Hologram Generation Technique Using Integral Photography Method

3-2 Hologram Generation Technique Using Integral Photography Method

OI Ryutaro, SENOH Takanori, YAMAMOTO Kenji, and KURITA Taiichiro

When a hologram is generated using a real photographic space as its object, one must basi- cally record the interference between beams refl ected through a coherent beam illuminated on the subject on one hand, and a reference beam on the other. This method essentially requires photography in a darkroom, however, and faces many other constraints when considering its use in ultra-realistic communication. In the fi eld of optical holography, on the other hand, the holocoder-hologram method where the fi rst exposure is used to take integral images of the subject through many lenses and a second exposure is used to generate a hologram based on integral images is already known. The use of this two-step photography in generating electronic holograms is ex- pected to enable the generation of holograms as electronic data of subjects taken under natural light beams, thereby expanding the applicable scope of holography. In transforming holocoder- holograms into electronic form, the coauthors have proposed a method that entails positioning hologram generation on the rear focus plane of the integral lens array, thereby transforming 3D image information recorded on integral images through a single Fourier transform operation into a complex amplitude distribution of the object beam on the hologram plane. This method makes it possible to perform transformation operation on all elemental images constituting the integral image independently of each other, and also enables fast transformation of high-resolution integral images based on many lenses through parallel calculation. Experiments conducted by the coauthors used integral images of 4096 × 2048 pixels generated by computer graphics as inputs, and demonstrated that 3D images of a subject can be reconstructed from holograms generated by using the proposed method. This paper presents the details of this method. Keywords Hologram, Integral photography, Computer-generated hologram, Real scene, Real-time

1 Introduction interference fringes as fi ne as its wavelength. The diffi culty of such operations currently lim- Holographic technology is a display meth- its its practical use in photographic fi lm and od that accurately records and reproduces the other limited fi elds that use special metal foils wave front of light emitted by a body, and with pictures drawn by means of electron which satisfi es binocular parallax, kinetic par- beams. If it becomes possible to perform all the allax, accommodation, and all other clues processes (recording, transmission and recon- through which humans sense the stereoscopic struction) of real-scene holograms in an elec- nature of an object [1]. For that reason, it is con- tronic and easy manner, then hopes run high sidered an ideal method of recording and repro- that this will bring about great advances in the ducing 3D images. However, a hologram re- fi eld of ultra-realistic communication. In par- quires the recording and reconstruction of ticular, this paper proposes the technology for

