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New technique for recording a Lippmann hologram
Volume 28, number 2
OPTICS COMMUNICATIONS
February 1979
NEW TECHNIQUE FOR RECORDING A LIPPMANN HOLOGRAM Toshihiro KUBOTA and Teruji OSE Institute of lndustrial Science, University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo, Japan Received 8 November 1978
A new Lippmann hologram technique is described in which a holographic stereogram is used as master hologram. A sharp and deep synthesized three-dimensional image can be obtained by this technique. Experimental results for this hologram and discussion of the image blur axe presented.
1. Introduction When a white light source is used to illuminate a Lippmann hologram, the reconstructed image is blurred because broadening of wavelength selectivity due to finite thickness of the hologram and because extended source of illumination. The blur increases as the hologram-to-image distance increases. Therefore, the image depth is restricted. In order to observe the deep image sharply, the increase of hologram thickness or the reduction of apparent source size is necessary. However, the former is difficult to develop the emulsion uniformly throughout the thickness and the latter sacrifices the image brightness. The image blur which is an inherent property of a Lippmann hologram does not exist for the case of an image hologram, that is, the case when the image is reconstructed on the hologram plane. Such a property of image hologram leads us to an idea that a sharp and deep synthesized three-dimensional image can be obtained from a Lippmann hologram when a holographic stereogram is used as master hologram. The use of a holographic stereogram was proposed by King et al. for a transmission hologram [1]. In this letter, we present a new technique for recording a Lippmann hologram using a holographic stereogram and the discussion of the image blur.
2. Description of the new technique The basic recording geometry is shown in fig. 1. We begin with the reconstruction of the holographic stereogram. A holographic stereogram consists of many elementary holograms [2]. One elementary hologram is formed for each two-dimensional transparency which shows the different perspective. Illumination of the stereogram with the wavefront conjugate to its reference wave produces the real images of the transparencies in space as well as a synthesized three-dimensional image of the object. Although the real image of the transparencies are reconstructed as many as the number of the elementary holograms, they are actually two-dimensional and are focused onto a certain plane. The photographic plate is set in this plane and a Lippmann hologram is recorded. The images of the transparencies now serve as the object of the hologram. When the Lippmann hologram is illuminated with the wavefront conjugate to its reference wave, the real image of the stereogram is produced. Eyes placed in that real image view the synthesized three-dimensional image. When 159
Volume 28, number 2 Illuminating Wave
Images of Transparencies
\
J Holographic Stereogram
OPTICS COMMUNICATIONS
February 1979
Reference Wave /
.... !VIII Photographic Plate
Fig. 1. Recording geometry of the Lippmann hologram. The real images of the transparencies reconstructed from the holographic stereogram are focused onto another photographic plate where the Lippmann hologram is formed.
the stereogram reconstructs the pseudoscopic image, the image from the Lippmann hologram appears orthoscopically. Because the images of all transparencies are focused on to the hologram plane, the recorded Lippmann hologram is exactly image hologram. Therefore, the sharp and deep three-dimensional image can be seen. Fig. 2 shows a photograph of the reconstructed image from the Lippmann hologram recorded by this method. The object is a model of molecule which is synthesized from the computer generated perspectives. The holographic stereogram consists of twenty elementary holograms. The width of each hologram is 5 mm. The illuminating source is the sun. The image appears in the extent of several centimeters before and behind the hologram but all balls and sticks are viewed without blur. The Lippmann hologram was recorded in dichromated gelatin. This recording material is suitable for a Lippmann hologram because the spectral response can be broadened by special development. The reason is probably that the grating period varies along the direction of the hologram thickness. Therefore, the light of many wavelength may contribute to the reconstruction of the image and the bright image can be obtained, though the variation of the grating period causes the increase of the image blur.
