- Email: [email protected]
Rotation selectivity of random phase encoding in volume holograms
Optics Communications 276 (2007) 62–66 www.elsevier.com/locate/optcom
Rotation selectivity of random phase encoding in volume holograms Ching-Cherng Sun a b
a,*
, Chih-Yuan Hsu a, Shih-Hsin Ma a, Wei-Chia Su
b
Department of Optics and Photonics, National Central University, Chung-Li 320, Taiwan The Graduate Institute of Photonics, National Changhua University of Education, Taiwan
Received 24 January 2007; received in revised form 26 March 2007; accepted 26 March 2007
Abstract We present the study of angular selectivity for holographic multiplexing based on random phase encoding by a ground glass. The rotational selectivity of the volume hologram is calculated theoretically and coincides with the experimental measurement. By controlling the parameters including rotational center, effective numerical aperture of both volume hologram and the ground glass, we can obtain different rotational selectivity applied to random phase encoding in volume holographic storage. 2007 Elsevier B.V. All rights reserved. Keywords: Random phase encoding; Volume holographic storage
1. Introduction Volume holography has been regarded as one of the most potential ways in data storage owing to high storage density in three dimensions, extreme high access rate and various available multiplexing schemes [1–4]. Among those multiplexing schemes, phase encoding, including random phase and orthogonal phase encoding, has been demonstrated for both data encryption and storage [5–22]. Generally, random phase encoding is performed by using a ground glass or a multi-mode fiber. Since the latter always presents obvious crosstalk so it is mostly applied to sensing instead of data storage. Therefore, random phase encoding for holographic multiplexing is always performed by using a ground glass. As an incident wave passing through a ground glass, the transmission light can be regarded as a combination of numerous spherical waves of random initial phase originated from the surface of the ground glass. The random initial phase is caused by the variation of the surface of the ground glass. When the ground glass is displaced, the wavefront on an observation plane is from the original one so that the shifted wavefront with random *
Corresponding author. Tel.: +886 3 4276240; fax: +886 3 4252897. E-mail address: [email protected] (C.-C. Sun).
0030-4018/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.03.082
phase cannot reconstruct the stored data in the hologram. The three-dimensional shifting selectivity of a ground glass has been proposed and demonstrated where shows that the horizontal direction, along the direction of the signal, is most sensitive, vertical is also sensitive and the longitudinal direction is less sensitive [14]. An alternative scheme, rotating a ground glass for holographic multiplexing has been proposed [22]. However, no study presents the theoretical calculation of the rotation selectivity of the volume hologram with random phase encoding. The rotation selectivity is important to not only holographic storage, but also in optical sensing when the hologram is applied to spatial filtering. In this paper, we present a study on the rotation selectivity of a volume hologram with random phase encoding. The theoretical calculation as well as the corresponding experiment is demonstrated. 2. Rotation selectivity The schematic diagram of the rotation multiplexing is shown in Fig. 1. Since the wavefront behind the glass can be treated as a superposition of the wavefronts emerged from a set of point sources with random-distributed initial phases as shown in Fig. 1, we may express the composite wavefront on the hologram plane [13,14]
C.-C. Sun et al. / Optics Communications 276 (2007) 62–66
xc=0
63
xc=0
yc=0
yc=0 Fig. 2. Three special locations of the illumination area on the ground glass in the simulation and experiment. Fig. 1. Schematic diagram of the rotational random phase encoding for volume hologram.
