-RS scanning, and (c) 1D-GS scanning.

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In order to obtain the high-quality display of 3D hologram based on angularly tiled mechanism, we integrate the compensation model into the CGH algorithm to produce the 3D hologram. The holograms of different objects at different vertical FOV are located at different vertical positions. The compensation position is determined on the established the scanning model in Eq. (12). Figure 8(a)–8(c) shows three frames of reconstructed holograms at different FOVA positions before compensation, while Fig. 8(d)–8(f) shows three frames at the same FOVA after compensation. In our full bandwidth system, we use three lasers to reconstruct colour holograms. The colour calibration includes three parts: (1) hologram size; (2) colour energy; and (3) conjugation alignment. In the proposed CIH display system, each pixel on the DMD supports a binary modulation through turning the direction of the micro mirror. This feature can produce grating-like effect, but main energy is delivered to a higher order direction due to the reflection of mirror. The reconstructed holograms have the conjugated image issue for all three colours as shown in Fig. 8(h)–8(j). For each channel, there is a square region defined by four spots (generated from the zero order reflection from both the SLM surface and the dead area between pixels). This area is divided by two regions, one of which is the conjugation zone and should be blocked. The target should be constructed by adjusting the illumination lights to make the useful regions of the red and green to cover the useful region of the blue (the smallest due to its shortest wavelength) as the white image shown in Fig. 8(k).

 figure: Fig. 8

Fig. 8 Position calibrated results, (a)–(c) before compensation, where the reconstructed holographic image is located at different FOVA positions when the scanner scans the holographic image. (d)–(f) after calibration, (g) original image, (h)–(j) the conjugated images of three colours, while (k) is the results after the adjustment.

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To provide aligned colour images, the DMD should have the same illumination directions from three lasers. We use dichroic filters and multiple mirrors to combine three different incident angle beams into the same direction. Figure 9(a) shows the reflection and transmission ratios of the dichroic filter for the CIH display system. After three different wavelengths beams (R/G/B) reflect off the DMD, different image sizes (scaling) are produced. In Fig. 9(b), a hologram size, (X,Y), can be expressed as X = mΔx, Y = nΔy, where Δx represents pixel size in X direction, Δy represents pixel size in Y direction, m and n are the pixel number in horizontal and vertical direction. Based on diffraction imaging theory [43-44], the horizontal and vertical extents of the holograms can be expressed as:

(Δx=λdm·Δa,Δy=λdn·Δb)
where λ represents the wavelength, d denotes the reconstructed hologram distance, m and n denote the horizontal and vertical pixel resolution of the DMD, and Δa and Δb represents the pixel size of DMD. The image lengths of three colour holograms in X direction can be expressed as:
{xR=mRΔxR=mRλRdm·ΔaxG=mGΔxG=mGλGdm·ΔaxB=mBΔxB=mBλBdm·Δa
where λR, λG, λB denote the wavelength of red, blue and green light, mR, mG, mB denote the pixel number of reconstructed hologram, The scaling relationship can be expressed as

 figure: Fig. 9

Fig. 9 Colour combing, (a) colour combining optical path and dichroic filter performance and (b) position calibration and colour size, where three views are located on the different vertical positions.

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mR:mG:mB=1λR:1λG:1λB

Based on Eq. (15), we integrated the scaling relationship into the CGH-based rendering algorithm where the three colour holograms are a fixed size. Figure 10(a) shows the reconstructed holographic images before size calibration, where the sizes are different for different colours. Figures 10(b) and 10(c) shows the reconstructed holographic images after size calibration and the original image, respectively. Moreover, we also calibrate the focal length of different wavelengths because the reconstructed distance is influenced as dr=dsDMDλc/scλDMD, where d, Sdmd, Sc, λc is the CGH parameters and DMD parameters. To calibrate colour intensity, we firstly use attenuation slices to adjust the three laser intensities individually to ensure a balanced displayed intensity. Secondly, we add the different weights for different colour holograms in the CGH calculations. Figure 10(e)–10(h) show the reconstructed holographic images by adjusting the value of three channels of the original Beijing Opera mask.

 figure: Fig. 10

Fig. 10 Reconstructed holographic images of (1) characters: (a) before size calibration, (b) after size calibration, (c) the original image; and (2) facial mask: (e)–(h) different intensities of colour lasers, (i) the original image.

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4.3 Reconstructed 3D holograms

We use 3ds Max [45,46] to design a 3D object model and to produce different parallax images. A layer-based CGH algorithm is used to compute holograms. The computed holograms are displayed through DMD and scanning system. The DMD, lasers, resonant scanner, and galvanometric scanner synchronously operate under the controlling of the developed software based controller on the Labview platform. Different parallax holograms are delivered into the corresponding FOV position. After the system is powered on, the DMD working parameters are configured and the 1D-RS begins to scan at 70 Hz. The control signals of DMD are triggered by the rising edge signal of the1D-RS. The DMD also synchronously controls three lasers. At the each rise edge of the trigger signal, the DMD presents a pattern. The DMD display time is set to 44 μs. The 1D-RS works at 70 Hz and the 1D-GS at 23.33 Hz. In this system, boustrophedonic scanning is used. During the half period of the 1D-RS scan (1/140 s), the DMD can display 162 patterns, which includes 54 sub-holograms (each sub-hologram is composed of three colours). Figure 11 shows the reconstructed holographic colour images at different viewing angles. The display’s FOV can reach 43.2°, which indicates the full bandwidth has been utilized. In this experiment, the full bandwidth of the DMD is achieved by three lasers when the frame-out signals directly control the lasers alternately. We also used a single laser to display the holographic images under the full bandwidth condition. In addition, this system reconstructs different views of a 3D object with all the images from all views exist together in the reconstruction, for the same single object with different parallax being viewed at different viewing angles. Moreover, the proposed system can display continuously sequential images because we use 1D-RS to synchronously control the DMD, lasers, and 1D-GS.

 figure: Fig. 11

Fig. 11 Reconstructed holographic colour images viewed from normal horizontally at an angle of (a) 0°, (b) + 1.6°, (c) + 21.6°, (d) −1.6°, and (e) −21.6°, respectively.

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Figure 12 shows the holographic colour images reconstructed at different depths, where there are four letter layers. When the four letter layers are located at the same depth position, the reconstructed holographic image has the same resolution, such as the image of Fig. 12(a). Subsequently the four letter layers are arranged at the different depths and the distance between two adjacent layers is set to be the same. The depth order of the letters is “C”, “P”, “D”, and “S”. When the camera focuses on a particular layer, the reconstructed holographic image of the corresponding layer has the highest resolution and minimum noise, while other layers have different resolutions, as shown in Fig. 12(b)–12(e), respectively. This experimental result show that our system can reconstruct holographic images at different depths according to the holographic distances used in the CGH, so a layer-based approach can be used to generate each image layer at different depths for a 3D holographic image.

 figure: Fig. 12

Fig. 12 Reconstructed holographic colour images of four letters, CPDS, taken by a camera, when (a) the four letters are located at the same depth and (b)-(e) the four letter layers are located at different depths with the camera focuses on the “C”, “P”, “D” and “S” layer, respectively.

