WO2003058352A1 - Phase-encoded multiplexing method using complex phase code in holographic memory system - Google Patents
Phase-encoded multiplexing method using complex phase code in holographic memory system Download PDFInfo
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- WO2003058352A1 WO2003058352A1 PCT/KR2002/000016 KR0200016W WO03058352A1 WO 2003058352 A1 WO2003058352 A1 WO 2003058352A1 KR 0200016 W KR0200016 W KR 0200016W WO 03058352 A1 WO03058352 A1 WO 03058352A1
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- G—PHYSICS
- G11—INFORMATION STORAGE
- G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
- G11B7/00—Recording or reproducing by optical means, e.g. recording using a thermal beam of optical radiation by modifying optical properties or the physical structure, reproducing using an optical beam at lower power by sensing optical properties; Record carriers therefor
- G11B7/12—Heads, e.g. forming of the optical beam spot or modulation of the optical beam
- G11B7/125—Optical beam sources therefor, e.g. laser control circuitry specially adapted for optical storage devices; Modulators, e.g. means for controlling the size or intensity of optical spots or optical traces
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- G02B26/00—Optical devices or arrangements for the control of light using movable or deformable optical elements
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- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/04—Processes or apparatus for producing holograms
- G03H1/10—Processes or apparatus for producing holograms using modulated reference beam
- G03H1/12—Spatial modulation, e.g. ghost imaging
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- G—PHYSICS
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- G11B7/00—Recording or reproducing by optical means, e.g. recording using a thermal beam of optical radiation by modifying optical properties or the physical structure, reproducing using an optical beam at lower power by sensing optical properties; Record carriers therefor
- G11B7/004—Recording, reproducing or erasing methods; Read, write or erase circuits therefor
- G11B7/0065—Recording, reproducing or erasing by using optical interference patterns, e.g. holograms
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- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/26—Processes or apparatus specially adapted to produce multiple sub- holograms or to obtain images from them, e.g. multicolour technique
- G03H1/2645—Multiplexing processes, e.g. aperture, shift, or wavefront multiplexing
- G03H2001/2675—Phase code multiplexing, wherein the sub-holograms are multiplexed according to spatial modulation of the reference beam
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Abstract
The present invention relates to a method for multiplexing phase code in holographic memory system, comprising the steps of outputting a complex phase code through complex phase code algorithm, whereby the complex phase code is used for an address beam when a phase is multiplexed-; modulating a phase of the address beam through a phase-type spatial light modulator; modulating amplitude of an object beam through signal amplification-type spatial light modulator; and interfering the amplitude-modulated object beam with the phase-modulated address beam using a photo refraction medium.
Description
PHASE-ENCODED MULTIPLEXING METHOD USING COMPLEX PHASE
CODE IN HOLOGRAPHIC MEMORY SYSTEM
Technical Field
The present invention relates to a method for multiplexing phase code using a
complex phase code ("CPC") in a holographic memory system, which can multiplex
data using a complex phase code generated based on a CPC algorithm.
Background Art
In recent times, rapid progress has occurred in the research and development of
a volume holographic memory system serving as an alternative as the next-generation
data storage system with massive storage capacity and fast access time since the
holographic memory system has high storage density and high play speed. With
respect to this, multiplexed recording schemes are substantially used for maximizing
the storage amount of the holographic memory system.
The method of multiplexing includes angular multiplexing in which the angle
of address is the input address of stored image, wavelength multiplexing using a light
source of varied wavelengths, and phase-code multiplexing using phases orthogonal
with each other. In particular, the phase-code multiplexing doesn't require
mechanical movement of an address beam nor variation of wavelength of light source.
Also the phase-code multiplexing allows for high-speed random access, high light
efficiency, and high storage capacity of information.
Fig. 1 represents the configuration of a holographic memory system using the
conventional phase code multiplexing. Referring to Fig. 1, the image (object beam) of
signal data 100 is transmitted through a signal amplitude spatial light modulator to
modulate the amplitude of the image. The phase code (address beam or basic beam)
130 is transmitted through an address phase spatial light modulator to modulate the
phase of the phase code by phase delay (0, π). The amplitude-modulated object beam
and phase-modulated address beam are transmitted through a focusing lens and
irradiated to photo refractive material 140. Thereafter, interference between the
object beam and the address beam irradiated to the photo refractive material 140 may
generate an interference pattern. Also, the interference pattern can be stored in the
photo refractive material 140.
In a phase-code multiplexing method, the object beam and address beam are
fixed in place, and the phase codes corresponding to each address beam are changed to
store a large amount of information in a photo refractive material. Therefore, in this
method, an orthogonal structure between the phase codes is crucial. Accordingly, not
only zero cross-correlation between the address beams that are coded with some phase
function, but also the correct phase modulation of pixels comprising the address beams
are required to enable highly dense information storage in the phase-code multiplexed
holographic memory without crosstalk. PMA (Piezo Mirror Array), CGH
(Computer-Generated Hologram), and P-SLM (Phase-Spatial Light Modulator) used in
the conventional phase-code multiplexing have the problem of not being able to
perform stable phase modulation without any errors. However, recent improvements in
the manufacturing technology of the P-SLM suggests a possibility to implement the
practical phase-code multiplexed holographic memory system. In the P-SLM, a phase
code like a binary code, for example (1, -1) representing phase section between 0 and π,
can be inputted in the orthogonal set like WHM (Walsh Hadamard Matrix) set.
