A floating type holographic display

Jung-Young Son; Chun-Hae Lee; Oleksii O. Chernyshov; Beom-Ryeol Lee; Sung-Kyu Kim

doi:10.1364/OE.21.020441

1. Introduction

Electro-holographic displays are still in the early stage of development, though the first effort of displaying hologram electronically had been done by Bell Lab. in late 1960th [1] and since then various techniques of obtaining holograms computationally have been developed [2–8]. To display a hologram with a proper viewing angle, a display medium which consists of pixels with sizes near 1µm is necessary. This size allows about 30° viewing angle. The 1µm pixel array based on giant magneto-resistive (GMR) material has already been introduced [9], though it is still in experimental stage. Its active surface size, 1.9 mm in width is too small to be used as a holographic display. Its size should at least be comparable to the current SLM (Spatial Light Modulator) for future use.

The main advantage of the holographic display is its ability to display a spatial image with a volume without any mechanically operating screen or a glass block as in volumetric images [10]. The spatial image is formed by the conjugate beam nature of the reconstructed image, i.e., the holographic image. Hence the illuminating beam from the display panel is converged to reconstruct the real image and the converging angle cannot be bigger than the crossing angle of the reference and object beams for recording the hologram because the crossing angle is defined by the maximum object beam angle to be recorded on the hologram. The crossing angle for a display chip with the pixel size 4.5µm is within the range 2.54° ~4.46° for the visible spectral range of 0.4 to 0.7µm. Since most of the display chips available today has the pixel size more than 4.5µm, the both end values of the angle range will be smaller than the values given above. These angle values are small but the actual viewing angle of the image is even smaller than them. Viewing the reconstructed image requires the viewers’ eyes to be located at the common space formed by the converging angles for two largest distance points forming the image. However, since the angle defining the common space is smaller than the converging angle and it appears at a certain distance from the reconstructed image, viewing the image without the support of a diffusive screen becomes very difficult. Since the distance becomes further away from the reconstructed image as its size increases, the difficulty of viewing the image increases more. Due to this problem, the reconstructed image is viewed through a diffusive screen or a lens. The diffusive screen helps to identify the presence of the spatially reconstructed image without viewing the active surface of the chip: Since the reconstructed image is originated from the active surface of the chip, the reconstructed image can only be seen with the active surface. However since the surface is much brighter than the image because the image is diffracted from the surface and the diffraction efficiency cannot be more than 10%, it is difficult to see the image without a diffusive screen. But the diffusive screen transforms the spatial image with a depth, i.e., the reconstructed image into a plane image and the lens forces the viewer to put his/her eye on near the focused point of the active surface. The former makes the spatial image property of the reconstructed image from the holographic display disappear. Since the spatial image property is the main feature of the holographic display, the display becomes just a plane image display. The latter makes the display very inconvenient to watch.

In this paper, for both preserving the spatial image nature of the holographic display and viewing the reconstructed image easily, several layers of PDLC (Polymer Dispersed Liquid Crystal) [11] sheets are used in the image space of the reconstructed image and a spherical mirror is used to magnify/demagnify the image. The PDLC layers preserve the depth of the image and widen the viewing angle more because they also have a diffusing property, and the spherical mirror enhances the spatial nature of the image. The image will be floated by the mirror. The floating distance of the image from the mirror will be easily controlled.

2. Viewing angle in a holographic display

The currently available display chips such as DMD (Digital Micromirror Device), LCD and LCoS chips are working as a 2 dimensional line grating. However, DMD works also like a blazed grating when it is On-state. Due to this diffraction grating nature, when a coherent laser beam illuminates the chip surfaces, a two dimensional diffraction pattern is created and the reconstructed image is accompanied with each of the beam forming the pattern [12]. The beam has the shape and size of the chips’ active surfaces and it keeps its size because the illuminating laser beam is collimated and covers the entire active surfaces of the chips. The object/image space where the object/the reconstructed image can be located will be centered on the each beam. To avoid the overlapping of the reconstructed image with the beam, it is necessary to make the reconstructed images appear in the surrounding space of the beam. In the image surface, each point of the reconstructed image is formed by rays from entire active surface of the chip. Figure 1 shows the recording and reconstructing geometries of a hologram on a chip. It shows that both bottom and top arrow tips of object $a$ which is in the object/image space are recorded on the entire active surface of the chip and reconstructed by rays from entire surface of the chip. The objects within the beam 2 space are recorded and reconstructed by a part of the hologram, where the beam 2 represents the maximum beam crossing angle allowed by the pixel sizes of the chips. The object rays exceeding the crossing angle of each chip cannot be recorded on the chip. Hence the object $b$ is recorded on the part of the hologram specified by $b^{'}$ but top arrow tip is only on the part $c^{'}$ . $b$ is reconstructed by the rays from the $b^{'}$ part of the chip, but the top arrow tip of $b$ is only by the rays from $c^{'}$ part. This means that the intensity of the reconstructed image $b$ will be continuously reduced as it goes from bottom to top. For the case of $c$ , the object part within the object space will be recorded on and reconstructed by the entire active surface of chip. But for the part within the beam 2 space, each object point is recorded only on a part of the surface. The part will be smaller as away from the top boundary of the object surface. The top arrow tip of $c$ is recorded on and reconstructed by $b^{'}$ part of the surface. This indicates that the reconstructed image will have a different brightness: The part within the image space will show the same brightness but the brightness will be continuously reduced as away from the image space.