Download Full Size | PPT Slide | PDF

5. Discussion

The maximum global switching rate for the DMD is 22.727 kHz and the full bandwidth is 17.8x109 bit/sec (1,024 pixels × 768 pixels × 22.727 k frame/s). The proposed system has a frame video of 23.33 Hz. Therefore, the total number of sub-holograms is 324 (17.8x109 / 23.33 frame/s / 3 colours/ 1,024 pixels / 768 pixels). In this proposed system, there are 54 horizontal sub-holograms in a row and 6 such rows stacked vertically, which indicates the full bandwidth of the DMD can be utilized. The total FOV angle is 43.2° due to each view zone covering 0.8° horizontally. Table 1 shows the display capability of the proposed system. The horizontal FOV is composed of 54 view zones for all R/G/B holograms under full bandwidth of the DMD. The horizontal viewing angle is ± 21.6°. The vertical FOVA is ± 1.6°. The DMD display frame rate is 22.727 kHz [22,270 = 3(R/G/B) × 54(views) × 70 Hz (resonant scanner) × 2]. The whole 3D hologram video frame is 23.33 Hz. The proposed system can display the information content of 17.5Gpixels/seconds from the DMD, with a FOVA of ± 21.6°H × ± 1.6°V, hologram size of 48 mm × 64 mm, and three colour hologram video at 23.33Hz.

Tables Icon

Table 1. Display capability of the proposed system

In the previous dynamic CIH system, there are 30 horizontal view zones (and sub-holograms) while there are 6 vertical view zones (and sub-hologram rows). The DMD bandwidth is 53.2% and total FOV angle is ± 12° × ± 1.6°. Compared with the existing dynamic CIH system, the propose method adopts similar optical configurations, while providing the double of horizontal fields to fully utilize the SLM’s bandwidth and double the hologram’s FOV. Compared with the auxiliary vertical resonant scanner vertical dither resonant scanner system, the proposed method provides a larger horizontal FOV and parallax, as well as vertical FOV, while optically, mechanically and electronically simpler than the system using the auxiliary vertical resonant scanner (AVRS). Moreover, in the existing dynamic CIH system, the DMD works at a master mode, while the controlling signals of two scanners are inconsecutive, which results in the mismatching the hologram and FOVA. At each a fixed period, the display system needs to restart a display task, which results in the discontinuous display. In this proposed system, hologram sequences can be continuously displayed because we used multiple methods, including DMD slave trigger display, 1D-RS master and repeatable triggers.

6. Conclusion and future work

Dynamic holographic video in CIH can be achieved by scanning a single low SBP but high bandwidth SLM to form the hologram array for integral optics. However, only half of the SLMs bandwidth was utilized previously due to the limitations of the galvanometer mirror scanner. Our work as reported in above proposes and demonstrates successfully an approach for a full bandwidth CIH display using a synchronized raster and cascaded galvanometric scanners. Two galvanometric horizontal scanners work in conjunction to increase the horizontal FOV of the display and utilize fully the SLMs bandwidth. This method doesn’t require a secondary high-speed vertical resonant dither scanner which we previously used to utilize the entire SLM bandwidth, thus making it easier to control and low in costs. This method can provide a reference for future scalable CIH displays.

The proposed system opens the door to scanning mechanisms capable of handling larger optical extents and higher frequencies. For future work, there can be three main directions. Firstly, multiple scanners can be used to distribute large optical information in horizontal and vertical directions. Fast extraction algorithms in star trackers [47-48] can be used to the layer-based CGH in the full bandwidth CIH display. Secondly, system scale-up can be considered with multiple SLMs contributing even more information into the final reconstructed holographic image, for large image size or wide fields-of-view, especially in the vertical direction (in this work we purposely redirect the information horizontally to facilitate probably a more important large horizontal FOV). Finally, a tileable CIH system should be explored to display more information for high quality and large size holographic 3D images.

Funding

CAPE Consortium (CAPE COIN3D-III).

Acknowledgments

This work was supported by a joint collaboration project under CAPE COIN3D-III between Disney Research and the University of Cambridge through the CAPE consortium.

References and links

1. H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011). [CrossRef]  

2. J. S. Chen, D. Chu, and Q. Smithwick, “Rapid hologram generation utilizing layer-based approach and graphic rendering for realistic three-dimensional image reconstruction by angular tiling,” J. Electron. Imaging 23(2), 023016 (2014). [CrossRef]  

3. J. S. Chen, Q. Smithwick, and D. Chu, “Implementation of shading effect for reconstruction of smooth layer-based 3D holographic images,” Proc. SPIE 8648, 86480R (2013). [CrossRef]  

4. J. S. Chen and D. P. Chu, “Improved layer-based method for rapid hologram generation and real-time interactive holographic display applications,” Opt. Express 23(14), 18143–18155 (2015). [CrossRef]   [PubMed]  

5. J. S. Chen and D. Chu, “Realization of real-time interactive 3D image holographic display,” Appl. Opt. 55(3), A127–A134 (2016). [CrossRef]   [PubMed]  

6. X. Xia, X. Liu, H. Li, Z. Zheng, H. Wang, Y. Peng, and W. Shen, “A 360-degree floating 3D display based on light field regeneration,” Opt. Express 21(9), 11237–11247 (2013). [CrossRef]   [PubMed]  

7. T. Kakue, T. Nishitsuji, T. Kawashima, K. Suzuki, T. Shimobaba, and T. Ito, “Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors,” Sci. Rep. 5(1), 11750 (2015). [CrossRef]   [PubMed]  

8. W. Matusik and H. Pfister, “3D TV: a scalable system for real-time acquisition, transmission, and autostereoscopic display of dynamic scenes,” ACM Trans. Graph. 23(3), 814–824 (2004). [CrossRef]  

9. S. Pastoor and M. Wöpking, “3-D displays: A review of current technologies,” Displays 17(2), 100–110 (1997). [CrossRef]  

10. M. Huebschman, B. Munjuluri, and H. Garner, “Dynamic holographic 3-D image projection,” Opt. Express 11(5), 437–445 (2003). [CrossRef]   [PubMed]  

11. S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008). [CrossRef]   [PubMed]  

12. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14(17), 7636–7641 (2006). [CrossRef]   [PubMed]  

13. M. T. Gruneisen, W. A. Miller, R. C. Dymale, and A. M. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt. 47(4), A32–A42 (2008). [CrossRef]   [PubMed]  

14. Y. Kim, E. Stoykova, H. Kang, S. Hong, J. Park, J. Park, and J. Hong, “Seamless full color holographic printing method based on spatial partitioning of SLM,” Opt. Express 23(1), 172–182 (2015). [CrossRef]   [PubMed]  

15. T. Ichikawa, T. Yoneyama, and Y. Sakamoto, “CGH calculation with the ray tracing method for the Fourier transform optical system,” Opt. Express 21(26), 32019–32031 (2013). [CrossRef]   [PubMed]  

16. H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015). [CrossRef]   [PubMed]  

17. G. Li, J. Jeong, D. Lee, J. Yeom, C. Jang, S. Lee, and B. Lee, “Space bandwidth product enhancement of holographic display using high-order diffraction guided by holographic optical element,” Opt. Express 23(26), 33170–33183 (2015). [CrossRef]   [PubMed]  

18. Y. Takaki and N. Okada, “Reduction of image blurring of horizontally scanning holographic display,” Opt. Express 18(11), 11327–11334 (2010). [CrossRef]   [PubMed]  

19. D. E. Smalley, Q. Y. J. Smithwick, V. M. Bove Jr, J. Barabas, and S. Jolly, “Anisotropic leaky-mode modulator for holographic video displays,” Nature 498(7454), 313–317 (2013). [CrossRef]   [PubMed]  

20. X. Xu, X. Liang, Y. Pan, R. Zheng, Z. A. Lum, P. P. M. Y. Lwin, and S. Solanki, “Development of full-color full-parallax digital 3D holographic display system and its prospects,” Proc. SPIE 8644, 864409 (2013). [CrossRef]  

21. J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7, 44656 (2017). [CrossRef]   [PubMed]  

22. Q. Smithwick, J. Chen, and D. Chu, “A Coarse Integral Holographic Display,” in SID International Symposium44(1), 310–313(2013).