Generally, to design a phase code using a phase code multiplexing method the
phase codes of the address beams have to comply with the following conditions of
equations 1 and 2.
[equation 1]
N
<C Cj> = λl ,k(x, • CJk (x,y k-l
[equation 2]
*=ι
In equation 2, the phase ^'■ • ■' /w represents address beam in accordance
with image jth stored image, and the phase wι=---->Φ w represents address beam to
recover the first stored image. Also, in equation 2 N means the number of pixels, and Q
and Cj (complex conjugate) means the phase code to be correlated. The auto-correlation
(j=l) and the cross-correlation (j≠l) should be approximated as a delta function and zero,
respectively, in order to restore the image data without crosstalk as shown in equation 3
[equation 3]
0, j≠l δ,« {
1, j=°l
WHM has been used for phase modulation of the phase spatial light modulator
generally and theoretically has the perfect orthogonal characteristics. WHM is
configured as equation 4 using a Walsh Hadamard conversion matrix,
[equation 4]
WHM is basically a square-type vector and has orthogonal characteristics when
a column vector is correlated with another column vector. That is, the square matrix,
H can comply with the condition of H*H r,—H rlH„-ni„ or 1^^^ Matrix, In.
Furthermore, vector components 1 and -1 indicate the phase delay in accordance with 0
and π.
However, accurate phase modulation of a spatial light modulator that represents
the modulation of 0 and π is required in order to apply the phase code by WHM to a
holographic memory system. Therefore, it is impossible to comply with the
characteristics of phase modulation in practicality.
Since the addresses of a general WHM algorithm have orders of a power of 2,
efficient usage of pixels will be inevitable in a spatial light modulator, and the number
of addresses is extremely limited. Therefore, a number of researchers have proposed
several methods of constructing a WHM in the form of N≠ 2 . For example, in 1993
R. Paley proposed various methods of constructing a WHM with an order N=4n^ an(j
Williamson presented a method of constructing a WHM with an order 172. X. Yang and
C. Denz et. al proposed an iterative decomposition algorithm using the WHM with an
order N=4p, with p being an odd integer and N is the order of a basic WHM based on
the method of Williamson to overcome the shortcomings of conventional methods. Also,
an algorithm that expands PSR (Pseudo Random Code) having minimum interference in
the same bandwidth of the spread spectrum communication system for application of a
holographic memory system to a two-dimensional PSR is proposed.
In order to achieve a practical holographic memory employing a phase-code
multiplexing method, it is important to generate an efficient phase-code in consideration
of the characteristics of a practical optical system. In other words, an efficient
phase-code has to guarantee an orthogonal structure between the address beams and
comply with random characteristics.
However, the conventional phase-codes may cause image crosstalk since DC
components are included between the address beams by regular arrangement of pixels.
Also, the conventional phase-codes can't generate the address beams as many as pixels
of spatial light modulator, so that applicability of the spatial light modulator is reduced.
Therefore, in order to implement a holographic memory system using
phase-code multiplexing efficiently, development of a phase-code algorithm is required
in which the phases between pixels are randomly distributed and the perfect orthogonal
structure is guaranteed.
Disclosure of the Invention
Therefore, the present invention was devised to resolve the problems associated
with the prior art. One object of the present invention is to provide a method for
phase-code multiplexing using complex phase-code in a holographic memory system
that can generate a complex phase-code using CPC algorithm. Another object of the
present invention is to provide a method for phase-code multiplexing using the complex
phase code in a holographic memory system that can multiplex an object beam using an
address beam generated based on the complex phase code.
According to a preferred embodiment to achieve this object, a method and an
apparatus for multiplexing phase code in a holographic memory system are provided as
follows. The method comprises the steps of generating a complex phase code through a
complex phase code algorithm, wherein the complex phase code is used as an address
beam when a phase is multiplexed, modulating the phase of the address beam through a
phase spatial light modulator, modulating the amplitude of an object beam through a
signal amplification spatial light modulator, and interfering the amplitude-modulated
object beam with the phase-modulated address beam using a light refraction medium.
Accordingly, the complex phase code is generated randomly.
Furthermore, the step of generating the complex phase code further comprises
the steps of a) setting up the block size of the complex phase code, b) generating a basic
complex phase code with a pair (ECPC, C-ECPC) based on the block size, wherein the
basic complex phase code includes a real vector component and an imaginary vector
component, c) identifying if the real vector component and the imaginary vector
component are independent from each other based on the basic complex phase code, d)
identifying if the pair of the basic complex phase code are orthogonal with each other
when the real vector component and the imaginary vector component are independent
from each other, e) identifying if RCE produced in advance is 1 when the pair of the
basic complex phase code are orthogonal with each other, and f) mapping the basic
complex phase code to a predetermined position of the block size of the complex phase
code according to the identified result.
Accordingly, the block size can have a square form.