Fig. 1 Hologram recording/reconstruction geometry for a display chip.

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The intensities of the reconstructed images corresponding to the object/a part of the object within the beam 2 space will be gradually reduced as away from the object/image space. Added on this intensity reduction, noises will also be accompanied with the reconstructed image because the object rays incident with more than the crossing angle will be scattered around the reconstructed image when the hologram is reconstructed. This is shown in Fig. 2 when a DMD chip is used as the display panel. Figure 2 is the reconstructed image of two slanted lines of forming an equilateral triangle with the height 20 mm. Each of the rectangular light patterns represents the active surface of the chip and is generated by the two dimensional blazed grating behavior of the DMD chip [12]. The four rectangular patterns represent the diffraction patterns which provide the brightest reconstructed image. The space surrounded by these beam patterns is the main volume where the reconstructed image can be located. The distances between the patterns are determined by the diffraction angles derived by the grating equation. Since the diffraction angle is almost two times of the maximum crossing angle between reference and object beams in recording a hologram on the active surface of the DMD chip, the surrounding space of each beam pattern extended to a half of the distance between two beam patterns is the space defined by the crossing angle. The size of the active surface is 10 mm × 6 mm. Figure 2 shows that each pattern is accompanied with a reconstructed image and another reconstructed image accompanied by the beam pattern specified by a dotted rectangular. The two lines accompanied with the top beam pattern clearly show that the thickness and brightness of the two lines are slowly decreasing. The starting position of the decreasing is specified by a broken line. The parts of the two lines starting from slightly above the broken line to the bottom are the line portions located at the beam 2 space and to the top at the object/image space. The beam pattern specified by the dotted rectangular is generated by the grating effect induced by the regularities in the fringe pattern of the hologram on the DMD. The line image induced by this beam pattern show the opposite behavior to the main beam pattern. The lines become thicker and brighter as goes to the bottom. The exact reason behind this behavior is not known yet.

Fig. 2 The reconstructed image of two slanted lines of forming an equilateral triangle.

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The viewing angle is the angle range in which viewers can view the reconstructed image from the active surfaces of the chips where a hologram is displayed. The angle is defined by the sizes of both object and the hologram, and the object distance from the hologram when the grain size is small enough to cover the incident beam angle of a ray from a point on the object surface. However, it is commonly represented by the beam crossing angle between reference and object beams in recording the hologram because the maximum possible crossing angle is determined by the smallest grain size in the photographic plate.

Hence the maximum possible viewing angle is usually defined by the maximum crossing angle between reference and object waves. However, this viewing angle defines the image space only but an actual viewing angle of viewing the reconstructed image is smaller than the crossing angle as mentioned before. The actual viewing angle of viewing full reconstructed image through the hologram is defined by both sizes of the image and the hologram, and the distance between them. This is also shown in Fig. 1. The image space is the spatial volume defined by the angle between the collimated reference beam incident normally to the active surface of the display chip/hologram and the object beam incident with the angle $θ$ which is determined by the pixel size of the chip. No object beams incident to the chip surface with the angles bigger than $θ$ cannot be recorded. Where $θ$ is the crossing angle between the reference beam, i.e., beam 1 and object beam, i.e., beam 2 is approximately given as [13],

θ \approx \frac{λ}{2 P_{P}}

Where

P_{P}

and

λ

represent the pixel size and wavelength of the laser used for recording the hologram, respectively. In recording the hologram, the image space becomes the object space where objects can be located. The same space is for the reconstructed image when the beam 1, i.e., the reference and the reconstructed beams are incident normally to the active surface. In this case, the starting distance of the image/object space,

d

is given as

h / \tan θ

, where

h

is the hologram size. When an object with the size

a

, at the distance

d + s

from the hologram is recorded as shown in Fig. 1, the whole reconstructed image of the object can only be seen at the common space of the beams for reconstructing top and bottom arrow tips of the image. The beams are coming from the whole active surface of the hologram.

