Three-dimensional reflection screens fabricated by holographic wavefront printer

Abstract. Several wavefront printers have been recently proposed. Since the printers can record an arbitrary computer-generated wavefront, they are expected to be useful for fabricating complex mirror arrays used in front projection 3-D screens without using real existing optics. We prototyped two transparent reflective screens using our hologram printer in experiments. These screens could compensate for a spherically distorted reference wave caused by a short projection distance to obtain an ideal reference wave. Owing to the use of the wavefront-printed screen, the 3-D display was simply composed of a normal 2-D projector and a screen without using extra optics. In our binocular system, reflected light rays converged to the left and right eyes of the observer and the crosstalk was less than 8%. In the light field system, the reflected light rays formed a spatially sampled light field and focused a virtual object in a depth range of ±30  mm with a ±13.5-deg viewing angle. By developing wavefront printing technology, a complex optics array may easily be printed by nonprofessionals for optics manufacturing.


Introduction
Static hologram printing services have been commercialized 1-3 for more than a decade. Also, compact desktop fullcolor printers 4 have recently been proposed. These printers basically use holographic stereograms (HS). Unlike an HS printer, fringe printers and wavefront printers [5][6][7][8][9] can theoretically record a hologram that reconstructs a very sharp point light source (3-D object point) that is located far from the hologram. In contrast to an HS printer, a wavefront printer records an arbitrary wavefront with full control of both the amplitude and phase distribution reconstructed by a computer-generated hologram 10 (CGH) displayed on a spatial light modulator (SLM). The number of pixels in a conventional SLM is insufficient to record a large hologram in a single shot; thus, computer-controlled X-Y linear stages are normally used and the entire hologram is divided into many subholograms.
A hologram generated by a wavefront printer is useful for static 3-D scene visualization applications 11,12 due to its ability to reproduce the deep focusing range of a 3-D point. However, it is also expected to be useful for fabricating large complex optical elements, such as microsize nonspherical lens arrays, anamorphic lens arrays, and multiple focallength lens arrays, 13 used in precisely designed 3-D displays. An appropriate subhologram size is one of the important factors that ensure the quality of resulting images. In this paper, we describe our wavefront printer, which uses a photopolymer as a holographic material, and discuss the subhologram size. Furthermore, we discuss two examples of reflective 3-D screens fabricated using the printer. In these screens, optical cells (subholograms) are formed by the numerical calculation of holograms, and they are also features of a different optical axis depending on the cell position.

Holographic Wavefront Printer
This section describes the optical settings of our hologram printer and the 3-D data printing method using the printer. Applications of static holograms are also described.

Wavefront Printer
Recently, Bruder et al. 14 have reported a large diffractive optical element, in which the divided wavefront of the designed optical function is reconstructed using a phase SLM and a large transparent-type holographic optical element (HOE) is stitched by writing many slightly different small HOEs. We also employ basically the same procedure to form reflective-type holograms and HOEs using an amplitude SLM with 4K resolution, as shown in Fig. 1. Bruder et al. claimed that a Fourier lens is needed to generate the phase function in a hologram printer using an amplitude SLM. However, we did not use a Fourier lens but electronic holography [15][16][17] technique to generate an arbitrary phase distribution. The optical system of our wavefront printer uses a collimated laser beam with 532-nm wavelength. First, the beam is split by a polarization beam splitter. The two beams are used as an object beam and a reference beam to record a subhologram as a reflection-type volume hologram. The object beam is modulated as a part of the entire wavefront on the hologram using subhologram data displayed on an SLM (JVC Kenwood Corporation D-ILA ® 4K2K LCOS). Undesirable lights, i.e., the transmission beam, high-order beam, and conjugate beam, are filtered out by a single-side band filter and a half-zone plate processing method [17][18][19] similar to an electronic holography system. [15][16][17] Then, the optical system demagnifies the modulated wavefront onto a holographic recording film made of covestro Bayfol ® HX102 photopolymer material. The reference beam is a plane wave and is incident perpendicular to the photopolymer from the opposite side of the object beam. Table 1 shows the specifications of the wavefront printer. Because the resolution of the motorized X-Y stage (Chuo Precision Industrial ALZ-230-C2P) is ∼4.0 μm, wavefronts will, in practice, be disconnected at the edge of each subhologram (Fig. 2). After recording of all the subholograms, the holographic recording material is then processed by bleaching 20 to obtain higher transmittance at visible-light wavelengths.