W ðx3 ; y 3 Þ ¼
Z
d=2
d=2
Z
d=2
A expfj/ðx1 ; y 1 Þg expfjkr1 gdx1 dy 1 ;
d=2
denote the coordinates of ðxc ; y c Þ as the center of the illumination spot and (0, 0) as the center of the rotational center, the coordinates of each point of the ground glass after rotation can be expressed
ð1Þ
x2 ¼ x1 cosðDhÞ ðy 1 þ y c Þ sinðDhÞ xc ;
where d is the dimension of the illumination region of the ground glass; A is the amplitude of each spherical wave 2 2 2 1=2 and r1 ¼ fðx3 x1 Þ þ ðy 3 y 1 Þ þ ðz3 z1 Þ g is the distance between the ground glass and the hologram; /ðx1 ; y 1 Þ is the initial phase of each point source, which is associated with the surface variation of the ground glass so expfj/ðx1 ; y 1 Þg is a random distributed function across the encoded wave. We assume that the hologram records the interference fringes formed by a plane wave and the reference wave described in Eq. (1). Now we use another wavefront, which passes through the rotated ground glass, to read the hologram. If the grating strength is weak that the amplitude transmittance of the hologram is proportional to the interference intensity, based on VOHIL model (volume hologram being integrator of light emitted from elementary light sources) [23], we can express the diffraction as Z L=2 Z d=2 Z d=2 Z d=2 Z d=2 D/ AR Ap AS
y 2 ¼ x1 sinðDhÞ þ ðy 1 þ y c Þ cosðDhÞ y c :
L=2
d=2
d=2
d=2
ð3Þ
In the reconstruction of the hologram, the same ground glass is used except it is rotated, so the initial phase of the reference and the reading light is the same. Through the calculation with use of Eqs. (2) and (3), we can obtain the relative diffraction intensity with respect to the rotation angle of the ground glass. Fig. 3 shows the simulation result for different illumination diameters, where the refractive index of the ordinary polarization is 2.34 for the wavelength of 514.5 nm, the distance (z0) between the ground glass and the crystal and the hologram is 10 cm and the hologram dimension along the signal direction is 10 mm. We may find that the hologram is more sensitive to the rotation when the distance z0 becomes smaller or the diameter of the illumination spot on the ground glass becomes larger.
d=2
expfj/ðx2 ; y 2 Þ j/ðx1 ; y 1 Þg expfjkðr2 r1 Þg
1 xc=0, yc=0,
ð2Þ
where AS, AR and Ap are the amplitudes of the signal, reference and reading lights, respectively, L is the thickness of the hologram along the direction of the signal, d is the diameter of the area of laser illumination on the ground glass, r2 ¼ fðx3 x2 Þ2 þ ðy 3 y 2 Þ2 þ ðz3 z2 Þ2 g1=2 , /ðx2 ; y 2 Þ is the initial phase of each point source on the ground glass used for encoding the reading wave. In the following analyses, the ground glass used for encoding the reference is the same as that used for the reading waves, but the position is different owing to rotation. Since there is a rotational center of the ground glass, the holographic selectivity will be a function of the location of the laser spot on the ground glass. Fig. 2 shows the three typical condition of the illumination condition. If we
Xc=1 cm, yc=0 cm
Normalized Diffraction Intensity
dx1 dy 1 dx2 dy 2 dx3 ;
Xc=3 cm, yc=0 cm Xc=0, yc=1 cm, Xc=0, yc=3 cm,
0 0
0.1
Rotational angle [Degree]
Fig. 3. Simulation of the rotational sensitivity of the volume hologram, where z0 = 10 cm and d = 1 cm.
