The effects of MPE on electro-holographic displays

Jung-Young Son; Manho Jeong

doi:10.1364/OE.22.002207

1. Introduction

The 3-D image from a typical 3-D display [1] looks having a continuous volume from the front to the back of the display panel/screen. However they don’t look floating due to the fact that the image cannot be separated from the panel/screen surface since it is focused on the surface. The holographic displays are different from the 3-D display because they can display a floating spatial image with a real volume. This is also the difference between the holographic and the volumetric images. The volumetric image has a real volume but is not floating because it is mostly either on a set of layered plates, a rotating screen, a translating screen or a curved surface with a varying radius of curvature [2]. This is why the holographic displays are the main concern of many researchers in the 3-D display areas. The known display devices for electro-holographic displays [3] are TeO2 AOM (Acousto-Optic Modulator) [4], SLMs (Spatial Light Modulator), LCD Panel and display chips. But lately display chips have gained their use in the holographic displays due to their simplicity and compatibility to plane images. Furthermore, the rapidly decreasing pixel sizes make them to fit more for the holographic displays. The size reached to less than 5µm which is smaller than that from the AOM. It is also reported that a display device with a 1µmpixel size for hologram display, though its size is in a few mm² [5]. This is why it is expected that the display chips/panels will be the main display devices for future holographic displays.

The image reconstruction in holography is based on the phase conjugation principle [6]. This principle indicates that all rays participated to record a hologram will be regenerated when a reconstruction beam illuminates the hologram and each of them retraces its own path to record the hologram. Hence the part of the original object, which was recorded on the hologram, will be completely reconstructed by the conjugate rays. This reconstructed image will preserve the original object shape, i.e., have a real volume and position, and look floating. The phase conjugation is possible within the coherence length of the recording and illuminating laser beam. The maximum floating distance of the reconstructed image from the hologram will be determined by the coherence length of the laser used for both recording and reconstruction. Hence a laser with a long coherence length is essential for the holographic display. This is why it is necessary to consider the safety of the holographic display for viewers’ eyes. It has been considered that the laser beams can be dangerous for human eye due to their much smaller focused beam size compared with those of the white lights [7]. The irradiance (Watt/m²) of the focused laser beam will be much higher than that of the white light. Due to this problem, the MPE for human eye has been set to 1 mW/cm² for the visible spectral range for up to 30,000 Seconds exposing [8]. The MPE value depends somewhat to the beam divergence angle of the laser beam but its influence is very small.

In this paper, the MPE value 1 mW/cm² is used to analyze its influence to the characteristics of the holographic displays.

2. Spectral response of human eye

The MPE value cannot be used directly to estimate its effect on the displays because the human eye responds only to the brightness. Hence the relationship between radiometric and photometric units should be found with use of the human eye’s spectral sensitivity in the visible spectral range. The standard Luminosity curve as shown in Fig. 1 gives the relationship. This curve actually represents the standardized spectral sensitivity of human eye. Human eye’s spectral sensitivity is different for daytime and night time. But Fig. 1 only shows the daytime vision, i.e., photopic vision based on CIE 1978 photopic eye sensitivity function for point source [9] because viewers watch displays under an illumination condition in most cases. The human eye is the most sensitive to the green color corresponding to the wavelength of 555nm for the photopic vision. The spectral sensitivity values are normalized by the luminance at 555nm which is set to 1. The luminance corresponding to the 555nm is given as 680 Lumens/W. This value informs that the illuminance corresponding to irradiance 1 mW/cm² is 0.68 Lumens/cm², i.e., 6800 Lumens/m² (Lux) at 555nm. The illuminance of other wavelengths corresponding to the laser power 1 mW/cm² will be found by multiplying the sensitivity value of each wavelength with 6800 Lux.

Fig. 1 Spectral response curve of human eye: Photopic vision.

