WO2002048800A1

WO2002048800A1 - Phase-encoded multiplexing method using a pseudo-random phase code in a holographic memory system

Info

Publication number: WO2002048800A1
Application number: PCT/KR2001/000318
Authority: WO
Inventors: Un-Su Kim
Original assignee: Maxsoft Co., Ltd; Kwangwoon University; Cho, Byung-Chul
Priority date: 2000-12-13
Filing date: 2001-03-03
Publication date: 2002-06-20
Also published as: KR20020046398A; AU2001237766A1

Abstract

The present invention pertains to a phase-encoded multiplexing method that uses pseudo-random phase code in a holographic memory system. The present invention is designed to provide the most effective phase-encoded multiplexing method for an HM system. First, an address beam is generated by PSR phase code. Then the phases of the address beam are modulated by the use of an Address Phase Spatial Light Modulator (APSLM), the amplitude of an object's beam is modulated by the use of a Signal Amplitude Spatial Light Modulator (SASLM), and the output of the APSLM is interfered with by the output of the SASLM by the use of a photo-refractive medium. In order to find an effective phase code, phase errors that had 0 %, 5 %, 10 %, 15 %, 20 % and 25 % error ratios were intentionally added to all the phase codes that were used in simulations of the use of the present invention. Through the use of a phase-encoded pseudo-random phase code, crosstalk effects are lower than with other phase codes, there is a relatively high SNR (signal-noise ratio), and it is possible to produce a large number of highly stable phase code address beams.

Description

PHASE-ENCODED MULTIPLEXING METHOD USING A PSEUDO¬

RANDOM PHASE CODE IN A HOLOGRAPHIC MEMORY SYSTEM

TECHNICAL FIELD

The present invention relates to a phase-encoded multiplexing method that uses a

pseudo-random phase code in a holographic memory system. More particularly, the

present invention relates to a phase-encoded multiplexing method in order to produce

multiple address beams and, at the same time, in order to effectively restrict crosstalk.

BACKGROUND ART

In the era of multimedia- there will be a tremendous increase in the amount of data

used by individuals and companies in voice, video, 3D video and NOD data (including text

or images). As a solution to this condition, a storage medium with higher storage

capacity is needed, and holographic memory (HM) is suitable for this purpose.

Amplitude represents the degree of brightness or darkness, and phase represents the

position of an object. A three-dimensional image can be produced by manipulating both

the amplitude and phase of an object in a two-dimensional picture.

In holograms, an object-reflected laser beam and an arbitrary laser beam from

another direction are stored on photographic film at the same time. If these two laser

beams cross at the same points on the photographic film- an interference pattern is produced that consists of many dark or bright lines which represent the amplitude and

phase of the object. Therefore, the photographic film that the interference pattern is

stored on is called a hologram and the technique of storing the hologram is called

holography.

Since it was discovered that data can be stored in a photo-refractive medium by

using a photo-refractive effect by which the refractive index of the medium is dependent

on the intensity of light, various multiplexing schemes more data in holographic memory

(HM) has been done.

Storage capacity of HM is dependent on the multiplexing method. Multiplexing

methods that have been disclosed so far are angle multiplexings, wavelength multiplexings

and phase code multiplexings. In the angle multiplexing methods, the angle of the

address beam represents the address of the stored image. In the wavelength multiplexing

methods, a light source with a changeable wavelength is used- In the phase-encoded

multiplexing methods, orthogonal phases are used.

In the angle multiplexing methods, the address beam is controlled to satisfy the

'Bragg angle' by means of an acousto-optic deflector (AOD), step motor or moving

windows.

Among the above-mentioned devices of controlling the address beam in the angle

multiplexing methods, a step motor has the disadvantage of causing crosstalk due to

mechanical errors. An AOD can precisely control the address beam electronically and also has the advantage of allowing fast random access. However, it has the disadvantage

that it needs complicated and high-priced system. A new method using moving windows

in spatial light modulator (SLM) has been disclosed, which diminishes the disadvantages

described above. However, because this method uses only the light that passes through

its windows, it has the disadvantage of reducing the efficiency of the use of light.

Wavelength multiplexing methods also require a high-priced and tunable coherent

light source that has precise, high-resolution wavelength selectivity.

On the other hand, the phase-encoded multiplexing methods have the advantage

that accurate and fast random access is possible by means of a comparatively simple

system that has no mechanical movement.

