OPTICAL REVIEW Vol. 20, No. 1 (2013) 13–18

A New Multiple-Exposure Scheme for Full-Color Full-Parallax Holographic Stereogram Fei YANG1 , Yuri MURAKAMI2 , and Masahiro YAMAGUCHI2 1 2

Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Yokohama 226-8503, Japan Global Scientific Information and Computing Center, Tokyo Institute of Technology, Meguro, Tokyo 152-8550, Japan

(Received October 28, 2012; Accepted November 29, 2012) We propose a new multiple-exposure scheme for full-color full-parallax holographic three-dimensional (3D) printer, in which two of three primary-color holograms are exposed at the same location on the recording medium. In this paper, the optimal combinations of colors for multiple exposure are experimentally derived. In addition, it is shown that the proposed method enables higher brightness, better color reproducibility, and high resolution through the experiment of recording and measurement of color-chart holographic stereogram. # 2013 The Japan Society of Applied Physics Keywords: holographic stereogram, full color, full parallax, photopolymer, color management, exposure scheme

1.

amount of exposure of each primary color in the triple exposure scheme. In this paper, we first evaluate the multiple exposure characteristics of the recording material, a photopolymer developed by Bayer MaterialScience AG.11,12) As a result, it was found that the diffraction efficiency of each color drastically changed depending on recording order. In addition, crosstalk was observed especially for triple-color exposure. On the basis of these results, this paper proposes a new method to record color HSs based on double-color exposure, i.e., two of three primary-color holograms are recorded at one position. By recording color chart holograms, it was shown that the proposed double-color exposure scheme enables high luminance, better color reproducibility, and fair spatial resolution.

Introduction

Full-color full-parallax holographic three-dimensional (3D) printers (holoprinters) automatically produce volume reflection holographic stereograms (HSs) by using three lasers with R (red), G (green), and B (blue) colors from 3D image data generated by a computer.1–7) Full-color 3D image can be observed under white light illumination based on the principle of Bragg diffraction by a volume reflection hologram. The brightness and resolution of HSs are important factors as a full-color full-parallax holographic display, as well as the color reproducibility. Full-color 3D HSs recorded by holoprinters are achieved by multiple exposures of R, G, and B elementary holograms,8) i.e., three primary-color holograms are exposed at the same position. Even though it enables highresolution image reproduction, the color reproducibility is suffered by the crosstalk among R, G, and B channels significantly, and the diffraction efficiency is decreased, especially in the case of silver halide recording materials.8) In our previous reports, we presented a space division recording scheme for better color reproduction.9) The color reproducibility was improved in space division exposure, and the fair color accuracy was confirmed through the evaluation using color chart hologram.10) However, the luminance and resolution of reconstructed image was decreased, because the area for recorded each primarycolor hologram becomes one third. When using photopolymer instead of silver halide as a recording material, it is easier to employ multiple exposures because of its higher dynamic range. In addition, the background noise of photopolymer is lower than that of silver halide, since the scattering in photopolymer is smaller than the silver halide material. However, we still observe the reduction of diffraction efficiency due to the multiple exposure, and hence the crosstalk between R, G, and B primary-color holograms cannot be ignored. In addition, the diffraction efficiency is susceptible to the exposure condition, such as the exposing order or the

2.

Optical System

2.1 Recording system In order to record full-color volume reflection HSs, we set up a holoprinter with three color lasers whose wavelength are 633 nm for R (He–Ne), 532 nm for G (diode-pumped solid state laser, DPSS), and 473 nm for B (DPSS).8–10) The optical recording system is shown in Fig. 1. The laser beams are switched by acousto-optic modulator (AOM) shutters, and divided into two beams with polarized beam splitter; one is reference beam and the other is object beam. The three object beams are combined into a single beam, and incident to a liquid crystal display (LCD) panel. The LCD is a twisted-nematic electronically addressed liquid crystal panel of 640
480 pixels, and image data are sent from a computer. The three reference beams are also combined into a single beam, and both reference and object beams are focused into a mask size at the position of the recording medium, where the reference beam is 30 off from the normal axis of the recording medium. In the case of spacedivision exposure, each primary-color elementary hologram is recorded at different position, while in the case of multiple-exposure, recorded primary-color elementary holograms are superposed. 13

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Fig. 1. (Color online) Setup of optical system for recording full-color holographic stereograms. L1 –L4 , M1 –M10 , AO , and AR represent lenses, mirrors, and apertures, respectively.