23. J. S. Chen, Q. Y. J. Smithwick, and D. P. Chu, “Coarse integral holography approach for real 3D color video displays,” Opt. Express 24(6), 6705–6718 (2016). [CrossRef]   [PubMed]  

24. T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18(19), 19504–19509 (2010). [CrossRef]   [PubMed]  

25. Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. A. Tanjung, C. Tan, and T. C. Chong, “Fast cgh computation using s-lut on gpu,” Opt. Express 17(21), 18543–18555 (2009). [CrossRef]   [PubMed]  

26. H. Zhang, Y. Zhao, L. Cao, and G. Jin, “Fully computed holographic stereogram based algorithm for computer-generated holograms with accurate depth cues,” Opt. Express 23(4), 3901–3913 (2015). [CrossRef]   [PubMed]  

27. Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015). [CrossRef]   [PubMed]  

28. Y. Zhao, L. Cao, H. Zhang, W. Tan, S. Wu, Z. Wang, Q. Yang, and G. Jin, “Time-division multiplexing holographic display using angular-spectrum layer-oriented method,” Chin. Opt. Lett. 14(1), 010005 (2016). [CrossRef]  

29. J. S. Chen, Q. Y. J. Smithwick, J. Li, and D. Chu, “Auxiliary Resonant Scanner to Increase the Scanning Capability for Coarse Integral Holographic Displays,” Chin. Opt. Lett. 15(4), 040901 (2017). [CrossRef]  

30. V. Westphal, S. Yazdanfar, A. M. Rollins, and J. A. Izatt, “Real-time, high velocity-resolution color Doppler optical coherence tomography,” Opt. Lett. 27(1), 34–36 (2002). [CrossRef]   [PubMed]  

31. L. K. Koay and N. A. A. Rahim, “Reviews: Torsional spring mechanism resonant scanner’s technology,” Journal of Mechanical Science & Technology 30(4), 1781–1798 (2016). [CrossRef]  

32. L. K. Koay, M. M. Ratnam, and H. Gitano-Briggs, “An Investigation on the Damping Characteristics of a Linear Optical Scanner,” Exp. Tech. 40(1), 271–284 (2016). [CrossRef]  

33. J. Kim, Y. Kawai, N. Inomata, and T. Ono, “Parametrically driven resonant micro-mirror scanner with tunable springs,” in Proceedings of IEEE 26th International Conference on Micro Electro Mechanical Systems (MEMS) (IEEE, 2013), pp. 580–583. [CrossRef]  

34. H. Urey, “Torsional MEMS scanner design for high-resolution display systems,” Proc. SPIE 4773, 27–37 (2002). [CrossRef]  

35. F. Filhol, E. Defay, C. Divoux, C. Zinck, and M. T. Delaye, “Resonant micro-mirror excited by a thin-film piezoelectric actuator for fast optical beam scanning,” Sens. Actuators A Phys. 123, 483–489 (2005). [CrossRef]  

36. C. Ataman and H. Urey, “Modeling and characterization of comb-actuated resonant microscanners,” J. Micromech. Microeng. 16(1), 9–16 (2006). [CrossRef]  

37. R. P. Aylward, “Advanced galvanometer-based optical scanner design,” Sens. Rev. 23(3), 216–222 (2003). [CrossRef]  

38. R. P. Aylward, “Advances and technologies of galvanometer-based optical scanners,” Proc. SPIE 3787, 158–164 (1999). [CrossRef]  

39. V. F. Duma, “Optimal scanning function of a galvanometer scanner for an increased duty cycle,” Opt. Eng. 49(10), 103001 (2010). [CrossRef]  

40. D. Matsuka, S. Fukushima, and M. Iwasaki, “Compensation for torque fluctuation caused by temperature change in fast and precise positioning of galvanometer scanners,” in Proceedings of IEEE International Conference on Mechatronics (ICM) (IEEE, 2015), pp. 642–647. [CrossRef]  

41. I. Tuchman, “Laser scanning and chopping methods using mechanical resonant devices,” Proc. SPIE 3787, 165–172 (1999). [CrossRef]  

42. M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, W. S. Christopher, and A. Wood, “3 D electronic holography display system using a 100-megapixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004). [CrossRef]  

43. U. Schnars and W. P. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002). [CrossRef]  

44. C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, “Digital recording and numerical reconstruction of lensless fourier holograms in optical metrology,” Appl. Opt. 38(22), 4812–4820 (1999). [CrossRef]   [PubMed]  

45. Autodesk 3ds Max 2012, https://knowledge.autodesk.com/support/3ds-max/downloads/caas/downloads/content/autodesk-3ds-max-2012-product-update-12.html (Accessed Jan. 2018)

46. L. Wu, R. W. Luo, and X. W. Chen, “Research on Realization of Dynamic Interaction by VRML and 3DS MAX,” Computer Simulation 1, 054 (2007).

47. M. Wei, F. Xing, and Z. You, “A real-time detection and positioning method for small and weak targets using a 1D morphology-based approach in 2D images,” Light Sci. Appl. 7, el8006 (2018).

48. S. Zhang, F. Xing, T. Sun, Z. You, and M. Wei, “Novel approach to improve the attitude update rate of a star tracker,” Opt. Express 26(5), 5164–5181 (2018). [CrossRef]   [PubMed]  