In 1977, T. Krile and Morozov presented the conditions that crosstalk in a plane

hologram with no angular selectivity can be diminished to a minimum by encoding the

reference beam. In 1982, E- Krai suggested the usage of orthogonal code for volume

hologram by using a random diffuser. In 1991, C. Denz and Y. Taketomi performed an

HM multiplexing experiment for Hadamard matrix (HAM) using a SLM for creating

orthogonality.

Generally, in phase-encoded multiplexing methods, the object beam and address

beam are fixed thereafter, and the address beam's phase code is changed, so lots of address

beams are multiplexed in order to store lots of data in a photo-refractive medium.

Therefore, it is important to maintain the orthogonality between phase codes. At this time, the accurate phase modulation of 0 and π, and the orthogonality between address beams,

must be guaranteed. Lots of simultaneous address beams are needed to achieve high

storage capacity.

In the case of the pure phase-encoded multiplexing method using a random diffuser,

it is possible to generate lots of addresses, but it is not guaranteed that their accurate

orthogonality can be maintained. As a result, there is the disadvantage that high crosstalk

occurs and accurate control of addresses is difficult. A Random diffuser is unsuitable for

use in a phase-encoded multiplexing method.

Also, in the case of a phase-encoded multiplexing method using HAM with an

SLM, there is some advantage in that HAM has its own orthogonality and, as a result, it is

easy to implement an HAM with SLM. However, because of phase modulation errors

resulting from the electronic and physical properties of the contemporary SLM that is used

for phase modulation, crosstalk can occur when lots of image data is stored and

reconstructed. Also, the well known documented method is only valid for the common

HAM whose order in power of 2, i-e-, N=2^r, with r integers. This represents only a very

small subset of positive integer. If only this HAM can be used in phase code multiplexing,

the inefficient utilization of currently available SLMs would be inevitable.

In the case of multiplexing many images by phase code through a photo-refractive

medium in order to diminish crosstalk that occurs in the process of image reconstruction,

crosstalk that occurs in the process of image storing is most diminished. For this, the auto-correlation components of the address beam must function similar to an impulse, and,

at the same time, the cross-correlation components of the address beam must do not exist.

That is, the complexly functioning address beams that are used in multiplexing have

orthogonality in order to diminish crosstalk, and accurate control of the SLM's phase and

amplitude is needed to dimmish crosstalk that occurs during reconstruction.

FIG- 1 is a schematic of an HM system using contemporary phase-encoded

multiplexing.

Referring to FIG. 1, the image of signal data (i-e-, the object beam) is modulated in

amplitude by being transmitted through a signal amplitude spatial light modulator

(SASLM); and the phase code (i.e., the address beam) is modulated in phase by being

transmitted through an address phase spatial light modulator (APSLM). The modulated

phase code has 0 or % phase lag. The amplitude-modulated object beam and phase-

modulated address beam are multiplexed by passing through lenses 160-1 and 160-2

respectively to a photo-refractive medium that generates interference- The beams from

the photo-re ractive medium are collected by lens 160-3 and the image signal is

reconstructed in output detector 150.

Generally, when the phase-encoded multiplexing method is compared with other

multiplexing methods, phase-encoded multiplexing has many advantages: mechanical

movement of the address beam is not needed, fast random access is available, there is high

efficiency in the use of light, and variation of wavelength is not needed. In the phase-encoded multiplexing method, each of the address beams consists of

plane waves that have uniform phase distribution, and phase codes that are used as address

beams are utilized accurately to store and reconstruct images. So, N units of orthogonal

phase code are needed to store N units of the hologram-

Typical phase-encoded multiplexing methods are a method that uses a random

diffuser or speckle pattern of glass fiber and a method that uses HAM having two values,

"+1" and "-1".

When a random diffuser or speckle pattern is used, there is some cross-correlation

component- So, it is impossible to generate an address beam that has perfect

orthogonality- Also, because crosstalk between reconstructed images is generated, the

signal-noise ratio (SNR) drops.

Also, because the HAM is expressed in the form of 2" pixel pattern, the SLM's

efficiency of pixel utilization is reduced. For example, when HAM is present in the use

of an SLM that consists of 100 (10 x 10) pixels, the number of usable pixels of the SLM is

fixed at 10⁶ such that half of the pixels are not used. Accordingly, the SLM's efficiency

of pixel utilization is low and the number of addresses is restricted.