2.2 Measurement system The system for the measurement of the color and diffraction efficiency of HSs is illustrated in Ref. 10, which quantifies the integral diffraction efficiency of diffuse-type holograms with a white light source. The light source used for the measurement is xenon lamp (Hamamatsu Photonics) with the power of 150 W, and the collimated light is used as illumination. Since the recorded hologram is volume reflection type, the spectrum of reconstructed light by white light illumination has peaks of narrow bandwidths at the wavelengths corresponding to R, G, B lasers, due to the Bragg diffraction. Then the diffraction efficiency is evaluated by the peak value of the diffracted spectra of holograms divided by the radiance of the illuminant spectrum at the same wavelength. For evaluating colors, CIE 1931 XYZ tristimulus values gi (i ¼ x; y; z) are calculated by Z ð1Þ gi ¼ Ci ðÞHðÞIðÞ d; where Ci ðÞ is CIE 1931 XYZ color matching functions, HðÞ is the spectral diffraction efficiency of a hologram, and IðÞ is the illumination spectrum, respectively. 3.

Multiple Exposure Characteristics of Photopolymer

3.1 Basic characteristics on monochromatic exposure In this paper, we used a photopolymer as a recording material, which is developed by Bayer MaterialScience AG.11,12) The exposure conditions of each color in monochrome exposure were first examined with different S/R ratio (S: object light, R: reference light) and exposure time.

Table 1.

Red Green Blue

Exposing condition in monochromatic exposure. Exposure energy (mJ/cm2 )

Diffraction efficiency (%)

19.28 35.19 8.41

45.13 29.76 13.00

As a result, it was found that the case of S/R ratio 1 : 5, 1 : 3, and 1 : 2 would be suitable for R, G, and B, respectively; these conditions were used in all the experiments below. In addition, the optimal exposure time which gives the highest diffraction efficiency was investigated. The exposure energy and diffraction efficiency for each color at this condition are shown in Table 1. We can see that the diffraction efficiency of blue is lower than two other colors. 3.2 Triple-color exposure characteristics This sub-section presents the experimental results examining the characteristics of triple-color exposure. First, we examined the influence of exposing order of R, G, and B holograms, where uniform-pattern HSs were recorded. The mean exposure energy was 5.85 mJ/cm2 (R), 11.59 mJ/cm2 (G), and 8.41 mJ/cm2 (B), respectively. We set the exposure energy of R and G lower than presented in Table 1, aiming to approximately equalize the diffraction efficiency of three colors. The photographs of the reconstructed images (uniform patch) are shown in Fig. 2. Especially, the reconstructed light of B was hardly obtained by RGB,

OPTICAL REVIEW Vol. 20, No. 1 (2013) Table 2.

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Triple exposing order and diffraction efficiency.

Exposing order RGB RBG GRB GBR BGR BRG

Diffraction efficiency (%) R G B 25.8 34.9 5.58 2.76 7.68 10.6

9.93 2.76 35.8 34.9 12.6 9.01

0.96 1.33 0.98 1.33 16 16.3

Table 3. Diffraction efficiency for different exposing order for double-color exposure. Exposed order RB BR GB BG

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R 20.8 20.2 — —

Diffraction efficiency (%) G B — — 37.0 37.1

7.52 3.58 19.6 10.7

RBG, GRB, and GBR orders and the diffraction efficiencies of them are shown in Table 2. From this result, we concluded that the best order for triple exposure was BGR or BRG. Next, crosstalk was examined. When R, G, and B elementary holograms are exposed at the same location of holographic material, the crosstalk may be observed in the diffraction efficiency. Namely, even though the amount of exposure is same for a certain color element, the diffraction efficiency of the color element is sometimes decreased or increased depending on the exposure amount of another color element. To investigate the influence of crosstalk, HSs of uniform pattern were recorded with changing the gray levels displayed on LCD. Figure 3 shows the relationship between the gray level of G channel and the diffraction efficiency, for the different gray levels of R channel, where the input level of B was constant as the single exposure. It can be seen that the diffraction efficiency of G is affected by the input level of R. The tendency depended on the exposing conditions and was difficult to be characterized. 3.3 Double-color exposure characteristics We also tested the case of double-color exposure, i.e., two of three primary-color holograms are exposed at the same position. Again, uniform color patches were recorded as changing the color order as well as the amount of exposure. Table 3 shows the diffraction efficiency of the recording conditions which give relatively high diffraction efficiency. The amounts of exposure were 6.89 mJ/cm2 (R), 3.11 mJ/cm2 (G), and 6.73 mJ/cm2 (B), respectively. Although the amounts of exposure were different from both single and triple exposure cases, we decided them to record holograms with high diffraction efficiency. The exposing orders are presented in Table 3. It was found that doublecolor exposure realizes high diffraction efficiency of B when using GB order.

4.