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C.-C. Sun et al. / Optics Communications 276 (2007) 62–66
3. Experimental result and discussion
Iris M
L
0.4
0.2
-0.8
-0.6
-0.4
-0.2
HWP
L
L
0.0
0.2
0.4
0.6
0.8
Rotational Angle [Degree]
Normalized Diffraction Intensity
1.0
0.8
0.6
0.4
0.2
0.0 -0.10
-0.05
0.00
0.05
0.10
Rotational Angle [Degree] 1.0
0.8
0.6
0.4
0.2
0.00
0.025
0.05
0.075
0.100
Rotational Angle [Degree]
M
HWP
0.6
0.0 -0.100 -0.075 -0.050 -0.025
PBS
GG
0.8
0.0
Normalized Diffraction Intensity
The experimental setup is shown in Fig. 4. A laser light of 514.5 nm was derived from an Argon laser made by Coherent Inc. The recording medium was a photorefractive crystal of Fe: LiNbO3, and the dimensions are 10 mm · 10 mm · 10 mm, where optics axis of the crystal was along x-axis. After expanded and collimated, the laser light was split into two parts by a polarized beam splitter (PBS). The first one was in extraordinary polarization, and the polarization was changed to ordinary polarization after passing through a half-wave plate. An iris was used to control the diameter of the spot size on the ground glass. After passing through the ground glass, the scattering lights served as the reference in reconstructing the hologram. The signal light was in ordinary polarization and was directed to the another side of the crystal. The intensity ratio on the ground glass between the signal and the reference was 9. Since the Bragg selectivity is a function of the illumination diameter on the ground glass and the laser light is in a Gaussian distribution, the spot profile will also be a factor related to the Bragg selectivity. Therefore, we measured the laser profile by using a CCD to catch the light pattern on the plane of the ground glass. After a calibration of the response of the CCD, we obtained the beam profile across the ground glass. Through fitting the profile with a Gauss curve, we used the curve to modify Eq. (2) by weighting the strength of the lights scattered from different location of the ground glass. In the simulation based on the weighting process, we found that the Bragg selectivity became smaller when the weighting factor was applied. It is easily to understand since the weighting factor reduces the effective diameter of the illumination area. The experimental measurement for different incident conditions (both in writing and reading processes) are shown in Figs. 5–7, where the dots are for the measurement results, the solid (dash) lines are for the simulation with (without) weighting factor and the dash lines. In the most conditions, the experimental measurements are within the
Normalized Diffraction Intensity
1.0
Ar+
Fig. 5. Normalized diffraction intensity vs. rotational angle when z0 = 10 cm and d = 1 cm. (a) xc = 0, yc = 0; (b) xc = 1 cm, yc = 0 and (c) xc = 0, yc = 1 cm.
LiNbO3 M
Detector
M
M
Power Meter
Fig. 4. The experimental setup. M, mirror; L, lens; HWP, half-wave plate; GG, ground glass.
area between the simulation with and without the weighting factor. Thus we can say that the theoretical simulation can be used to predict the Bragg selectivity of the hologram with rotational random phase encoding. Besides, we find that the most sensitive condition occurs when the center of the laser spot is located at the y-axis on the ground glass.
C.-C. Sun et al. / Optics Communications 276 (2007) 62–66 1.0
Normalized Diffraction Intensity
Normalized Diffraction Intensity
1.0
0.8
0.6
0.4
0.2
0.8
0.6
0.4
0.2
0.0
0.0 -0.4
-0.2
0.0
0.2
-0.4
0.4
0.0
0.2
0.4
1.0
Normalized Diffraction Intensity
Normalized Diffraction Intensity
1.0
0.8
0.6
0.4
0.2
-0.05
0.00
0.05
0.8
0.6
0.4
0.2
0.0 -0.10
0.10
-0.05
0.00
0.05
0.10
Rotational Angle [Degree]
Rotational Angle [Degree] 1.0
Normalized Diffraction Intensity
1.0
Normalized Diffraction Intensity
-0.2
Rotational Angle [Degree]
Rotational Angle [Degree]
0.0 -0.10
65
0.8
0.6
0.4
0.2
0.0 -0.100 -0.075 -0.050 -0.025
0.000
0.025
0.050
0.075
0.100
0.8
0.6
0.4
0.2
0.0 -0.100 -0.075 -0.050 -0.025
Rotational Angle [Degree]
Fig. 6. Normalized diffraction intensity vs. rotational angle when z0 = 5 cm and d = 1 cm. (a) xc = 0, yc = 0; (b) xc = 1 cm, yc = 0 and (c) xc = 0, yc = 1 cm.
0.000
0.025
0.050
0.075
0.100
Rotational Angle [Degree]
Fig. 7. Normalized diffraction intensity vs. rotational angle when z0 = 10 cm and d = 2.5 cm. (a) xc = 0, yc = 0, (b) xc = 1 cm, yc = 0, (c) xc = 0, yc = 1 cm.
