Discrete pattern, apparatus, method, and program storage device for generating and implementing the discrete pattern

• US 6,865,325 B2
• Filed: 04/11/2003
• Issued: 03/08/2005
• Est. Priority Date: 04/19/2001
• Status: Active Grant

• Current Assignee: AU Optronics Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Ide, Tsuyoshi, Taira, Yoichi, Mizuta, Hideyuki, Nishikai, Akiko
• Primary Examiner(s): ULLAH, AKM E
• Application Number:
  US10/413,168
• Publication Number:
  US 20030210210A1
• Time in Patent Office: 697 Days
• Field of Search: 385120-126, 385/141, 385/147, 257/14, 257/24, 257/321, 345/30
• US Class Current: 385/120
• CPC Class Codes: G02B 6/0043 provided on the surface of the light guide
• CPC Class Codes: G02B 6/0061 to provide homogeneous light output intensity
• CPC Class Codes: G02B 6/0065 Manufacturing aspects; Material aspects
• CPC Class Codes: G02B 6/0086 Positioning aspects

Abstract

A discrete pattern, formed by dots discretely arranged in two dimensions, is provided wherein the dots are generated in a low discrepancy sequence. The dots are preferably generated in a discrete pattern wherein the square of discrepancy D satisfies the formula,
D≦0.13N^−1.15  (1)
Further, the method provides for generation of, and the appartus provides implementation of, a discrete pattern even when the filling factor rapidly changes by automatically generating or deleting dots.

Claims

1. A disease pattern, formed by dots discretely arranged in two dimensions, wherein said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,

D≦

0.13N<sup>−

1.15</sup> 

 

(1)

such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x,y) is a diagonal line, $\begin{array}{cc}D<br><br>\left(L_x,L_y;<br><br>N\right)=\int <br><br>{\int <br><br>}_{L_x<br><br>x<br><br>\text{\hspace{1em}<br><br>}<br><br>L_y}<br><br>{\left[\frac{A<br><br>\left(x,y\right)}{N}-\frac{x<br><br>\text{\hspace{1em}<br><br>}<br><br>y}{L_x<br><br>L_y}\right]}^2<br><br>\frac{d<br><br>\text{\hspace{1em}<br><br>}<br><br>x<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y}{L_x<br><br>L_y}& \left(2\right)\end{array}$

and wherein S₁ that is obtained by expression $\begin{array}{cc}{S}_1<br><br>\left(r_1,r_2\right)={\int <br><br>}_{r_1}^{r_2}<br><br>d<br><br>r\left|g_1<br><br>\left(r;<br><br>r_1,r_2\right)-g_{a<br><br>\text{\hspace{1em}<br><br>}<br><br>v}\right|& \left(3\right)\end{array}$

is equal to or smaller than 0.7, such that g, is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of g(r) over a range of from r₁ to r₂, and g_av is the average value of g₁ within the range of from r₁ to r₂;

such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r₁ and r₂ are chosen as one and four times the value of the lattice constant Dr respectively; and

the dot filling rate is a value obtained by multiplying the square of the maximum diameter of a dot by the number of dots, and dividing the product by the size of the area, wherein said discrete pattern is disposed so that an average radius distribution function in said predetermined blocks becomes sufficiently smooth.

2. An optical member, on which a discrete pattern is formed by dots discretely arranged in two dimensions, wherein said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,

D≦

0.13N<sup>−

1.15</sup> 

 

(1)

such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x,y) is a diagonal line, $\begin{array}{cc}D<br><br>\left(L_x,L_y;<br><br>N\right)=\int <br><br>{\int <br><br>}_{L_x<br><br>x<br><br>\text{\hspace{1em}<br><br>}<br><br>L_y}<br><br>{\left[\frac{A<br><br>\left(x,y\right)}{N}-\frac{x<br><br>\text{\hspace{1em}<br><br>}<br><br>y}{L_x<br><br>L_y}\right]}^2<br><br>\frac{d<br><br>\text{\hspace{1em}<br><br>}<br><br>x<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y}{L_x<br><br>L_y}& \left(2\right)\end{array}$

and wherein S₁ that is obtained by expression

3. A light guide plate, used for a light-transmitting liquid crystal display device, on which a discrete pattern is formed by dots discretely arranged in two dimensions, wherein said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,