Also, the method may further comprise the step of repeatedly executing step b)
~ step f) until all the basic complex phase codes are mapped to the block size.
The method may further comprise the step of outputting the complex phase
codes if all the basic complex phase codes are mapped to the block size of the complex
phase code.
Firstly, the block size of the basic complex phase codes can be basically
predetermined.
Also, the basic complex phase codes can be randomly generated.
Furthermore, the basic complex phase codes are generated using a
mathematical equation as follows:
Zγ—a+ib, z2 =c+id
b=c=0, a=d=±l.
Also, if the real vector component and the imaginary vector component are
independent from each other the mathematical equation is the following:
N(R): real vector component,
N(I): imaginary vector component,
PXY(N(R), N(I)): probability density function.
The RCE is generated in accordance with the block size of the complex phase code
using an RCE algorithm and stored in a buffer.
The method may further comprise the step of regenerating the basic complex
phase code in pair in the step b) if the real vector component and the imaginary vector
component are not independent or not orthogonal with each other.
The photo refractive material may be either light polymer or crystal.
According to another preferred embodiment to achieve the object, a method
and an apparatus for generating a complex phase code using a complex phase code
algorithm is provided. The method comprises the steps of a) setting up the block size of
the complex phase code, b) generating a basic complex phase code with a pair (ECPC,
C-ECPC) based on the block size, wherein the basic complex phase code includes a real
vector component and an imaginary vector component, c) identifying if the real vector
component and the imaginary vector component are independent from each other based
on the basic complex phase code, d) identifying if the pair of the basic complex phase
code are orthogonal with each other when the real vector component and the imaginary
vector component are independent from each other, e) identifying if RCE produced in
advance is 1 when the pair of the basic complex phase code are orthogonal with each
other, and f) mapping the basic complex phase code to a predetermined position of the
block size of the complex phase code according to the identified result.
The block size can have a square form.
The method may further comprise the step of repeatedly executing the step b) ~
step f) until all the basic complex phase codes are mapped to the block size.
The method may further comprise the step of outputting the complex phase
codes if all the basic complex phase codes are mapped to the block size of the complex
phase code. The block size of the basic complex phase codes can be basically
predetermined.
The basic complex phase codes can be randomly generated.
The RCE can be generated in accordance with the block size of the complex
phase code using an RCE algorithm and stored in a buffer.
The method may further comprise the step of regenerating the basic complex
phase code in pair in the step b) if the real vector component and the imaginary vector
component are not independent or not orthogonal with each other.
According to another preferred embodiment, a storage media readable by
digital processor is provided. The storage media stores a program to execute the process
for generating a complex phase code in order to perform the method for multiplexing
the phase code in a holographic memory system. The process comprises the steps of
generating a complex phase code through a complex phase code algorithm, wherein the
complex phase code is used as an address beam when a phase is multiplexed,
modulating the phase of the address beam through a phase spatial light modulator,
modulating the amplitude of an object beam through a signal amplification spatial light
modulator, and interfering the amplitude-modulated object beam with the
phase-modulated address beam using light refraction medium.
According to still another preferred embodiment, a storage media readable by
digital processor is provided. The storage media stores a program to execute the process
for generating a complex phase code in order to perform the method for multiplexing
the phase code in a holographic memory system.
The complex phase code is generated by performing the process comprising the
steps of a) setting up the block size of the complex phase code, b) generating a basic
complex phase code with a pair (ECPC, C-ECPC) based on the block size, wherein the
basic complex phase code includes a real vector component and an imaginary vector
component, c) identifying if the real vector component and the imaginary vector
component are independent from each other based on the basic complex phase code, d)
identifying if the pair of the basic complex phase code are orthogonal with each other
when the real vector component and the imaginary vector component are independent
from each other, e) identifying if RCE produced in advance is 1 when the pair of the
basic complex phase code are orthogonal with each other, f) mapping the basic complex
phase code to a predetermined position of the block size of the complex phase code
according to the identified result, g) executing the step b) ~ step f) repeatedly until all
the basic complex phase codes are mapped to the block size, h) outputting the complex
phase codes if the all the basic complex phase codes are mapped to the block size of the
complex phase code, and i) regenerating the basic complex phase code in a pair in the
step b) if the real vector component and the imaginary vector component are not
independent or not orthogonal with each other.
Brief Description of the Drawings
Fig. 1 represents the configuration of a holographic memory system using the
conventional phase code multiplexing.
Fig. 2 is a flowchart representing the procedure for generating a complex phase
code in the holographic memory system according to the preferred embodiment of the
present invention.
Fig. 3 represents a block table of a complex phase code (CPC) with M x M
blocks according to the preferred embodiment of the present invention.
Fig. 4 represents a table used to compare the number of address according to
CPC with that of the address according to other phase codes according to the
preferred embodiment of the present invention.
Fig. 5 a and 5b represent tables used to show the distribution of vector element
of complex phase code with 8 x 8 according to the preferred embodiment of the
present invention.
Fig. 6a and 6b are diagrams to show the real vector element of complex phase
code with 8 x 8 on a two-dimensional plane according to the preferred embodiment
of the present invention.