Overlap Print for Better 3-D Scene Reconstruction
The dividing process in the hologram recording causes phase discontinuity between the subholograms (cells), and the reconstructed holographic image also has severe split lines and phase discontinuity, as shown in Fig. 3(a), which shows a reconstructed image with 648-μm cell size and 648-μm cell pitch printed using our printer. 21 One possible solution to this problem is to use a subhologram size smaller than the spatial resolution of the observer's eyesight. In the case of static hologram application, the cell size should be less than 87 μm when the hologram is observed at a distance of 30 cm and the resolution of the observer eyesight is 1 deg ∕60. However, the phase discontinuity at the neighboring subholograms also causes image degradation due to the diffraction effect, particularly when the subhologram is too small. From the viewpoint of diffraction, the cell size should be large unless 3-D objects or scenes are placed very close to the hologram. 11,21 The wavefront reconstructed by one subhologram is considered to be the same as that reproduced by a hologram with a finite square aperture. When the subhologram width is D, the finite aperture P ðxÞ on the x-axis is expressed by E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 3 2 6 ; 2 1 9 When the distance between the hologram and a point light source is d and the wavefront of the point light source is recorded on the hologram, the wavefront reconstructed by the subhologram is the convolution of the entire hologram and the finite aperture. The Fourier transform of the finite aperture is expressed as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 3 2 6 ; 1 0 8 The resolution Δy i along the x-axis can be expressed in the same manner. For example, when λ ¼ 532 nm, D ¼ 87 μm, and d ¼ 50 mm, then Δx i is 611 μm, which is seven times larger than the subhologram size, and the resulting 3-D image may be blurred.
Overlap printing is one solution to this contradicting cellsize problem. Since the photopolymer can record multiple wavefronts in one subhologram, by using a larger cell size D and shifting each subhologram by D∕2 in vertically and horizontally, a large aperture size and small cell size can be simultaneously achieved while concealing the dark areas of split lines. Figure 3(b) shows an image reconstructed by overlapping 648-μm subholograms with a 324-μm shift.

Real/Virtual 3-D Data Visualization Applications
Three-dimensional data of both real and virtual objects were recorded using our wavefront printer. CGHs of a real object, a miniature Buddha statue, and a virtual object, computer graphics (CG) data of Venus, were calculated on the raysampling plane by a fast calculation method. Perspective images with a number of 544 × 544 viewpoints were rendered for each hologram using conventional CG software and each view had 512 × 512 resolution. The resulting hologram had the same number of pixels as the input perspective images, 278;528 × 278;528 pixels in total. For the real object, 47 images from different viewpoints were taken using a handheld camera, which were combined by Autodesk ® 123D Catch 22 to form a solid 3-D object. The conversion from the 47 2-D pictures to the 3-D object was fully automated and the data were transferred to conventional CG software.
The generated hologram was divided into 155 × 155 subholograms because we used a cell size of 3600 × 1800 pixels in the wavefront printer in this experiment. Since the recorded holograms have the wavelength selectivity inherent to reflection-type volume holograms, white-light illumination was used in this experiment.

Reflection 3-D Screen and Application
In this section, projection 3-D video displays employing a digitally designed HOE (DDHOE) are introduced. The DDHOE was fabricated using the wavefront printer and has several advantages over conventional volume-type HOE, [23][24][25][26][27] which are shaped by an analog hologram recording procedure. Since a DDHOE is recorded by stitching many small optical cells, it can easily provide a microscale optical element array without any additional cost. It can also provide complex optical functions, such as a multiple focal-length lens array 13 printed using numerical data because an SLM can ideally reproduce any complex amplitude. It can also be used to compose nonspherical lens array without using real existing optics before the DDHOE is manufactured.

Transparent Glasses-Free Binocular Display
Some glasses-free 3-D displays are now commercially available 28,29 but 3-D glasses are more commonly used. Some advantages of 3-D glasses are their low crosstalk, the 2-D/3-D compatibility of the video screen, and the low cost.
In glasses-free 3-D displays, a lenticular lens array or a parallax barrier array is often used 30,31 to converge light emitted from the screen to the L/R eye positions of the human observer. A major disadvantage of these arrays is that the resolution may be reduced along the horizontal axis. 30 Visual artifacts including view reversals 30 as well as the visibility of the light-guiding array components 31 are also problems.
Here, we consider a binocular 3-D display application of the DDHOE. 32,33 Figure 5 shows our experimental setup of the glasses-free system. The system consists of a 2-D projector and a DDHOE screen that was printed using the hologram printer. The projector (Sanwa Supply 400-PRJ021, resolution of 1280 × 720) was used without any modification (the focusing distance was set to ∼520 mm by adjusting the focusing dial). The left image is projected on odd lines on the screen and right image is projected on even lines. The DDHOE was designed to selectively reflect even lines to the right eye of humans. The observation distance was set to 700 mm from the screen.

