Touch display system with reduced moiré patterns

1. A display device, comprising:

an array of display pixels comprising display pixel apertures that are periodic along two orthogonal directions, x and y, at spatial frequencies f x and f y , respectively; and

a first array of electrodes overlaid on the array of display pixel apertures, the first array of electrodes comprised of a metal mesh having conductors with a width that is less than 3% of a pixel pitch of the array of display pixels, the metal mesh having openings formed between the conductors that are periodic along a first direction u 1 at an angle θ u1 relative to x, and along a second direction v 1 at an angle θ v1 relative to y, and at spatial frequencies f u1 and f v1 , respectively, and wherein the parameter set {θ u1 , f x , f u1 } satisfies the following criteria:

|tan θ u1 | is within the range of 0.26 to 0.28, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /3−1/6), where m 1 is a positive integer; or

|tan θ u1 | is within the range of 0.38 to 0.48, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /3+1/6); or

|tan θ u1 | is within the range of 0.52 to 0.56, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /2−1/4); or

|tan θ u1 | is within the range of 0.59 to 0.62, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /3−1/4); or

|tan θ u1 | is within the range of 0.7 to 0.8, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /3−1/12).

2. The display device of claim 1 , wherein the parameter set {θ v1 , f y , f v1 } satisfies the following criteria:

|tan θ v1 | is within the range of 0.26 to 0.28, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /3−1/6), where n 1 is a positive integer; or

|tan θ v1 | is within the range of 0.38 to 0.48, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /3+1/6); or

|tan θ v1 | is within the range of 0.52 to 0.56, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /2−1/4); or

|tan θ v1 | is within the range of 0.59 to 0.62, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /3−1/4); or

|tan θ v1 | is within the range of 0.7 to 0.8, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /3−1/12).

3. The display device of claim 2 , further comprising:

a second array of electrodes overlaid on the first array of electrodes, the second array of electrodes comprised of a metal mesh having openings that are periodic along a third direction u 2 at an angle θ u2 relative to x, and along a fourth direction v 2 at an angle θ v2 relative to y, and at spatial frequencies f u2 and f v2 , respectively, and wherein the parameter set {θ 2 , f x , f u2 } satisfies the following criteria:

|tan θ u2 | is within the range of 0.26 to 0.28, and |f x /(f u2 *cos θ u2 )| is within 1/12 of (m 2 /3−1/6), where m 2 is a positive integer; or

|tan θ u2 )| is within the range of 0.38 to 0.48, and |f x /(f u2 *cos θ u2 )| is within 1/12 of (m 2 /3+1/6); or

|tan θ u2 )| is within the range of 0.52 to 0.56, and |f x /(f 2 *cos θ u2 )| is within 1/12 of (m 2 /2−1/4); or

|tan θ u2 | is within the range of 0.59 to 0.62, and |f x /(f u2 *cos θ u2 )| is within 1/12 of (m 2 /3−1/4); or

|tan θ u2 | is within the range of 0.7 to 0.8, and |f x /(f u2 *cos θ u2 )| is within 1/12 of (m 2 /3−1/12); and

wherein the parameter set {θ v2 , f y , f v2 } satisfies the following criteria:

|tan θ v2 | is within the range of 0.26 to 0.28, and |f y /(f 2 *cos θ v2 )| is within 1/12 of (n 2 /3−1/6), where n 2 is a positive integer; or

|tan θ v2 | is within the range of 0.38 to 0.48, and |f y /(f 2 *cos θ v2 )| is within 1/12 of (n 2 /3+1/6); or

|tan θ v2 | is within the range of 0.52 to 0.56, and |f y /(f 2 *cos θ v2 )| is within 1/12 of (n 2 /2−1/4); or

|tan θ v2 | is within the range of 0.59 to 0.62, and |f y /(f v2 *cos θ v2 )| is within 1/12 of (n 2 /3−1/4); or

|tan θ v2 | is within the range of 0.7 to 0.8, and |f y /(f v2 *cos θ v2 )| is within 1/12 of (n 2 /3−1/12).

4. The display device of claim 3 , wherein n 1 is not equal to n 2 , and further wherein m 1 is not equal to m 2 .

5. The display device of claim 1 , wherein the metal mesh has a square unit cell.

6. The display device of claim 1 , wherein the electrodes comprise capacitive touch sensor electrodes.

7. The display device of claim 1 , wherein each display pixel comprises three primary-colored subpixels.

8. The display device of claim 7 , wherein f x =f y =f, and wherein x is perpendicular to y.

9. The display device of claim 8 , wherein:

each of |tan θ u1 | and |tan θ v1 | lies within one of the following ranges: 0.26-0.28, 0.38-0.48, 0.52-0.56, 0.59-0.62, 0.7-0.8;

