WO2003096103A1

WO2003096103A1 - Method for producing a photopolymer-based multiview vhoe using optimized exposure-time schedule

Info

Publication number: WO2003096103A1
Application number: PCT/KR2002/000522
Authority: WO
Inventors: Eun-Soo Kim; Jung-Sik Koo; Byung-Chul Cho
Original assignee: Maxsoft Co., Ltd.
Priority date: 2002-03-26
Filing date: 2002-03-26
Publication date: 2003-11-20
Also published as: AU2002243052A1

Abstract

The present invention relates to a method for producing a photopolymer-based multiview VHOE using an optimal exposure schedule. The multiview VHOE according to the present invention is characterized in that the multiview VHOE is produced by recording a predetermined number diffraction gratings according to a predetermined exposure time, wherein said exposure time is calculated by a predetermined model A= a0 + a1t + a2t2 + a3t3 + a4t4 where, A is cumulative grating strength, t is said exposure time, and a0, a1, a2, a3 and a4 are coefficients.

Description

METHOD FOR PRODUCING A PHOTOPOLYMER-BASED MULTIVIEW

VHOE USING OPTIMIZED EXPOSURE-TIME SCHEDULE

Field of the invention

The present invention relates to a method for producing a photopolymer-based

multiview VHOE using optimal exposure schedule.

Background of the invention

Three-dimensional(3D) image display technology is the fundamental

technology of the next generation multimedia information communication.

Accordingly, 3D image display technologies are being competitively developed by

advanced countries. According to a recommendation of the CCIR working group,

predecessor of the ITU, 3D display technology must comply with three requirements:

(1) be an autostereoscopic type that does not cause eye fatigue, (2) have higher

resolution than the conventional flat panel display, and (3) provide compatibility with

the conventional 2D display and multiple seeing and hearing. Articles of the CCIR

recommendation have become the core of 3D image display technology, and various

solutions for satisfying them have been developed.

Recently, a multiview stereo 3D display system using VHOE(volume

holographic optical element) has been proposed as a new approach to implement a natural 3D image display. The multiview stereo 3D display system records the

diffraction gratings corresponding to the number of views on the optical diffraction

medium by an angular multiplexing method to produce NHOE, and time-divisionally

projects multiview images on NHOE to display the multiview stereo images. Thus, the

physical-optical characteristics affect the number of recording views and reproducing

views. Recently, many studies on a photopolymer, a new optical recording medium,

have been extensively conducted.

Generally, diffraction efficiency characteristics, multiview characteristics

related to the angular selectivity, crosstalk characteristics between the reproduced

diffraction beams, and a uniform diffraction efficiency of each view are required in the

3D image display system using NHOE. Especially, the optimal exposure time schedule

for effectively recording multiview diffraction gratings on the photopolymer is required

for the restored images corresponding to each view that are reproduced as uniform

diffraction beams.

Detailed description of the present invention

It is the primary object of the present invention to provide a method for an

optimal exposure schedule of a photopolymer(Dupont's HRF-150-100) to implement a

photopolymer-based multiview NHOE in the multiview stereo 3D image display system.

Also, another object of the present invention is to implement an 8-view VHOE. More particularly, the object of the present invention is to propose a cumulative

grating strength dependent on the exposure that is mathematically modeled by using a

fourth-order polynomial function and induces the optimal exposure schedule for

recording multiview gratings on the photopolymer.

Also, the object of the present invention is to propose the applicability of the

optimal exposure schedule of the present invention to the system for displaying

multiview stereo 3D image through implementing 8-view NHOE by recording 8-view

gratings on the photopolymer according to the optimized exposure schedule.

To achieve aforementioned objects, according to the preferred embodiment of

the present invention, there is provided a multiview NHOE, characterized in that the

multiview NHOE is produced by recording a predetermined number of diffraction

gratings according to a predetermined exposure time, wherein the exposure time is

A=a₀+a₁t+a₂t²+aJ³+a ⁴ calculated by a predetermined model as follows:

where, A is cumulative grating strength, t is the exposure time, and , , ,

and are coefficients.

The multiview NHOE is exposed to a light source of a predetermined

wavelength during the pre-exposure time and the pre-exposure time is 15 seconds. Also,

the wavelength is 532 nm, and the predetermined number of diffraction gratings is 8.

Also, the multiview NHOE is made of a photopolymer, and more particularly, the

photopolymer is Dupont's HRF-150-100. According to another preferred embodiment of the present invention, there is

provided a multiview NHOE, characterized in that the multiview NHOE is produced by

recording diffraction gratings according to a predetermined exposure time

corresponding to a predetermined number of diffraction gratings, wherein the exposure

time corresponding to each diffraction grating is calculated by a predetermined model

as follows:

— =a₀+a₁ t_n+a₂ t_n ²+a₃ t_n ³+a₄ t _n ⁴ m

where, A is cumulative grating strength, t_n is the exposure time corresponding

to each diffraction grating, and , , , and are coefficients.