Fig. 7a and 7b represent illustrative three-dimensional diagrams to show the
real vector element of complex phase code with 8 x 8 on a three-dimensional plane
according to the preferred embodiment of the present invention.
Fig. 8a and 8b represent illustrative diagrams to display the real vector element
of complex phase code with 8 x 8 as three-dimensional space phase according to the
preferred embodiment of the present invention.
Fig. 9a and 9b are diagrams to show the imaginary vector element of complex
phase code with 8 x 8 on a two-dimensional plane according to the preferred
embodiment of the present invention.
Fig. 10a and 10b represent illustrative three-dimensional diagrams to show the
imaginary vector element of a complex phase code with 8 x 8 on a three-dimensional
plane according to the preferred embodiment of the present invention.
Fig. 11a and lib represent illustrative diagrams to display the imaginary vector
element of complex phase code with 8 x 8 as a three-dimensional space phase according
to the preferred embodiment of the present invention.
Fig. 12a and 12b represent illustrative diagrams to show the principle of
generating CPC by REC according to the preferred embodiment of the present
invention.
Best Modes for carrying out the Invention
Hereinafter, preferred embodiments of the present invention will be described in
more detail with reference to the accompanying drawings.
Fig. 2 is a flowchart representing the procedure for generating a complex phase
code in the holographic memory system according to the preferred embodiment of the
present invention. Referring to Fig. 2, the size of the CPC (Complex Phase Code,
hereinafter "CPC") is set up (S310). That is, the range of the horizontal axis is set up as
x=0, x=n and the range of the vertical axis is set up as y=0, y=n regarding the size of the
CPC. For example, if n=8, the size of the CPC is 8 x 8 matrix. Accordingly, a pixel
means a complex phase value.
If the size of the CPC is determined, each block size of ECPCP (Elemental
Complex Phase Code Pair) is set up (S315). Accordingly, a CPC may include multiple
ECPCP. If the size of the CPC is 8X8 and that of the ECPCP is 2X2, the CPC may
5 comprise 16 ECPCP. The ECPCP includes a pair, that is, an ECPC (elementary
complex phase code) and a C-ECPC (counter part-elemental complex phase code) in
accordance with ECPC that the inner product of ECPC and C-ECPC is zero.
If the block of the ECPCP is set up, the coordinate of the vertical axis is setup
by y=y+l (S320). Also, the coordinate of horizontal axis is setup by x=x+l (S325). For
10 example, if the initial condition is set up as x=0 and y=0, x axis and y axis of CPC are
x=l and y=l. If the coordinate of the CPC is set up, also ECPC and C-ECPC are
generated (S330). In more detail, the ECPC and the C-ECPC are randomly generated.
For example, if the block of the ECPCP is set up by 2X2, then ECPC and C-ECPC may
be randomly generated as below.
l τλ
It is determined that the real number and the complex number are independent
from each other based on the vector components of the ECPC and the C-ECPC (S335).
The value of complex phase in accordance with the pixels of the ECPC and the C-ECPC
is defined as N(R) and N(I) respectively. A four-phase section comprising the CPC is
20 shown as equation 9 in the form of a Jones vector.
[equation 9]
V(R,I)= exp( π) =-1 = VR .) exp( π/2) =t = ^D exp(-/π/2) —-i = ^2
In detail probability density functions of N(R) and N(I) are defined as X and Y since
N(R) and N(I) must comply with the same probability of each other. Thus, if the
probability density function X and Y comply with the condition as in equation 10, it can
be proven that they are independent statistically like equation 11 that follows,
[equation 10]
[equation 11]
Pj_:V(R))=PY(V(l))=0.5
In order to generate the CPC, a phase element N(R) and N(I) must have the
same probability and comply with the condition of being independent from each other.
This means a complex phase having only a real part and a complex phase having only
an imaginary part are generated with the same probability independently. Also, this
means correlation between -π/2 and π/2, and 0 and π is zero in the complex
inner-product space.
In order to suppress the correlation of inner product of the address beam
including vector component in the holographic memory system, the complex phase
has to be canceled from each other completely.
If the generated ECPC and C-ECPC are not independent from each other then
the process goes to S330, and the ECPC and the C-ECPC are regenerated.
However, if the ECPC and the C-ECPC are independent respectively, a
determination is made whether the inner product between the ECPC and the C-ECPC is
zero (S340). The ECPC and the C-ECPC have four complex phase values respectively.
Each of the complex phase values means a pixel, so that the ECPC and the C-ECPC
include four pixels respectively. For example, the number of cases for "N(R)" and
"N(I)" with the phase element of the ECPCP by 2X2 block is represented as equation 5
by a combination 4C2.
[equation 5]
L V(R) V(P)\ Y V(R) V(I)1 V(R) V(I)\
Ml, M3 and M5 correspond with the ECPC, while M2, M4 and M6 correspond with
the C-ECPC. Also, R means real number and I means imaginary number respectively.
Also, N means phase element. Therefore, the ECPCP is generated and comprised of Ml
and M2, M3 and M4, and M5 and M6 respectively.
In this case, inner product of Ml and M2, M3 and M4, and M5 and M6 must be
zero to be generated as the CPC.