[f/(f u1 *cos θ u1 )] lies within one of the following ranges, where m 1 is a positive integer:

a. (m 1 /3−1/4)-(m 1 /3−1/12), if |tan θ u1 | lies within 0.26-0.28;

b. (m 1 /3+1/2)-(m 1 /3+1/4), if |tan θ u1 | lies within 0.38-0.48;

c. (m 1 /2−1/3)-(m 1 /2−1/6), if |tan θ u1 | lies within 0.52-0.56;

d. (m 1 /3−1/3)-(m 1 /3−1/6), if |tan θ u1 | lies within 0.59-0.62;

e. (m 1 /3−1/6)-(m 1 /3), if |tan 74 u1 | lies within 0.7-0.8; and

[f/(f v1 *cos θ v1 )] lies within one of the following ranges, where n 1 is a positive integer:

f. (n 1 /3−1/4)-(n 1 /3−1/12), if |tan θ v1 | lies within 0.26-0.28;

g. (n 1 /3+1/12)-(n 1 /3+1/4), if |tan θ v1 | lies within 0.38-0.48;

h. (n 1 /2−1/3)-(n 1 /2−1/6), if |tan θ v1 | lies within 0.52-0.56;

i. (n 1 /3−1/3)-(n 1 /3−1/6), if |tan θ v1 | lies within 0.59-0.62; and

j. (n 1 /3−1/6)-(n 1 /3), if |tan θ v1 | lies within 0.7-0.8.

10. A method of manufacturing a touch-sensitive display device, comprising:

overlaying a first array of electrodes on an array of display pixel apertures, the array of display pixels comprising display pixel apertures that are periodic along two orthogonal directions, x and y, at spatial frequencies f x and f y , respectively, the first array of electrodes comprised of a metal mesh having conductors with a width that is less than 3% of a pixel pitch of the array of display pixels, the metal mesh having openings formed between the conductors that are periodic along a first direction u 1 at an angle θ u1 relative to x, and along a second direction v 1 at an angle θ v1 relative to y, and at spatial frequencies f u1 and f v1 , respectively, such that the parameter set {θ u1 , f x , f u1 } satisfies the following criteria:

|tan θ u1 | is within the range of 0.26 to 0.28, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /3−1/6), where m 1 is a positive integer; or

|tan θ u1 | is within the range of 0.38 to 0.48, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /3+1/6); or

|tan θ u1 | is within the range of 0.52 to 0.56, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /2−1/4); or

|tan θ u1 | is within the range of 0.59 to 0.62, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /3−1/4); or

|tan θ u1 | is within the range of 0.7 to 0.8, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /3−1/12).

11. The method of claim 10 , wherein the first array of electrodes is overlaid on the array of display pixel apertures such that the parameter set {θ v1 , f y , f v1 } satisfies the following criteria:

|tan θ v1 | is within the range of 0.26 to 0.28, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /3−1/6), where n 1 is a positive integer; or

|tan θ v1 | is within the range of 0.38 to 0.48, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /3+1/6); or

|tan θ v1 | is within the range of 0.52 to 0.56, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /2−1/4); or

|tan θ v1 | is within the range of 0.59 to 0.62, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /3−1/4); or

|tan θ v1 | is within the range of 0.7 to 0.8, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /3−1/12).

12. The method of claim 11 , further comprising:

overlaying a second array of electrodes on the first array of electrodes, the second array of electrodes comprised of a metal mesh having openings that are periodic along a third direction u 2 at an angle θ u2 relative to x, and along a fourth direction v 2 at an angle θ v2 relative to y, and at spatial frequencies f u2 and f v2 , respectively, such that the parameter set {θ u2 , f x , f u2 } satisfies the following criteria:

|tan θ u2 | is within the range of 0.26 to 0.28, and |f x /(f u2 *cos θ u2 )| is within 1/12 of (m 2 /3−1/6), where m 2 is a positive integer; or

|tan θ u2 | is within the range of 0.38 to 0.48, and |f x /(f 2 *cos θ u2 )| is within 1/12 of (m 2 /3+1/6); or

|tan θ u2 | is within the range of 0.52 to 0.56, and |f x /(f u2 *cos θ u2 )| is within 1/12 of (m 2 /2−1/4); or

|tan θ u2 | is within the range of 0.59 to 0.62, and |f x /(f u2 *cos θ u2 )| is within 1/12 of (m 2 /3−1/4); or

|tan θ u2 | is within the range of 0.7 to 0.8, and |f x /(f 2 *cos θ u2 )| is within 1/12 of (m 2 /3−1/12); and

such that the parameter set {θ v2 , f y , f v2 } satisfies the following criteria:

|tan θ v2 | is within the range of 0.26 to 0.28, and |f y /(f v2 *cos θ v2 )| is within 1/12 of (n 2 /3−1/6), where n 2 is a positive integer; or

|tan θ v2 | is within the range of 0.38 to 0.48, and |f y /(f v2 *cos θ v2 )| is within 1/12 of (n 2 /3+1/6); or

|tan θ v2 | is within the range of 0.52 to 0.56, and |f y /(f v2 *cos θ v2 )| is within 1/12 of (n 2 /2−1/4); or

|tan θ v2 | is within the range of 0.59 to 0.62, and |f y /(f v2 *cos θ v2 )| is within 1/12 of (n 2 /3−1/4); or

|tan θ v2 | is within the range of 0.7 to 0.8, and |f y /(f v2 *cos θ v2 )| is within 1/12 of (n 2 /3−1/12).