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3. Image space and solid angle

To convert this illuminance value to the brightness (Luminance), it is necessary to know the solid angle corresponding to the cross sectional area of the space where the reconstructed image from the hologram is directed. This space is the image space of a holographic display [10]. In this space, any point of composing the image will be formed by rays from all hologram points and appear without contacting with other beams which are generated in the process of reconstruction, including the 0th order diffracted beam, except those induced by the hologram itself [11]. Since the crossing angle $θ_{C}$ ( $= 2 \sin^{- 1} (λ / 4 P_{P})$ ) between reference and object beams defines the maximum object beam angle which can be recorded on the hologram, the reconstructed image from the hologram can only appear within the space determined by $θ_{C}$ . Where $λ$ and $P_{P}$ are illuminating wavelength and pixel size of a chip, respectively. Hence the image space is determined by the crossing angle [12]. Figure 2 shows the image space. In a typical display chip, when a collimated laser beam illuminates the chip’s active surface, it works like a 2 dimensional line grating due to its regular pixel arrangement [11]. Hence a diffraction pattern appears as shown in Fig. 2. This pattern consists of a set of regularly aligned diffracted beams. Each beam has the shape and size of the chip’s active surface, i.e., the hologram when it fills completely the surface. In Fig. 2, only nine beams surrounding the (0,0)^th order beam are shown, and all the lines are in the plane formed by $y -$ axis and bisecting line of the hologram. The distance between neighboring order beams are determined by the diffraction angle which is given as $θ_{D} (= \sin^{- 1} (λ / P_{P}))$ . Hence $θ_{D} \approx 2 θ_{C}$ when $θ_{D} \leq 20^{o}$ . The distance between beams in each of vertical ( $y -$ axis) and horizontal ( $x -$ axis) directions is determined as $r \tan θ_{D}$ , where $r$ is the distance of (0,0)^th order beam from the hologram. The origin of the coordinate is the center of the (0,0)^th order beam.

Fig. 2 Diffracted pattern from a display chip: L₀, L₁, L₂, L₃, L₄, L₅ and L₆, represent (0,0)^th, (0,1)^th, (1,0)^th, (0,-1)^th, (−1,0)^th, (−1,-1)^th, (1,1)^th order beams, respectively, and L₇ and L₈ are the cross sectional areas of image spaces for (0,1)^th and (1,0)^th order beams, respectively.

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The reconstructed image from the hologram on the surface is accompanied by each of these beams. Hence the image space is defined for each diffracted beam. This indicates two things: First one is that the line connecting the centers of each beam and the hologram represents the reference and illuminating beam direction of the hologram for the beam. All the connecting lines have virtually the same direction as the illuminating beam specified by the solid arrow in the center of the figure, though they are directed differently in reality. The second is that when $P_{P} < λ$ , there will not be any diffracted beam except (0,0)^th. In this case, there will be only one reconstructed image accompanied by the (0,0)^th beam and heating due to the presence of evanescent waves.

Since the crossing angle is approximately an half of the diffraction angle, it is possible to think that the image space is the half space between two neighboring order beams. However, this is not true because the image space cannot be defined until the two adjacent diffracted beams are completely separated at point $P_{S}$ . The distance at which two adjacent diffracted beams in $y -$ axis is completely separated is $d_{d} = h / \tan θ_{D}$ . At $d_{d}$ , the two diffracted beams are separated by distance $h$ which represents the vertical size of the active surface. The space which starts at point $P_{S}$ and expands with the angle corresponding to $θ_{D}$ , occupies only the gap between (0,0)^th and (0,1)^th order beams. The image space of (0,1)^th order beam will be within the space as shown in Fig. 2. The horizontal size of the image space’s cross sectional area will be $r \tan θ_{D}$ because it includes a half distance between diffracted beams in both left and right sides of the horizontal direction. To define the vertical size $h_{I}$ of the cross sectional area of the (0,1)^th order beam’s image space, Fig. 2 is simplified as in Fig. 3 to show clearly the image space. Figure 3(a) is the simplified view of Fig. 2 and Fig. 3(b) shows the image space.

Fig. 3 Simplified image of Fig. 2 for the identification of image space: (a) Simplified image of Fig. 2 and (b) the magnified view of image space.

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In Fig. 3(a), the line 1 is originated from the center of the hologram and passes the mid-point of the gap between the beams (0,0)^th and (0,1)^th. The line 3 represents the line connecting the bottom edge point $A$ on the bisecting line of the hologram to the top tip of the arrow representing $h_{I}$ . The line 2 the line connecting top edge point on the bisecting line of the hologram to the bottom tip of the arrow representing $h_{I}$ . The crossing angle of lines 2 and 3 is $θ_{C}$ , The line 4 is parallel to and $h / 2$ distanced from the line connecting the centers of both the hologram and beam (0,1)^th. Hence the lines 1, 2, 3 and 4 are in the same plane formed by the bisecting line and $y -$ axis, and the crossing angles of lines 1 and 3, and 2 and 3 are $θ_{D} / 2$ and $θ_{C}$ , respectively, When $θ_{D} \leq 20^{o}$ , the lines 1 and 2 are almost parallel to each other. The lines 3 and 4 work like the lower and upper edges of the reference (reconstruction) beam, respectively, and the lines 2 and 2’ upper and lower edges of the object beam, respectively. These beams cover the entire hologram. Hence the lines 2 and 3 which are crossed at point $C$ with the angle $θ_{C}$ , define the image space of the (0,1)^th order beam as specified in Fig. 3(b). All image points (all object points) within this space will be formed by rays from entire area of the hologram (will contribute a ray to each point within the hologram) because any point in this space makes the angle smaller than or equal to $θ_{C}$ , with the hologram. $h_{I}$ can be defined by the similar triangle relationship between two triangles of $C$ with the bisector line and with $y -$ axis, respectively. $h_{I}$ , $d$ and the cross sectional area $A_{C}$ are calculated as,