References

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  1. H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
    [Crossref]
  2. J. S. Chen, D. Chu, and Q. Smithwick, “Rapid hologram generation utilizing layer-based approach and graphic rendering for realistic three-dimensional image reconstruction by angular tiling,” J. Electron. Imaging 23(2), 023016 (2014).
    [Crossref]
  3. J. S. Chen, Q. Smithwick, and D. Chu, “Implementation of shading effect for reconstruction of smooth layer-based 3D holographic images,” Proc. SPIE 8648, 86480R (2013).
    [Crossref]
  4. J. S. Chen and D. P. Chu, “Improved layer-based method for rapid hologram generation and real-time interactive holographic display applications,” Opt. Express 23(14), 18143–18155 (2015).
    [Crossref] [PubMed]
  5. J. S. Chen and D. Chu, “Realization of real-time interactive 3D image holographic display,” Appl. Opt. 55(3), A127–A134 (2016).
    [Crossref] [PubMed]
  6. X. Xia, X. Liu, H. Li, Z. Zheng, H. Wang, Y. Peng, and W. Shen, “A 360-degree floating 3D display based on light field regeneration,” Opt. Express 21(9), 11237–11247 (2013).
    [Crossref] [PubMed]
  7. T. Kakue, T. Nishitsuji, T. Kawashima, K. Suzuki, T. Shimobaba, and T. Ito, “Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors,” Sci. Rep. 5(1), 11750 (2015).
    [Crossref] [PubMed]
  8. W. Matusik and H. Pfister, “3D TV: a scalable system for real-time acquisition, transmission, and autostereoscopic display of dynamic scenes,” ACM Trans. Graph. 23(3), 814–824 (2004).
    [Crossref]
  9. S. Pastoor and M. Wöpking, “3-D displays: A review of current technologies,” Displays 17(2), 100–110 (1997).
    [Crossref]
  10. M. Huebschman, B. Munjuluri, and H. Garner, “Dynamic holographic 3-D image projection,” Opt. Express 11(5), 437–445 (2003).
    [Crossref] [PubMed]
  11. S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
    [Crossref] [PubMed]
  12. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14(17), 7636–7641 (2006).
    [Crossref] [PubMed]
  13. M. T. Gruneisen, W. A. Miller, R. C. Dymale, and A. M. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt. 47(4), A32–A42 (2008).
    [Crossref] [PubMed]
  14. Y. Kim, E. Stoykova, H. Kang, S. Hong, J. Park, J. Park, and J. Hong, “Seamless full color holographic printing method based on spatial partitioning of SLM,” Opt. Express 23(1), 172–182 (2015).
    [Crossref] [PubMed]
  15. T. Ichikawa, T. Yoneyama, and Y. Sakamoto, “CGH calculation with the ray tracing method for the Fourier transform optical system,” Opt. Express 21(26), 32019–32031 (2013).
    [Crossref] [PubMed]
  16. H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
    [Crossref] [PubMed]
  17. G. Li, J. Jeong, D. Lee, J. Yeom, C. Jang, S. Lee, and B. Lee, “Space bandwidth product enhancement of holographic display using high-order diffraction guided by holographic optical element,” Opt. Express 23(26), 33170–33183 (2015).
    [Crossref] [PubMed]
  18. Y. Takaki and N. Okada, “Reduction of image blurring of horizontally scanning holographic display,” Opt. Express 18(11), 11327–11334 (2010).
    [Crossref] [PubMed]
  19. D. E. Smalley, Q. Y. J. Smithwick, V. M. Bove, J. Barabas, and S. Jolly, “Anisotropic leaky-mode modulator for holographic video displays,” Nature 498(7454), 313–317 (2013).
    [Crossref] [PubMed]
  20. X. Xu, X. Liang, Y. Pan, R. Zheng, Z. A. Lum, P. P. M. Y. Lwin, and S. Solanki, “Development of full-color full-parallax digital 3D holographic display system and its prospects,” Proc. SPIE 8644, 864409 (2013).
    [Crossref]
  21. J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7, 44656 (2017).
    [Crossref] [PubMed]
  22. Q. Smithwick, J. Chen, and D. Chu, “A Coarse Integral Holographic Display,” in SID International Symposium44(1), 310–313(2013).
  23. J. S. Chen, Q. Y. J. Smithwick, and D. P. Chu, “Coarse integral holography approach for real 3D color video displays,” Opt. Express 24(6), 6705–6718 (2016).
    [Crossref] [PubMed]
  24. T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18(19), 19504–19509 (2010).
    [Crossref] [PubMed]
  25. Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. A. Tanjung, C. Tan, and T. C. Chong, “Fast cgh computation using s-lut on gpu,” Opt. Express 17(21), 18543–18555 (2009).
    [Crossref] [PubMed]
  26. H. Zhang, Y. Zhao, L. Cao, and G. Jin, “Fully computed holographic stereogram based algorithm for computer-generated holograms with accurate depth cues,” Opt. Express 23(4), 3901–3913 (2015).
    [Crossref] [PubMed]
  27. Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
    [Crossref] [PubMed]
  28. Y. Zhao, L. Cao, H. Zhang, W. Tan, S. Wu, Z. Wang, Q. Yang, and G. Jin, “Time-division multiplexing holographic display using angular-spectrum layer-oriented method,” Chin. Opt. Lett. 14(1), 010005 (2016).
    [Crossref]
  29. J. S. Chen, Q. Y. J. Smithwick, J. Li, and D. Chu, “Auxiliary Resonant Scanner to Increase the Scanning Capability for Coarse Integral Holographic Displays,” Chin. Opt. Lett. 15(4), 040901 (2017).
    [Crossref]
  30. V. Westphal, S. Yazdanfar, A. M. Rollins, and J. A. Izatt, “Real-time, high velocity-resolution color Doppler optical coherence tomography,” Opt. Lett. 27(1), 34–36 (2002).
    [Crossref] [PubMed]
  31. L. K. Koay and N. A. A. Rahim, “Reviews: Torsional spring mechanism resonant scanner’s technology,” Journal of Mechanical Science & Technology 30(4), 1781–1798 (2016).
    [Crossref]
  32. L. K. Koay, M. M. Ratnam, and H. Gitano-Briggs, “An Investigation on the Damping Characteristics of a Linear Optical Scanner,” Exp. Tech. 40(1), 271–284 (2016).
    [Crossref]
  33. J. Kim, Y. Kawai, N. Inomata, and T. Ono, “Parametrically driven resonant micro-mirror scanner with tunable springs,” in Proceedings of IEEE 26th International Conference on Micro Electro Mechanical Systems (MEMS) (IEEE, 2013), pp. 580–583.
    [Crossref]
  34. H. Urey, “Torsional MEMS scanner design for high-resolution display systems,” Proc. SPIE 4773, 27–37 (2002).
    [Crossref]
  35. F. Filhol, E. Defay, C. Divoux, C. Zinck, and M. T. Delaye, “Resonant micro-mirror excited by a thin-film piezoelectric actuator for fast optical beam scanning,” Sens. Actuators A Phys. 123, 483–489 (2005).
    [Crossref]
  36. C. Ataman and H. Urey, “Modeling and characterization of comb-actuated resonant microscanners,” J. Micromech. Microeng. 16(1), 9–16 (2006).
    [Crossref]
  37. R. P. Aylward, “Advanced galvanometer-based optical scanner design,” Sens. Rev. 23(3), 216–222 (2003).
    [Crossref]
  38. R. P. Aylward, “Advances and technologies of galvanometer-based optical scanners,” Proc. SPIE 3787, 158–164 (1999).
    [Crossref]
  39. V. F. Duma, “Optimal scanning function of a galvanometer scanner for an increased duty cycle,” Opt. Eng. 49(10), 103001 (2010).
    [Crossref]
  40. D. Matsuka, S. Fukushima, and M. Iwasaki, “Compensation for torque fluctuation caused by temperature change in fast and precise positioning of galvanometer scanners,” in Proceedings of IEEE International Conference on Mechatronics (ICM) (IEEE, 2015), pp. 642–647.
    [Crossref]
  41. I. Tuchman, “Laser scanning and chopping methods using mechanical resonant devices,” Proc. SPIE 3787, 165–172 (1999).
    [Crossref]
  42. M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, W. S. Christopher, and A. Wood, “3 D electronic holography display system using a 100-megapixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
    [Crossref]
  43. U. Schnars and W. P. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
    [Crossref]
  44. C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, “Digital recording and numerical reconstruction of lensless fourier holograms in optical metrology,” Appl. Opt. 38(22), 4812–4820 (1999).
    [Crossref] [PubMed]
  45. Autodesk 3ds Max 2012, https://knowledge.autodesk.com/support/3ds-max/downloads/caas/downloads/content/autodesk-3ds-max-2012-product-update-12.html (Accessed Jan. 2018)
  46. L. Wu, R. W. Luo, and X. W. Chen, “Research on Realization of Dynamic Interaction by VRML and 3DS MAX,” Computer Simulation 1, 054 (2007).
  47. M. Wei, F. Xing, and Z. You, “A real-time detection and positioning method for small and weak targets using a 1D morphology-based approach in 2D images,” Light Sci. Appl. 7, el8006 (2018).
  48. S. Zhang, F. Xing, T. Sun, Z. You, and M. Wei, “Novel approach to improve the attitude update rate of a star tracker,” Opt. Express 26(5), 5164–5181 (2018).
    [Crossref] [PubMed]

2018 (2)

M. Wei, F. Xing, and Z. You, “A real-time detection and positioning method for small and weak targets using a 1D morphology-based approach in 2D images,” Light Sci. Appl. 7, el8006 (2018).