4. Summary The reason is that the rotation of the ground glass in such a case is equivalent to the displacement of the ground glass in the horizontal direction, which is the most sensitive direction.
In this paper, we develop the theoretical model to calculate rotational selectivity of the volume hologram with random phase encoding by a ground glass. In the simulation, we first regard the wavefront scattered by the ground glass
66
C.-C. Sun et al. / Optics Communications 276 (2007) 62–66
as a composite one of various spherical waves with specific initial phase. In taking consideration of the beam profile of the illumination spot on the ground glass, the simulation coincides with the experimental result. As a result, we find that the hologram becomes more sensitive to the rotation when the area of the illumination spot increases and the distance between the ground glass and the volume hologram decreases. Besides, the location of the illumination spot is important to the Bragg selectivity. When the illumination spot is located at the y-axis other than (0, 0), the hologram will be most sensitive to the rotation of the ground glass. Acknowledgement This study was sponsored by the National Science Council with the Contract No. NSC95-2221-E-008-155, and by the Ministry of Economic Affairs of the Republic of China with the Contract No. 95-EC-17-A-07-S1-011. References [1] P.J. van Heerden, Appl. Opt. 2 (1963) 393. [2] D. Psaltis, F. Mok, Sci. Am. 23 (1995) 70.
[3] E.N. Leith, A. Kozma, J. Upatnieks, J. Marks, N. Massey, Appl. Opt. 5 (1966) 1303. [4] H.J. Coufal, D. Psaltis, G.T. Sincerbox (Eds.), Holographic Data Storage, Springer, 2000. [5] J.T. LaMacchia, D.L. White, Appl. Opt. 7 (1968) 91. [6] J.F. Heanue, M.C. Bashaw, L. Hesselink, Science 265 (1994) 749. [7] C. Denz, G. Pauliat, G. Roosen, Opt. Commun. 85 (1991) 171. [8] C.C. Sun, R.H. Tsou, W. Chang, J.Y. Chang, M.W. Chang, Opt. Quantum Electron. 28 (1996) 1509. [9] J.F. Heanue, M.C. Bashaw, L. Hesselink, Appl. Opt. 34 (1995) 6012. [10] Q. Gao, R. Kostuk, Appl. Opt. 36 (1997) 4853. [11] G. Unnikrishnan, Joby Joseph, K. Singh, Appl. Opt. 37 (1998) 8181. [12] H. Lee, S.K. Jin, Appl. Phys. Lett. 62 (1993) 2191. [13] C.C. Sun, W.C. Su, B. Wang, Y. Ouyang, Opt. Commun. 175 (2000) 67. [14] C.C. Sun, W.C. Su, Appl. Opt. 40 (2001) 1253. [15] C.C. Sun, W.C. Su, B. Wang, A.E.T. Chiou, Opt. Commun. 191 (2001) 209. [16] C.C. Sun, Y.M. Chen, W.C. Su, Opt. Eng. 40 (2001) 160. [17] C.C. Sun, C.Y. Hsu, C.H. Wu, W.C. Su, Opt. Eng. 42 (2003) 2788. [18] Y. Jeong, B. Lee, Appl. Opt. 41 (2002) 4085. [19] C.C. Sun, Y.M. Chen, W.C. Su, Opt. Eng. 40 (2001) 160. [20] T.C. Teng, W.J. Zhong, S.H. Ma, C.C. Sun, Appl. Opt. 46 (2007) 1456. [21] S.H. Shin, B. Javidi, Opt. Lett. 26 (2001) 1161. [22] C.C. Chang, K.L. Russel, G.K. Wu, Appl. Phys. B 72 (2001) 307. [23] C.C. Sun, Opt. Eng. 42 (2003) 1184.
