- Email: [email protected]
Digital Holography Display (2)
Available online at www.sciencedirect.com
Physics Procedia 19 (2011) 278–284
International Conference on Optics in Precision Engineering and Nanotechnology 2011
Digital Holography Display (2) Cheok Peng Lee a , A. Asundi b , Yang Yu a , Zhen Zhong Xiao a a
b
Ngee Ann Polytechnic, Centre for Applied Photonics and Laser Technology, 535 Clementi Road S’pore 599489, Singapore
Nanyang Technological University, School of Mechanical and Aerospace Engineering, Nanyang Avenue S’pore 639798, Singapore
Abstract This paper describes the extension work from the last Digital Holography Projector System. From the developed works shows that, some unforeseen factors have created the difficulties for the system alignment. Such factors are the DMD frame rate, light source and diffractive zero order. It is really the challenging development works to achieve the virtual 3D model display on the high speed rotation screen. The three most key factors are emphasizing: 1) The display device’s frame rate; 2) The light source orientation angle; and 3) The zero order filtering optic. 1) This device’s is the digital micro mirror, in short is DMD. It is the high speed switching device has developed by the most recent technology. The switching frame rate can go up as high as 291fps. At first, the 8 bits depth file must be digitalized and stored for DMD onboard Ram. The digitalized data are transmitting from the PC USB to DMD onboard Ram. Instead of the data are downloading directly from the PC to DVI or VGA during display, this downloading method cause slower down the display speed, which is the common frame rate of 30Hz. Next, the onboard Ram data then transfer to the DMD mirror’s for display, at the 8 bits 291 fps speed. At this frame rate, the 0
0
display 2D image can almost cover for 1 of out of the 360 in 1 revolution. 0
0
2) This laser light source must be installed such that free for orientated in any arbitrary angle from 22 to 45 . Which is normalized to the DMD mirrors and the brief sketch show on figure (a). The purpose of orientated the light source is ensure that multi diffractive order would be reflected straight from the mirrors. (This multi diffractive order is the phenomenon of the digital micro mirror’s characteristic). This mean, the reconstruct images would be followed the DMD normalized direction reflected up to fibre conduit . Moreover, this orientated method install of the laser light source is making space for other optical lenses or device driver/controller. Because, all equipments and components can be easy line up and mounted in the compartment. 3) This solid 6mm diameter fibre conduit is implemented to transmit the higher diffractive image, it is also the brightest and clearer image as compare to other lower order images. This means many of the lower order and blurred images would be neglected for display and consider as the energy lost.
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Organising Committee of the ICOPEN 2011 conference doi:10.1016/j.phpro.2011.06.161
279
Cheok Peng Lee et al. / Physics Procedia 19 (2011) 278–284
© 2011Published Publishedbyby Elsevier B.V. Selection and/or peer-review under responsibility of the Organising Committee of © 2010 Elsevier B.V. the ICOPEN 2011 conference Keywords:volumetric rotation diffuser, zero order, fiber conduit
1. INTRODUCTION For the beginning of this paper, the author would like to refresh some of the theorem that has been described and investigated previously such as Fourier, Fresnel and Fraunhofer. The working principle can be classified into three common types: pure-amplitude, pure-phase and compound, which it both amplitude and phase. The wave front information, such as reference and object wave are simulated from the algorithm and at the same time numerically reconstructed and displayed on the Silicon Liquid Crystal Based Spatial Light Modulator or Digital Micro-mirror Devices. Both devices has been tested in our system for the CGH process, however only the digital micro mirror is adopted in this system. Because, none of the dry display material can show the clearer 3D digital holography image as compare to conventional type holography. Whereas, this DMD device has the highest switching speed to display the multiple 2D frames in the short time, as short as 291 fps. The virtual 3D objects are basically formed by many of the 2D imagery. Begins, the digitalized holography data are transferred to the on board Ram of the DMD PCB card from the PC USB. A while later, the data are downloading from the Ram to DMD mirror’s directly and at the same time display at the 8 bits 291 fps speed. Instead of send from PC to DVI or VGA port at 8 bits 30 Hz frame rate. These digitalized holography data is converted from the Fraunhofer principle, thus a simulated object must be placed within the Fraunhofer region to satisfy the condition. However, the conversion is virtual simulated by the ver.4 3D Max and 32 bits LABVIEW. The generated digital hologram data have been given the low diffraction efficienct. The off-axis method for reconstruction is demonstrated shown in Fig (2).