S. Zhang, F. Xing, T. Sun, Z. You, and M. Wei, “Novel approach to improve the attitude update rate of a star tracker,” Opt. Express 26(5), 5164–5181 (2018).
[Crossref] [PubMed]

2017 (2)

J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7, 44656 (2017).
[Crossref] [PubMed]

J. S. Chen, Q. Y. J. Smithwick, J. Li, and D. Chu, “Auxiliary Resonant Scanner to Increase the Scanning Capability for Coarse Integral Holographic Displays,” Chin. Opt. Lett. 15(4), 040901 (2017).
[Crossref]

2016 (5)

2015 (7)

T. Kakue, T. Nishitsuji, T. Kawashima, K. Suzuki, T. Shimobaba, and T. Ito, “Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors,” Sci. Rep. 5(1), 11750 (2015).
[Crossref] [PubMed]

J. S. Chen and D. P. Chu, “Improved layer-based method for rapid hologram generation and real-time interactive holographic display applications,” Opt. Express 23(14), 18143–18155 (2015).
[Crossref] [PubMed]

Y. Kim, E. Stoykova, H. Kang, S. Hong, J. Park, J. Park, and J. Hong, “Seamless full color holographic printing method based on spatial partitioning of SLM,” Opt. Express 23(1), 172–182 (2015).
[Crossref] [PubMed]

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
[Crossref] [PubMed]

G. Li, J. Jeong, D. Lee, J. Yeom, C. Jang, S. Lee, and B. Lee, “Space bandwidth product enhancement of holographic display using high-order diffraction guided by holographic optical element,” Opt. Express 23(26), 33170–33183 (2015).
[Crossref] [PubMed]

H. Zhang, Y. Zhao, L. Cao, and G. Jin, “Fully computed holographic stereogram based algorithm for computer-generated holograms with accurate depth cues,” Opt. Express 23(4), 3901–3913 (2015).
[Crossref] [PubMed]

Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
[Crossref] [PubMed]

2014 (1)

J. S. Chen, D. Chu, and Q. Smithwick, “Rapid hologram generation utilizing layer-based approach and graphic rendering for realistic three-dimensional image reconstruction by angular tiling,” J. Electron. Imaging 23(2), 023016 (2014).
[Crossref]

2013 (5)

J. S. Chen, Q. Smithwick, and D. Chu, “Implementation of shading effect for reconstruction of smooth layer-based 3D holographic images,” Proc. SPIE 8648, 86480R (2013).
[Crossref]

X. Xia, X. Liu, H. Li, Z. Zheng, H. Wang, Y. Peng, and W. Shen, “A 360-degree floating 3D display based on light field regeneration,” Opt. Express 21(9), 11237–11247 (2013).
[Crossref] [PubMed]

T. Ichikawa, T. Yoneyama, and Y. Sakamoto, “CGH calculation with the ray tracing method for the Fourier transform optical system,” Opt. Express 21(26), 32019–32031 (2013).
[Crossref] [PubMed]

D. E. Smalley, Q. Y. J. Smithwick, V. M. Bove, J. Barabas, and S. Jolly, “Anisotropic leaky-mode modulator for holographic video displays,” Nature 498(7454), 313–317 (2013).
[Crossref] [PubMed]

X. Xu, X. Liang, Y. Pan, R. Zheng, Z. A. Lum, P. P. M. Y. Lwin, and S. Solanki, “Development of full-color full-parallax digital 3D holographic display system and its prospects,” Proc. SPIE 8644, 864409 (2013).
[Crossref]

2011 (1)

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

2010 (3)

2009 (1)

2008 (2)

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

M. T. Gruneisen, W. A. Miller, R. C. Dymale, and A. M. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt. 47(4), A32–A42 (2008).
[Crossref] [PubMed]

2007 (1)

L. Wu, R. W. Luo, and X. W. Chen, “Research on Realization of Dynamic Interaction by VRML and 3DS MAX,” Computer Simulation 1, 054 (2007).

2006 (2)

L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14(17), 7636–7641 (2006).
[Crossref] [PubMed]

C. Ataman and H. Urey, “Modeling and characterization of comb-actuated resonant microscanners,” J. Micromech. Microeng. 16(1), 9–16 (2006).
[Crossref]

2005 (1)

F. Filhol, E. Defay, C. Divoux, C. Zinck, and M. T. Delaye, “Resonant micro-mirror excited by a thin-film piezoelectric actuator for fast optical beam scanning,” Sens. Actuators A Phys. 123, 483–489 (2005).
[Crossref]

2004 (2)

W. Matusik and H. Pfister, “3D TV: a scalable system for real-time acquisition, transmission, and autostereoscopic display of dynamic scenes,” ACM Trans. Graph. 23(3), 814–824 (2004).
[Crossref]

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, W. S. Christopher, and A. Wood, “3 D electronic holography display system using a 100-megapixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[Crossref]

2003 (2)

M. Huebschman, B. Munjuluri, and H. Garner, “Dynamic holographic 3-D image projection,” Opt. Express 11(5), 437–445 (2003).
[Crossref] [PubMed]

R. P. Aylward, “Advanced galvanometer-based optical scanner design,” Sens. Rev. 23(3), 216–222 (2003).
[Crossref]

2002 (3)

H. Urey, “Torsional MEMS scanner design for high-resolution display systems,” Proc. SPIE 4773, 27–37 (2002).
[Crossref]

V. Westphal, S. Yazdanfar, A. M. Rollins, and J. A. Izatt, “Real-time, high velocity-resolution color Doppler optical coherence tomography,” Opt. Lett. 27(1), 34–36 (2002).
[Crossref] [PubMed]

U. Schnars and W. P. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

1999 (3)

C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, “Digital recording and numerical reconstruction of lensless fourier holograms in optical metrology,” Appl. Opt. 38(22), 4812–4820 (1999).
[Crossref] [PubMed]

I. Tuchman, “Laser scanning and chopping methods using mechanical resonant devices,” Proc. SPIE 3787, 165–172 (1999).
[Crossref]

R. P. Aylward, “Advances and technologies of galvanometer-based optical scanners,” Proc. SPIE 3787, 158–164 (1999).
[Crossref]

1997 (1)

S. Pastoor and M. Wöpking, “3-D displays: A review of current technologies,” Displays 17(2), 100–110 (1997).
[Crossref]

Ahrenberg, L.

Ataman, C.

C. Ataman and H. Urey, “Modeling and characterization of comb-actuated resonant microscanners,” J. Micromech. Microeng. 16(1), 9–16 (2006).
[Crossref]

Aylward, R. P.

R. P. Aylward, “Advanced galvanometer-based optical scanner design,” Sens. Rev. 23(3), 216–222 (2003).
[Crossref]

R. P. Aylward, “Advances and technologies of galvanometer-based optical scanners,” Proc. SPIE 3787, 158–164 (1999).
[Crossref]

Barabas, J.