Rotation selectivity of random phase encoding in volume holograms Ching-Cherng Sun a b
a,*
, Chih-Yuan Hsu a, Shih-Hsin Ma a, Wei-Chia Su
b
Department of Optics and Photonics, National Central University, Chung-Li 320, Taiwan The Graduate Institute of Photonics, National Changhua University of Education, Taiwan
Received 24 January 2007; received in revised form 26 March 2007; accepted 26 March 2007
Abstract We present the study of angular selectivity for holographic multiplexing based on random phase encoding by a ground glass. The rotational selectivity of the volume hologram is calculated theoretically and coincides with the experimental measurement. By controlling the parameters including rotational center, effective numerical aperture of both volume hologram and the ground glass, we can obtain different rotational selectivity applied to random phase encoding in volume holographic storage. 2007 Elsevier B.V. All rights reserved. Keywords: Random phase encoding; Volume holographic storage
1. Introduction Volume holography has been regarded as one of the most potential ways in data storage owing to high storage density in three dimensions, extreme high access rate and various available multiplexing schemes [1–4]. Among those multiplexing schemes, phase encoding, including random phase and orthogonal phase encoding, has been demonstrated for both data encryption and storage [5–22]. Generally, random phase encoding is performed by using a ground glass or a multi-mode fiber. Since the latter always presents obvious crosstalk so it is mostly applied to sensing instead of data storage. Therefore, random phase encoding for holographic multiplexing is always performed by using a ground glass. As an incident wave passing through a ground glass, the transmission light can be regarded as a combination of numerous spherical waves of random initial phase originated from the surface of the ground glass. The random initial phase is caused by the variation of the surface of the ground glass. When the ground glass is displaced, the wavefront on an observation plane is from the original one so that the shifted wavefront with random *
Corresponding author. Tel.: +886 3 4276240; fax: +886 3 4252897. E-mail address: [email protected] (C.-C. Sun).
0030-4018/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.03.082
phase cannot reconstruct the stored data in the hologram. The three-dimensional shifting selectivity of a ground glass has been proposed and demonstrated where shows that the horizontal direction, along the direction of the signal, is most sensitive, vertical is also sensitive and the longitudinal direction is less sensitive [14]. An alternative scheme, rotating a ground glass for holographic multiplexing has been proposed [22]. However, no study presents the theoretical calculation of the rotation selectivity of the volume hologram with random phase encoding. The rotation selectivity is important to not only holographic storage, but also in optical sensing when the hologram is applied to spatial filtering. In this paper, we present a study on the rotation selectivity of a volume hologram with random phase encoding. The theoretical calculation as well as the corresponding experiment is demonstrated. 2. Rotation selectivity The schematic diagram of the rotation multiplexing is shown in Fig. 1. Since the wavefront behind the glass can be treated as a superposition of the wavefronts emerged from a set of point sources with random-distributed initial phases as shown in Fig. 1, we may express the composite wavefront on the hologram plane [13,14]
C.-C. Sun et al. / Optics Communications 276 (2007) 62–66
xc=0
63
xc=0
yc=0
yc=0 Fig. 2. Three special locations of the illumination area on the ground glass in the simulation and experiment. Fig. 1. Schematic diagram of the rotational random phase encoding for volume hologram.