Brief description of the drawings

FIG. 1 shows the concept of the multiview 3D display system using VHOE.

FIG. 2 shows the system for measuring the exposure time to implement

multiview NHOE according to the present invention.

FIG. 3 shows the change of diffraction efficiency according to the pre-exposure

time.

FIG. 4a shows the diffraction efficiency change according to the preferred

embodiment of the present invention.

FIG. 4b shows the diffraction efficiency change according to another preferred embodiment of present invention.

FIG. 4c shows the diffraction efficiency change according to another preferred

embodiment of present invention.

FIG. 4d shows the diffraction efficiency change according to another preferred

embodiment of present invention.

FIG. 5 shows the change distribution of the cumulative grating strength

according to the repeated experiment of the present invention.

FIG. 6 shows the final exposure time schedule for implementing 8-view NHOE

by use of a photopolymer according to the preferred embodiment of the present

invention.

FIG. 7 shows the final detected 8 diffraction beams that are diffracted from the

8-view NHOE according to the preferred embodiment of the present invention.

Embodiments

Hereinafter, the preferred embodiment of the present invention will be

described with accompanying drawings.

Technology for displaying a multiview 3D stereo image using NHOE uses the

principal that when multiview gratings are generated in the conventional volume

hologram having high angular selectivity due to the Bragg's condition, the multiview

images that are projected into the volume hologram are diffracted toward predetermined directions. Thus, in order to time-divisionally implement the required

multiview stereo images, a high-density recording technique of a hologram for

effectively recording and reproducing gratings corresponding to the number of views is

required. In particular, it is possible to implement multiview NHOE by recording the

gratings corresponding to the number of views on the photopolymer according to the

optimal exposure schedule, and display multiview stereo images by diffraction beams

reproduced when the multiview images are time-divisionally projected into the NHOE.

FIG. 1 shows the concept of the multiview 3D display system using NHOE.

Referring to FIG. 1, after producing multiview NHOE 101 by angular multiplexing and

recording the reference beam and object beam according the number of views (both in

the form of plane wave) on the photopolymer, the multiview stereo 3D image display

system for displaying multiview images on spatially-different view points by the

combination of the VHOE 101 and LCD panel 103 is shown. Through synchronizing

the projecting direction of a reference beam being projected into the NHOE 101 with

the multiview images that are displayed on the LCD panel 103, multiview images are

time-divisionally displayed on each view point.

Hereinafter, the method for analyzing the optimized pre-exposure time in order

to implement multiview NHOE will be described. Generally, since the conventional

photopolymer is insensitive to the initial exposure and the formation of gratings linearly

increases as the exposure time continues, the pre-exposure time according to the optical characteristics of the photopolymer is needed in order to effectively record gratings.

Namely, the pre-exposure schedule is needed to activate the molecules of the

photopolymer.

FIG. 2 shows the system for measuring the exposure time to implement

multiview VHOE according to the present invention. Referring to FIG. 2, the system

for measuring the exposure time for implementing the multiview VHOE comprises a

light source 210, plural shutters 203, a collimating system 205, a beam splitter 207,

plural imaging lenses 209, plural mirrors 211, plural Fourier lenses 213, and a light

detector 217. By use of the system for measuring the exposure time for implementing

the multiview NHOE, the optimal exposure time and schedule for recording multiview

gratings according to the grating efficiency and physical characteristics of the

photopolymer can be induced. In the preferred embodiment of the present invention, the

optimal pre-exposure time for producing 8-view NHOE, which is used in the multiview

stereo 3D image display system, can be induced.

In the preferred embodiment of the present invention, being confirmed as the

optimized angle by measuring the diffraction efficiency change due to the angle

between two interference beams, the angle of two interference beams that are both

projected to the photopolymer is 27°. Also, the light source 201 in the present invention

is an Νd-YAG laser having a 532 am wavelength. The intensities of each beam are 65

/_W/c_tf. Also, since the system for measuring exposure time according to the present invention controls the beams by use of the electrical shutter 203, the system can shut

two beams simultaneously, and only the recording beam during reproduction.

FIG. 3 shows the change of diffraction efficiency according to the pre-exposure

time. Referring to FIG. 3, the graphs show the changes of diffraction efficiency relative

to the pre-exposure time when the pre-exposure times are 8, 10, 15, 20, and 30 seconds,

respectively. As shown in FIG. 3, the optimized diffraction efficiency is shown at 15

seconds. Thus, when multiview NHOE is implemented by use of a photopolymer in the

preferred embodiment of the present invention, the NHOE is pre-exposed for 15

seconds. When the pre-exposure time of 15 seconds that is measured in the present

invention is converted into the exposure energy, 15 seconds of pre-exposure time

corresponds to lmJVcn . Also, in the preferred embodiment of the present invention, the

saturation time for using the linear increasing part can be determined as 160 seconds.