In order to create an effective HM system using phase code, certain conditions are

required: the availability of many addresses; minimum crosstalk between adjacent images;

and, at the same time, insensitivity to phase modulation error that occurs when the phase

code is applied to a real system. In practical applications, when phase code is modulated by the use of an SLM, it is difficult to modulate correctly all of the SLM's pixels by 0 and

π in phase due to the non-linearity that is generated by electrical and physical effects.

DISCLOSURE OF INVENTION

The present invention specifically addresses and alleviates the above-mentioned

deficiencies associated with prior art- It is a primary object of the present invention to

provide a phase-encoded multiplexing method that uses pseudo-random phase code that

efficiently generates phase code by use of a computer program-

To achieve the above-mentioned object, according to the first part of the

embodiment of the present invention, the phase-encoded multiplexing method using

pseudo-random phase code (PSR) comprises the steps of: generating an address beam by

the use of the pseudo-random phase code; modulating phase of the address beam by the

use of an Address Phase Spatial Light Modulator (APSLM); modulating amplitude of an

object beam by the use of an Signal Amplitude Spatial Light Modulator (SASLM); and

interfering an output of the APSLM with an output of SASLM by the use of a photo-

refractive medium.

The PSR is randomly produced by a computer program.

The step of generating the address beam by the use of pseudo-random phase code

comprises the steps of producing one-dimensional phase code by the use of a feedback

shift register and expanding the one-dimensional phase code to two-dimensional phase code.

The one-dimensional phase code has 2^m-l bits through performing XOR operation

between i ^tb (i<=m) and m ^th bit of the m bits shift register, the result of the XOR operation

is inputted to the i ^th bit of the m bits shift register by feedback.

The step of expanding the one-dimensional phase code to the two-dimensional

code comprises the steps of: sequentially sampling a row of pseudo-random phase code, on

the assumption that the one-dimensional phase code is the row of pseudo-random phase

code; deciding whether each bit of the row of pseudo-random phase code has the value of 0

or 1; producing a two-dimensional pseudo-random phase code by sequentially expanding

the row of pseudo-random phase code, if each bit of the row of pseudo-random phase code

has the value "1"; and producing a two-dimensional pseudo-random phase code by

reversing bits of the row of pseudo-random phase code and sequentially expanding the row

of pseudo-random phase code by the use of the reversed bits.

The number of two-dimensional pseudo-random phase code is produced as

follows:

_PSR = 2(2" - l)²(m - 1)(« - 1)

wherein n represents the two-dimensional pseudo-random phase code consisting of

n x n pixels, and m is the number of bits in the m bits feedback shift register-

According to the second part of the embodiment of the present invention, a

computer-readable medium with stored computer-executable instructions for producing pseudo-random phase code performs the steps of producing a one-dimensional phase code

by the use of a feedback shift register and expanding the one-dimensional phase code to

two-dimensional phase code.

BRIEF DESCRIPTION OF DRAWINGS

FIG- 1 is a schematic representation of contemporary geometry for the phase-

encoded multiplexing method utilized in the HM system;

FIG. 2a to 2d show 4 different types of two-dimensional phase code for phase-

encoded multiplexing that are generated by use of a computer program;

FIG. 3 is a schematic representation of the feedback shift register for generating

pseudo-random phase code;

FIG. 4 is a flow chart showing the procedure for generating two-dimensional

pseudo-random phase code by the use of a computer program, in accordance with the

preferred embodiment of the present invention;

FIG.5 is a result graph of the SNR for the 4 phase codes that is obtained by varying

the phase error ratio from 0% to 25% in consideration of the SLM's phase errors that occur

during phase modulation due to non-linearity;

FIG. 6a and 6b are normalized result graphs showing the auto-correlation

component and cross-correlation component between two arbitrarily selected phase codes

that are generated by the use of pure random code (PR); FIG. 7a and 7b are normalized result graphs showing the auto-correlation

that are generated by the use of random code with equality (ER);

FIG. 8a and 8b are normalized result graphs showing the auto-correlation

that are generated by the use of HAM;

FIG. 9a and 9b are normalized result graphs showing the auto-correlation

that are generated by the use of pseudo-random phase code (PSR);

FIG. 10a, 10b, 10c and lOd are result graphs showing cross-correlation between

two phase codes that are arbitrarily selected from 500 phase codes generated by the use of

PR, ER, HC and PSR respectively

FIG. 11a and lib are result graphs showing mean and standard deviation

(consisting of variance in the size of pixels in the address beam) in the cross-correlation

between phase codes that are generated by the use of PR, ER, HAM and PSR.