W ðx3 ; y 3 Þ ¼
Z
d=2
d=2
Z
d=2
A expfj/ðx1 ; y 1 Þg expfjkr1 gdx1 dy 1 ;
d=2
denote the coordinates of ðxc ; y c Þ as the center of the illumination spot and (0, 0) as the center of the rotational center, the coordinates of each point of the ground glass after rotation can be expressed
ð1Þ
x2 ¼ x1 cosðDhÞ ðy 1 þ y c Þ sinðDhÞ xc ;
where d is the dimension of the illumination region of the ground glass; A is the amplitude of each spherical wave 2 2 2 1=2 and r1 ¼ fðx3 x1 Þ þ ðy 3 y 1 Þ þ ðz3 z1 Þ g is the distance between the ground glass and the hologram; /ðx1 ; y 1 Þ is the initial phase of each point source, which is associated with the surface variation of the ground glass so expfj/ðx1 ; y 1 Þg is a random distributed function across the encoded wave. We assume that the hologram records the interference fringes formed by a plane wave and the reference wave described in Eq. (1). Now we use another wavefront, which passes through the rotated ground glass, to read the hologram. If the grating strength is weak that the amplitude transmittance of the hologram is proportional to the interference intensity, based on VOHIL model (volume hologram being integrator of light emitted from elementary light sources) [23], we can express the diffraction as Z L=2 Z d=2 Z d=2 Z d=2 Z d=2 D/ AR Ap AS
y 2 ¼ x1 sinðDhÞ þ ðy 1 þ y c Þ cosðDhÞ y c :
L=2
d=2
d=2
d=2
ð3Þ
In the reconstruction of the hologram, the same ground glass is used except it is rotated, so the initial phase of the reference and the reading light is the same. Through the calculation with use of Eqs. (2) and (3), we can obtain the relative diffraction intensity with respect to the rotation angle of the ground glass. Fig. 3 shows the simulation result for different illumination diameters, where the refractive index of the ordinary polarization is 2.34 for the wavelength of 514.5 nm, the distance (z0) between the ground glass and the crystal and the hologram is 10 cm and the hologram dimension along the signal direction is 10 mm. We may find that the hologram is more sensitive to the rotation when the distance z0 becomes smaller or the diameter of the illumination spot on the ground glass becomes larger.
d=2
expfj/ðx2 ; y 2 Þ j/ðx1 ; y 1 Þg expfjkðr2 r1 Þg
1 xc=0, yc=0,
ð2Þ
where AS, AR and Ap are the amplitudes of the signal, reference and reading lights, respectively, L is the thickness of the hologram along the direction of the signal, d is the diameter of the area of laser illumination on the ground glass, r2 ¼ fðx3 x2 Þ2 þ ðy 3 y 2 Þ2 þ ðz3 z2 Þ2 g1=2 , /ðx2 ; y 2 Þ is the initial phase of each point source on the ground glass used for encoding the reading wave. In the following analyses, the ground glass used for encoding the reference is the same as that used for the reading waves, but the position is different owing to rotation. Since there is a rotational center of the ground glass, the holographic selectivity will be a function of the location of the laser spot on the ground glass. Fig. 2 shows the three typical condition of the illumination condition. If we
Xc=1 cm, yc=0 cm
Normalized Diffraction Intensity
dx1 dy 1 dx2 dy 2 dx3 ;
Xc=3 cm, yc=0 cm Xc=0, yc=1 cm, Xc=0, yc=3 cm,
0 0
0.1
Rotational angle [Degree]
Fig. 3. Simulation of the rotational sensitivity of the volume hologram, where z0 = 10 cm and d = 1 cm.
64
C.-C. Sun et al. / Optics Communications 276 (2007) 62–66
3. Experimental result and discussion
Iris M
L
0.4
0.2
-0.8
-0.6
-0.4
-0.2
HWP
L
L
0.0
0.2
0.4
0.6
0.8
Rotational Angle [Degree]
Normalized Diffraction Intensity
1.0
0.8
0.6
0.4
0.2
0.0 -0.10
-0.05
0.00
0.05
0.10
Rotational Angle [Degree] 1.0
0.8
0.6
0.4
0.2
0.00
0.025
0.05
0.075
0.100
Rotational Angle [Degree]
M
HWP
0.6
0.0 -0.100 -0.075 -0.050 -0.025
PBS
GG
0.8
0.0
Normalized Diffraction Intensity