OI Ryutaro et al. 21 recording real-scene holograms electronically. Taking pictures of a subject from numerous It is known that integral photography—where- viewpoints, on the other hand, is known to pro- by pictures are taken of a subject through a lens vide 3D information including horizontal par- plate consisting of many convex lenses—en- allax, vertical parallax, and the imaging of ob- ables 3D information of the subject including ject points constituting the subject or scene. its horizontal and vertical parallax to be record- This is called integral photography [2]. More- ed [2]. The coauthors have observed that it is over, the holocoder-hologram has also been possible to generate holograms (interference proposed in the past as an optical technology [5]. fringes) as electronic data by obtaining the This technology uses images taken from many complex amplitude of the object beam on the viewpoints as the original, thereby obtaining hologram plane by performing Fourier trans- holograms of the subject optically. This meth- form on each element independently, after add- od utilizes still integral images and the holo- ing an appropriate initial phase to data obtained gram’s recording plane to prepare holograms of by means of this integral photography [3]. The still real-scene images taken under a natural following describes this method. beam. But since this preparation of holograms requires an optical system including many 2 3D recording method for subject lenses of very high precision, the method was images not put to practical use. Moreover, when the integral photography is applied as an electronic 2.1 Holographic recording medium, it is still necessary to conduct expo- The generation of real-scene holograms re- sure in a darkroom, which limits its scope of quires that interference fringes between the co- application. herent beam and reference beam refl ected from the subject should be photographed regardless 2.2 Recording using integral of whether employing a photographic technol- photography ogy or technology based on CCD/CMOS or Integral photography is also one of the other electronic image sensor. Therefore, pic- methods used for recording and reconstructing tures of holograms had to be taken in a special- images of a subject in a 3D manner. This is a ized darkroom environment with extremely beam reconstruction type of 3D recording tech- low vibration. nology and entails taking photos with a natural When one uses computer graphics (CG)— beam (incoherent beam) applied to the subject, where the structure of the subject is known—as as is similarly done in ordinary TV photogra- the original pictures, however, the desired ho- phy. lograms can be generated by creating the co- Since outdoor photography is affected by herent object beam refl ected from the CG ob- sunlight, photography by means of an incoher- ject in a computer and calculating the complex ent beam is an indispensable requirement. Fig- sum of that beam with the reference beam sim- ure 1 shows the principles of recording and re- ilarly obtained through calculation. This meth- constructing 3D images by using integral od is already known as the computer-generated photography. When taking pictures, the subject hologram (CGH) [4]. If it were hypothetically is recorded through a lens array composed of easy to obtain a complete structural model and many convex lenses (elemental lenses) as the texture of real-scene objects and scenes in shown in Fig. 1 (a). At that time, the recording an easy real-time manner, the CGH method plane receives many miniscule images (ele- could be used to generate holograms. However, mental images) obtained by observing the sub- under present conditions it is very diffi cult to ject from different angles. The recording plane obtain a detailed and faithful real-scene struc- is positioned at the focal point distance of each tural model and texture applicable to holo- lens, so that the pixels constituting the elemen- grams. tal images will match the direction of the paral-

22 Journal of the National Institute of Information and Communications Technology Vol.57 Nos.1/2 2010 lel beam that passed through the corresponding reconstruct the horizontal and vertical parallax, elemental lens. Similarly, the light emitted and imaging position of the subject. However, from one point on the subject plane is sampled the width of reconstructed beams cannot be in the same number as that of elemental lenses less than the diameter of convex lenses consti- constituting the lens array. That is, one can see tuting the lens array. For that reason, the sub- that the number of elemental lenses corre- ject image to be reconstructed will have blurs sponds to the number of beams recorded. as large as the diameter of lenses constituting Next, as shown in Fig. 1 (b), after the ele- the lens array [6]. mental image is reversed at recording, the natural beam (incoherent beam) is applied similarly 3 Generation of holograms using from the direction where the subject was pres- integral photography ent at the time of photography. Then, passing an image through the lens eye of the same array 3.1 Conversion from integral as at the time of photography causes the beam photography emitted by the elemental image to be refracted When a hologram is prepared from an inte- by the lens array, resulting in the reconstruction grally photographed recording plane, a coher- of a beam equivalent to that emitted from the ent beam is ﬁ rst applied to illuminate the re- subject at the time of recording. cording plane as shown in Fig. 2, thereby Integral photography makes it possible to reconstructing the coherent object beam. More- over, when a reference beam that can interfere with the one used in illumination is irradiated on the hologram plane, the square of the absolute value of the complex sum of the coherent object beam and reference beam is recorded on the hologram’s recording plane as an amplitude hologram. A hologram recorded this way can be used to reconstruct the original 3D image of the subject [5]. Conducting this process optically required a lens array with high positional precision and an exposure process for holograms based on a coherent beam (laser). Replacing the hologram generation process with calculation operations (a) Capturing of 3D image enables the creation of holograms without

(b) Reconstruction of 3D image

Fig.1 Recording and reconstruction by integral photography Fig.2 Recording by holocoder-hologram