FIG. 12a is a graph showing the SNRs (signal-noise ratio) for PR, ER, HAM and

PSR phase codes by repeating 500 addresses, when the size of the address has 32x32

pixels;

FIG. 12b is a graph showing the SNRs for PR, ER, HAM and PSR when the size of

the address is 64x64, 128x128 and 256x256 pixels. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, the preferred embodiment of the present invention will be described

with reference to accompanying drawings.

FIG. 2a to 2d show 4 different types of two-dimensional phase code for phase-

encoded multiplexing that are generated by the use of a computer program-

FIG- 2a shows pure random code (PR). Though it is easy to generate PR by the

use of a random diffuser, an optical fiber speckle pattern, and other devices, because there

is a high probability that "-1" and "+1" are concentrated in a specific region, it cannot have

high cross-correlation-

Also, when cross-correlation is produced by phase codes, irregular cross-

correlation is produced because the concentration of the phase value of "-1" and "+1" get

randomly distributed. When the size of pixels of address beams is n x n, because a pixel

can have the phase values of "-1" and "+1" at the same time, _PR, the number of addresses

beams of PR, can be given by

M_PR = (20 "

FIG- 2b shows random code with equality (ER) that makes up for the deficiency of

PR.

In the case of using ER, the whole region is classified by optional blocks (2 x 2, 4 x

4, ...., m x m) with equal possibility, and the phase values "-1" and "+1" are generated with

equal possibility by the computer program, so that the concentration of cross-correlation components in a specific region is restricted. As a result, the situation that the same codes

concentrate in a specific region is reduced partially.

Also, in the case of using ER, cross-correlation components and the number of

address beams are both dependent on the level of unit blocks not being in accordance with

each other.

To calculate the number of address beams, let a unit block be m x m (m-level). The

number of combination for this block is given by

Where M_B-_ER s the number of combination of m-level in ER. When the size of

the address beam is n x n pixels and the block level is /n-level, A _ER, the number of

addresses beams produced by the combination „C_r is as follows:

FIG. 2c shows HAM as an orthogonal code that is easy to realize with an SLM.

However, since HAM is expressed only in the form of 2" pixels pattern, the number of

addresses beams is restricted. That is, when an SLM with 10 x 10 pixels is used, the

number of pixels that can be utilized is 2 x 2 , so the efficiency of SLM pixel usage drops

approximately by 56%. Also, since the non-linearity of commercial SLMs and the irregularity of glass

thickness, an HAM method that requires the accurate phase modulation of components is

not easily applied to an HM system using an SLM in comparison with other methods-

_HC, the number of addresses beams of HC, is as follows:

_HC = 2"

FIG. 2d shows pseudo-random phase code (PSR). In the bandwidth diffusion

communication system, PSR is used for encoding data in order to have minimum

interference in the spread-spectrum communication system-

PSR.

Referring to FIG. 3, PSR constitutes a class of binary random codes using shift

resister. The feedback shift register performs the XOR operation between the arbitrary tth

bit and the last mth bit on its own, and the result of the XOR operation is inputted to rth bit

by feedback.

The output value that is defined by each code (bit) of register, (i-e-, "1" and "0") is

repeated by 2^m as a maximum cycle in the register having m bits. However, when initial

condition of the shift register is all "0", the output of the XOR operation becomes 0, so the

real cycle becomes 2^m-l. The output of the feedback shift register results in one-

dimensional PSR. It is apparent to those skilled in the art that there are many possible

ways of producing one-dimensional PSR. Here, two-dimensional PSR can be produced by the use of one-dimensional PSR

having 2/n-l bits. First, one-dimensional PSR becomes a column of two-dimensional

PSR, and the generated one-dimensional PSR code's values are sampled in order. If the

value of the sampled code is "1," then the original one-dimensional PSR is placed in the

same row orderly. Otherwise (i.e., if the value of sampled code is "0"), then whole codes

of one-dimensional PSR are reversed and placed in that row- Two-dimensional PSR is

produced by means of this procedure. A detailed description of this procedure is

provided later with FIG. 4.