Fibre conduit
Diffuser is rotating at 360
DMD & Laser Compartment
Fig. 1
0
280
Cheok Peng Lee et al. / Physics Procedia 19 (2011) 278–284
diffractive images
Green Laser
diffractive images
0
22 - 45
0
Digital Micro Mirror Fig. 2 A single complex of arbitrary hologram amplitude and phase values hologram matrix is given as follows:
ha (m, n)
§ 2S · U¸ exp¨ i i O ¹ © * Qdmdn ' ³³ EO ( x, y) exp[ jI ( x, y)]E R x, y
O
U
With
U'=
x [ y K
and
Q
1 (cos T cos T ' ) 2
In most practical situations, both Where
' 2
T
and
' 2
d2
(1.1)
(1.2)
(1.3)
T ' are very small and Q | 1 from (1.3 )
EO denotes a 3D Max object rotating in y-axis at any arbitrary viewing angle in x-y plane, E R* Denotes the reference propagate wave front in free space at any arbitrary Fresnel sensitive distance.
In this case, the development will only focus on amplitude distribution, neglecting the phase contribution complex function. The hologram process is described mathematically for complex amplitude for object wave and given by:
E O ( x, y )
aO ( x, y ) exp( i M O ( x, y ) )
(1.4)
E R ( x, y )
a R ( x, y ) exp( i M R ( x, y ) )
(1.5)
281
Cheok Peng Lee et al. / Physics Procedia 19 (2011) 278–284
Where a O , a R ,
M O , M R denote the object and reference wave real amplitude and phase respectively. The equation
is rewritten to summarize all intensity at any point on the digital images: A Taylor series :
[ x 2 K x 2 1 > [ x 2 K x 2 @ U d 3
2
2d
2d
8
d
....
(1.6)
The higher order terms can be neglected due to it small value so as to compare to the wavelength. As a result the following expression becomes: i § 2S · ª S * m x 2 n y 2 º»dmdn H (m, n) exp¨ i d ¸ x³³ Eo ( x, y) exp[ jI ( x, y)]ER x, y exp i (1.7) « Od © O ¹ ¬ Od ¼
Another more stringent approximation for Fraunhofer approximation is also considered. This is the further simplifies from the Fresnel approximation [8]. The following is another expression for the Fresnel approximation:
H (m, n)
If z >>
2S k k D j ( x 2 y 2 ) ½ j ( xm yn ) e jkz j 2 z ( m 2 n 2 ) 2z e dmdn ¾e Oz ³D ³ ®u([ , n)e jO z ¿ ¯
(1.8)
k ( x 2 y 2 ) max condition satisfied, the expression can be rewritten as follow as the Fraunhofer 2 k
approximation:
H (m, n)
2S
D
( xm yn ) j e jkz j 2 z ( m 2 n 2 ) ^u ([ , n)`e Oz e dmdn ³ ³ jO z D
Y
n X
dice object is created by 3D Max
(1.9)
m
hologram fringe is converted from LABVIEW Fig. 3
282
Cheok Peng Lee et al. / Physics Procedia 19 (2011) 278–284
2ˊMETHODOLOGY For this experiment, we have tested to display of 291 fps for this high switching speed DMD. This high display frame rate has to be synchronized with motor speed at 900 rpm. That mean the motor 1 revolution must be mixed with the delivered of the 291 frames. Because of this high switching speed mirrors, the displayed images can almost 0 0 cover 1 per frame for out of the 360 ( 291 frames
360
0
) which it’s the motor rotated in 1 revolution. This
amplitude type of DMD device has the capability to accommodate of 5,461 frames for onboard memory. This accommodation of number of frames is referring to the 8 bit depth of PNG file. The dice images have be briefly sketch in the later part of this section in Fig 2.0. The most challenging part is the alignment for the reconstructed holography images into the size of diameter 10mm fibre. At the “on” stage of DMD characteristic, the mirrors are reflecting the multiple images and they are separated apart in between at the array format. However, the alignment is only required the higher, clearer and brightest order. Nevertheless, the rest of the useless remaining order must be filtered off. It is tedious and complicated works, if adapts the pure mechanical system set up. In view of this, the