OI Ryutaro et al. 23 needing a darkroom for exposure [7]. When replacing the process for optically （5） preparing holograms with CGH, people gener- ally use a method that involves tracing the propagation of object beams by approximation Then the approximation of Equation（4） holds in the Fresnel region of the Kirchhoff diffrac- and the following equation is obtained. tion integration equation. Here, assuming an aperture and screen as （6） shown in Fig. 3, when a wave having a complex amplitude of Ψ(x, y) passes the opening and illuminates a screen at distance z, then the Here, g (x, y) denotes the complex amplitude complex amplitude distribution Ψ’(x', y' ) pro- distribution (transformed data) in the opening; duced on the screen is expressed by the follow- u(x', y' ) denotes the complex amplitude distri- ing equations: bution (transforming data) produced on the screen. （1） Figure 4 shows the hologram preparation process using integral photography. First, as-

suming a complex amplitude of g0(x0, y0) for （2） the elemental image, one should determine the

beam distribution g1(x1, y1) formed on the incidence plane of the convex lens when this prop- （3） agates over focal point distance f of the lens array. This can be expressed by Equation（6） as Here, the aperture function f (x', y' ) is based on follows: an aperture of 1 and a masking of 0 with λ as the wavelength of the light source. （7） Developing r to the primary term in relation to z will produce an equation as shown below. Next, one should determine the beam distribu- （4） tion g2(x1, y1) formed on the exit plane of the convex lens. The resulting amplitude will re- Moreover, when the tertiary term is sufﬁ ciently main unchanged relative to the beam distribu- small relative to the wavelength and is: tion on the incidence plane of the lens, with

Fig.3 Diffraction and propagation of beams in Fig.4 Generation of holograms based on inte- the Fresnel region gral images

24 Journal of the National Institute of Information and Communications Technology Vol.57 Nos.1/2 2010 only the phase being changed and resulting in the following: （11）

（8） Let the Fourier transforms of u(x', y'), g(x, y) and p(x, y) be U(ξ, η), G(ξ, η) and P(ξ, η), re- The calculations performed so far can be deter- spectively, and we obtain the following: mined independently for each elemental image. （12） Furthermore, one should also determine the

beam distribution g3( y2, y2) on the hologram Then determining the Fourier transforms of plane placed at distance l from the lens array. g(x, y) and p(x, y), and performing a reverse Again by using Equation（6） , this becomes as Fourier transform on the product thereof will follows: produce u(x', y'). The Fourier transform of the transfer function can be analytically determined and will be as follows: （9）

（13） Note that the calculations in Equation（9） must absolutely be performed on the entire hologram Therefore, Equation（9） , which is the Fresnel plane, and not just for each elemental image. transform, can actually be calculated by multi-

Last but not least, determining the square plying the Fourier transform of g2(x1, y1) by of the absolute value of the sum (complex sum) P(ξ, η) and performing a reverse Fourier trans- of the complex amplitude distribution obtained form on the result (two FFTs). With this calcu-

from Equation（9） and the reference beam will lation method, transformed data g3(x2, y2) can produce an amplitude hologram. be obtained with the same sampling interval Here, it is notable that distance l between and aperture width as those of transformed data

the hologram location and the lens array is as g2(x1, y1). desired, and that the location for hologram In the hologram generation process using preparation may be either immediately behind integral photography, Fresnel transform of the or far from the lens array. same size as the hologram plane must be used In concrete calculations, Equations（7） and in calculations of object beam propagation （9） must be calculated at least twice, domi- from the exit plane of the lens array to the ho- nated by the amount of calculations for this logram plane shown in Fig. 4. Hypothetically, Fresnel transform. Conversely, the amount of if fast operations are used based on FFT, per- calculations for Equation（8） —the modulation forming those calculations will ultimately take of the phase component from the convex lens— much time. is comparably and negligibly small. For efﬁ cient calculation of the Fresnel 3.2 Conversion method with easy transform as shown in Equation（6） , there is a parallel calculation solution method [8] that transforms this into a When holograms are prepared in a special combination of Fourier transforms and then ap- location in the hologram preparation process plies FFT. Here, by ignoring the constant term using integral photography, transformation can and using a convolution integral to then be performed more efﬁ ciently without af- write Equation（6） , we have the following: fecting the image quality. As shown in Fig. 5, let the complex amplitude distribution formed （10） by a single elemental image on the hologram