\begin{array}{l} h_{I} = h (r - d) / d \\ d = {h (1 + \tan θ_{D} \tan θ_{C})} / {\tan θ_{C} (1 + \tan^{2} θ_{D})}, \\ A_{C} = h_{I} r \tan θ_{D} \end{array}

respectively, by the triangle ABC in Fig. 3.

h_{I}

is rewritten as,

h_{I} = {(r \tan θ_{C} - h) + \tan θ_{D} \tan θ_{C} (r \tan θ_{D} - h)} / (1 + \tan θ_{D} \tan θ_{C})

For the solid angle calculation,

A_{C}

cannot be used because the distance is not normal to this area as shown in Fig. 3(b). Hence the solid angle

S_{A}

in steradian, corresponding to the image space is calculated as,

S_{A} = {h^{'}}_{I} r \tan θ_{D} / r'^{2} = 2 r \sin θ_{D} \sin (θ_{C} / 2) (1 + \tan θ_{D} \tan (θ_{C} / 2) / (r - d),

where

r'

and

h_{I}'

are expressed as

r' = (r - d) / \cos (θ_{D} - θ_{C} / 2)

and

h_{I}' = 2 r' \tan (θ_{C} / 2)

, respectively as shown by Fig. 3(b).

From Eq. (1), $d$ is linearly proportional to $h$ , it will be larger as $h$ becomes larger. It is further increased as $λ$ becomes shorter and $P_{P}$ larger, i.e., the angles $θ_{C}$ and $θ_{D}$ become smaller. As $d$ increases, $S_{A}$ also increases. The image space for (1,0)^th order beam is specified as the vertically extended quadrangle in its left side as shown in Fig. 2. The vertical size of this quadrangle has also the size of $r \tan θ_{D}$ . Similar procedure as above can be applied to find its horizontal width. The (0,-1)^th and (−1,0)^th order beams will also have the same image space as the (0,1)^th and (1,0)^th order beams, respectively. But the position of the space is on its top for the (0,-1)^th and its right side for the (−1,0)^th. The reconstructed image accompanied with the (0,0)^th order beam is the brightest but it is very much noisy. However, the images accompanied by the (0,1)^th, (1,0)^th, (0,-1)^th and (−1,0)^th order beams are less bright but more clear than that by the (0,0)^th order beam. Since the intensity distribution of the diffracted beams are described by ${Sinc}^{2} (x, y)$ [13], the reconstructed images which are within the space defined by the (0,1)^th, (1,0)^th, (0,-1)^th and (−1,0)^th order beams will be brighter than those in outside. This is why the image spaces are defined within the space. Among these image spaces, that of (0,1)^th beam is most frequently used due to its convenient location within the space.

4. Brightness and spectral response of holographic image

As mentioned in Section 3, since the reconstructed image is accompanied by each of the beam in the diffraction pattern, the intensity of each reconstructed beam is given as $I_{L} E_{D G} E_{h}$ , where $I_{L}$ , $E_{D G}$ and $E_{h}$ represent the power of the illuminating laser beam, the diffraction efficiency defining the intensity of each beam in the diffraction pattern and diffraction efficiency of the hologram, respectively. Hence the brightness of the holographic image, $B_{H}$ in Nits can be represented as,

B_{H} = 680 I_{L} E_{D G} E_{h} S_{e} / A_{I} S_{A},

where,

S_{e}

and

A_{I}

represent human eye’s spectral sensitivity as shown in Fig. 1 and reconstructed image’s surface area, respectively. The brightness will be reduced as

A_{I}

increases because the diffracted energy will be spread over the reconstructed image. In Eq. (4),