author has implemented the optical set-up, which is the fibre conduit. Hence, this setting up time has been tremendously reduced during the exploration. Simplicity the alignment is moving of the X, Y or XY axis direction of the fibre support. However, this method also has its disadvantages: (1) Physically measured and calibrated diffractive images from the lower order to the next higher order in between distance at the mirrors “on” stage, and (2) The fibre and images size must in the mixing ratio. Otherwise only part of the image can display. Further of the development works, the author looks into the symmetry and non-symmetry objects and from the experimented results obtained, the symmetry object is more direct and easy to achieve. Alternatively, the nonsymmetry objects are given that more steps to fulfil. Because of it complexity, in this paper, only focuses on the symmetry instead of the non-symmetry. The Fig ( 4 ) shows for the dice display at the different angle. Finally, the reconstructed 2D multiple dice imagers are transmitted through the solid fibre and displayed on the high speed rotation diffuser. The diameter of 200mm transparent acrylic tube shields is sited on the rotation diffuser for protecting the audience when the motor is rotating at the high speed.
Fig. 4. The audience viewing from number of 1,2, 3 and 4 position
Cheok Peng Lee et al. / Physics Procedia 19 (2011) 278–284
283
From Fig (5) any of the arbitrary position can only see at that particular face dice number. After many of the 0
exploration, from the result showing, the audience can view from any of the different angle out of the 360 . Although, this set up proven that each arbitrary position show the different of the dice face. Whereas, the resolution is blurs and also have the discontinues boundary from the face to face during changes of the numbers.. The figure 2.1 shows the changes of the face to face, but only the various faces are show at here :
Fig. 5
3. CONCLUSION AND DISSCUSSION In this paper, the Fraunhofer diffraction set up is explored and discussed using the fast switching DMD device. The reconstructed images are tested on volumetric display media by the high speed rotation diffuser. As a result, the DMD is capable to display 291 fps images and also show the dice on the diffuser. Although, this set up has proved that can show the virtual 3D object, whereas it is only good for small screen. As for the large dimension screen will still require a larger system. On the other hand, the high rotation diffuser as a volumetric display can be easily achieve, provided using the fast switching rate digital micro mirror. As for the colour display and non-symmetry object is our future direction. This project is funded by Ngee Ann Polytechnic and TOTE BOARD.
ACKNOWLEDGEMENTS The author would like to thank Prof Yu Yingjie and Dr Zheng HuaDong from Shanghai University for providing valuable guidance and consultation during the project integration. Moreover, the author also wishes to express his gratitude to Mr. Chan Kwan Yew, Mr. Chia Yong Poo and Prof A. Asundi for their invaluable advice and guidance for this research and development. Last but not least, the author would also like to thank for the Ngee Ann Polytechnic and TOTE Board for funding of this project.
284
Cheok Peng Lee et al. / Physics Procedia 19 (2011) 278–284
REFERENCE 1.
Ulf Schars and Werner Jueptner., Digital Holography, Springer-Verlag, Berlin Heidelberg, Ch 2 (2005)
2.
Etienne Cuche, Pierre Marquet, and Christian Depeursinge.,” Spatial filtering for zero-Order and twin-image elimination in digital off-axis holography”, APPLIED OPTICS, Vol. 39, No. 23 / 10 August 2000.