Here, transfer function p(x, y) is: plane be g4(x3, y3). Moreover, let the hologram plane be near the rear focal plane at distance d from the lens exit end, and use function h de-

OI Ryutaro et al. 25 ﬁ ned by the equation below to notate the phase tain the following: term as follows: （18）（14） 2 2 The terms including (x3 + y3 ) also delete each As such, the optical ﬁ eld produced on the holo- other, thereby obtaining the following: gram plane by complex amplitude distribution immediately after the lens can be written by （19） modifying Equation（6） as follows:

（15） Here, Equation（19） is such that, when the hologram plane is d = f on the focal plane, the 2 2 Then by performing the Fresnel transform terms including (x0 + y0 ) in the integration can from the elemental image to the incidence end also be deleted, so that a complete Fourier of the lens, and substituting Equations（7） and transform [9] will be formed on the rear focal （8） that express phase modulation by the lens, plane, including the phase terms of beam distri- the optical ﬁ eld produced by a single elemental bution on the front focal plane with the elemen- image on the hologram plane can be written as tal image in place. Since this complex ampli- follows: tude distribution is the object beam to be determined, when the hologram plane is the rear focal plane, the complex amplitude on the （16） hologram plane of beam propagation before and after the convex lens can be directly determined by performing Fourier transform on the

Here, the Fourier transform of h(x1, y1:d ) will complex amplitude of the elemental image for become: each element, instead of performing operations based on Equations（7） ,（8） , and（9） . Figure 6 shows the proposed method of （17） generating holograms. Assuming that the lens array is composed of convex lenses with focal due to its relations with Equation（13） . There- point distance f, the beam distribution on holo-

fore, by substituting Equation（17） in Equation gram plane g4(x3, y3) when using the method （16） and omitting the constant terms, we ob- shown in Fig. 6 will eventually be obtained with the following equation by using Equation （19）.

（20）

An amplitude hologram is obtained from the square of the absolute value of the sum (complex sum) of the ﬁ nally obtained beam distribu-

tion g4(x3, y3) and the reference beam. In Equation （20）, FFT operation can be used as Fourier transform. When compared with the case where holograms are prepared at Fig.5 Beam distribution before and after the a desired location at distance l from the lens rear focal plane of the lens array, operations can be performed more efﬁ -

26 Journal of the National Institute of Information and Communications Technology Vol.57 Nos.1/2 2010 ciently. Moreover, at that time, if the beam dis- logram generation. tribution g4(x3, y3) formed on the hologram plane is obtained at the same sampling distance 3.3 Initial phase and aperture width as those of source elemental Elemental images taken using integral pho- image g0(x0, y0), then the object beams pro- tography technology record the amplitude of a duced by element images on the hologram beam alone and do not record phase information plane will not overlap, but appear in a manner in a strict sense. For that reason, an appropriate that covers the entire hologram without gaps. initial phase must be given to obtain the com-

This means that operations on the object beams plex amplitude distribution g0(x0, y0) of elemen- on the hologram plane can be performed com- tal images in transformation Equation （20）. pletely independently for each elemental im- In CGH, random phase [10] is often superim- age, and that parallel calculations can be per- posed, assuming that the subject surface fol- formed on computers of the distributed memory lows the Lambert reﬂ ection model. The initial type. When parallel operations are performed, phase of integrally taken elemental images is operation units can be divided to the number of similarly set to a random phase. Therefore, the elemental images (equal to the number of lens- complex amplitude distribution g0(x0, y0) of ob- es) at the maximum, which can realize high ject beams on the surfaces of elemental images speed mounting. is expressed by using the luminance distribu-