s

is the distance between the starting point of the common space and the reconstructed image. If

g

and

ϕ

represent the distance between the reconstructed image and the starting point of the common space and the actual viewing angle of viewing the whole reconstructed image of the object, respectively,

g

and

ϕ

is calculated as,

\begin{array}{l} g = \frac{a (d + s)}{h - a} \\ ϕ = \tan^{- 1} \frac{h}{d + s} - \tan^{- 1} \frac{a}{d + s} = \tan^{- 1} \frac{(h - a) (d + s)}{{(d + s)}^{2} + a h} \end{array}

For Eq. (2), the relationship

\tan^{- 1} θ_{1} - \tan^{- 1} θ_{2} = \tan^{- 1} {(θ_{1} - θ_{2}) / (1 + θ_{1} θ_{2})}

[14] is used and

d = h / \tan θ

. Since

θ > ϕ

, i.e., the viewing angle of the real image of a hologram is smaller than the crossing angle of the reference and object beams,

θ

will be the maximum possible viewing angle of the real image of the object reconstructed from the hologram. Equation (2) indicates that when

a

is not smaller than

h

. i.e.,

a \geq h

,

ϕ

becomes equal to or smaller than 0, i.e.,

ϕ \leq 0

. This means that the whole reconstructed image cannot be viewed at any location of the space in front of the hologram. The whole reconstructed image of the object can only be seen when its size is smaller than that of the hologram. Furthermore, since the distance of viewing the image will be farther away from the image as

a

closes to

h

, the real image reconstructed from the display panel with a chip size can hardly be seen by viewers. This is why a diffuser plate or a lens is needed to view the real image. In Fig. 3,

g

and

ξ = ϕ / θ

versus

γ

are plotted for two different cases of

s

, such as

s = a d / h

(Fig. 3(a)) and

s = χ d

(

χ

is a proportional constant) (Fig. 3(b)), when

h

,

P_{P}

and

λ

are 10 mm, 10.8µm and 532nm, respectively.

s = a d / h

and

s = χ d

represent the cases when the object position is varying but the object height is always equal to the height of the object/image space at

s

position and when the object position is fixed but its height is varying with the ratio

γ = a / h

, respectively.

γ

represents the relative size of the reconstructed image/object to the hologram. Since

ϕ

in Eq. (2) is small, it is simplified as

ϕ \approx (1 - γ) h / (1 + γ (or χ)) d

for

s = γ d or χ d

. Since

d = h / \tan θ

and

\tan θ \approx θ

, when

θ

is small,

ϕ

is reduced as,

ϕ \approx \frac{1 - γ}{1 + γ (or χ)} θ \to ξ \approx \frac{1 - γ}{1 + γ (or χ)}

Equation (3) informs that

ξ

is a function of

γ

and becomes smaller as

γ

increases. For

s = χ d

,

ξ

is linearly proportional to

γ

and has the maximum value

1 / (1 + χ)

when

γ = 0

.

θ / (1 + χ)

is the maximum value of

ϕ

. This means that as the object size and/or the object/reconstructed image distance increase,

ϕ

will be reduced more. Figure 3 shows that the increasing rate of

g

values increases more with increasing

γ

values and it increases sharply as

γ

closes to 1 for both

s

values. However, the decreasing rate of

ξ

decreases as

γ

closes to 1 for

s = γ d

but linearly for

s = d

. The maximum value of

ξ

is 0.5 when

s = d

as shown in Fig. 3(b). The

γ

and

ξ

values corresponding to

g = 1 m

are 0.615 and 0.22, respectively for

s = γ d

, and 0.545 and 0.228, respectively, for

s = d

. For the case of

g = 3 m

,

γ

and

ξ

values are 0.806 and 0.108, respectively for

s = γ d

, and 0.788 and 0.111, respectively, for

s = d

. The differences between

γ

and

ξ

values for the cases are reduced for the

g = 3 m

case. These two examples inform that the reconstructed image size is bigger but the actual viewing angle is smaller for

s = γ d

than for

s = d

for the same

g

value. However, the differences between the two cases reduce as

g

increases.

Fig. 3 Plotting of $g$ and $ξ = ϕ / θ$ versus $γ$ : (a) $s = a d / h$ and (b) $s = χ d$ for $h = 10 mm$ , $P_{P} = 10.8 μm$ , $λ = 0.532 μm$ .