D≦

0.13N<sup>−

1.15</sup> 

 

(1)

such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x,y) is a diagonal line, $\begin{array}{cc}D<br><br>\left(L_x,L_y;<br><br>N\right)=\int <br><br>{\int <br><br>}_{L_x<br><br>x<br><br>\text{\hspace{1em}<br><br>}<br><br>L_y}<br><br>{\left[\frac{A<br><br>\left(x,y\right)}{N}-\frac{x<br><br>\text{\hspace{1em}<br><br>}<br><br>y}{L_x<br><br>L_y}\right]}^2<br><br>\frac{d<br><br>\text{\hspace{1em}<br><br>}<br><br>x<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y}{L_x<br><br>L_y}& \left(2\right)\end{array}$

and wherein S₁ that is obtained by expression (3) $\begin{array}{cc}{S}_1<br><br>\left(r_1,r_2\right)={\int <br><br>}_{r_1}^{r_2}<br><br>d<br><br>r\left|g_1<br><br>\left(r;<br><br>r_1,r_2\right)-g_{a<br><br>\text{\hspace{1em}<br><br>}<br><br>v}\right|& \left(3\right)\end{array}$

is equal to or smaller than 0.7, such that, g₁ is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of g(r) over a range of from r₁ to r₂, and g_av is the average value of g₁ within the range of from r₁ to r₂, such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r₁ and r₂ are chosen as one and four times the value of the lattice constant Dr respectively; and

the dot filling rate is a value obtained by multiplying the square of the maximum diameter of a dot by the number of dots, and dividing the product by the size of the area, wherein said discrete pattern is disposed so that an average radius distribution function in said predetermined blocks becomes sufficiently smooth.

4. A side light device comprising:

a light guide plate, on which a discrete pattern is formed by dots discretely arranged in two dimensions, wherein said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,

D≦

0.13N<sup>−

1.15</sup> 

 

(1)

such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x,y) is a diagonal line, $\begin{array}{cc}D<br><br>\left(L_x,L_y;<br><br>N\right)=\int <br><br>{\int <br><br>}_{L_x<br><br>x<br><br>\text{\hspace{1em}<br><br>}<br><br>L_y}<br><br>{\left[\frac{A<br><br>\left(x,y\right)}{N}-\frac{x<br><br>\text{\hspace{1em}<br><br>}<br><br>y}{L_x<br><br>L_y}\right]}^2<br><br>\frac{d<br><br>\text{\hspace{1em}<br><br>}<br><br>x<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y}{L_x<br><br>L_y}& \left(2\right)\end{array}$

and wherein S₁ that is obtained by expression $\begin{array}{cc}{S}_1<br><br>\left(r_1,r_2\right)={\int <br><br>}_{r_1}^{r_2}<br><br>d<br><br>r\left|g_1<br><br>\left(r;<br><br>r_1,r_2\right)-g_{\mathrm{av}}\right|& \left(3\right)\end{array}$

is equal to or smaller than 0.7, such that, g₁ is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of a(r) over a range of from r₁ to r₂, and g_av is the average value of g₁ within the range of from r₁ to r₂;

such that, when the dots are arranged in a square lattice to satisfy a given tilling rate, r₁ and r₂ are chosen as one and four times the value of the lattice constant Dr respectively; and

the dot filling rate is a value obtained by multiplying the square of the maximum diameter of a dot by the number of dots, and dividing the product by the size of the area;

said light device further comprising;

a light source for projecting light onto said light guide plate; and

a reflector for reflecting said light projected by said light source and transmitting said reflected light to said light guide plate, wherein said discrete pattern is disposed so that an average radius distribution function in said predetermined blocks becomes sufficiently smooth.

5. A discrete pattern generation method in a computer system to generate a discrete pattern formed of discrete dots disposed two-dimensionally comprising the steps of:

providing a predetermined block;

providing a filling factor distribution function of said dots;

providing areas of said dots;

generating at least two dots according to said filling factor distribution function for said predetermined blocks;

moving using predetermined functions said generated dots and updating thereof to new coordinate values;

judging a distance between dots of which said new coordinate values have been obtained;

generating or deleting new dots with regard to said distance; and

employing said predetermined functions to update coordinate values of dots including said generated dots.