D. E. Smalley, Q. Y. J. Smithwick, V. M. Bove, J. Barabas, and S. Jolly, “Anisotropic leaky-mode modulator for holographic video displays,” Nature 498(7454), 313–317 (2013).
[Crossref] [PubMed]

Benzie, P.

Blanche, P. A.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Bove, V. M.

D. E. Smalley, Q. Y. J. Smithwick, V. M. Bove, J. Barabas, and S. Jolly, “Anisotropic leaky-mode modulator for holographic video displays,” Nature 498(7454), 313–317 (2013).
[Crossref] [PubMed]

Cameron, C. D.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, W. S. Christopher, and A. Wood, “3 D electronic holography display system using a 100-megapixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[Crossref]

Cao, L.

Chen, J.

J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7, 44656 (2017).
[Crossref] [PubMed]

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

Q. Smithwick, J. Chen, and D. Chu, “A Coarse Integral Holographic Display,” in SID International Symposium44(1), 310–313(2013).

Chen, J. S.

Chen, X. W.

L. Wu, R. W. Luo, and X. W. Chen, “Research on Realization of Dynamic Interaction by VRML and 3DS MAX,” Computer Simulation 1, 054 (2007).

Chong, T. C.

Christopher, W. S.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, W. S. Christopher, and A. Wood, “3 D electronic holography display system using a 100-megapixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[Crossref]

Chu, D.

J. S. Chen, Q. Y. J. Smithwick, J. Li, and D. Chu, “Auxiliary Resonant Scanner to Increase the Scanning Capability for Coarse Integral Holographic Displays,” Chin. Opt. Lett. 15(4), 040901 (2017).
[Crossref]

J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7, 44656 (2017).
[Crossref] [PubMed]

J. S. Chen and D. Chu, “Realization of real-time interactive 3D image holographic display,” Appl. Opt. 55(3), A127–A134 (2016).
[Crossref] [PubMed]

J. S. Chen, D. Chu, and Q. Smithwick, “Rapid hologram generation utilizing layer-based approach and graphic rendering for realistic three-dimensional image reconstruction by angular tiling,” J. Electron. Imaging 23(2), 023016 (2014).
[Crossref]

J. S. Chen, Q. Smithwick, and D. Chu, “Implementation of shading effect for reconstruction of smooth layer-based 3D holographic images,” Proc. SPIE 8648, 86480R (2013).
[Crossref]

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

Q. Smithwick, J. Chen, and D. Chu, “A Coarse Integral Holographic Display,” in SID International Symposium44(1), 310–313(2013).

Chu, D. P.

Collings, N.

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

Coomber, S. D.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, W. S. Christopher, and A. Wood, “3 D electronic holography display system using a 100-megapixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[Crossref]

Crossland, B.

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
[Crossref]

Defay, E.

F. Filhol, E. Defay, C. Divoux, C. Zinck, and M. T. Delaye, “Resonant micro-mirror excited by a thin-film piezoelectric actuator for fast optical beam scanning,” Sens. Actuators A Phys. 123, 483–489 (2005).
[Crossref]

Delaye, M. T.

F. Filhol, E. Defay, C. Divoux, C. Zinck, and M. T. Delaye, “Resonant micro-mirror excited by a thin-film piezoelectric actuator for fast optical beam scanning,” Sens. Actuators A Phys. 123, 483–489 (2005).
[Crossref]

Divoux, C.

F. Filhol, E. Defay, C. Divoux, C. Zinck, and M. T. Delaye, “Resonant micro-mirror excited by a thin-film piezoelectric actuator for fast optical beam scanning,” Sens. Actuators A Phys. 123, 483–489 (2005).
[Crossref]

Duma, V. F.

V. F. Duma, “Optimal scanning function of a galvanometer scanner for an increased duty cycle,” Opt. Eng. 49(10), 103001 (2010).
[Crossref]

Dymale, R. C.

Filhol, F.

F. Filhol, E. Defay, C. Divoux, C. Zinck, and M. T. Delaye, “Resonant micro-mirror excited by a thin-film piezoelectric actuator for fast optical beam scanning,” Sens. Actuators A Phys. 123, 483–489 (2005).
[Crossref]

Flores, D.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Fukushima, S.

D. Matsuka, S. Fukushima, and M. Iwasaki, “Compensation for torque fluctuation caused by temperature change in fast and precise positioning of galvanometer scanners,” in Proceedings of IEEE International Conference on Mechatronics (ICM) (IEEE, 2015), pp. 642–647.
[Crossref]

Garner, H.

Gitano-Briggs, H.

L. K. Koay, M. M. Ratnam, and H. Gitano-Briggs, “An Investigation on the Damping Characteristics of a Linear Optical Scanner,” Exp. Tech. 40(1), 271–284 (2016).
[Crossref]

Gruneisen, M. T.

Gu, T.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Hong, J.

Hong, S.

Huebschman, M.

Ichihashi, Y.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
[Crossref] [PubMed]

Ichikawa, T.

Inomata, N.

J. Kim, Y. Kawai, N. Inomata, and T. Ono, “Parametrically driven resonant micro-mirror scanner with tunable springs,” in Proceedings of IEEE 26th International Conference on Micro Electro Mechanical Systems (MEMS) (IEEE, 2013), pp. 580–583.
[Crossref]

Ito, T.

T. Kakue, T. Nishitsuji, T. Kawashima, K. Suzuki, T. Shimobaba, and T. Ito, “Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors,” Sci. Rep. 5(1), 11750 (2015).
[Crossref] [PubMed]

T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18(19), 19504–19509 (2010).
[Crossref] [PubMed]

Iwasaki, M.

D. Matsuka, S. Fukushima, and M. Iwasaki, “Compensation for torque fluctuation caused by temperature change in fast and precise positioning of galvanometer scanners,” in Proceedings of IEEE International Conference on Mechatronics (ICM) (IEEE, 2015), pp. 642–647.
[Crossref]

Izatt, J. A.

Jang, C.

Jeong, J.

Jia, J.

J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7, 44656 (2017).
[Crossref] [PubMed]

Jin, G.

Jolly, S.

D. E. Smalley, Q. Y. J. Smithwick, V. M. Bove, J. Barabas, and S. Jolly, “Anisotropic leaky-mode modulator for holographic video displays,” Nature 498(7454), 313–317 (2013).
[Crossref] [PubMed]

Jüptner, W.

Jüptner, W. P.

U. Schnars and W. P. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

Kakue, T.

T. Kakue, T. Nishitsuji, T. Kawashima, K. Suzuki, T. Shimobaba, and T. Ito, “Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors,” Sci. Rep. 5(1), 11750 (2015).
[Crossref] [PubMed]

Kang, H.

Kawai, Y.

J. Kim, Y. Kawai, N. Inomata, and T. Ono, “Parametrically driven resonant micro-mirror scanner with tunable springs,” in Proceedings of IEEE 26th International Conference on Micro Electro Mechanical Systems (MEMS) (IEEE, 2013), pp. 580–583.
[Crossref]

Kawashima, T.

T. Kakue, T. Nishitsuji, T. Kawashima, K. Suzuki, T. Shimobaba, and T. Ito, “Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors,” Sci. Rep. 5(1), 11750 (2015).
[Crossref] [PubMed]

Kim, J.

J. Kim, Y. Kawai, N. Inomata, and T. Ono, “Parametrically driven resonant micro-mirror scanner with tunable springs,” in Proceedings of IEEE 26th International Conference on Micro Electro Mechanical Systems (MEMS) (IEEE, 2013), pp. 580–583.
[Crossref]

Kim, Y.