3.
Ulf Schnars and Werner P O Juptner.,”Digital recording and numerical reconstruction of holograms“, INSTITUTE OF PHYSICS PUBLISHING, 2002.
4.
Huadong Zheng, Yingjie Yu, Haiyan Qian, Anand Asundi.,” Reduction of Speckle Noise By Multi-Kinoforms in Holographic Three-Dimensional Display”,Shanghai University, Project no: 075115001, 2008.
5.
Huadong Zheng, Yingjie Yu, Tao Wang, Anand Asundi.,” A Dynamic Three-Dimensional Display Technique Based on Liquid Crystal Spatial Light Modulator “.,Proc. of SPIE Vol. 7000, 70001U, 2008.
6.
Andrew Jones, Magnus Lang, Graham Fyffe, Xueming Yu, Jay Busch, Paul Debevec, Ian McDowall, Mark Bolas, “Achieving Eye Contact in a One-to-Many 3D Video Teleconferencing System”, University of Southern California Institute for Creative Technologies, Fakespace Labs, University of Southern California School of Cinematic Arts.
7.
Andrew Jones, Paul Debevec, Ian McDowall, Hideshi Yamada, Mark Bolas, “Rendering for an Interactive 0
360 Light Field Display”, University of Southern California Institute for Creative Technologies, Fakespace Labs, Sony Corporation, University of Southern California School of Cinematic Arts, ACM SIGGRAPH conference proceedings 8.
JOSEPH W. GOODMAN, “INTRODUCTION TO FOURIER OPTICS”, Page 63-81, McGRAW HILL INTERNATIONAL EDITIONS ( SECOND EDITION ) ch4, Fresnel and Fraunhofer.
9.
David Abookasis and Joseph Rosen Ben-Gurion University of the Negev, Department of Electrical and Computer Engineering, “Fourier, Fresnel and Image CGH of three-dimensional objects observed from many different projections” ,Proc. of SPIE Vol. 5531, page 273-284.
Physics Procedia 19 (2011) 278–284
International Conference on Optics in Precision Engineering and Nanotechnology 2011
Digital Holography Display (2) Cheok Peng Lee a , A. Asundi b , Yang Yu a , Zhen Zhong Xiao a a
b
Ngee Ann Polytechnic, Centre for Applied Photonics and Laser Technology, 535 Clementi Road S’pore 599489, Singapore
Nanyang Technological University, School of Mechanical and Aerospace Engineering, Nanyang Avenue S’pore 639798, Singapore
Abstract This paper describes the extension work from the last Digital Holography Projector System. From the developed works shows that, some unforeseen factors have created the difficulties for the system alignment. Such factors are the DMD frame rate, light source and diffractive zero order. It is really the challenging development works to achieve the virtual 3D model display on the high speed rotation screen. The three most key factors are emphasizing: 1) The display device’s frame rate; 2) The light source orientation angle; and 3) The zero order filtering optic. 1) This device’s is the digital micro mirror, in short is DMD. It is the high speed switching device has developed by the most recent technology. The switching frame rate can go up as high as 291fps. At first, the 8 bits depth file must be digitalized and stored for DMD onboard Ram. The digitalized data are transmitting from the PC USB to DMD onboard Ram. Instead of the data are downloading directly from the PC to DVI or VGA during display, this downloading method cause slower down the display speed, which is the common frame rate of 30Hz. Next, the onboard Ram data then transfer to the DMD mirror’s for display, at the 8 bits 291 fps speed. At this frame rate, the 0
0
display 2D image can almost cover for 1 of out of the 360 in 1 revolution. 0
0
2) This laser light source must be installed such that free for orientated in any arbitrary angle from 22 to 45 . Which is normalized to the DMD mirrors and the brief sketch show on figure (a). The purpose of orientated the light source is ensure that multi diffractive order would be reflected straight from the mirrors. (This multi diffractive order is the phenomenon of the digital micro mirror’s characteristic). This mean, the reconstruct images would be followed the DMD normalized direction reflected up to fibre conduit . Moreover, this orientated method install of the laser light source is making space for other optical lenses or device driver/controller. Because, all equipments and components can be easy line up and mounted in the compartment. 3) This solid 6mm diameter fibre conduit is implemented to transmit the higher diffractive image, it is also the brightest and clearer image as compare to other lower order images. This means many of the lower order and blurred images would be neglected for display and consider as the energy lost.