Note that limiting the location for prepar- tion A(x0, y0) of integrally taken elemental im- ing holograms to the rear focal plane of the in- ages as follows: tegral lens will do nothing but fi x the relative positional relationship between integrally pho- （21） tographed elemental images and holograms. In ordinary integral photography, pictures are taken of a subject positioned at a desired location In Equation（21） , note that rnd(x0,y0) is a a certain distance away from the lens array, so uniform random number in the interval [0,1). that images of the subject as reconfi gured from a hologram generated by the abovementioned 3.4 Color 3D image transformation method can be produced natu- The discussion above regarded a case using rally in a 3D manner at a desired location from a coherent beam with single wavelength λ. In the hologram plane. In other words, when this holographic technology, the basic principle is is regarded as a function of recording and re- to record 3D images of a subject by using a constructing 3D images, there are no special single wavelength. However, recording holo- constraints due to the proposed method of ho- grams with the three colors (red, green and blue) of coherent beams as in TV broadcasting, and also illuminating with coherent beams of the same wavelength at reconstruction will enable the reconfi guration of 3D color holographic images. In the proposed method, the same applies to generating holograms from integrally taken original pictures. Coherent beams near the cen- tral wavelength of RGB fi lters in a color cam- era at the time of integral photography can be used to transform images into holograms corresponding to the three primary colors, in order Fig.6 Method of generating holograms with to prepare color holograms. easy parallel calculation

OI Ryutaro et al. 27 4 Optimal design of elemental pling interval Δp of the original picture, calcu- images as the result of lation wavelength λ, and the number of samples discretization (M or N ). For simplifi cation, the following discussion When FFT or other discrete numerical cal- will be based on the assumption that the hori- culation is used in generating holograms from zontal and vertical sampling intervals are equal integrally taken original pictures, the focal (M = N), and that the aperture widths are also point distance of the integral lens, the number equal, being rectangular (NΔp). of samples of elemental images, and various When one thinks of determining the distri- other design values must be determined to en- bution of complex amplitudes of object beams sure proper mounting. on the hologram plane by using FFT in Equa- With the algorithm of the commonly used tion（20） , one can choose N as two’s power to discrete Fourier transform, let the transformed perform effi cient transformation. As an exam- function be set to g(m, n) and the Fourier spec- ple, when using a value from Table 1 as a pa- trum on Fourier transform plane j-k be G( j, k), rameter to generate a hologram from an inte- with their relationship being expressed by the gral image, one can see from the relationship in following equation: Equation（25） that focal point distance f of the integral lens in the calculation is 0.582 mm. （22） In integral photography, it is known that the ratio of the lens diameter in photography The following equation is conversely the result to the lens diameter in reconstruction will be of rewriting Equation （20） to determine the the lateral magnifi cation of the image to be beam distribution on the hologram plane from reconstructed (i.e., magnifi cation of the im- integrally taken elemental images with the age height), and that the ratio of the lens fo- numbers of horizontal and vertical samples set cal point distance in photography to the focal to M and N, respectively, and the sampling in- point distance in reconstruction will become terval set to Δp, in order to Fourier-transform it the longitude magnifi cation in reconstruction as data discretely sampled in a limited aperture. (i.e., magnifi cation of depth). Therefore, if, hypothetically, the focal point distance of the （23） elemental lens in integral imaging as shown in Fig. 7 is 12 mm, then the optimal design lens Here, let the conditions be that the elemental pitch (diameter) in photography will be 1.583 image, size (aperture), and sampling interval of mm, and the reconstructed holographic image the element hologram calculated from the ele- at that time will be strain-free as a 3D image. mental images and this elemental image are Moreover, in that case, the view angle that al- equal, and that the element holograms do not lows for the subject by integral imaging will be overlap but are laid throughout without gaps, about 7.54 degrees. thereby obtaining the following relational equations from a comparison of the phase ter- 5 Generation and reconstruction minals in Equations（22） and（23） . of holograms by computer simulation （24） Computer simulation was conducted to （25） generate holograms based on the proposed From this, one can see that focal point distance method from integrally taken original pictures. f in calculations of the process for generating holograms from original pictures recorded in 5.1 Preparation of integral images integral photography is determined by sam- Here, in preparation for the original pic-