Proposed Exposing Scheme Based on Double-Color Exposure

Recording full-color HSs can be realized by multiple exposure or space division exposure of R, G, and B elementary holograms as showing in Figs. 4(a) and 4(b). In the multiple-exposure scheme, the whole area of the hologram is used for every color, while only 1/3 is devoted in space division scheme. This results in the reduction of gross diffraction efficiency in the space division scheme. On the other hand the diffraction efficiency is decreased in multiple exposures, and the crosstalk affects the color reproduction as explained above. Therefore, we propose a new scheme of recording fullcolor HSs based on double exposure. Taking account of the low diffraction efficiency of blue hologram, blue element is exposed over whole surface, and R + B and G + B elements are arranged as shown in Fig. 4(c). Since green and red elements occupy 1/2 of the whole hologram, their diffraction efficiencies become half compared with the results shown in Table 3, but still expected to be higher than space division and triple exposure cases. Note that the diffraction efficiencies of space division and double-color exposure cannot be completely expected from the results of Tables 1 and 3, because neighboring elementary holograms interact each other. The spatial resolution of the proposed exposure scheme is higher than the case of space division, though lower than the triple exposure scheme. 5.

Experimental Results

This section presents the results of recording full-color holograms of a color chart by different three methods including the proposed one. For color reproducibility, we introduced color management techniques to the recording process of holograms. 5.1 Color management in holoprinter Previously, we reported the results of color management of full-color HSs,10) in which holograms were recorded on silver halide material by space division exposure. The same color management model is used to control the recorded color on the photopolymer in this paper. Before introducing color management model, we have to decide the amount of exposure energy of each primary color, considering white balance. More specifically, exposure energy should be decided so that the reproduced light becomes white when the input grey level of LCD is 255 for all the three colors. Then, any colors can be reproduced by controlling the three (R, G, and B) input grey levels of LCD. We decided exposure energy for three kinds of exposure schemes so that the xy chromatic coordinates of the white corresponds to that of the CIE D65 standard illuminant. The results are as follows: – Space division: 3.1 mJ/cm2 (R), 2.28 mJ/cm2 (G), 8.41 mJ/cm2 (B) – Double: 6.89 mJ/cm2 (R), 3.11 mJ/cm2 (G), 6.73 mJ/cm2 (B)

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F. YANG et al. 16.0% R

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 2. (Color) Reconstruction image at different recording orders by triple exposure. 10
10 elementary holograms are recorded in each color patch. The exposing order is (a) RGB, (b) RBG, (c) GRB, (d) GBR, (e) BGR, and (f ) BRG, respectively.

Diffraction effciency

14.0% 12.0%

B

10.0% 8.0%

G

6.0% 4.0% 2.0% 0.0%

Diffraction efficiency of Green channel

0

50

100 150 Gray Level of LCD Image

200

250

Fig. 5. The relationship between gray levels of LCD and diffraction efficiency by double color exposure.

12.00% 10.00% 8.00% R=0 6.00%

R=128 R=255

4.00% 2.00% 0.00% 0

64

128

192

256

Green channel

(a)

Fig. 3. Diffraction efficiency in green channel with red channel of 0, 128, and 255 with exposing amount red: 9.36 mJ/cm2 ; green: 5.63 mJ/cm2 .

(b)

(a)

(b)

(c)

Fig. 4. (Color) Three exposing patterns for full-color holographic stereograms. (a) Space division exposure, (b) triple-color exposure, and (c) double-color exposure (proposed method).

(c) Table 4. Diffraction efficiency of each exposing scheme after white balancing (in %).

Space division Double exposure Triple exposure

R

G

B

7.3 13.4 13

2 7.7 4.1

4.21 10.7 7.5

– Triple: 3.1 mJ/cm2 (R), 1.66 mJ/cm2 (G), 5.89 mJ/cm2 (B) The diffraction efficiencies of three exposure schemes under this condition are shown in Table 4. The diffraction efficiencies became lower than the previous experiment because the exposure energy was adjusted on the basis of the

Fig. 6. (Color) Left: reproduced images of (a) space division exposure, (b) double-color exposure, (c) triple-color exposure with the average of color difference of 24 color patches. Right: color difference between reproduced and original color chart under the same xenon lamp in CIE 1931 L a b color space, respectively.

lowest diffraction efficiency among R, G, and B primary color holograms. After deciding exposure energy, we introduce a color management model. The color management model used in this paper is described explicitly in Ref. 10. The model describe the relationship between a set of RGB signals sent to LCD and XYZ tristimulus values reproduced from the recorded holograms. The model consists of a 3-by-3 matrix

OPTICAL REVIEW Vol. 20, No. 1 (2013)

Scheme Space division Double exposure Triple exposure

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Chromaticity of primary colors and white with each exposure scheme. R