According to the procedure, the size of PSR address beams that are generated from

address beams having n x n pixels, _PSR, is as follows:

_PSR = 2(2^M - l)²(m - l)(/- - l)

To use two-dimensional PSR having _PS addresses, two-dimensional PSR is

finally produced by changing "0" code value into "-1."

FIG. 4 is a flow chart showing the procedure of generating two-dimensional PSR

by the use of a computer program, in accordance with the preferred embodiment of the

present invention-

Referring to FIG- 4, all bits of the m-stage feedback shift register are initialized at

0(Step 401). One-dimensional PSR is produced by the above-mentioned procedure(Step

403). If the produced PSR code's value is "1," the code's value is not altered. If the

produced PSR code's value is "0," the code's value is converted to "-1" (Step 405). Let two variables, A and B, represent the column and row of a two-dimensional

matrix for storing two-dimensional PSR. The value of A and B are initialized at 0 and the

size of the matrix to be generated is stored in n (Step 407). Here, n results from n x n

pixels.

If the row variable B is equal to or greater than n-1 (Step 409), A is increased by 1

for the purpose of increasing the column of the two-dimensional matrix (Step 421). Then

0 is inputted to row B for the purpose of setting it as the first row of the two-dimensional

matrix (Step 423), and the procedure then returns to Step 409.

If the row variable B is less than n-1, the values located in PSR [A][B] of the PSR

matrix are stored in a buffer temporarily (Step 411). If the values stored in a buffer are

more than "0" (for example, "1"), PSR_[A]p_] is inputted to PSR_[A+i_][B_] (Step 415). If the

values stored in a buffer are equal to or less than "0," -PSRfA_jp_] is inputted to PSR_[A_{+ [B]}

for inversing the phase code (Step 425). The matrix row variable B is increased by 1

(Step 417) and two-dimensional PSR is produced (Step 419).

It is apparent to those skilled in the art that there are many possible ways of

producing two-dimensional PSR. TABLE 1

Table 1 shows the number of two-dimensional address beams that are produced by

PR, RE (2nd level), RE (4th level), HAM and PSR. In accordance with the list in Table 1

of the general cases that can occur, PR produces the greates number of address beams (in

the quantity of 2J7 x ID⁷¹) and HC produces the least number- However, these numerical

values are for only the general cases that can occur, so there may be some limits in

applying them to a real HM system.

Phase errors that have 0%, 5%, 10%, 15%, 20% and 25% error ratios are

intentionally imposed to all phase codes that are used in the simulation of the present

invention for the purpose of considering phase modulation error caused by the real SLM's

optical properties.

If f(x, y) is an exact phase code representing an address and g(x, y) is a phase code

with phase error, the address code with phase error can be represented by

g(^χ, y) =f(^χ> y) + > y)

where e(x, y) is a phase error function that is imposed randomly on the exact phase value of "-1" or "+1" mf(x, y).

If phase code that is generated by this method is similar to the phase code that is

generated by a real SLM, one patter of is acting as one address in multiplexing when phase

code is propagating to the photo-refractive medium in the form of complex function

through the lens depicted in FIG. 1.

In order to investigate the effects of crosstalk that is caused by these addresses, the

correlation between addresses is examined as follows:

J oo . CO G_t (fx y) G_} Xξ-fx, η-fy) dξdη

where G(fi, fy) represents a Furrier Transformation of an address beam g(x, y), Gi

and Gj represent the ith and jth address beams respectively, and FT represents the Furrier

Transformation.

To restrict the appearance of crosstalk in an HM system, the following condition

must be satisfied. That is, the auto-correlation component of the address beam must be

estimated into a delta function, and the cross-correlation component of the address beam

must be removed. This property is satisfied by

( 1 if i= j

FT{\g x,y)\²}

1 0 if iΦj

The formula below represents the SNR, which represents the multiplexing

capability, of phase code by the ratio of the value of the auto-correlation component to the value of the cross-correlation component. As it is shown in the formula below, the auto¬

correlation component is inversely proportional to the SNR, so the SNR is improved by

restricting the appearance of auto-correlation.