6. The discrete pattern generation method according to claim 5, wherein said step of generating dots according to a filling factor distribution function comprises a step of generating dots in a boundary region of said block and a step of generating dots inside said boundary region of said block.

7. The discrete pattern generation method according to claim 6, wherein said step of employing predetermined functions to move dots comprises a step of moving dots along said boundary region and a step of moving said dots two-dimensionally inside said boundary region.

8. The discrete pattern generation method according to claim 5, wherein said step of generating dots according to a tilling factor distribution function comprises a step of employing a low-discrepancy sequence method to generate dots.

9. The discrete pattern generation method according to claim 5, wherein said discrete pattern is a binarized pattern of an optical intensity modulation element or a variable-density image of an optical component.

20. A discrete pattern generation system for generating discrete patterns comprising:

an execution means for the method according to claim 5;

a storage means to store position coordinates of dots forming said generated discrete pattern;

a printer means to output position coordinates stored in said storage means; and

a pattern acceptance element to which discrete pattern is formed by said printer means.

21. The discrete pattern generation system according to claim 20, wherein said system generates a binarized pattern of an optical intensity modulation element or a variable-density image of an optical component.

10. A program for making a computer to execute the steps of:

providing a predetermined block;

providing said filing factor distribution function of dots;

providing said area of dots;

generating at least two dots according to said filling factor distribution function for said predetermined blocks;

moving employing predetermined functions said generated dots and updating thereof to new coordinate values;

judging a distance between said dots of which said new coordinate values have been obtained;

generating or deleting new dots with regard to said distance; and

employing said predetermined functions to update coordinate values of dots including said generated dots.

11. The program according to claim 10, wherein said step of generating dots according to a filling factor distribution function comprises a step of generating dots in a boundary region of said block and a step of generating dots inside said boundary region of said block.

12. The program according to claim 11, wherein said step of employing predetermined functions to move dots comprises a step of moving dots along said boundary region and a step of moving said dots two-dimensionally inside said boundary region.

13. The program according to claim 10, wherein said step of generating dots according to a filling factor distribution function comprises a step of generating a low-discrepancy sequence method for generation.

14. The program according to claim 10, wherein said discrete pattern is binarized patterns of optical intensity modulation elements or variable-density images of optical components.

15. A computer readable storage medium storing a computer executable program, said program making said computer to execute a generation method for discrete patterns formed of discrete dots disposed two-dimensionally, said storage medium making a computer system to execute the steps of:

providing a predetermined block;

providing a filling factor distribution function of said dots;

providing areas of said dots;

generating at least two dots according to said filling factor distribution function for said predetermined blocks;

moving using predetermined functions said generated dots and updating thereof to new coordinate values;

judging a distance between dots of which said new coordinate values have been obtained;

generating or deleting new dots with regard to said distance; and

employing said predetermined functions to update coordinate values of dots including said generated dots.

16. The storage medium according to claim 15, wherein said step of generating dots according to a filling factor distribution function comprises a step of generating dots in a boundary region of said block and a step of generating dots inside said boundary region of said block.

17. The storage medium according to claim 15, wherein said step of employing predetermined functions to move dots comprises a step of moving dots along said boundary region and a step of moving said dots two-dimensionally inside said boundary region.

18. The storage medium according to claim 15, wherein said step of generating dots according to a filling factor distribution function comprises a step of employing a low-discrepancy sequence method to generate dots.

19. The storage medium according to claim 15, wherein said discrete pattern is binarized patterns of light intensity modulation elements of optical components or a variable-density image.

22. A binarized pattern generation method for generating a binarized patterns of a variable-density image formed of discrete dots disposed two-dimensionally, said binary pattern generation method making a computer system to execute the steps of:

providing a predetermined block;

determining a number of dots disposed in said predetermined block;

determining said dot position coordinates so that said dots contained in a rectangular block having a lateral size of Lx and a longitudinal size of Ly satisfy formula (1);

D≦

0.13N<sup>−

1.15</sup> 

 

(1)

(wherein N in formula (1) denotes a number of dots contained in said block and D is given by formula (2) in the condition in that a number of dots contained in a rectangular region having a diagonal line extending from a reference coordinate (0, 0) to an arbitrary coordinate (x, y) is A (x, y);