The origin in FIG. 3 represents the actual exposure time except for the pre-exposure

time.

Hereinafter, the optimal exposure schedule for implementing multiview NHOE

after applying optimal pre-exposure time will be described. In order to implement the

system for displaying multiview stereo 3D image using NHOE, a diffraction beam in

the form of a plane wave having a relatively large radius and NHOE having high

diffraction efficiency and high angular selectivity for recording multiview gratings are

needed. Thus, the effective pre-exposure time and the optimal exposure schedule for recording multiview grating are very important steps in order to implement the optimal

multiview NHOE. In the preferred embodiment of the present invention, a cumulative

grating strength (i.e., the function of exposure energy), is used as a parameter indicating

the grating recording level, and the cumulative grating strength can be induced by

calculating the root of the diffraction beam's intensity and then integrating the root.

Also, since the cumulative grating strength is the total energy recorded on the

photopolymer, analogous diffraction efficiency can be obtained by distributing the

cumulative grating strength according to the number of views.

FIG. 4a shows the diffraction efficiency change according to the preferred

embodiment of present invention. Referring to FIG. 4a, the diffraction efficiencies of 8

holograms that are recorded by the angular multiplexing method with the same

exposure time are shown. The 20 seconds resulting from dividing 160 seconds of

saturation time by 8 (the number of holograms) are applied to each grating. In the

preferred embodiment of the present invention, in order to analyze the characteristics of

multiview diffraction efficiency obtained through the iterated experiments after

applying these pre-conditions, the following mathematical parameter is used.

Formula 1

Formula 2

Formula 3

Formula 1 through Formula 3 are for the calculating mean, variance, and

deviation, where m represents the mean of diffraction efficiency, M represents the

number of gratings, E represents diffraction efficiency, and represents deviation

of the diffraction efficiency.

Although the mean and deviation of the diffraction efficiency of each grating

can be calculated, since the change distribution of diffraction efficiency cannot be

determined exactly by mean or deviation, the preferred embodiment of the present

invention induces a coefficient of variation as a new parameter to analyze the diffraction

efficiency of each grating. Generally, although it is possible to estimate the relative

diffraction efficiency distribution of each view by comparing each deviation when the

diffraction efficiency means of the two results are the same, if the means of the two

results are different or continuously change then it is difficult to estimate the relative

diffraction grating distribution with deviations. Thus, in order to analyze the relative

distribution change of plural results having different means and deviations, the

coefficient of variance of Formula 4 in consideration of the mean and the deviation simultaneously is needed.

Formula 4

The preferred embodiment of the present invention shows an analysis of the

optimal diffraction efficiency distribution of 8 images that are reproduced by use of the

coefficient of variation in Formula 4. Also, in the preferred embodiment of the present

invention, a mathematical model of an exposure schedule as an approach for multiplex

recording on a photopolymer to obtain analogous diffraction efficiencies of each

multiview diffraction beam can be derived.

Table 1 shows the difference between the derived polynomial and the original

data in the maximum error ratio to express the relationship between the exposure time

and the cumulative grating strength in the form of a polynomial.

Table 1

Accordingly, based on the result of Table 1, the exposure schedule for implementing multiview NHOE is mathematically modeled by using a fourth-order

polynomial function of Formula 5 in the preferred embodiment of the present invention.

Formula 5

A = a ₀+ a _±t+ a ₂t²+ a₃t³+a ₄t⁴

Formula 5 is based on the sixth-order polynomial function, which is

conventionally used in the field of volume hologram memory using photopolymer, and

is derived by applying the maximum error ratio of the preferred embodiment of the

present invention. As indicated above, A represents the cumulative grating strength, t

represents cumulative exposure time, and arj through a₄ are coefficients that are used to

represent the cumulative graph. Because 8 gratings must be recorded with regard to the

8-view NHOE, the exposure time can be determined by dividing the stabilized

cumulative grating strength of Formula 6 by 8. At this time, with regard to Formula 6,

each exposure time t_n for n(l ≤ n ≤ 8) can be calculated.

Formula 6

FIG. 4a shows the diffraction efficiency change according to another preferred

embodiment of present invention.

FIG. 4b shows the measured diffraction efficiency distribution after recording

gratings on the photopolymer by applying the exposure time schedule that is calculated by Formula 6 according to the preferred embodiment of the present invention.

The results of repeatedly performing the aforementioned step after obtaining

the cumulative grating strength by the same method are shown in FIGS. 4c and 4d. In

FIGS. 4a-4d, the thick dashed line represents the mean of the diffraction efficiency, and

the thin dashed line represents the deviation of the diffraction efficiency.