A. SNR[dB] = 10 log IO-^:

Where A. and C. represent normalized auto-correlation and normalized cross-

correlation respectively- Also, if the desired data image is restored continuously among

the multiplexed several data images in HM system, the restored data image might have

some errors in the point of threshold detection due to the lack of uniformity and the

irregular cross-correlation values. Accordingly, the mean value and standard deviation of

auto-correlation components have to be maintained as low as possible. Generally, the

mean value for random signals is as follows:

^{1 "} A E{χ) ≡= m_x = j__∞ ^χ ^^dx

Where E(x) and m_x represent the mean value for x. p(x) represents the possibility

density function of x, which means the possibility of generating x. Accordingly, an

variance and standard deviation of x axe represented as follows:

The effect of crosstalk upon phase codes used in simulations and the stability of

address beams can be analyzed by using a mean value. By this means, a standard deviation

for correlation and an efficient phase code that able to be used with stability in an HM

system can be proposed based on the results of analysis.

Hereinafter, in order to investigate the most efficient phase code for use in an HM

system, the results of the analyses of cross-correlated values and the number of addresses

produced by PR, ER, HC and PSR presently in use are explained.

All phase codes that were used in the simulation intentionally included phase errors

that had 0%, 5%, 10%, 15%, 20% and 25% error ratios for the purpose of considering

phase modulation errors caused by a real SLM's optical properties. Moreover, the

samples used consisted of 501 phase code addresses that were generated in sequence by a

computer program-

Also, to analyze the effect of changes in the magnitude of the address beam, the

simulation was performed using 32 x 32, 64 x 64, 256 x 256 and 512 x 512 pixels.

during phase modulation due to non-linearity.

To obtain approximate statistics, the SNR for produced phase codes uses the mean

values of auto-correlation components and cross-correlation components for 501 phase

codes that have 32 x 32 pixels and are generated by a computer program. Referring to FIG. 5, HAM has the highest SNR of 7%, but there is a relatively

strong effect of phase error after about 10%. It means that if there is no phase error,

HAM is an ideal orthogonal code. But, in the case that a large quantity of images are

stored by the SLM, on account of the SLM's nonlinear phase property and the phase error

that can occur in an optical system, the reconstructed images are more likely to be

corrupted by crosstalk-

However, in spite of non-linear random phase errors, other phase codes that have

random phase properties are less affected by phase errors. FIG. 5 also shows that PSR has

the least influenced phase error among the four because PSR is designed to have

orthogonal property-

FIG. 6a and 9b are normalized result graphs showing auto-correlation components

and cross-correlation components between two arbitrarily phase codes that are generated

by the use of PR, ER, HAM and PSR respectively.

Referring to FIG. 6a to 9b, the auto-correlation and the cross-correlation were

obtained by correlating between two arbitrary address phase code whose size was 32x32

pixels and which was selected among 500 different phase code created with the methods of

PR, ER, HAM and PSR, respectively- It can be appreciated that auto correlation

components are approximated to a delta function, but cross-correlation components are

shown to have different phase codes. After cross-correlating phase codes 500 times, the

maximum values obtained for each phase code were 0.16, 0.11, 0.14 and 0.054 respectively. FIG. 10a, 10b, 10c and lOd are result graphs showing cross-correlation between

PR, ER, HC and PSR respectively.

In the phase-encoded multiplexing method for an HM system, to prevent the

degradation of a recalled image that is part of continuous images, the cross-correlation

value between address beams must be low and, at the same time, almost uniform. Also,

address beams have to be orthogonal in relation to each other in order to have high storage

capacity.

FIG- 11a and lib are result graphs that show (through variation in the size of pixels

in an address beam) the mean and standard deviation in cross-correlation between phase

codes that are generated by the use of PR, ER, HAM and PSR. That is, the mean value

and standard deviation that result from cross-correlation 500 times using each phase code

are obtained by changing the number of address beam pixels to 32 x 32, 64 x 64, 128 x 128

and 256 x 256-

Referring to FIG. 11a and lib, the vertical axis represents the number of pixels and

the mean value for cross-correlation decreases in inverse proportion to the number of

pixels. Similarly, . the standard deviation of cross-correlation also decreases in inverse

proportion to the number of pixels.

FIG. 11a and lib show that, based on the distribution of mean values and the

standard deviation during cross-correlation, PSR has a mean value 2 or 3 times lower than the PR's mean value according to the number of pixels and also 1.5 or 2 times lower than

the HAM's mean value.