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Organising Committee of the ICOPEN 2011 conference doi:10.1016/j.phpro.2011.06.161
279
Cheok Peng Lee et al. / Physics Procedia 19 (2011) 278–284
© 2011Published Publishedbyby Elsevier B.V. Selection and/or peer-review under responsibility of the Organising Committee of © 2010 Elsevier B.V. the ICOPEN 2011 conference Keywords:volumetric rotation diffuser, zero order, fiber conduit
1. INTRODUCTION For the beginning of this paper, the author would like to refresh some of the theorem that has been described and investigated previously such as Fourier, Fresnel and Fraunhofer. The working principle can be classified into three common types: pure-amplitude, pure-phase and compound, which it both amplitude and phase. The wave front information, such as reference and object wave are simulated from the algorithm and at the same time numerically reconstructed and displayed on the Silicon Liquid Crystal Based Spatial Light Modulator or Digital Micro-mirror Devices. Both devices has been tested in our system for the CGH process, however only the digital micro mirror is adopted in this system. Because, none of the dry display material can show the clearer 3D digital holography image as compare to conventional type holography. Whereas, this DMD device has the highest switching speed to display the multiple 2D frames in the short time, as short as 291 fps. The virtual 3D objects are basically formed by many of the 2D imagery. Begins, the digitalized holography data are transferred to the on board Ram of the DMD PCB card from the PC USB. A while later, the data are downloading from the Ram to DMD mirror’s directly and at the same time display at the 8 bits 291 fps speed. Instead of send from PC to DVI or VGA port at 8 bits 30 Hz frame rate. These digitalized holography data is converted from the Fraunhofer principle, thus a simulated object must be placed within the Fraunhofer region to satisfy the condition. However, the conversion is virtual simulated by the ver.4 3D Max and 32 bits LABVIEW. The generated digital hologram data have been given the low diffraction efficienct. The off-axis method for reconstruction is demonstrated shown in Fig (2).
Fibre conduit
Diffuser is rotating at 360
DMD & Laser Compartment
Fig. 1
0
280
Cheok Peng Lee et al. / Physics Procedia 19 (2011) 278–284
diffractive images
Green Laser
diffractive images
0
22 - 45
0
Digital Micro Mirror Fig. 2 A single complex of arbitrary hologram amplitude and phase values hologram matrix is given as follows:
ha (m, n)
§ 2S · U¸ exp¨ i i O ¹ © * Qdmdn ' ³³ EO ( x, y) exp[ jI ( x, y)]E R x, y
O
U
With
U'=
x [ y K
and
Q
1 (cos T cos T ' ) 2
In most practical situations, both Where
' 2
T
and
' 2
d2
(1.1)
(1.2)
(1.3)
T ' are very small and Q | 1 from (1.3 )
EO denotes a 3D Max object rotating in y-axis at any arbitrary viewing angle in x-y plane, E R* Denotes the reference propagate wave front in free space at any arbitrary Fresnel sensitive distance.
In this case, the development will only focus on amplitude distribution, neglecting the phase contribution complex function. The hologram process is described mathematically for complex amplitude for object wave and given by:
E O ( x, y )
aO ( x, y ) exp( i M O ( x, y ) )
(1.4)
E R ( x, y )
a R ( x, y ) exp( i M R ( x, y ) )
(1.5)
281
Cheok Peng Lee et al. / Physics Procedia 19 (2011) 278–284
Where a O , a R ,
M O , M R denote the object and reference wave real amplitude and phase respectively. The equation
is rewritten to summarize all intensity at any point on the digital images: A Taylor series :
[ x 2 K x 2 1 > [ x 2 K x 2 @ U d 3
2
2d
2d
8
d
....