Spherical wave from the projector
The size of the screen was chosen to be 100 mm × 100 mm. As shown in Fig. 6(a), the incident angle of the ray at the top edge of the screen is 10.9 deg to the normal vector, whereas the angle at the bottom edge of the screen is 0 because the projector has a diverging angle in the vertical direction. The DDHOE is designed to converge whole light rays toward the observer's eye height (271 mm), as shown in Fig. 6(b).
The horizontal reflection function was designed in the same manner as the above-mentioned vertical function. The incident light from the projector is a spherical wave (radius of 520 mm), and the incident angle at the side edges was calculated to be 5.5 deg to the normal vector, as shown in Fig. 7(a). Figure 7(b) shows the reflection from even lines of the DDHOE. All the reflected rays converge at the right eye position, which is 31 mm from the center of the projector.

Printing the DDHOE
The screen used for the binocular display consists of many planar micromirrors with a dedicated tilt angle to the optical axis. These micromirrors were printed by the interference between two planewaves inside the wavefront hologram printer. A plane wave with an arbitrary incident angle was generated accordingly using the Lohmann CGH technique. 10 Complex amplitude of a plane wave P 1ðx;yÞ with an incident angle of θ to the x-axis and incident angle of φ to the y-axis is expressed by E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 3 2 6 ; 3 9 5 P 1ðx;yÞ ¼ e −i 2π λ ðx·sin θþy·sin φÞ ; where λ is the wavelength. The reference beam R 1ðx;yÞ is written using the following equation: The amplitude hologram I 1ðx;yÞ , which is displayed on the SLM, is written as the square of the complex sum of the object beam P 1ðx;yÞ and the reference beam R 1ðx;yÞ and expressed by E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 6 3 ; 4 2 4 I 1ðx;yÞ ¼ jP 1 þ R 1 j 2 ¼ 2 · cos 2π λ ðx · sin θ þ y · sin φÞ þ jP 1 j 2 þ jR 1 j 2 : Hologram I 1ðx;yÞ is numerically calculated using a computer with a 32-bit floating-point number (approximately seven-digit accuracy) then rounded off to an 8-bit unsigned integer to be displayed on the SLM. Table 2 shows the specifications of the prototype DDHOE screen.

Binocular 3-D display
The prototype binocular screen was glued to a glass substrate (1.0 mm thickness) and placed at a distance of 500 mm from the projection lens. Figures 8(a)-8(c) depict the reflection function of the prototype DDHOE. Figure 8(a) is a photograph taken in a dark room using a smoke machine (Antari Z-800 II); the projector displays a solid green square on the screen. Incident light from the projector to the screen has a diverging angle and the reflected light converges to the positions of two human eyes. The bright square area just below the converged light is a direct reflection at the DDHOE glass substrate (zeroth-order beam), and this component appears a different position from the first-order diffracted beam. The images in Figs. 8(b) and 8(c) show the results of examining crosstalk. A horizontal strip pattern consisting of only odd lines is projected onto the DDHOE. According to the design, only the left image should be bright. A bright strip is visible in Fig. 8(b), which was from the left-eye position, whereas it is invisible in Fig. 8(c), which was taken from the right-eye position. The opposite result was obtained when a strip pattern consisting of even lines was projected on the screen (images not shown). The crosstalk light components were measured by a lux meter (Konica Minolta ® CL-200A) and the maximum leakage power was 8% for both the R image to the left and the L image to the right eye. Figures 9(a)-9(d) show the result of optical reconstruction. The images in Figs. 9(a) and 9(c) were taken using a digital camera from the left-eye position, and those in Figs. 9(b) and 9(d) were taken from the right-eye positon. The observed left-eye image and right-eye image had the designed disparity, as shown in Figs. 9(c) and 9(d); thus, the 3-D virtual image could be seen without using glasses. Since the DDHOE screen has wavelength selectivity in accordance with the principle of volume holograms, the screen can be used for white-light illumination from a projector. The DDHOE screen also has high transmittance for visible light (400 to 760 nm), allowing background objects to be seen through the prototype screen, as shown in Fig. 10.