Fig. 2. Photograph of the reconstructed image from the Lippmann hologram recorded by the geometry shown in fig. 1. The object is a model of molecule. The hologram was recorded in dichromated gelatin and the sun was used for reconstructing it. 160
Volume 28, number 2
OPTICS COMMUNICATIONS
February 1979
3. Image blur of the described Lippmann hologram We now discuss the image blur of the Lippmann hologram described above. The image blur of a Lippmann hologram can be analyzed in terms of Fresnel-Kirchhoff diffraction theory [3]. The blur due to broadening of wavelength selectivity is estimated as follows. Let the wavelength of the illuminating wave required to extinguish the diffracted wave changes from that of light used for recording by AX. A change in wavelength AX results in a change in direction of the diffracted wave A0 from that of the object wave 00, as illustrated in fig. 3 (a). This causes the image blur. Assuming that the incidence angle of the illuminating wave is the same as that of the reference wave Or, AX and A0 in air are written as AX-
X2
4 c o s 2 0 0 + n 2 -- 1
t n 2 _ sin 00 sin Or + X/cos200 + n 2 -- 1X/cos20r + n 2 -- 1 X 4 c ° s 2 0 0 + n2 - 1
sin Or - sin 00
at -
(1) t
n2_sinOosinOr+X/cos2Oo+n2_lx/cos2Or+n2_t
cos0 0
'
where X is the wavelength of light used for recording, t is the hologram thickness, and n is the refractive index of the hologram. 0 O, Or, and X are the values in air. Diameter D of the point image located at a distance r from the hologram is then given by D = 2r] A0 ].
(2)
The relation between D and r is shown in fig. 4 by solid lines for various values of the hologram thickness t. Next we estimate the blur due to finite source size of illumination. A change in direction of the illuminating wave A0' from that o f the reference wave results in a change in direction of the diffracted wave A0 from that of the object wave, as illustrated in fig. 3 (b). Then A0 is written as A0 = (COS0r/COS 00)A0' ,
(3)
assuming that the wavelength of the illuminating wave equals to that of light used for recording. The diameter of the point image due to this blur is also given by eq. (2). A typical case that the hologram is illuminated with the sun is shown in fig. 4 by dashed line. When the image is formed at a distance of 25 cm from the hologram the diameter o f the image blur is 2 mm. This is approximately equivalent to the blur for the case that the hologram thickness is 20/am. When the image of the elementary holograms overlap each other due to these blur, the viewer's eyes placed in this image plane will see the plural images of the transparencies at the same time. As a result, the synthesized three.
White Light [ 'NK 0 r ~ ,
X+AX / Diffracted
Extended Source ,l' L X~ 0r/-d
Diffracted . J r " , , Wave
: 12 I
(a)
(b)
Fig. 3. Image blur of a Lippmann hologram. (a) Blur due to broadening of wavelength selectivity, (b) blur due to finite source size of illumination. 161
Volume 28, number 2
OPTICS COMMUNICATIONS
February 1979
i
2~ =488nrn 8o= 0 ° 2
t 1 ~ ~ S u n-
& =150° n =1.5
J
j
ArT- 15--'"
1//
E
1
0 0
./" t
50
50/~m
100
150 r(mm)
200
250
Fig. 4. Diameter D of the point image as a function of image distance r from the hologram for various hologram thickness t (solid line) and for illumination with the sun (dashed line).
dimensional image appears unsharply. The synthesized image, however, remains sharply as long as the images of the elementary holograms do not overlap because the Lippmann hologram is exactly image hologram for all transparencies. Therefore, a sharp and deep three-dimensional image can be reconstructed even with an extended white light source by choosing the width of the elementary holograms and the interval between the successive holograms so that the images of these holograms do not overlap each other in the final reconstruction.
4. Conclusions When a Lippmann hologram is illuminated with a white light source, the image blur increases as the hologramto-image distance increases. The problem of the image blur of a Lippmann hologram may be solved using a holographic stereogram as master hologram. By this technique, a sharp and deep synthesized three-dimensional image can be obtained. For a conventional Lippmann hologram, the object to be recorded is restricted to be relatively small and still. The restriction for the object is now removed by this technique and the large and deep objects, e.g. outdoor scene, human face, or even computer generated non-existent object can be used as the object for Lippmann hologram. The authors acknowledge Konishiroku Photo Ind. Co., Ltd. for willingly lending the holographic stereogram which was used as master hologram for recording the Lippmann hologram. The authors also acknowledge Dainippon Printing Co., Ltd. Central Research Institute for performing the experimental work. Part of this work was supported by a Scientific Research Grant-In-Aid from the Ministry of Education, Japanese Government.
References
[1 ] M.C. King, A.M. Noll and D.H. Berry, Appl. Opt. 9 (1970)471. [2] T. Kasahara, Y. Kimura and S. Tanaka, Japan. J. Appl. Phys. 8 (1969) 124; T. Kasahara, Y. Kir~ura and M. Kawai, Applications of holography, eds. E.S. Barrekette, W.E. Kock, T. Ose, J. Tsujiuchi and G.W. Stroke (Plenum Press, New York, 1971) p. 19. [3] H.M. Smith, Principles of holography (Wiley-lnterscience, New York, 1969) p. 54.