$\begin{array}{cc}D<br><br>\left(L_x,L_y;<br><br>N\right)=\int <br><br>{\int <br><br>}_{L_x<br><br>{\mathrm{xL}}_y}<br><br>{\left[\frac{A<br><br>\left(x,y\right)}{N}-\frac{\mathrm{xy}}{L_x<br><br>L_y}\right]}^2<br><br>\frac{\mathrm{dxdy}}{L_x<br><br>L_y}& \left(2\right)\end{array}$

and S₁ given by formula (3) is equal to or less than 0.7;

$\begin{array}{cc}{S}_1<br><br>\left(r_1,r_2\right)={\int <br><br>}_{r_1}^{r_2}<br><br>d<br><br>r\left|g_1<br><br>\left(r;<br><br>r_1,r_2\right)-g_{\mathrm{av}}\right|,& \left(3\right)\end{array}$

wherein g₁ in formula (3) is a value obtained from dividing an average radius distribution function g(r) by an integral value ranging from r₁ to r₂ and g_av is a mean value of g₁ ranging from r₁ to r₂. When dots are disposed in a shape of a tetragonal lattice to satisfy a given filling factor, r₁ and r₂ are specified to an equal value and a quadruple value of a lattice constant Dr, respectively. A filling factor of dots is the value defined in that a square of a maximum diameter of a dot is multiplied by a number of dots, then thus calculated value is divided by an area of said region);

setting said predetermined position coordinates as initial positions;

changing said dot position coordinates so that dots of which said position coordinates have been determined do not overlap with each other; and

employing a plurality of said boundary conditions to adjoin said predetermined blocks to generate a discrete pattern of a predetermined size.

23. The binarized pattern generation method according to claim 22, wherein said step of changing position coordinates comprising the steps of:

calculating repulsion regarding a predetermined dot from another dot existing in the vicinity of said dot;

displacing said predetermined dot according to a magnitude of said repulsion;

a step of calculating repulsion regarding said displaced dot;

and summing up repulsion regarding dots within a predetermined range.

24. The binarized pattern generation method according to claim 22, wherein said step of changing position coordinates employs repulsion which remains steady as against said distance between dots at a wavelength equal to or less than a principal wavelength and decreases according to increase of said distance between dots exceeding a predetermined value.

31. A generation system of binarized patterns including discrete patterns comprising:

an execution means to execute the method according to claim 22;

a storage means to store position coordinates of dots forming said generated binarized patterns;

a printer means to output position coordinates stored in said storage means; and

a pattern acceptance element to discrete pattern is formed by said printer means.

25. A computer executable program for making a computer system to execute a generation method for binarized patterns of a variable-density image formed of discrete dots disposed two-dimensionally, said program making said computer system execute the steps of:

providing a predetermined block;

determining a number of dots disposed in said predetermined block;

determining said dot position coordinates so that said dots contained in a rectangular block having a lateral size of Lx and a longitudinal size of Ly satisfy formula (1);

D≦

0.13N<sup>−

1.15</sup> 

 

(1)

(wherein N in formula (1) denotes a number of dots contained in said block and D is given by formula (2) in the condition that a number of dots contained in a rectangular region having a diagonal line extending from a reference coordinate (0, 0) to an arbitrary coordinate (x, y) is A (x, y);

$\begin{array}{cc}D<br><br>\left(L_x,L_y;<br><br>N\right)=\int <br><br>{\int <br><br>}_{L_x<br><br>{\mathrm{xL}}_y}<br><br>{\left[\frac{A<br><br>\left(x,y\right)}{N}-\frac{\mathrm{xy}}{L_x<br><br>L_y}\right]}^2<br><br>\frac{\mathrm{dxdy}}{L_x<br><br>L_y}& \left(2\right)\end{array}$

and S₁ given by formula (3) is equal to or less than 0.7;