Five situations showing the orthogonal structure of complex inner product
space are indicated like equation 6 as follows:
[equation 6]
MΛ • j2=( e 2 + e 2 )+< 2 + e 2 )=(-ι-ι)+(ι+i)
Mz3 - Mz4= ( 2'2π)2+( 2 2 )2= (1)2+ ( 2
»2π.
A/* • -z6= ( β'~) + ( β Jτ. ) = (1)'+ (-0
λ-/.7 • M28=( β i 'X -^VO X e " )=(-! X l)+(i X -i)
■M* ' A^10=( '2π X e m)+( e 2 X e 2 )=( 1 X - 1 )+(- X /)
The equation 6 shows the correlation to become "0" by mutual influence of
vector component of complex phase. The orthogonal structure in the complex inner
product space indicates independence among the inner products. Therefore, the
correlation among the complex phase has to be canceled completely to suppress the
correlation of the inner product of the address beam including vector component in the
holographic memory system. Also, this indicates the component of mutual correlation
between phase section -π/2 and π/2, 0 and π.
If the inner product of ECPC and C-ECPC is zero, it is checked if the
RCE[x] [y] stored in the buffer is 1 (S345).
The ECPC and the C-ECPC need to be distributed randomly. Therefore, the
CPC designed according to the ECPC and the C-ECPC has to guarantee perfect
orthogonal structure among the address beams theoretically. This is the condition to
generate the CPC with ECPCP, which comprises n n pixels and has constant block
size.
In order to arrange the ECPCP randomly and mutually, a generated algorithm
RCE (Random Code with Equality) that complies with equations 10 and 11 for 2 phase
components can be used. The RCE is a random code, in which each code can be
obtained by generating the phase components of 1 and -1 with equal probability;
accordingly the same phase components are prevented from concentrating in a specific
region (this concentration causes a correlation component).
Therefore, 1 or -1 generated at random by the RCE algorithm in advance is
stored in the buffer to map the ECPC and the C-ECPC generated with a pair for each
coordinate of the CPC.
If RCE[x][y] is 1, the ECPC is mapped to CPC[x][y](S350). However, if
RCE[x][y] is not 1, the C-ECPC is mapped to CPC[x][y] (S355). Therefore, the CPC
can prevent phase components from concentrating in a specific region if the ECPCP is
mapped to the CPC by this method.
After the mapping to the CPC is finished, it is checked if the horizontal
coordinate of the CPC, x is n (S360). If x is not n, the process returns to the S235, the
ECPCP pair is generated with x being incremented by 1, and it is checked if the inner
product is zero. If x is n, it is checked that the vertical coordinate of the CPC, if y is n
(S365).
If y is not n, the process returns to the S320, the ECPCP pair is generated with y
being incremented by 1, and it is checked if the inner product is zero. If y is n, the
phase codes that fit the size of the CPC set up in the step S310 are filled, and are
inputted to photo refractive material by irradiated light (S370).
Although not shown in Fig. 2, the number of the address beam by the CPC can
be same as the number of the object beam. That is, if the number of the object beam is
30, the number of the address beam generated to the CPC is 30.
Therefore, if a CPC is generated and outputted as in Fig. 2, an ECPC and a C-ECPC are
regenerated and another CPC can be generated repeatedly. Those skilled in this art will
know how to modify this Method for generating the CPC.
Furthermore, if the ECPCP by mXm block is arranged as the address beam in
accordance with the number of the pixels, nXn, the number of the address can be
shown by equation 12.
[equation 12]
The CPC can be generated by restricting MXM block among the ECPCPs for
accurate phase control modulation while a practical light experiment is made as shown
in Fig. 3. Referring to Fig. 3, since ECPCP are generated in a pair and the CPC
consists of four ECPCPs, the CPC includes two ECPCP pairs. ECPCP(0,0),
ECPCP(1,0), ECPCP(0,1) and ECPCP(1,1) can represent phase components
respectively. For example, suppose that ECPC by mXm can be expressed as below.
/ 1
■BCTCP'-[-, .ι]
Then, ECPCP(0,0), ECPCP(1,0), ECPCP(0,1) and ECPCP(1,1) can represent i, 1, -I and
-1 respectively. M means the size of basic block to be arranged in accordance with the
selected ECPCP.
Therefore, the number of the address beam that can be generated by arranging
the ECPCP in MXM block can be expressed as equation 13.
Fig. 4 represents a table used to compare the number of address according to
CPC with that of an address according to the other phase codes according to the
preferred embodiment of the present invention. Referring to Fig. 4, the RCE has the
greatest address beam as 1.6096X10Λ199. To the contrary, the WHM has the smallest
address beam as 4.295 X10Λ9 (2Λn). However, this result represents the number of
cases possible to occur overall. Especially, regarding RCE as well as WHM, it is
impossible to apply all of the number of cases to a holographic memory system.
However, regarding CPCpRand CPCRCEi is easy to apply them to the address beam
since it is numerous that the number of cases that the phase component inputted
initially are different.
Hereinafter, the present invention will be described using two CPCs.