Primary color coordinates (CIE xy-chromaticity) G

ð0:70; 0:30Þ ð0:70; 0:30Þ ð0:70; 0:30Þ

ð0:16; 0:80Þ ð0:16; 0:80Þ ð0:16; 0:80Þ

which converts XYZ to RGB and tone reproduction curves. In this model, the crosstalk among three channels was not considered. Therefore, crosstalk becomes one of the reasons to degrade the color reproduction accuracy. To make the model, we need xy chromaticity coordinates of the three primary colors, XYZ tristimulus values of the white, and tone reproduction curves of the three primary colors. In order to obtain the former two, we recorded the holograms of uniform color patches with the size of 5
5 mm2 , where the input grey levels are ð255; 255; 255Þ for white, ð255; 0; 0Þ for R, ð0; 255; 0Þ for G, and ð0; 0; 255Þ for B. Then, the reproduced spectra were measured by a spectroradiometer. The results are shown in Table 5. In order to obtain the tone reproduction curve, we investigated the relation between the input grey level (R, G, and B) of the LCD and the diffraction efficiency of the recorded holograms. In this experiment, we exposed color patches with the size of 5 mm
5 mm, and changed the input gray levels from 0 to 255 every 64. The relation between each gray level for R, G, and B and their diffraction efficiency is shown in Fig. 5 in the case of double color exposure scheme. From this result, we assumed the tone curve linearity in the range of gray levels from 0 to 192 and implemented it to the 1D look-up table (LUT) in the following experiment. In the case of both space division and triple exposure, tone curve linearity can be assumed in the range of 0–255. 5.2 Reconstruction of color chart Full-color HSs of the color chart (GretagMacbethColorChecker, MCC) were recorded by three exposure schemes. The XYZ tristimulus values of original MCC were measured by using spectroradiometer under the xenon lamp illumination. The RGB signals used to record HSs were calculated on the basis of the matrix and the tone curves explained in the previous section. The color chart was recorded on the hologram plane. Each color patch consists of 28
28 elementary holograms, where the pitch and the size of the elementary holograms were 200
200 m2 . The reconstructed image of the color chart is shown in Fig. 6. In addition, in order to evaluate the result, we compared the colors reproduced by the hologram with those of a real color chart, under the same xenon lamp, and the CIELAB color difference E was calculated using the following formula: L ¼ 116f ðY=Yn Þ  16; a ¼ 500½ f ðX=Xn Þ  f ðY=Yn Þ; b ¼ 200½ f ðY=Yn Þ  ðZ=Zn Þ;

White point

B

ð0:13; 0:05Þ ð0:12; 0:07Þ ð0:13; 0:05Þ

ð0:36; 0:36Þ ð0:27; 0:32Þ ð0:33; 0:33Þ

1.2 Space division

Yave=0.28 Double exposure Yave=0.29 Triple exposure Yave=0.20

1 0.8 Y values

Table 5.

F. YANG et al.

0.6 0.4 0.2 0 0

6

12

18

24

Color chart serial number

Fig. 7. Y values of 24 color patches pattern recorded by three different exposure schemes. The caption of Yave presents the average of Y values.

f ð!Þ ¼ ð!Þ1=3 ; ! > 0:008856; 7:787ð!Þ þ 16 f ð!Þ ¼ ; ! < 0:008856; 116 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi EL a b ¼ ðL1  L2 Þ2 þ ða1  a2 Þ2 þ ðb1  b2 Þ2 :

ð2Þ

From these results, it was confirmed that the proposed double-color exposure scheme realizes the lowest color error. In addition, we found that the spatial resolution is higher than that of space division exposure. Figure 7 shows Y values in XYZ color space of 24 color patches, which correspond to the luminance of the reconstruction image. We can see that the double exposure achieved approximately same brightness as that of space division exposure, and higher brightness than triple-color exposure. 6.

Conclusions

In this paper, we proposed a new exposing scheme for full-color full-parallax holographic 3D printer using photopolymer as a recording medium. The proposed method is based on double-color exposure. The adjustment of exposing condition of the proposed method is less complicated than triple exposure case, because only two colors are multiexposed. In addition, the spatial resolution of the proposed method is higher than that of space division exposure, while it is lower than that of triple-color exposure. Since the diffraction efficiency of blue was lower than those of red and green, we arranged blue elementary holograms at twice density of red and green, which realizes better diffraction efficiency. From the results of recording the color chart holograms, it was confirmed that the proposed double-color

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exposure scheme realizes the highest color accuracy. In addition, the brightness is comparable to that of space divisition case, and higher than triple exposure case. Though the number of blue elements is twice of that of red and green in this paper, the proposed scheme can be modified according to the characteristics of recording material. Acknowledgments The authors wish to thank Bayer MaterialScience AG for providing the photopolymer material, and Toppan Printing Co., Ltd. for the support on the development of the holoprinter system. References 1) M. Yamaguchi, N. Ohyama, and T. Honda: Appl. Opt. 31 (1992) 217. 2) M. A. Klug, M. W. Halle, and P. M. Hubel: Proc. SPIE 1667 (1992) 110. 3) M. A. Klug, A. Klein, W. Plesniak, A. Kropp, and B. Chen: Proc. SPIE 3011 (1997) 78.

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