162
OPTICS COMMUNICATIONS
February 1979
NEW TECHNIQUE FOR RECORDING A LIPPMANN HOLOGRAM Toshihiro KUBOTA and Teruji OSE Institute of lndustrial Science, University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo, Japan Received 8 November 1978
A new Lippmann hologram technique is described in which a holographic stereogram is used as master hologram. A sharp and deep synthesized three-dimensional image can be obtained by this technique. Experimental results for this hologram and discussion of the image blur axe presented.
1. Introduction When a white light source is used to illuminate a Lippmann hologram, the reconstructed image is blurred because broadening of wavelength selectivity due to finite thickness of the hologram and because extended source of illumination. The blur increases as the hologram-to-image distance increases. Therefore, the image depth is restricted. In order to observe the deep image sharply, the increase of hologram thickness or the reduction of apparent source size is necessary. However, the former is difficult to develop the emulsion uniformly throughout the thickness and the latter sacrifices the image brightness. The image blur which is an inherent property of a Lippmann hologram does not exist for the case of an image hologram, that is, the case when the image is reconstructed on the hologram plane. Such a property of image hologram leads us to an idea that a sharp and deep synthesized three-dimensional image can be obtained from a Lippmann hologram when a holographic stereogram is used as master hologram. The use of a holographic stereogram was proposed by King et al. for a transmission hologram [1]. In this letter, we present a new technique for recording a Lippmann hologram using a holographic stereogram and the discussion of the image blur.
2. Description of the new technique The basic recording geometry is shown in fig. 1. We begin with the reconstruction of the holographic stereogram. A holographic stereogram consists of many elementary holograms [2]. One elementary hologram is formed for each two-dimensional transparency which shows the different perspective. Illumination of the stereogram with the wavefront conjugate to its reference wave produces the real images of the transparencies in space as well as a synthesized three-dimensional image of the object. Although the real image of the transparencies are reconstructed as many as the number of the elementary holograms, they are actually two-dimensional and are focused onto a certain plane. The photographic plate is set in this plane and a Lippmann hologram is recorded. The images of the transparencies now serve as the object of the hologram. When the Lippmann hologram is illuminated with the wavefront conjugate to its reference wave, the real image of the stereogram is produced. Eyes placed in that real image view the synthesized three-dimensional image. When 159
Volume 28, number 2 Illuminating Wave
Images of Transparencies
\
J Holographic Stereogram
OPTICS COMMUNICATIONS
February 1979
Reference Wave /
.... !VIII Photographic Plate
Fig. 1. Recording geometry of the Lippmann hologram. The real images of the transparencies reconstructed from the holographic stereogram are focused onto another photographic plate where the Lippmann hologram is formed.
the stereogram reconstructs the pseudoscopic image, the image from the Lippmann hologram appears orthoscopically. Because the images of all transparencies are focused on to the hologram plane, the recorded Lippmann hologram is exactly image hologram. Therefore, the sharp and deep three-dimensional image can be seen. Fig. 2 shows a photograph of the reconstructed image from the Lippmann hologram recorded by this method. The object is a model of molecule which is synthesized from the computer generated perspectives. The holographic stereogram consists of twenty elementary holograms. The width of each hologram is 5 mm. The illuminating source is the sun. The image appears in the extent of several centimeters before and behind the hologram but all balls and sticks are viewed without blur. The Lippmann hologram was recorded in dichromated gelatin. This recording material is suitable for a Lippmann hologram because the spectral response can be broadened by special development. The reason is probably that the grating period varies along the direction of the hologram thickness. Therefore, the light of many wavelength may contribute to the reconstruction of the image and the bright image can be obtained, though the variation of the grating period causes the increase of the image blur.