28 Journal of the National Institute of Information and Communications Technology Vol.57 Nos.1/2 2010 tures, CG pictures that simulate the subject × 16 pixels, and then two-dimensional FFT was with a two-layer depth as shown in the layout performed based on the DC component as the in Fig. 8 were used to prepare integral images image center. The data obtained was the distri- of 4096 pixels horizontally by 2048 pixels ver- bution of complex amplitudes of object beams tically. Table 2 lists the parameters used in pre- in the hologram’s recording plane, as deter- paring integral images. Here, the focal point mined independently of the elemental images. distance and aperture of the lens were set to 10 Calculations were also performed on the inter- times their respective settings listed in Table 1. ference fringes between the object beam ob- Figure 9 shows the original pictures prepared. tained and the reference beam. Here, it was as- One can see that the original pictures have the sumed that the reference beam was to enter arrangement structure of the elemental lens. from the direction vertical to the hologram. The

Moreover, one can also see changes in the im- reference beam R( y) used in calculations for the age of the subject appearing in the elemental off-axis hologram that enters at angle θ can be image according to the distance of the subject. given by the equation below. Here, k denotes the wave number (k = 2π/λ). 5.2 Hologram generation Next, the algorithm shown in Fig. 10 was （26） followed to transform the data into hologram data. First, a random phase of 0 to 2π was given The beam that enters a hologram vertically be- to the elemental image composed in units of 16 comes a reference beam having constant ampli-

Table 1 Examples of settings made in hologram Table 2 Parameters used in recording integral generation images

Sampling interval : Δp 4.8μm Focal point 5.82mm distance of lens : f Number of horizontal and vertical 16 samples : N Aperture diameter 0.768mm of lens : D Calculated wavelength : λ(He-Ne 633nm red Elemental image 16 horizontally × 16 size : N vertically Lens aperture diameter : NΔp 0.0768mm Number of 256 horizontally × 128 Lens focal point distance in elemental images vertically 0.582mm calculation : f Total number of 4096 pixels horizontally × pixels 2048pixels vertically

Fig.7 Examples of settings made on the ele- Fig.8 Layout of the subject in recording integral mental lens in integral imaging images

OI Ryutaro et al. 29 Fig.9 Integral image (4096 × 2048 pixels) used in experiments

Table 3 Parameters used in hologram generation Fig.10 Processing to generate holograms from integral images Total number of 4096 pixels horizontally × hologram pixels 2048 pixels vertically 4.8μm Pixel pitch : Δp (horizontally & vertically) Elemental hologram 16 horizontally × 16 dimensions vertically

Wavelength : λ 633nm (He-Ne red)

Focal point distance 0.582mm (calculated value) of lens : f Reference beam Parallel beam (in-line) Fig.11 Hologram pattern generated (DC = 127) tude on the entire screen obtained by substitut- Conversely, Fig. 12 (b) shows that the subject ing θ = 0 in Equation（26） , and after all, the placed far from the recording plane is sharply hologram is nothing but the real portion of the imaged, but the subject placed close to the re- object beam. Table 3 lists the settings used in cording plane is reconstructed as being blurred. hologram generation; Figure 11 shows the ho- These results show that 3D composition of the lograms obtained. subject space is correctly maintained by the proposed method of hologram generation. 5.3 Hologram reconstruction Here, the lens focal point distance and aperture Holograms obtained using the abovemen- in hologram generation are one-tenth the inte- tioned method were reconstructed by computa- gral image, respectively, and one can see that tional reconstruction to observe the images. the distance to the subject is reduced in re- Here, how imaging is performed on a plane sponse to the magnifi cation. By comparing the separated by distance -z from the hologram’s subject shown in Fig. 8 with the position of the recording plane is reproduced. Figure 12 shows reconstructed hologram image, it was con- hologram images reconstructed over two diffi rmed that the ratio of longitudinal magnifi ca- ferent distances from the hologram plane. Fig- tion to transverse magnifi cation of the subject ure 12 (a) shows a reconstructed image at a was correctly stored as well. distance close to the hologram plane. In Fig. 8, the subject placed close to the integral record- 6 Conclusion ing plane is sharply imaged, and one can see here that the subject placed far from the record- This paper described a method of generating plane is reconstructed as being blurred. ing electronic holograms by using integral pho-