Figs. 5a and 5b represent tables used to show the distribution of vector element
of complex phase code with 8 8 according to the preferred embodiment of the
present invention. Referring to Figs. 5a and 5b, two ECPCP samples having 2X2
pixels were selected as the vector element of the CPC. Also, CPCRCE having 8 8
pixels can be generated using RCE algorithm having 4X4 pixels. This will be
described by referring to Figs. 12a and 12b in further detail.
Figs. 12a and 12b represent illustrative diagrams to show the principle of
generating CPC by REC according to the preferred embodiment of the present invention.
Referring to Figs. 12a and 12b, Fig. 12a represents the process in generating a CPC
having the size of M X M comprising 2 X 2 ECPC and C-ECPC using the RCE
having the size of M/2 X M/2.
Fig. 12b is an illustrative diagram when M = 8. That is, the ECPC and C-ECPC
having 2 X 2 pixels generate two CPCs having 8 X 8 pixels by an RCE algorithm
having 4 X 4 pixels
The vector element by 8X8 can be represented as a three-dimensional spatial
coordinate and phase expression, as well as a two-dimensional phase code in
accordance with real part normalized to 1 as shown in Figs. 6a ~ 8b. Accordingly, if it is
expressed as real part, only the phase components corresponding to 1 of the vector
element in Figs. 5a and 5b are expressed.
Therefore, the phase component is shown only when the phase component of
real part is 1 as shown in Figs. 7a and 7b. Also, the phase corresponding to vector
component 1 is expressed as zero when the real part is represented in the complex space
as shown in Figs. 8a and 8b. Also, the vector component of the CPC by 8X8 is
expressed and represented as a two-dimensional phase code, three-dimensional spatial
coordinate, and phase expression in accordance with the imaginary part also as shown in
Figs. 9a ~ 10b.
The vector components of the CPC, i and -i are expressed as two conjugate
complex numbers, zι== +ib' z2=c÷id (b=c=0? a=d=±l) as in equation 8. Therefore,
it is expressed in normalization as 1 and -1 respectively in the three-dimensional space
coordinate as shown in Figs. 10a and 10b. 1 and -1 are expressed as phase section, -π/2
and π/2 in the real complex space as shown in Figs. 11a and lib.
Industrial Applicability
As described above, according to a method for phase-code multiplexing using a
complex phase code in a holographic memory system of the present invention, the
complex phase code that complies with random distribution and guarantees an
orthogonal structure can be generated.
According to a method for phase-code multiplexing using a complex phase
code in a holographic memory system of the present invention, efficient application of
P-SLM and implementation of the stable phase code address beam are possible.
According to a method for phase-code multiplexing using a complex phase
code in a holographic memory system of the present invention, the application of code
will become easier since the number of address are not limited.
Although a preferred embodiment of a method for phase-code multiplexing
using complex phase code in a holographic memory system is described in detail above,
the scope of the present invention is not limited within the field of the present invention
disclosed in the following claims. Also, it is understood that those skilled in this art can
change the present invention in various details of form and construction without
departing from the spirit and the scope of the invention.
Claims
1. A method for multiplexing phase code in a holographic memory system,
comprising the steps of:
generating a complex phase code through a complex phase code algorithm,
wherein the complex phase code is used as an address beam when a phase is
multiplexed;
modulating the phase of the address beam through a phase spatial light
modulator;
modulating the amplitude of an object beam through a signal amplification
spatial light modulator; and
interfering the amplitude-modulated object beam with the phase-modulated
address beam using photo refractive material.
2. The method according to claim 1, wherein the complex phase code is
randomly generated.
3. The method according to claim 1, wherein the step of generating complex
phase code further comprises the steps of: a) setting up the block size of the complex phase code;
b) generating basic complex phase code with a pair (ECPC, C-ECPC) based on
the block size, wherein the basic complex phase code includes a real vector component
and an imaginary vector component;
c) identifying if the real vector component and the imaginary vector component
are independent from each other based on the basic complex phase code;
d) identifying if the pair of the basic complex phase code are orthogonal with
each other when the real vector component and the imaginary vector component are
independent from each other;
e) identifying if RCE produced in advance is 1 when the pair of the basic
complex phase code are orthogonal with each other; and
f) mapping the basic complex phase code to a predetermined position of the
block size of the complex phase code according to the identified result.
4. The method according to claim 3, wherein the block size is a square form.
5. The method according to claim 3, further comprising the step of:
executing the step b) ~ step f) repeatedly until all the basic complex phase
codes are mapped to the block size.
6. The method according to claim 5, further comprising the step of:
outputting the complex phase codes if all the basic complex phase codes are
mapped to the block size of the complex phase code.
7. The method according to claim 3, wherein the block size of the basic
complex phase codes is basically predetermined.
8. The method according to claim 3, wherein the basic complex phase codes are
randomly generated.
9. The method according to claim 3, wherein the basic complex phase codes are
generated using a mathematical equation, and further wherein the mathematical
equation is
b=c=0, a=d=+l.
10. The method according to claim 3, wherein if the real vector component and
the imaginary vector component are independent from each other the mathematical
equation is
PxAV(R ,V(I) =Pj_ V(Ry)PY(V(r) N(R): real vector component,
N(I): imaginary vector component, and
PXY(N(R), N(I)): probability density function.