Koay, L. K.

L. K. Koay and N. A. A. Rahim, “Reviews: Torsional spring mechanism resonant scanner’s technology,” Journal of Mechanical Science & Technology 30(4), 1781–1798 (2016).
[Crossref]

L. K. Koay, M. M. Ratnam, and H. Gitano-Briggs, “An Investigation on the Damping Characteristics of a Linear Optical Scanner,” Exp. Tech. 40(1), 271–284 (2016).
[Crossref]

Kong, D.

Lee, B.

Lee, D.

Lee, S.

Li, G.

G. Li, J. Jeong, D. Lee, J. Yeom, C. Jang, S. Lee, and B. Lee, “Space bandwidth product enhancement of holographic display using high-order diffraction guided by holographic optical element,” Opt. Express 23(26), 33170–33183 (2015).
[Crossref] [PubMed]

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Li, H.

Li, J.

Liang, X.

X. Xu, X. Liang, Y. Pan, R. Zheng, Z. A. Lum, P. P. M. Y. Lwin, and S. Solanki, “Development of full-color full-parallax digital 3D holographic display system and its prospects,” Proc. SPIE 8644, 864409 (2013).
[Crossref]

Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. A. Tanjung, C. Tan, and T. C. Chong, “Fast cgh computation using s-lut on gpu,” Opt. Express 17(21), 18543–18555 (2009).
[Crossref] [PubMed]

Lin, W.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Liu, X.

Lum, Z. A.

X. Xu, X. Liang, Y. Pan, R. Zheng, Z. A. Lum, P. P. M. Y. Lwin, and S. Solanki, “Development of full-color full-parallax digital 3D holographic display system and its prospects,” Proc. SPIE 8644, 864409 (2013).
[Crossref]

Luo, R. W.

L. Wu, R. W. Luo, and X. W. Chen, “Research on Realization of Dynamic Interaction by VRML and 3DS MAX,” Computer Simulation 1, 054 (2007).

Lwin, P. P. M. Y.

X. Xu, X. Liang, Y. Pan, R. Zheng, Z. A. Lum, P. P. M. Y. Lwin, and S. Solanki, “Development of full-color full-parallax digital 3D holographic display system and its prospects,” Proc. SPIE 8644, 864409 (2013).
[Crossref]

Magnor, M.

Masuda, N.

Matsuka, D.

D. Matsuka, S. Fukushima, and M. Iwasaki, “Compensation for torque fluctuation caused by temperature change in fast and precise positioning of galvanometer scanners,” in Proceedings of IEEE International Conference on Mechatronics (ICM) (IEEE, 2015), pp. 642–647.
[Crossref]

Matusik, W.

W. Matusik and H. Pfister, “3D TV: a scalable system for real-time acquisition, transmission, and autostereoscopic display of dynamic scenes,” ACM Trans. Graph. 23(3), 814–824 (2004).
[Crossref]

Miller, W. A.

Munjuluri, B.

Nakayama, H.

Nishitsuji, T.

T. Kakue, T. Nishitsuji, T. Kawashima, K. Suzuki, T. Shimobaba, and T. Ito, “Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors,” Sci. Rep. 5(1), 11750 (2015).
[Crossref] [PubMed]

Norwood, R. A.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Oi, R.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
[Crossref] [PubMed]

Okada, N.

Ono, T.

J. Kim, Y. Kawai, N. Inomata, and T. Ono, “Parametrically driven resonant micro-mirror scanner with tunable springs,” in Proceedings of IEEE 26th International Conference on Micro Electro Mechanical Systems (MEMS) (IEEE, 2013), pp. 580–583.
[Crossref]

Osten, W.

Pan, Y.

X. Xu, X. Liang, Y. Pan, R. Zheng, Z. A. Lum, P. P. M. Y. Lwin, and S. Solanki, “Development of full-color full-parallax digital 3D holographic display system and its prospects,” Proc. SPIE 8644, 864409 (2013).
[Crossref]

Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. A. Tanjung, C. Tan, and T. C. Chong, “Fast cgh computation using s-lut on gpu,” Opt. Express 17(21), 18543–18555 (2009).
[Crossref] [PubMed]

Park, J.

Pastoor, S.

S. Pastoor and M. Wöpking, “3-D displays: A review of current technologies,” Displays 17(2), 100–110 (1997).
[Crossref]

Peng, Y.

Peyghambarian, N.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Pfister, H.

W. Matusik and H. Pfister, “3D TV: a scalable system for real-time acquisition, transmission, and autostereoscopic display of dynamic scenes,” ACM Trans. Graph. 23(3), 814–824 (2004).
[Crossref]

Rahim, N. A. A.

L. K. Koay and N. A. A. Rahim, “Reviews: Torsional spring mechanism resonant scanner’s technology,” Journal of Mechanical Science & Technology 30(4), 1781–1798 (2016).
[Crossref]

Ratnam, M. M.

L. K. Koay, M. M. Ratnam, and H. Gitano-Briggs, “An Investigation on the Damping Characteristics of a Linear Optical Scanner,” Exp. Tech. 40(1), 271–284 (2016).
[Crossref]

Rokutanda, S.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Rollins, A. M.

Sakamoto, Y.

Sasaki, H.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
[Crossref] [PubMed]

Schnars, U.

U. Schnars and W. P. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

Seebacher, S.

Senoh, T.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
[Crossref] [PubMed]

Shen, W.

Shimobaba, T.

T. Kakue, T. Nishitsuji, T. Kawashima, K. Suzuki, T. Shimobaba, and T. Ito, “Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors,” Sci. Rep. 5(1), 11750 (2015).
[Crossref] [PubMed]

T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18(19), 19504–19509 (2010).
[Crossref] [PubMed]

Smalley, D. E.

D. E. Smalley, Q. Y. J. Smithwick, V. M. Bove, J. Barabas, and S. Jolly, “Anisotropic leaky-mode modulator for holographic video displays,” Nature 498(7454), 313–317 (2013).
[Crossref] [PubMed]

Smith, A. P.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, W. S. Christopher, and A. Wood, “3 D electronic holography display system using a 100-megapixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[Crossref]

Smith, M. A.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, W. S. Christopher, and A. Wood, “3 D electronic holography display system using a 100-megapixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[Crossref]

Smithwick, Q.

J. S. Chen, D. Chu, and Q. Smithwick, “Rapid hologram generation utilizing layer-based approach and graphic rendering for realistic three-dimensional image reconstruction by angular tiling,” J. Electron. Imaging 23(2), 023016 (2014).
[Crossref]

J. S. Chen, Q. Smithwick, and D. Chu, “Implementation of shading effect for reconstruction of smooth layer-based 3D holographic images,” Proc. SPIE 8648, 86480R (2013).
[Crossref]

Q. Smithwick, J. Chen, and D. Chu, “A Coarse Integral Holographic Display,” in SID International Symposium44(1), 310–313(2013).

Smithwick, Q. Y. J.

Solanki, S.

X. Xu, X. Liang, Y. Pan, R. Zheng, Z. A. Lum, P. P. M. Y. Lwin, and S. Solanki, “Development of full-color full-parallax digital 3D holographic display system and its prospects,” Proc. SPIE 8644, 864409 (2013).
[Crossref]

Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. A. Tanjung, C. Tan, and T. C. Chong, “Fast cgh computation using s-lut on gpu,” Opt. Express 17(21), 18543–18555 (2009).
[Crossref] [PubMed]

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S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Stanley, M.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, W. S. Christopher, and A. Wood, “3 D electronic holography display system using a 100-megapixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[Crossref]

Stoykova, E.