FIG. 12a is a graph showing the SNRs (signal-noise ratio) for PR, ER, HAM and

PSR phase codes by repeating 500 addresses, when the size of the address has 32x32 pixels,

and FIG. 12b is a graph showing the SNRs for PR, ER, HAM and PSR when the size of the

address is 64x64, 128x128 and 256x256 pixels.

Referring to 12a and 12b, the SNR always increases in proportion to the size of

address. However, it is appreciated that SNR for PSR is about 1.5 times higher than other

phase codes.

The SNR for PSR and other phase codes increases in line with an increase in the

number of pixels. Accordingly, in the case that PSR is used for a phase code multiplexing

method in an HM system that has phase modulation errors, it is possible to embody

relatively high SNR and stable phase code address beams.

Table 2

Table 2 shows comparative results for mean value and standard deviation after

cross-correlating phase codes 500 times that have 32 x 32 pixels. The results from cross-

correlation show that the mean value and standard deviation for PSR is 2 times lower than

that for other phase codes. And because this result is in inverse proportion to the SNR, a

relatively high SNR can be deduced from this result.

Also, because the standard deviation that the transition of cross-correlation can be

measured by is the lowest, it is appreciated that the cross-correlation components are

almost stable.

The present invention is not limited to the above-mentioned embodiment, and

diverse modifications of the present invention are possible to the one skilled in the art.

The cross-correlation properties of PSR phase code according to the present

invention (in which the phase code uses 32 x 32 address beams) show that PSR has

relatively high SNR in comparison with other phase codes, since the mean value for PSR phase code is 0.067. Therefore, the effects of crosstalk occur 2 times less than with other

phase codes.

INDUSTRIAL APPLICABILITY

Also, because PSR phase code's standard deviation according to the present

invention is lower than other with other phase codes, the possibility of crosstalk affecting

reconstructed images is lower than with any other phase codes.

Also, because the PSR phase code used in the present invention has relatively high

SNR, it is possible to realize stable address beams.

Claims

1. A phase-encoded multiplexing method that uses pseudo-random phase code in a

holographic memory system, comprising the steps of:

generating address beam by the use of the pseudo-random phase code;

modulating phase of the address beam by the use of an Address Phase Spatial

Light Modulator (APSLM);

modulating amplitude of an object beam by the use of a Signal Amplitude Spatial

Light Modulator (SASLM); and

interfering an output of the APSLM with an output of the SASLM by the use of a

photo-refractive medium.

2- The method stated in Claim 1, wherein the pseudo-random phase code is

randomly produced by a computer program-

3- The method stated in Claim 1, wherein the step of generating the address beam

by the use of the pseudo-random phase code comprises the steps of:

producing one-dimensional phase code by the use of a feedback shift register; and

expanding the one-dimensional phase code to two-dimensional phase code.

4. The method stated in Claim 3, wherein the one-dimensional phase code has 2^m-l bits through performing XOR operation between i ^th (i<-m) and m ^th bit of a m bits shift

register, and a result of the XOR operation is inputted to the i ^th bit of the m bits shift

register by feedback.

5. The method stated in Claim 4, wherein the step of expanding the one-

dimensional phase code to the two-dimensional phase code comprises the steps of:

sequentially sampling a row of pseudo-random phase code, on the assumption that

the one-dimensional phase code is the row of pseudo-random phase code;

deciding whether each bit of the row of pseudo-random phase code has the value

"0" or "1";

producing a two-dimensional pseudo-random phase code by sequentially

expanding the row of pseudo-random phase code, if each bit of the row of pseudo-random

phase code has the value "1"; and

producing a two-dimensional pseudo-random phase code by reversing bits of the

row of pseudo-random phase code and sequentially expanding the row of pseudo-random

phase code by the use of the reversed bits.

6- The method stated in Claim 5, wherein a size of the two-dimensional pseudo¬

random phase code is produced as follows:

M_PS = 2(2^m - l)²(m - l)(n - 1) wherein n represents the two-dimensional pseudo-random phase code consisting of

n x n pixels and m is the number of bits in the m bits feedback shift register.