(1.6)
The higher order terms can be neglected due to it small value so as to compare to the wavelength. As a result the following expression becomes: i § 2S · ª S * m x 2 n y 2 º»dmdn H (m, n) exp¨ i d ¸ x³³ Eo ( x, y) exp[ jI ( x, y)]ER x, y exp i (1.7) « Od © O ¹ ¬ Od ¼
Another more stringent approximation for Fraunhofer approximation is also considered. This is the further simplifies from the Fresnel approximation [8]. The following is another expression for the Fresnel approximation:
H (m, n)
If z >>
2S k k D j ( x 2 y 2 ) ½ j ( xm yn ) e jkz j 2 z ( m 2 n 2 ) 2z e dmdn ¾e Oz ³D ³ ®u([ , n)e jO z ¿ ¯
(1.8)
k ( x 2 y 2 ) max condition satisfied, the expression can be rewritten as follow as the Fraunhofer 2 k
approximation:
H (m, n)
2S
D
( xm yn ) j e jkz j 2 z ( m 2 n 2 ) ^u ([ , n)`e Oz e dmdn ³ ³ jO z D
Y
n X
dice object is created by 3D Max
(1.9)
m
hologram fringe is converted from LABVIEW Fig. 3
282
Cheok Peng Lee et al. / Physics Procedia 19 (2011) 278–284
2ˊMETHODOLOGY For this experiment, we have tested to display of 291 fps for this high switching speed DMD. This high display frame rate has to be synchronized with motor speed at 900 rpm. That mean the motor 1 revolution must be mixed with the delivered of the 291 frames. Because of this high switching speed mirrors, the displayed images can almost 0 0 cover 1 per frame for out of the 360 ( 291 frames
360
0
) which it’s the motor rotated in 1 revolution. This
amplitude type of DMD device has the capability to accommodate of 5,461 frames for onboard memory. This accommodation of number of frames is referring to the 8 bit depth of PNG file. The dice images have be briefly sketch in the later part of this section in Fig 2.0. The most challenging part is the alignment for the reconstructed holography images into the size of diameter 10mm fibre. At the “on” stage of DMD characteristic, the mirrors are reflecting the multiple images and they are separated apart in between at the array format. However, the alignment is only required the higher, clearer and brightest order. Nevertheless, the rest of the useless remaining order must be filtered off. It is tedious and complicated works, if adapts the pure mechanical system set up. In view of this, the author has implemented the optical set-up, which is the fibre conduit. Hence, this setting up time has been tremendously reduced during the exploration. Simplicity the alignment is moving of the X, Y or XY axis direction of the fibre support. However, this method also has its disadvantages: (1) Physically measured and calibrated diffractive images from the lower order to the next higher order in between distance at the mirrors “on” stage, and (2) The fibre and images size must in the mixing ratio. Otherwise only part of the image can display. Further of the development works, the author looks into the symmetry and non-symmetry objects and from the experimented results obtained, the symmetry object is more direct and easy to achieve. Alternatively, the nonsymmetry objects are given that more steps to fulfil. Because of it complexity, in this paper, only focuses on the symmetry instead of the non-symmetry. The Fig ( 4 ) shows for the dice display at the different angle. Finally, the reconstructed 2D multiple dice imagers are transmitted through the solid fibre and displayed on the high speed rotation diffuser. The diameter of 200mm transparent acrylic tube shields is sited on the rotation diffuser for protecting the audience when the motor is rotating at the high speed.