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With $γ$ and $χ$ values, $g$ is rewritten as,

g = \frac{1 + γ (or χ)}{(1 - γ)} γ d \approx \frac{h γ {1 + γ (or χ)}}{θ (1 - γ)}

Equation (4) informs that

g \times θ

is also a function of

γ

, and

g

is linearly proportional to

a = γ h

and inversely proportional to

θ

.

g

will be increased as object/reconstructed image size increases but be decreased as the crossing angle increases, Since

ϕ

increases as

θ

increases, the condition of viewing the reconstructed image will be improved as

θ

increases;

g

is reducing and

ϕ

is increasing. This is the desired condition of viewing the reconstructed image.

3. Floating the reconstructed image

As mentioned before, the brightness difference between the reconstructed image and the active surface of the chip and the small active viewing angle make difficult to view reconstructed image. This difficulty can be overcome by a diffuser which is located at the place where the reconstructed image appears. But since this diffuser works like a screen of projecting the reconstructed image on it, the image will be seen without interference of the active surface however the presence of the diffuser will deprive the spatial image property of the holographic display and also eliminates the depth in the reconstructed image by diffusing it. One way of preserving the depth and the property of the spatial image in holographic display is using a diffuser with a low diffusing power and optics for floating image. As an example of the diffuser with a low diffusing power is PDLC. PDLC is an electro-optical material which can be used as an On/Off switch of light [11]. It is almost non-transparent when no voltage, however, it becomes transparent with a voltage and at the same time diffuses light by its haziness. Figure 4 shows PDLC’s performances. PDLC sheets are put on a fluorescent lamp. When a single PDLC sheet is put on the lamp, the lamp is not seen but most parts of the sheet looks bright when the sheet is off. However, the lamp is clearly seen with some haziness around the lamp when the sheet is on. When two sheets are put on, the brightness is reduced for both On and Off cases compared with the single sheet cases. Furthermore the bright area is also reduced when the sheet is off but the haziness is more than the single sheet case. For three sheets, the brightness is further reduced and the haziness is increased more than the two sheet case when the sheets are on. All these cases, the lamp keeps its shape though haziness is added on the lamp image. This haziness is the main force of reducing the brightness of the active surface and makes visible the reconstructed image.

Fig. 4 Performances of PDLC.

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When a diffuser is used, it is not possible to identify the exact shape of the lamp, i.e., the shape itself is distorted. This figure informs that the haziness in a sheet causes a weak diffusing and the haziness adds with more sheets, i.e., the diffusing power increases more. Since the diffusing power caused by the haziness will distorts the image if it induces the same effect as the diffuser, it is necessary to choose an optimum number of sheets to make the reconstructed image more visible while preserving the spatial depth.

If the spatial depth of the reconstructed image is preserved, the spatial image property of the holographic display can be preserved by hiding the diffuser. One way of hiding is imaging again the reconstructed image on the diffuser surface with a spherical mirror as shown in Fig. 5. Figure 5 is the schematics of a floating image type holographic display. This is a kind of floating imaging systems, It consists of a spherical mirror for main imaging optics, a monitor/TV for the background image generation, a half mirror for directing the reconstructed image to the spherical mirror, a PDLC layer in the reconstructed image space to make visible the reconstructed and a holographic display as the source of generating the floating image. The reconstructed image from the holographic display which will appear near the PDLC layer will be magnified/demaginfied by the spherical mirror and imaged on the front space of the mirror. The background image from the monitor/TV which will appear near the spherical mirror will provide a background scene for the re-imaged reconstructed image.

Fig. 5 A floating image type holographic display.

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4. A floating image type holographic display

The schematic of the holographic display part is shown in Fig. 6. The display part consists of a DMD chip with full HD resolution, 1920 × 1080 as a main display panel and a reconstructing laser beam with wavelength 532 nm. This DMD has the pixel size of 10.8µm [15]. Since each pixel of the DMD is slanted either 12° or $- 12^{0}$ to its substrate when it is operating, the reconstructed image will be either more than 24° or less than $- 24^{0}$ away from the reconstructing beam by the addition of the crossing angle.

Fig. 6 The schematics of the holographic display part.