The experimental setup is shown in Fig. 4. A laser light of 514.5 nm was derived from an Argon laser made by Coherent Inc. The recording medium was a photorefractive crystal of Fe: LiNbO3, and the dimensions are 10 mm · 10 mm · 10 mm, where optics axis of the crystal was along x-axis. After expanded and collimated, the laser light was split into two parts by a polarized beam splitter (PBS). The first one was in extraordinary polarization, and the polarization was changed to ordinary polarization after passing through a half-wave plate. An iris was used to control the diameter of the spot size on the ground glass. After passing through the ground glass, the scattering lights served as the reference in reconstructing the hologram. The signal light was in ordinary polarization and was directed to the another side of the crystal. The intensity ratio on the ground glass between the signal and the reference was 9. Since the Bragg selectivity is a function of the illumination diameter on the ground glass and the laser light is in a Gaussian distribution, the spot profile will also be a factor related to the Bragg selectivity. Therefore, we measured the laser profile by using a CCD to catch the light pattern on the plane of the ground glass. After a calibration of the response of the CCD, we obtained the beam profile across the ground glass. Through fitting the profile with a Gauss curve, we used the curve to modify Eq. (2) by weighting the strength of the lights scattered from different location of the ground glass. In the simulation based on the weighting process, we found that the Bragg selectivity became smaller when the weighting factor was applied. It is easily to understand since the weighting factor reduces the effective diameter of the illumination area. The experimental measurement for different incident conditions (both in writing and reading processes) are shown in Figs. 5–7, where the dots are for the measurement results, the solid (dash) lines are for the simulation with (without) weighting factor and the dash lines. In the most conditions, the experimental measurements are within the
Normalized Diffraction Intensity
1.0
Ar+
Fig. 5. Normalized diffraction intensity vs. rotational angle when z0 = 10 cm and d = 1 cm. (a) xc = 0, yc = 0; (b) xc = 1 cm, yc = 0 and (c) xc = 0, yc = 1 cm.
LiNbO3 M
Detector
M
M
Power Meter
Fig. 4. The experimental setup. M, mirror; L, lens; HWP, half-wave plate; GG, ground glass.
area between the simulation with and without the weighting factor. Thus we can say that the theoretical simulation can be used to predict the Bragg selectivity of the hologram with rotational random phase encoding. Besides, we find that the most sensitive condition occurs when the center of the laser spot is located at the y-axis on the ground glass.
C.-C. Sun et al. / Optics Communications 276 (2007) 62–66 1.0
Normalized Diffraction Intensity
Normalized Diffraction Intensity
1.0
0.8
0.6
0.4
0.2
0.8
0.6
0.4
0.2
0.0
0.0 -0.4
-0.2
0.0
0.2
-0.4
0.4
0.0
0.2
0.4
1.0
Normalized Diffraction Intensity
Normalized Diffraction Intensity
1.0
0.8
0.6
0.4
0.2
-0.05
0.00
0.05
0.8
0.6
0.4
0.2
0.0 -0.10
0.10
-0.05
0.00
0.05
0.10
Rotational Angle [Degree]
Rotational Angle [Degree] 1.0
Normalized Diffraction Intensity
1.0
Normalized Diffraction Intensity
-0.2
Rotational Angle [Degree]
Rotational Angle [Degree]
0.0 -0.10
65
0.8
0.6
0.4
0.2
0.0 -0.100 -0.075 -0.050 -0.025
0.000
0.025
0.050
0.075
0.100
0.8
0.6
0.4
0.2
0.0 -0.100 -0.075 -0.050 -0.025
Rotational Angle [Degree]
Fig. 6. Normalized diffraction intensity vs. rotational angle when z0 = 5 cm and d = 1 cm. (a) xc = 0, yc = 0; (b) xc = 1 cm, yc = 0 and (c) xc = 0, yc = 1 cm.
0.000
0.025
0.050
0.075
0.100
Rotational Angle [Degree]
Fig. 7. Normalized diffraction intensity vs. rotational angle when z0 = 10 cm and d = 2.5 cm. (a) xc = 0, yc = 0, (b) xc = 1 cm, yc = 0, (c) xc = 0, yc = 1 cm.
4. Summary The reason is that the rotation of the ground glass in such a case is equivalent to the displacement of the ground glass in the horizontal direction, which is the most sensitive direction.
In this paper, we develop the theoretical model to calculate rotational selectivity of the volume hologram with random phase encoding by a ground glass. In the simulation, we first regard the wavefront scattered by the ground glass
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