Sun, T.

Suzuki, K.

T. Kakue, T. Nishitsuji, T. Kawashima, K. Suzuki, T. Shimobaba, and T. Ito, “Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors,” Sci. Rep. 5(1), 11750 (2015).
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Sweiti, A. M.

Takaki, Y.

Tan, C.

Tan, W.

Tanjung, R. B. A.

Tay, S.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

Thomas, J.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
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I. Tuchman, “Laser scanning and chopping methods using mechanical resonant devices,” Proc. SPIE 3787, 165–172 (1999).
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S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
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C. Ataman and H. Urey, “Modeling and characterization of comb-actuated resonant microscanners,” J. Micromech. Microeng. 16(1), 9–16 (2006).
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H. Urey, “Torsional MEMS scanner design for high-resolution display systems,” Proc. SPIE 4773, 27–37 (2002).
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S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[Crossref] [PubMed]

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Wakunami, K.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
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Watson, P. J.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, W. S. Christopher, and A. Wood, “3 D electronic holography display system using a 100-megapixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
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Wood, A.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, W. S. Christopher, and A. Wood, “3 D electronic holography display system using a 100-megapixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
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M. Wei, F. Xing, and Z. You, “A real-time detection and positioning method for small and weak targets using a 1D morphology-based approach in 2D images,” Light Sci. Appl. 7, el8006 (2018).

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X. Xu, X. Liang, Y. Pan, R. Zheng, Z. A. Lum, P. P. M. Y. Lwin, and S. Solanki, “Development of full-color full-parallax digital 3D holographic display system and its prospects,” Proc. SPIE 8644, 864409 (2013).
[Crossref]

Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. A. Tanjung, C. Tan, and T. C. Chong, “Fast cgh computation using s-lut on gpu,” Opt. Express 17(21), 18543–18555 (2009).
[Crossref] [PubMed]

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H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
[Crossref] [PubMed]

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S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
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Yao, J.

J. Jia, J. Chen, J. Yao, and D. Chu, “A scalable diffraction-based scanning 3D colour video display as demonstrated by using tiled gratings and a vertical diffuser,” Sci. Rep. 7, 44656 (2017).
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S. Zhang, F. Xing, T. Sun, Z. You, and M. Wei, “Novel approach to improve the attitude update rate of a star tracker,” Opt. Express 26(5), 5164–5181 (2018).
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M. Wei, F. Xing, and Z. You, “A real-time detection and positioning method for small and weak targets using a 1D morphology-based approach in 2D images,” Light Sci. Appl. 7, el8006 (2018).

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Zhang, S.

Zhao, Y.

Zheng, R.

X. Xu, X. Liang, Y. Pan, R. Zheng, Z. A. Lum, P. P. M. Y. Lwin, and S. Solanki, “Development of full-color full-parallax digital 3D holographic display system and its prospects,” Proc. SPIE 8644, 864409 (2013).
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C. Ataman and H. Urey, “Modeling and characterization of comb-actuated resonant microscanners,” J. Micromech. Microeng. 16(1), 9–16 (2006).
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M. Wei, F. Xing, and Z. You, “A real-time detection and positioning method for small and weak targets using a 1D morphology-based approach in 2D images,” Light Sci. Appl. 7, el8006 (2018).

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U. Schnars and W. P. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

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D. E. Smalley, Q. Y. J. Smithwick, V. M. Bove, J. Barabas, and S. Jolly, “Anisotropic leaky-mode modulator for holographic video displays,” Nature 498(7454), 313–317 (2013).
[Crossref] [PubMed]

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H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
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J. S. Chen, Q. Y. J. Smithwick, and D. P. Chu, “Coarse integral holography approach for real 3D color video displays,” Opt. Express 24(6), 6705–6718 (2016).
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T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18(19), 19504–19509 (2010).
[Crossref] [PubMed]

Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. A. Tanjung, C. Tan, and T. C. Chong, “Fast cgh computation using s-lut on gpu,” Opt. Express 17(21), 18543–18555 (2009).
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[Crossref] [PubMed]

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4(1), 6177 (2015).
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Figures (12)

Fig. 1
Fig. 1 The principle of CIH displays, (a) layer-based algorithm for calculating a 3D hologram, (b) static CIH display, and (c) dynamic CIH display.
Fig. 2
Fig. 2 CIH display with Hybrid Resonant Scanner (HRS): horizontal resonant scanner and vertical galvanometer. Lens L1 to L4 are attached lens array (virtual).
Fig. 3
Fig. 3 The principle of HRS.
Fig. 4
Fig. 4 Scanning pattern, (a) scanning timing and (b) scanning trajectory.
Fig. 5
Fig. 5 The scanning coordinate relationships.
Fig. 6
Fig. 6 Experimental setup, (a) entire system overview, (b) the laser and DMD configurations, and (c) the HRS configurations.
Fig. 7
Fig. 7 Scanning simulation by using ZEMAX, (a) 3D optical path of the HRS scanner, (b) 1D-RS scanning, and (c) 1D-GS scanning.
Fig. 8
Fig. 8 Position calibrated results, (a)–(c) before compensation, where the reconstructed holographic image is located at different FOVA positions when the scanner scans the holographic image. (d)–(f) after calibration, (g) original image, (h)–(j) the conjugated images of three colours, while (k) is the results after the adjustment.
Fig. 9
Fig. 9 Colour combing, (a) colour combining optical path and dichroic filter performance and (b) position calibration and colour size, where three views are located on the different vertical positions.
Fig. 10
Fig. 10 Reconstructed holographic images of (1) characters: (a) before size calibration, (b) after size calibration, (c) the original image; and (2) facial mask: (e)–(h) different intensities of colour lasers, (i) the original image.
Fig. 11
Fig. 11 Reconstructed holographic colour images viewed from normal horizontally at an angle of (a) 0°, (b) + 1.6°, (c) + 21.6°, (d) −1.6°, and (e) −21.6°, respectively.
Fig. 12
Fig. 12 Reconstructed holographic colour images of four letters, CPDS, taken by a camera, when (a) the four letters are located at the same depth and (b)-(e) the four letter layers are located at different depths with the camera focuses on the “C”, “P”, “D” and “S” layer, respectively.

Tables (1)

Tables Icon

Table 1 Display capability of the proposed system

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

G(x,y,z)= n G n (x,y)
Q n (x,y)= P n (x,y)×exp[ j k 2 ( x 2 z nx + y 2 z ny ) ]
Q(x,y)= n=1 N Q n (x,y)
f R = 1 2π k t 4 lJ
t= l Sϕ
ΔhΔθ nλ 2
v = w 2( q , w ) q
A = Q + η y w
η y = q , G Q q , w
{ μ x =tan μ x = B x z 0 +h μ y =tan μ y = B y z 0
[ C x C y μ x μ y ]=[ 1 0 0 0 0 1 0 0 1 f 0 1 0 0 1 f 0 1 ][ B x B y μ x μ y ]
[ D x D y D y ]=[ C x + z 1 × μ x C y + z 1 × μ y z 0 + z 1 ]
( Δx= λd m·Δa ,Δy= λd n·Δb )
{ x R = m R Δ x R = m R λ R d m·Δa x G = m G Δ x G = m G λ G d m·Δa x B = m B Δ x B = m B λ B d m·Δa
m R : m G : m B = 1 λ R : 1 λ G : 1 λ B

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