Fig. 2. Photograph of the reconstructed image from the Lippmann hologram recorded by the geometry shown in fig. 1. The object is a model of molecule. The hologram was recorded in dichromated gelatin and the sun was used for reconstructing it. 160
Volume 28, number 2
OPTICS COMMUNICATIONS
February 1979
3. Image blur of the described Lippmann hologram We now discuss the image blur of the Lippmann hologram described above. The image blur of a Lippmann hologram can be analyzed in terms of Fresnel-Kirchhoff diffraction theory [3]. The blur due to broadening of wavelength selectivity is estimated as follows. Let the wavelength of the illuminating wave required to extinguish the diffracted wave changes from that of light used for recording by AX. A change in wavelength AX results in a change in direction of the diffracted wave A0 from that of the object wave 00, as illustrated in fig. 3 (a). This causes the image blur. Assuming that the incidence angle of the illuminating wave is the same as that of the reference wave Or, AX and A0 in air are written as AX-
X2
4 c o s 2 0 0 + n 2 -- 1
t n 2 _ sin 00 sin Or + X/cos200 + n 2 -- 1X/cos20r + n 2 -- 1 X 4 c ° s 2 0 0 + n2 - 1
sin Or - sin 00
at -
(1) t
n2_sinOosinOr+X/cos2Oo+n2_lx/cos2Or+n2_t
cos0 0
'
where X is the wavelength of light used for recording, t is the hologram thickness, and n is the refractive index of the hologram. 0 O, Or, and X are the values in air. Diameter D of the point image located at a distance r from the hologram is then given by D = 2r] A0 ].
(2)
The relation between D and r is shown in fig. 4 by solid lines for various values of the hologram thickness t. Next we estimate the blur due to finite source size of illumination. A change in direction of the illuminating wave A0' from that o f the reference wave results in a change in direction of the diffracted wave A0 from that of the object wave, as illustrated in fig. 3 (b). Then A0 is written as A0 = (COS0r/COS 00)A0' ,
(3)
assuming that the wavelength of the illuminating wave equals to that of light used for recording. The diameter of the point image due to this blur is also given by eq. (2). A typical case that the hologram is illuminated with the sun is shown in fig. 4 by dashed line. When the image is formed at a distance of 25 cm from the hologram the diameter o f the image blur is 2 mm. This is approximately equivalent to the blur for the case that the hologram thickness is 20/am. When the image of the elementary holograms overlap each other due to these blur, the viewer's eyes placed in this image plane will see the plural images of the transparencies at the same time. As a result, the synthesized three.
White Light [ 'NK 0 r ~ ,
X+AX / Diffracted
Extended Source ,l' L X~ 0r/-d
Diffracted . J r " , , Wave
: 12 I
(a)
(b)
Fig. 3. Image blur of a Lippmann hologram. (a) Blur due to broadening of wavelength selectivity, (b) blur due to finite source size of illumination. 161
Volume 28, number 2
OPTICS COMMUNICATIONS
February 1979
i
2~ =488nrn 8o= 0 ° 2
t 1 ~ ~ S u n-
& =150° n =1.5
J
j
ArT- 15--'"
1//
E
1
0 0
./" t
50
50/~m
100
150 r(mm)
200
250
Fig. 4. Diameter D of the point image as a function of image distance r from the hologram for various hologram thickness t (solid line) and for illumination with the sun (dashed line).
dimensional image appears unsharply. The synthesized image, however, remains sharply as long as the images of the elementary holograms do not overlap because the Lippmann hologram is exactly image hologram for all transparencies. Therefore, a sharp and deep three-dimensional image can be reconstructed even with an extended white light source by choosing the width of the elementary holograms and the interval between the successive holograms so that the images of these holograms do not overlap each other in the final reconstruction.
4. Conclusions When a Lippmann hologram is illuminated with a white light source, the image blur increases as the hologramto-image distance increases. The problem of the image blur of a Lippmann hologram may be solved using a holographic stereogram as master hologram. By this technique, a sharp and deep synthesized three-dimensional image can be obtained. For a conventional Lippmann hologram, the object to be recorded is restricted to be relatively small and still. The restriction for the object is now removed by this technique and the large and deep objects, e.g. outdoor scene, human face, or even computer generated non-existent object can be used as the object for Lippmann hologram. The authors acknowledge Konishiroku Photo Ind. Co., Ltd. for willingly lending the holographic stereogram which was used as master hologram for recording the Lippmann hologram. The authors also acknowledge Dainippon Printing Co., Ltd. Central Research Institute for performing the experimental work. Part of this work was supported by a Scientific Research Grant-In-Aid from the Ministry of Education, Japanese Government.
References
[1 ] M.C. King, A.M. Noll and D.H. Berry, Appl. Opt. 9 (1970)471. [2] T. Kasahara, Y. Kimura and S. Tanaka, Japan. J. Appl. Phys. 8 (1969) 124; T. Kasahara, Y. Kir~ura and M. Kawai, Applications of holography, eds. E.S. Barrekette, W.E. Kock, T. Ose, J. Tsujiuchi and G.W. Stroke (Plenum Press, New York, 1971) p. 19. [3] H.M. Smith, Principles of holography (Wiley-lnterscience, New York, 1969) p. 54.
162