A_{I}

has the unit of

m^{2}

. The required brightness of the reconstructed image should not be less than the typical brightness of flat panel displays, which is considered as 300 Nits (Lumens/m²·sr) [14], where “sr” represents the solid angle, Steradian. Hence

B_{H}

should be not smaller than 300 Nits. This condition and the MPE value induce the following relationships:

10 {W/m}^{2} \geq I_{L} E_{D G} E_{h} / A_{I} \geq (15 / 34) S_{A} / S_{e}

These relationships define both intensity and spectral characteristics of the reconstructed image. The relationship

A_{I} \geq 0.1 I_{L} E_{D G} E_{h} m^{2}

reveals that the reconstructed image size should not be smaller than the value defined by 0.1 times of the diffracted intensity of the image. The second relationship

(15 / 34) S_{A} / S_{e} \leq 10 {W/m}^{2}

indicates that

(15 / 34) S_{A} / S_{e}

shouldn’t exceed 1 mW/cm² (10W/m²). In Fig. 4, the relationship is depicted for entire visible spectral range with 5nm interval for pixel sizes of 0.8, 1, 2 and 3 µm when

r

and

h

values are set to 1 m and 10 mm, respectively. Figure 4 shows that the visible spectral range is intact for pixel sizes larger than 2 µm, however, for

P_{P} \leq 2 μm

, the displayable spectral range becomes narrower than the visible. The narrowing will be more as the pixel size decreases and the brightness increases.

Fig. 4 Spectral Response of Electro-holographic displays based on display chips/panels.

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Figure 4 shows that when $P_{P} = 0.8 and 1 μm$ , the spectral range is reduced to 407 nm ~676 nm and 404 nm ~684 nm, respectively. When the brightness value is assumed to 500 Nits, the spectral range is further reduced to 409 nm ~677 nm for $P_{P} = 0.8 μm$ and 414nm ~668nm for $P_{P} = 1 μm$ . These reduced spectral ranges may not cause any reduction in displayable color varieties when the three primary colors for holographic displays are in the reduced spectral range. When $h$ is set to 0.25m and 0.5m, the spectral range is further reduced with the increasing sizes. However, the reducing ratio decreases slightly as $r$ increases. Figure 5 shows the spectral response for the cases of $r =$ 3, 6 and 8m for $h = 0.5 m$ . For all $r$ values, $P_{P} = 2 and 3 μm$ cases show more changes in spectral range than $P_{P} = 0.8 and 1 μm$ cases. And furthermore, $d$ can be more than 6 m for the shorter wavelengths. Due to this, the spectral curves for $P_{P} = 2 and 3 μm$ are missing when $r = 3 m$ and a part of the curve is missing for $P_{P} = 3 μm$ when $r = 6 m$ . The spectral range of $h = 0.5 m$ and $P_{P} = 0.8 μm$ case is calculated as 426 nm ~665 nm. This range is about 50nm less than the visible range.

Fig. 5 Spectral responses of Electro-holographic display for $h = 0.5 m$ when $r =$ 3 (a), 6 (b) and 8m (c).

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5. Conclusion

The analysis so far informs that the safety problem of using lasers in holographic display can be avoided by setting the reconstructed image size to not smaller than the value defined by 0.1 times of the diffracted intensity of the image. However, the displayable spectral range will always be smaller than the visible for pixel sizes smaller than $2 μm$ . As the panel size increases, the range for higher pixel sizes becomes also smaller than the visible.

Acknowledgments

This work was partly supported by GigaKOREA project, [GK13D0100, Development of Telecommunications Terminal with Digital Holographic Table-top Display] and the IT R&D program of MKE/KEIT [K1001810035337, development of interactive wide viewing zone SMV optics of 3D display].

References and links

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6. M. Gower and D. Proch (Eds.), Optical Phase Conjugation (Springer, 1994).

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8. www.psi.manchester.ac.uk

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10. J.-Y. Son, B.-R. Lee, O. O. Chernyshov, K.-A. Moon, and H. Lee, “Holographic display based on a spatial DMD array,” Opt. Lett. 38(16), 3173–3176 (2013). [CrossRef] [PubMed]

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14. Personal communication with Dr. Dae-Sik Kim of Digital media and communication Div., Samsung Electronics.

The effects of MPE on electro-holographic displays

Abstract

1. Introduction

2. Spectral response of human eye

3. Image space and solid angle

4. Brightness and spectral response of holographic image

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (5)

Equations (5)

Optics Express