11. The method according to claim 3, wherein the RCE is generated in
accordance with the block size of the complex phase code using an RCE algorithm and
stored in a buffer.
12. The method according to claim 3, further comprising:
regenerating the basic complex phase code in a pair in the step b) if the real
vector component and the imaginary vector component are not independent or not
orthogonal with each other.
13. The method according to claim 1, wherein the photo refractive material is
either a light polymer or a crystal.
14. A method for generating a complex phase code using a complex phase code
algorithm
comprising the steps of:
a) setting up the block size of the complex phase code; b) generating basic complex phase code with a pair (ECPC, C-ECPC) based on
the block size, wherein the basic complex phase code includes a real vector component
and an imaginary vector component;
c) identifying if the real vector component and the imaginary vector component
are independent from each other based on the basic complex phase code;
d) identifying if the pair of the basic complex phase code are orthogonal with
each other when the real vector component and the imaginary vector component are
independent from each other;
e) identifying if RCE produced in advance is 1 when the pair of the basic
complex phase code are orthogonal with each other; and
f) mapping the basic complex phase code to a predetermined position of the
block size of the complex phase code according to the identified result.
15. The method according to claim 14, wherein the block size is a square form.
16. The method according to claim 14, further comprising the step of:
executing the step b) ~ step f) repeatedly until all the basic complex phase
codes are mapped to the block size.
17. The method according to claim 16, further comprising the step of: outputting the complex phase codes if the all the basic complex phase codes are
mapped to the block size of the complex phase code.
18. The method according to claim 14, wherein the block size of the basic
complex phase codes is basically predetermined.
19. The method according to claim 14, wherein the basic complex phase codes
are randomly generated.
20. The method according to claim 14, wherein the basic complex phase codes
are generated using a mathematical equation, and further wherein the mathematical
equation is
z^—a+ϊb, z2—c+id
b=c=0, a=d=±l.
21. The method according to claim 14, wherein if the real vector component
and the imaginary vector component are independent from each other the mathematical
equation is
N(R): real vector component, N(I): imaginary vector component, and
PXY(N(R), N(I)): probability density function.
22. The method according to claim 14, wherein the RCE is generated in
accordance with the block size of the complex phase code using an RCE algorithm and
stored in a buffer.
23. The method according to claim 14, further comprising:
regenerating the basic complex phase code in a pair in the step b) if the real
vector component and the imaginary vector component are not independent or not
orthogonal with each other.
24. A storage media readable by digital processor, wherein the storage media
stores a program to execute the process when generating complex phase code in order to
perform the method for multiplexing the phase code in a holographic memory system,
and further wherein the process comprises the steps of:
generating a complex phase code through a complex phase code algorithm,
wherein the complex phase code is used as an address beam when a phase is
multiplexed;
modulating the phase of the address beam through a phase spatial light modulator;
modulating the amplitude of object beam through a signal amplification spatial
light modulator; and
interfering the amplitude-modulated object beam with the phase-modulated
address beam using a light refraction medium.
25. A storage media readable by digital processor, wherein the storage media
stores a program to execute the process in generating a complex phase code in order to
perform the method for multiplexing the phase code in a holographic memory system,
and further wherein the complex phase code is generated by performing the process
comprising the steps of:
a) setting up the block size of the complex phase code;
b) generating basic complex phase code with a pair (ECPC, C-ECPC) based on
the block size, wherein the basic complex phase code includes a real vector component
and an imaginary vector component;
c) identifying if the real vector component and the imaginary vector component
are independent from each other based on the basic complex phase code;
d) identifying if the pair of the basic complex phase code are orthogonal with
each other when the real vector component and the imaginary vector component are
independent from each other; e) identifying if RCE produced in advance is 1 when the pair of the basic
complex phase code are orthogonal with each other; and
f) mapping the basic complex phase code to a predetermined position of the
block size of the complex phase code according to the identified result.
26. The storage media according to claim 25, wherein the block size is a square
form.
27. The storage media according to claim 25, wherein the basic complex phase
codes are randomly generated.
28. The storage media according to claim 25, wherein the RCE is generated in
accordance with the block size of the complex phase code using an RCE algorithm and
stored in a buffer.
29. An apparatus for multiplexing phase code in a holographic memory system
comprising:
means for generating complex phase code through a complex phase code
algorithm, wherein the complex phase code is used as an address beam when a phase is
multiplexed; phase spatial light modulator for modulating the phase of the address beam;
signal amplification spatial light modulator for modulating the amplitude of
object beam; and
means for interfering the amplitude-modulated object beam with the
phase-modulated address beam using a light refraction medium.
30. An apparatus for generating complex phase code using a complex phase
code algorithm
comprising:
a) means for setting up the block size of the complex phase code;
b) means for generating basic complex phase code with a pair (ECPC,
C-ECPC) based on the block size, wherein the basic complex phase code includes a real
vector component and an imaginary vector component;
c) means for identifying if the real vector component and the imaginary vector
component are independent from each other based on the basic complex phase code;
d) means for identifying if the pair of the basic complex phase code are
orthogonal with each other when the real vector component and the imaginary vector
component are independent from each other;
e) means for identifying if RCE produced in advance is 1 when the pair of the
basic complex phase code are orthogonal with each other; and f) means for mapping the basic complex phase code to a predetermined position
ock size of the complex phase code according to the identified result.