$\begin{array}{cc}{S}_1<br><br>\left(r_1,r_2\right)={\int <br><br>}_{r_1}^{r_2}<br><br>d<br><br>r\left|g_1<br><br>\left(r;<br><br>r_1,r_2\right)-g_{\mathrm{av}}\right|,& \left(3\right)\end{array}$

wherein g₁ in formula (3) is a value obtained from dividing an average radius distribution function g(r) by an integral value ranging from r₁ to r₂ and g_av is a mean value of g₁ ranging from r₁ to r₂, when dots are disposed in a shape of a tetragonal lattice to satisfy a given filling factor, r₁ and r₂ are specified to an equal value and a quadruple value of a lattice constant Dr, respectively. A filling factor of dots is the value in the condition that a square of a maximum diameter of a dot is multiplied by a number of dots, then thus calculated value is divided by an area of said region);

setting said predetermined position coordinates as initial positions;

changing said dot position coordinates so that dots of which said position coordinates have been determined do not overlap with each other; and

employing a plurality of predetermined boundary conditions to adjoin said predetermined blocks to generate discrete patterns of predetermined sizes.

26. The program according to claim 25, wherein said step of changing position coordinates comprises the steps of:

calculating repulsion regarding a predetermined dot from another dot existing in the vicinity of said dot;

displacing said predetermined dot according to a magnitude of said repulsion;

calculating repulsion regarding said displaced dot; and

summing up repulsion regarding dots within a predetermined range.

27. The program according to claim 25, wherein said step of changing position coordinates employs repulsion which remains steady as against said distance between dots at a wavelength equal to or less than a principal wavelength, and which decreases according to increase of said distance between dots exceeding a predetermined value.

28. A computer readable storage medium storing a program for making a computer execute a generating method for binarized patterns of a variable-density image formed of discrete dots disposed two dimensionally, said program making said computer execute the steps of:

providing a predetermined block;

determining a number of dots disposed in said predetermined block;

determining said dot position coordinates so that said dots contained in a rectangular block having a lateral size of Lx and a longitudinal size of Ly satisfy formula (1);

D≦

0.13N<sup>−

1.15</sup> 

 

(1)

(wherein N in formula (1) denotes a number of dots contained in said block and D is given by formula (2) in the condition that a number of dots contained in a rectangular region having a diagonal line extending from a reference coordinate (0, 0) to an arbitrary coordinate (x, y) is A (x, y);

$\begin{array}{cc}D<br><br>\left(L_x,L_y;<br><br>N\right)=\int <br><br>{\int <br><br>}_{L_x<br><br>{\mathrm{xL}}_y}<br><br>{\left[\frac{A<br><br>\left(x,y\right)}{N}-\frac{\mathrm{xy}}{L_x<br><br>L_y}\right]}^2<br><br>\frac{\mathrm{dxdy}}{L_x<br><br>L_y}& \left(2\right)\end{array}$

and S₁ given by formula (3) is equal to or less than 0.7;

$\begin{array}{cc}{S}_1<br><br>\left(r_1,r_2\right)={\int <br><br>}_{r_1}^{r_2}<br><br>d<br><br>r\left|g_1<br><br>\left(r;<br><br>r_1,r_2\right)-g_{\mathrm{av}}\right|,& \left(3\right)\end{array}$

wherein g₁ in formula (3) is a value obtained from dividing an average radius distribution function g(r) by an integral value ranging from r₁ to r₂ and g_av is a mean value of g₁ ranging from r₁ to r₂, when dots are disposed in a shape of a tetragonal lattice to satisfy a given filling factor, r₁ and r₂ are specified to an equal value and a quadruple value of a lattice constant Dr, respectively. A filling factor of dots is the value defined in that a square of a maximum diameter of a dot is multiplied by a number of dots, then thus calculated value is divided by an area of said region);

setting said predetermined position coordinates as initial positions;

changing said dot position coordinates so that dots of which said position coordinates have been determined do not overlap with each other; and

employing a plurality of predetermined boundary conditions to adjoin said predetermined blocks to generate discrete patterns of predetermined sizes.

29. The program according to claim 28, wherein said step of changing said position coordinates comprises:

calculating repulsion regarding a predetermined dot from another dot existing in the vicinity of said dot;

displacing said predetermined dots according to a size of said repulsion;

calculating repulsion regarding said displaced predetermined dots; and

summing up said repulsion regarding dots within a predetermined range.

30. The program according to claim 28, wherein said step of changing position coordinates employs repulsion which remains steady as against said distance between dots at a wavelength equal to or less than a principal wavelength, and which decreases according to increase of said distance between dots exceeding a predetermined value.