Diffraction Light Field Display
Light field displays have the ability to induce the accommodation of human eyes as well as motion parallax. Since Lippmann first reported 34 a static integral photography display, many light field video displays have been proposed. [34][35][36][37][38][39] In these displays, numerous elemental images are arranged vertically and horizontally, and a microlens array (MLA) is used to control the directions of light rays    25 and other applications of the HOE have been reported. However, in the previous research, the HOEs were fabricated by copying a phase distribution generated by real existing optics, such as MLAs, objective lenses, or optical diffusers.
Here, we propose a light field screen made from a DDHOE. Since a DDHOE is fabricated by recording a numerically generated phase distribution without using any optical molds, complex optical functions for the light field screen can be easily realized by nonprofessionals for using optical hardware.
The system consists of a 2-D projector and a DDHOE light field screen, as shown in Fig. 11(a). A 4K projector (Sony ® VPL-VW515, 3840 × 2160 resolution.) was used because the light field system 41 requires more pixels than the former binocular system. The screen is a reflectiontype light field screen, thus, basically, consists of arbitrarily tilted concave micromirrors. The DDHOE was designed to compensate the spherical wave from the projector to a parallel wave for the same reason, as described in Sec. 3.1.1. Figure 11(b) shows the fabricated light field screen. The projection distance was set to 567.5 mm in accordance with the diverging angle of the projector and the height of the DDHOE screen. The observation distance was not set in this system; thus, the principal rays reflected by the elemental mirrors exited at an angle of 9.8 deg to the normal vector of the screen.

Fabrication of light field DDHOE screen
The prototype DDHOE screen is composed of numerous tilted mirrors. The phase modulation P 2ðx;yÞ of a concave mirror, whose focal length is f (mm), can be written as follows: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 7 ; 3 2 6 ; 6 1 5 where k is the wave number. The tilt angle ðθ; φÞ of the mirror can be described by Eq. (4). The reference beam in the wavefront printer is always incident normal to the SLM; thus, the complex amplitude of the reference beam can be written as Eq. (5). In total, an amplitude hologram I 2ðx;yÞ that reconstructs a tilted concave mirror function is written as follows: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 8 ; 3 2 6 ; 5 0 1 The hologram calculation was performed on Visual Studio ® C++ 2012, and the resulting amplitude holograms were stored in an HDD as bitmap data. Each bitmap was retrieved and displayed on the SLM to modulate the illumination beam from the laser (Cobolt Samba™ 100 mW at 532 nm) in the printer. In the printing of prototype DDHOE, an SLM with a center area of 2800 × 1400 pixels was used to generate the object beam. The printing time for one 100 × 100 mm DDHOE was ∼16 h. The waiting time to reduce the vibration of the printer hardware accounts for more than 60% of the total printing time (2.0 s in each cell). An active vibration-cancelling system would help to solve this problem. Reducing the exposure time through the use of a more powerful laser may be another means of reducing the long printing time. The resulting DDHOE parameters used for the light field display are shown in Table 3.

Light field display
The prototype light field screen was fixed in front of a 2-D projector at a distance of 567.5 mm. CG software (Blender 2.76) was used for rendering virtual 3-D objects to form 17,391 elemental images. Figures 12(a)-12(d) show reconstructed light field images taken by a digital camera from different positions. To obtain Figs. 12(a) and 12(b), a heartshaped object was placed 25 mm behind the screen, and a flower pattern was placed 25 mm in front of the screen. Motion parallax can be clearly observed in these images. When a virtual object was placed farther than 30 mm from the screen, the reconstructed image gradually became blurred. Figures 12(c) and 12(d) also show "logo" contents taken by a digital camera (Canon ® EOS-5DMK2, 180 mm, F3.5). An ellipse was placed 25 mm behind the screen and letters were placed 25 mm in front of the screen. The viewing angle of the light field display was ∼27 deg, which is equivalent to the designed parameter. The prototype screen has wavelength selectivity and the green component of the projected light is visible from the observer, as shown in Fig. 13. The viewing angle of our system is restricted owing to the limited range of the diffraction angle in our wavefront hologram printer. The direct reflection of the projector light from the screen is slightly below the first-order diffracted light component; thus, it does not hinder the reconstructed light field image.

Conclusion
In this paper, a wavefront printer that records reflective volume holograms and several of its applications were described. The overlap printing technique used in our wavefront printer can effectively conceal the stitch lines between subholograms. The generation of large holograms for visualizing static 3-D scene is the most promising application of the printer while it is also useful for fabricating optical screens with relatively complex optical functions determined by numerical calculation. A 10-cm prototype glasses-free binocular display and a prototype light field display with a viewing angle of 27 deg were reported in this paper. In both prototypes, we used a commercially available 2-D projector and a screen that was printed using our wavefront printer, and the expected 3-D images were observed. Because of a hardware limitation of our printer, experiments were undertaken at a wavelength of 532 nm. The fabrication of full-color-capable HOEs will be considered in future.