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The reconstructed image is on the PDLC sheet. Since the DMD chip works as a blazed grating [16] when it displays a hologram, each of many different diffraction order beams accompanies with the reconstructed image. Hence it is necessary to select a reconstructed image with the highest brightness. This image appears in the space surrounded by the four beams shown in Fig. 2. Hence it is necessary to use a mask to select the brightest reconstructed image and to blocks other images. Figure 7 shows the depth preserving performance of PDLC sheets in the display system in Fig. 5. To show the depth preserving property of different numbers of PDLC sheet layers, three letters A, B and C with 150mm distance between them are made to a hologram with use of ray tracing method [17]. The sheet layers which are distanced 0.7m from the spherical mirror are located at the place of the reconstructed image “A”. “A” is the farthest letter among them. It appears about 1 m distance from the DMD, “B” about 850 mm and “C” 700 mm. When no diffuser is used, it is impossible to see the reconstructed image due to the very bright image of the active surface, though the reconstructed image is there in the space. Its presence can be identified by locating a camera detector or a diffuser at each reconstructed image location. The images in Fig. 7 are taken without the camera objective, except “no diffuser” case in the left side of 1st row. The camera detector plane is located at the focused image plane of each letter. This is why no image of active surface is shown in these figures and the letter “A” appears to be the largest because its magnified image size fills the detector. It is closest to the spherical mirror surface. Figure 7 shows the reconstructed images of letters “A”, “B” and “C” with a diffuser, no diffuser and PDLC sheets of 1, 2 and 3. For all cases, “A”, “B” and “C” are appearing at 1.75m, 1.21m and 1m distances from the spherical mirror, respectively and have the sizes of 36mm × 24mm, 26mm × 15mm and 14mm × 10mm, respectively, except the “with diffuser” case. In this case, only “A” is valid. No other letters are available. The “A” looks very blurred. This blurring is not different from that in Fig. 2. For the “No Diffuser” case, only a bright spot is viewed but the reconstructed images of letters “A”, “B” and “C” are identified at different distances. For different numbers of PDLC sheets, the letters with different distances are not different from those of the “No Diffuser” case, though the images become hazier as the number of sheets increases. Figure 7 informs that the PDLC sheets are preserving the spatial depth and image shape as the no diffuser case but images are hazed more with more sheets.

Fig. 7 Depth retaining performance of the PDLC sheets.

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Figure 8 shows the performance of the display system. The floating image includes the reconstructed image and a background image. The reconstructed image is a rotating globe with a 6 frames/sec, which was made as a hologram based on the ray tracing method. One of the globe holograms is also shown in Fig. 8. This image appears at 1.75m distance from the spherical mirror surface and has a diameter of 75mm. The images are taken with a camera by seeing the display system directly. Three PDLC sheets are used at the focused image plane of the reconstructed image of the hologram on DMD active surface for this figure. The bright spot in the images is the active surface image of the DMD.

Fig. 8 The performances of the floating image type holographic display.

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Since the surface is located at 1.7 m distance from the spherical mirror and this distance is more than two times of the focal length of the spherical mirror, 500 mm. the image will appear as a bright spot. The spot brightness is much reduced but still visible. The spot sizes for different numbers of PDLC sheets are also shown in Fig. 8. The size reduces with increasing numbers. In fact, when 5 sheets are used, the spot becomes almost invisible but still the depth is preserved. However, the brightness of the image is much reduced due to the increased haziness. The manufacture specification of the PDLC’s haziness is 5% [18]. Even with the spot, the PDLC sheet allows viewing the reconstructed image. The background image is not identifiable in these figures because the distance between the globe and the background is more than 1 m. However, both images are viewed very well by eyes. The background image can be used to enhance the visual effect of and to provide more information on the reconstructed image.

5. Conclusion

The brighter active surface image of a display chip makes almost invisible the holographic image. Viewing the image through a diffuser is eliminating the spatial depth in the image and depriving the spatial image property of the holographic image because it works as a screen. The problems caused by using a diffuser can be overcome by using PDLC sheets instead of the diffuser. The haziness in the PDLC sheet reduces the brightness of the active surface image and makes the reconstructed image visible while preserving the spatial image depth. The spatial image property of the holographic image can be enhanced with use of an imaging system based on a spherical mirror. It maximizes the spatial image property of the holographic image by making the image floating in the space.

For the further development of the holographic display, it is necessary to figure out the optimum number of PDLC sheets to be used and its relationships to its haziness and other system parameters such as the brightness of the active surface, image size and brightness, and so on in the future.

Acknowledgments

This work was partly supported by the Korean Ministry of Culture, Sports and Tourisms and the Korea Creative Content Agency under the Culture Technology Research and Development Program 2013, by the IT R&D program of MKE/KEIT (K1001810039169, Development of Core Technologies of Holographic 3D Video System for Acquisition and Reconstruction of 3D Information and by the IT R&D program of MKE/KEIT [K1001810035337, development of interactive wide viewing zone SMV optics of 3D display] and in part by the Korea Institute of Science and Technology under the Tangible Social Media Platform Project.

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A floating type holographic display

Abstract

1. Introduction

2. Viewing angle in a holographic display

3. Floating the reconstructed image

4. A floating image type holographic display

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (8)

Equations (4)

Optics Express