30 Journal of the National Institute of Information and Communications Technology Vol.57 Nos.1/2 2010 ing, thereby obtaining the distribution of complex amplitudes of object beams on the hologram plane, and thereby eventually generating holograms in a quick manner. Moreover, the paper clarifi ed the relationship between the focal point distance of the lens array best suited for using a fast Fourier transform (FFT) and the sampling interval for (a) Reconstructed image at distance of 12.58mm elemental images in the transformation process from integral images to holograms. The experiments conducted involved generating and reconstructing holograms by means of the proposed method by using CG-generated integral images of 4096 × 2048 pixels. From the observation results of the images reconstructed, the coauthors confi rmed the possibil- (b) Reconstructed image at distance of 24.58mm ity of obtaining 3D images that correctly repro- duce the depth relationship of the subject space. Fig.12 Reconstructed image of a hologram (how imaging is performed at a constant Hopes run high that by performing all the distance from the hologram plane) processes of real-scene holograms (recording, transmission and reconstruction) electronically tography. One can perform Fourier transform and easily in the future, then great progress will on each element independently after adding an be made in the fi eld of ultra-realistic communi- initial phase to data obtained by integral imag- cation.

References 1 R.Oi, M.Okui, “A Method for Displaying a Real-scene Fresnel Hologram,” The Institute of Image Informa- tion and Television Engineers (ITE) Technical Report, Vol. 30, No. 43, pp. 3–6 (2006) 2 M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” Journal of Physics, 4 serie, Ⅶ , pp. 821–825, 1908. 3 R.Oi, T.Mishina, M.Okui, Y.Nojiri, and F.Okano, “A Fast Hologram Calculation Method for Real Objects,” Journal of The Institute of Image Information and Television Engineers (ITE), Vol. 61, No. 2, pp. 198–203 (2007) 4 B. R. Brown and A. W. Lohmann, “Computer generated binary holograms,” IBM Journal of Research and Development, 13, pp. 160–167, 1969. 5 R. V. Pole, “3-D Imagery and holograms of objects illuminated in white light,” Applied Physics Letter, 10, pp. 20–22, 1967. 6 J. Arai, H. Hoshino, M. Okui, and F. Okano, “Effects of Focusing on the Resolution Characteristics of Inte- gral Photography,” Journal of Optical Society of America, Vol. 20, No. 6, pp. 996–1004, 2003. 7 T. Mishina, M. Okui, and F. Okano, “Generation of holograms using integral photography,” in Three Di- mensional TV Video and Display Ⅲ, Proc. SPIE5599, pp. 114–122, 2004. 8 Y.Matsuo, K.Yamane, “Rader Holography,” pp. 80-81, The Institute of Electronics and Communication Engineers of Japan (1980) 9 Y.Yamaguchi, “Applied Optics,” pp.189-201, The Japan Society of Applied Physics, Ohmsha (1998)

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(Accepted Sept. 9, 2010)

OI Ryutaro, Dr. Sci. SENOH Takanori, Dr. Eng. Senior Researcher, 3D Spatial Image Expert Researcher, 3D Spatial Image and Sound Group, Universal Media and Sound Group, Universal Media Research Center Research Center Optical Wave Propagation Analysis, Electronic Holography, 3D Image Holography, 3D Imaging Technology, Technology Image Sensor

YAMAMOTO Kenji, Dr. Eng. KURITA Taiichiro, Dr. Eng. Senior Researcher, 3D Spatial Image Group Leader, 3D Spatial Image and Sound Group, Universal Media and Sound Group, Universal Media Research Center Research Center Electronic Holography, 3D Image Television System, Information Technology Display, 3D Image Technology

32 Journal of the National Institute of Information and Communications Technology Vol.57 Nos.1/2 2010