Fig. 4. The audience viewing from number of 1,2, 3 and 4 position
Cheok Peng Lee et al. / Physics Procedia 19 (2011) 278–284
283
From Fig (5) any of the arbitrary position can only see at that particular face dice number. After many of the 0
exploration, from the result showing, the audience can view from any of the different angle out of the 360 . Although, this set up proven that each arbitrary position show the different of the dice face. Whereas, the resolution is blurs and also have the discontinues boundary from the face to face during changes of the numbers.. The figure 2.1 shows the changes of the face to face, but only the various faces are show at here :
Fig. 5
3. CONCLUSION AND DISSCUSSION In this paper, the Fraunhofer diffraction set up is explored and discussed using the fast switching DMD device. The reconstructed images are tested on volumetric display media by the high speed rotation diffuser. As a result, the DMD is capable to display 291 fps images and also show the dice on the diffuser. Although, this set up has proved that can show the virtual 3D object, whereas it is only good for small screen. As for the large dimension screen will still require a larger system. On the other hand, the high rotation diffuser as a volumetric display can be easily achieve, provided using the fast switching rate digital micro mirror. As for the colour display and non-symmetry object is our future direction. This project is funded by Ngee Ann Polytechnic and TOTE BOARD.
ACKNOWLEDGEMENTS The author would like to thank Prof Yu Yingjie and Dr Zheng HuaDong from Shanghai University for providing valuable guidance and consultation during the project integration. Moreover, the author also wishes to express his gratitude to Mr. Chan Kwan Yew, Mr. Chia Yong Poo and Prof A. Asundi for their invaluable advice and guidance for this research and development. Last but not least, the author would also like to thank for the Ngee Ann Polytechnic and TOTE Board for funding of this project.
284
Cheok Peng Lee et al. / Physics Procedia 19 (2011) 278–284
REFERENCE 1.
Ulf Schars and Werner Jueptner., Digital Holography, Springer-Verlag, Berlin Heidelberg, Ch 2 (2005)
2.
Etienne Cuche, Pierre Marquet, and Christian Depeursinge.,” Spatial filtering for zero-Order and twin-image elimination in digital off-axis holography”, APPLIED OPTICS, Vol. 39, No. 23 / 10 August 2000.
3.
Ulf Schnars and Werner P O Juptner.,”Digital recording and numerical reconstruction of holograms“, INSTITUTE OF PHYSICS PUBLISHING, 2002.
4.
Huadong Zheng, Yingjie Yu, Haiyan Qian, Anand Asundi.,” Reduction of Speckle Noise By Multi-Kinoforms in Holographic Three-Dimensional Display”,Shanghai University, Project no: 075115001, 2008.
5.
Huadong Zheng, Yingjie Yu, Tao Wang, Anand Asundi.,” A Dynamic Three-Dimensional Display Technique Based on Liquid Crystal Spatial Light Modulator “.,Proc. of SPIE Vol. 7000, 70001U, 2008.
6.
Andrew Jones, Magnus Lang, Graham Fyffe, Xueming Yu, Jay Busch, Paul Debevec, Ian McDowall, Mark Bolas, “Achieving Eye Contact in a One-to-Many 3D Video Teleconferencing System”, University of Southern California Institute for Creative Technologies, Fakespace Labs, University of Southern California School of Cinematic Arts.
7.
Andrew Jones, Paul Debevec, Ian McDowall, Hideshi Yamada, Mark Bolas, “Rendering for an Interactive 0
360 Light Field Display”, University of Southern California Institute for Creative Technologies, Fakespace Labs, Sony Corporation, University of Southern California School of Cinematic Arts, ACM SIGGRAPH conference proceedings 8.
JOSEPH W. GOODMAN, “INTRODUCTION TO FOURIER OPTICS”, Page 63-81, McGRAW HILL INTERNATIONAL EDITIONS ( SECOND EDITION ) ch4, Fresnel and Fraunhofer.
9.
David Abookasis and Joseph Rosen Ben-Gurion University of the Negev, Department of Electrical and Computer Engineering, “Fourier, Fresnel and Image CGH of three-dimensional objects observed from many different projections” ,Proc. of SPIE Vol. 5531, page 273-284.