7. A computer-readable medium having stored thereon computer-executable

instructions for producing pseudo-random phase code, comprising the steps of:

producing a one-dimensional phase code by the use of a feedback shift register;

and

expanding the one-dimensional phase code to two-dimensional phase code.

8. The medium stated in Claim 7, wherein the one-dimensional phase code has 2^m-

1 bits through performing XOR operation between i^th (i<=m) and m^th bit of a m bits shift

register by feedback.

9. The medium stated in Claim 7, wherein the step of expanding the one-

sequentially sampling a row of pseudo-random phase code, on the assumption that

the one-dimensional phase code is the row of pseudo-random phase code;

deciding whether each bit of the row of pseudo-random phase code has the value

"0" or "1"; producing a two-dimensional pseudo-random phase code by sequentially

phase code has the value "1"; and

producing a two-dimensional pseudo-random phase code by reversing bits of the

phase code by the use of the reversed bits.

10. The medium stated in Claim 9, wherein a size of the two-dimensional pseudo¬

random phase code is produced as follows:

_PS = 2(2" - lf(m - l)(n - 1)

wherein n represents the two-dimensional pseudo-random phase code consisting of

n n pixels and m is the number of bits in the m bits feedback shift register-

AMENDED CLAIMS

[received by the International Bureau on 12 April 2002 (12.04.02); original claims 1,5 and 7 amended; original claims 3,4 and 8 cancelled; remaining claims unchanged (3 pages)]

1. [AMENDED] A phase-encoded multiplexing method that uses pseudo-random

phase code in a holographic memory system, comprising the steps of:

producing one-dimensional phase code by the use of a feedback shift register;

expanding the one-dimensional phase code to two-dimensional phase code to

generate an address beam by the use of the pseudo-random phase code;

modulating phase of the address beam by the use of an Address Phase Spatial

Light Modulator (APSLM);

modulating amplitude of an object beam by the use of a Signal Amplitude Spatial

Light Modulator (SASLM); and

interfering an output of the APSLM with an output of the SASLM by the use of a

photo-refractive medium,

wherein the one-dimensional phase code has 2!"-l bits through performing XOR

operation between i^th (i<=m) and m^tb bit of a m bits shift register, and a result of the XOR

operation is inputted to the i^Λ bit of the m bits shift register by feedback.

2. The method stated in Claim 1, wherein the pseudo-random phase code is

randomly produced by a computer program.

3. [DELETED]

4. [DELETED]

5. [AMENDED] The method stated in Claim 1, wherein the step of expanding the

one-dimensional phase code to the two-dimensional phase code comprises the steps of:

sequentially sampling a row of pseudo-random phase code, on the assumption that

the one-dimensional phase code is the row of pseudo-random phase code;

deciding whether each bit of the row of pseudo-random phase code has the value

"0" or "1";

producing a two-dimensional pseudo-random phase code by sequentially

phase code has the value "1"; and

producing a two-dimensional pseudo-random phase code by reversing bits of the

phase code by the use of the reversed bits.

6. The method stated in Claim 5, wherein a size of the two-dimensional pseudo¬

random phase code is produced as follows:

ps_R = 2(2^m - l)²(rn - l)(n - l)

wherein n represents the two-dimensional pseudo-random phase code consisting of n x n pixels and m is the number of bits in the m bits feedback shift register.

7- [AMENDED] A computer-readable medium having stored thereon computer-

executable instructions for producing pseudo-random phase code, comprising the steps of:

producing a one-dimensional phase code by the use of a feedback shift register;

and

expanding the one-dimensional phase code to two-dimensional phase code,

wherein the one-dimensional phase code has 2^m-l bits through performing XOR

operation between i^th (i<=m) and m ^th bit of a m bits shift register, and a result of the XOR

operation is inputted to the i ^th bit of the m bits shift register by feedback.

8. [DELETED]

9. The medium stated in Claim 7, wherein the step of expanding the one-

sequentially sampling a row of pseudo-random phase code, on the assumption that

the one-dimensional phase code is the row of pseudo-random phase code;

deciding whether each bit of the row of pseudo-random phase code has the value

-O" _or « .

producing a two-dimensional , pseudo-random phase code by sequentially STATEMENT UNDER ARTICLE 19

I/We amended claims under the article 19 of PCT-

Qaims 1, 5 and 7 replaced by amended claims bearing the same numbers;

Claims 3, 4 and 8 deleted; all other claims unchanged.