When analyzing the results shown in FIGS. 4a-4d, the more the experiments are

repeated, the higher the mean and the lower the deviation. Table 2 shows the results

numerically.

Table 2

Namely, Table 2 shows the mean, variance and coefficient of variation of the

results, calculated by use of Formula 1, Formula 3 and Formula 5. Referring to Table 2,

since the coefficient of variation v is 63.42% in the first exposure time schedule, then

the diffraction efficiency of the multiview is distributed within the relatively broad

63.42% range centering around the mean. However,, as the experiments are performed repeatedly, the coefficient of variation v rapidly declines to 40.95%, 24.91%, and 3.58%.

The reduction of the coefficient of variation indicates that the diffraction efficiencies of

each diffraction beam become higher and distribute analogously. Thus, through the

repetition using the mathematical model of the proposed exposure time schedule, the

analogous diffraction efficiency of multiplexed gratings can be obtained.

Hereinafter, an experiment of implementing the 8-view NHOE and the

experimental results will be described in detail. In the preferred embodiment of the

present invention, the exposure time schedule of a photopolymer(Dupont's HRF-150-

100) to record an 8-view grating by using the result of the 3^rd repetition is determined,

and the 8-view NHOE can be implemented by the exposure time schedule.

FIG. 5 shows the change distribution of the cumulative grating strength

according to the repeated experiments of the present invention. Referring to FIG. 5, the

cumulative grating strength obtained through repeating the experiment by using the

mathematical model of the proposed exposure time schedule is shown. It can be

understood from FIG. 5 that the graph of the cumulative grating strength approaches a

straight line. Thus the diffraction efficiencies of each view point are distributed

analogously. Also, the exposure time schedule for the optimal diffraction efficiency can

be determined by repeating the experiments.

FIG. 6 shows the final exposure time schedule for implementing the 8-view

NHOE by use of the photopolymer according to the preferred embodiment of the present invention.

Referring to FIG. 6, through angular multiplex recording an 8-view grating on

photopolymer(HRF-150-100, Dupont) with rotating the 8-view grating by 1.8° using

the optimized exposure time schedule, the 8-view NHOE can be implemented. Also,

through time-divisionally projecting the reference beam on the implemented 8-view

VHOE, each diffraction beam can be obtained from the 8-view grating.

8-view NHOE according to the preferred embodiment of the present invention.

Referring to FIG. 7, each figure indicates that analogous patterns of beams appear at all

8 view points according to the angle.

Although the present invention has been described with the preferred

embodiment, the spirit and the scope of the present invention will be determined only

by the following claims. Also, it will be apparent for those skilled in the art that

modifications or amendments to the aforementioned embodiment within the spirit and

the scope of the present invention are possible without departing from the boundary of

the claimed invention.

Industrial applicability

According to the present invention, it is possible to implement NHOE based on a photopolymer(HRF-150-100) using the optimal exposure time schedule. Also,

according to the present invention, an 8-view NHOE can be implemented. Namely, the

cumulative grating strength dependent on the exposure energy is mathematically

modeled by using a fourth-order polynomial function, and the optimal exposure time

schedule of the photopolymer for recording the given multiple gratings is calculated.

Further, by implementing the 8-view NHOE by using a conventional photopolymer and

providing proof through experiments, the mathematical expression of the optimal

exposure time schedule according to the present invention can be applied to the actual

system implementation.

Claims

1. A multiview NHOE, characterized in that

said multiview NHOE is produced by recording a predetermined number of

diffraction gratings according to a predetermined exposure time,

wherein said exposure time is calculated by a predetermined model as follows:

A = a ₀+ a _χt+ a ₂t²+ a ₃t³+ a ₄t⁴

where, A is cumulative grating strength, t is said exposure time, and , ,

, and are coefficients.

2. The multiview NHOE as stated in claim 1, characterized in that said multiview

NHOE is exposed to a light source of a predetermined wavelength during the pre-

exposure time.

3. The multiview NHOE as stated in claim 2, characterized in that said pre-exposure

time is 15 seconds.

4. The multiview NHOE as stated in claim 2, characterized in that said wavelength is

532 nm.

5. The multiview NHOE as stated in claim 1, characterized in that said predetermined number of diffraction gratings is 8.

6. The multiview NHOE as stated in claim 1, characterized in that said multiview

NHOE is made of a photopolymer.

7. The multiview NHOE as stated in claim 6, characterized in that said photopolymer is

Dupont's HRF-150-100.

8. A multiview NHOE, characterized in that

said multiview NHOE is produced by recording diffraction gratings according

to a predetermined exposure time corresponding to a predetermined number of

diffraction gratings,

wherein said exposure time corresponding to each diffraction grating is

calculated by a predetermined model as follows:

where, A is cumulative grating strength, t_n is said exposure time corresponding

to each diffraction grating, and are coefficients.