Priority Applications (3)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| PCT/KR2002/000016 WO2003058352A1 (en) | 2002-01-05 | 2002-01-05 | Phase-encoded multiplexing method using complex phase code in holographic memory system |
| AU2002219682A AU2002219682A1 (en) | 2002-01-05 | 2002-01-05 | Phase-encoded multiplexing method using complex phase code in holographic memory system |
| KR10-2002-0000562A KR100452061B1 (en) | 2002-01-05 | 2002-01-05 | Phase-encoded multiplexing method and apparatus using complex phase code in holographic memory system |
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| PCT/KR2002/000016 WO2003058352A1 (en) | 2002-01-05 | 2002-01-05 | Phase-encoded multiplexing method using complex phase code in holographic memory system |
| KR10-2002-0000562A KR100452061B1 (en) | 2002-01-05 | 2002-01-05 | Phase-encoded multiplexing method and apparatus using complex phase code in holographic memory system |
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| Publication Number | Publication Date |
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Family
ID=28793663
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| PCT/KR2002/000016 WO2003058352A1 (en) | 2002-01-05 | 2002-01-05 | Phase-encoded multiplexing method using complex phase code in holographic memory system |
Country Status (2)
| Country | Link |
|---|---|
| KR (1) | KR100452061B1 (en) |
| WO (1) | WO2003058352A1 (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2005057559A1 (en) * | 2003-12-08 | 2005-06-23 | Koninklijke Philips Electronics N.V. | Holographic storage device |
| CN100378818C (en) * | 2005-03-31 | 2008-04-02 | 富士通株式会社 | Recording and reproducing apparatus |
| CN103513557A (en) * | 2013-10-12 | 2014-01-15 | 北京工业大学 | Coaxial digital holography phase retrieval imaging method of continuous Terahertz waves |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE102006003741B4 (en) | 2006-01-18 | 2009-08-27 | Seereal Technologies S.A. | Method for coding a computer-generated hologram |
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| KR930022124A (en) * | 1992-04-03 | 1993-11-23 | 윌리엄 이. 힐러 | Multiphase Optical Modulation Method and System |
| US5339177A (en) * | 1990-04-06 | 1994-08-16 | University Of Southern California | Incoherent/coherent source array for multiplexed holographic recording and readout |
| EP0632348A1 (en) * | 1993-06-28 | 1995-01-04 | International Business Machines Corporation | Volume holographic storage system |
| EP1065658A1 (en) * | 1998-02-27 | 2001-01-03 | Hideyoshi Horimai | Method and apparatus for optical information, method and apparatus for reproducing optical information, apparatus for recording/reproducing optical information, and optical information recording medium |
| KR20020046398A (en) * | 2000-12-13 | 2002-06-21 | 김은수 | Phase-encoded multiplexing method by using pseudo random phase code in holographic memory system |
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| TW464794B (en) * | 1997-11-12 | 2001-11-21 | Lucent Technologies Inc | System and method for holographic storage using a holographic optical element |
| US6178019B1 (en) * | 1999-05-03 | 2001-01-23 | Lucent Technologies, Inc. | System and method for controlling the selectivity of a holographic memory system |
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2002
- 2002-01-05 KR KR10-2002-0000562A patent/KR100452061B1/en not_active IP Right Cessation
- 2002-01-05 WO PCT/KR2002/000016 patent/WO2003058352A1/en not_active Application Discontinuation
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5339177A (en) * | 1990-04-06 | 1994-08-16 | University Of Southern California | Incoherent/coherent source array for multiplexed holographic recording and readout |
| KR930022124A (en) * | 1992-04-03 | 1993-11-23 | 윌리엄 이. 힐러 | Multiphase Optical Modulation Method and System |
| EP0632348A1 (en) * | 1993-06-28 | 1995-01-04 | International Business Machines Corporation | Volume holographic storage system |
| EP1065658A1 (en) * | 1998-02-27 | 2001-01-03 | Hideyoshi Horimai | Method and apparatus for optical information, method and apparatus for reproducing optical information, apparatus for recording/reproducing optical information, and optical information recording medium |
| KR20020046398A (en) * | 2000-12-13 | 2002-06-21 | 김은수 | Phase-encoded multiplexing method by using pseudo random phase code in holographic memory system |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2005057559A1 (en) * | 2003-12-08 | 2005-06-23 | Koninklijke Philips Electronics N.V. | Holographic storage device |
| CN100378818C (en) * | 2005-03-31 | 2008-04-02 | 富士通株式会社 | Recording and reproducing apparatus |
| CN103513557A (en) * | 2013-10-12 | 2014-01-15 | 北京工业大学 | Coaxial digital holography phase retrieval imaging method of continuous Terahertz waves |
Also Published As
| Publication number | Publication date |
|---|---|
| KR100452061B1 (en) | 2004-10-08 |
| KR20020028164A (en) | 2002-04-16 |
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