13. The method of claim 12 , wherein n 1 is not equal to n 2 , and further wherein m 1 is not equal to m 2 .

14. The method of claim 10 , wherein the metal mesh has a square unit cell.

15. The method of claim 10 , wherein the electrodes comprise capacitive touch sensor electrodes.

16. The method of claim 10 , wherein each display pixel comprises three primary-colored subpixels.

17. The method of claim 16 , wherein f x =f y =f.

18. The method of claim 17 , wherein:

each of |tan θ u1 | and |tan θ v1 | lies within one of the following ranges: 0.26-0.28, 0.38-0.48, 0.52-0.56, 0.59-0.62, 0.7-0.8;

[f/(f u1 *cos θ u1 )] lies within one of the following ranges, where m 1 is a positive integer:

a. (m 1 /3−1/4)-(m 1 /3−1/12), if |tan θ u1 | lies within 0.26-0.28;

b. (m 1 /3+1/12)-(m 1 /3+1/4), if |tan θ u1 | lies within 0.38-0.48;

c. (m 1 /2−1/3)-(m 1 /2−1/6), if |tan θ u1 | lies within 0.52-0.56;

d. (m 1 /3−1/3)-(m 1 /3−1/6), if |tan θ u1 | lies within 0.59-0.62;

e. (m 1 /3−1/6)-(m 1 /3), if |tan θ u1 | lies within 0.7-0.8; and

[f/(f v1 *cos θ v1 )] lies within one of the following ranges, where n 1 is a positive integer:

f. (n 1 /3−1/4)-(n 1 /3−1/12), if |tan θ v1 | lies within 0.26-0.28;

g. (n 1 /3+1/12)-(n 1 /3+1/4), if |tan θ v1 | lies within 0.38-0.48;

h. (n 1 /2−1/3)-(n 1 /2−1/6), if |tan θ v1 | lies within 0.52-0.56;

i. (n 1 /3−1/3)-(n 1 /3−1/6), if |tan θ v1 | lies within 0.59-0.62; and

j. (n1/3−1/6)-(n 1 /3), if |tan θ v1 | lies within 0.7-0.8.

19. A display device having a capacitive touch-sensitive sensor, the display device comprising:

an array of display pixels comprising display pixel apertures that are periodic along two orthogonal directions, x and y, at spatial frequencies f x and f y , respectively;

a first array of electrodes overlaid on the array of display pixel apertures, the first array of electrodes comprised of a metal mesh having conductors with a width that is less than 3% of a pixel pitch of the array of display pixels, the metal mesh having openings formed between the conductors that are periodic along a first direction u 1 at an angle θ u1 relative to x, and along a second direction v 1 at an angle θ v1 relative to y, and at spatial frequencies f u1 and f v1 , respectively, and wherein the parameter set {θ u1 , f x , f u1 } satisfies the following criteria:

|tan θ u1 | is within the range of 0.26 to 0.28, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /3−1/6), where m 1 is a positive integer; or

|tan θ u1 | is within the range of 0.38 to 0.48, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /3+1/6); or

|tan θ u1 | is within the range of 0.52 to 0.56, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /2−1/4); or

|tan θ u1 | is within the range of 0.59 to 0.62, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /3−1/4); or

|tan θ u1 | is within the range of 0.7 to 0.8, and |f x /(f u1 *cos θ u1 )| is within 1/12 of (m 1 /3−1/12); and

wherein the parameter set {θ v1 , f y , f v1 } satisfies the following criteria:

|tan θ v1 | is within the range of 0.26 to 0.28, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /3−1/6), where n 1 is a positive integer; or

|tan θ v1 | is within the range of 0.38 to 0.48, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /3+1/6); or

|tan θ v1 | is within the range of 0.52 to 0.56, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /2−1/4); or

|tan θ v1 | is within the range of 0.59 to 0.62, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /3−1/4); or

|tan θ v1 | is within the range of 0.7 to 0.8, and |f y /(f v1 *cos θ v1 )| is within 1/12 of (n 1 /3−1/12); and

a second array of electrodes overlaid on the first array of electrodes, the second array of electrodes comprised of a metal mesh having openings that are periodic along a third direction u 2 at an angle θ u2 relative to x, and along a fourth direction v v2 at an angle θ v2 relative to y, and at spatial frequencies f u2 and f v2 , respectively, and wherein the parameter set {θ u2 , f x , f 2 } satisfies the following criteria:

|tan θ u2 | is within the range of 0.26 to 0.28, and |f x /(f u2 *cos θ u2 )| is within 1/12 of (m 2 /3−1/6), where m 2 is a positive integer; or

|tan θ u2 | is within the range of 0.38 to 0.48, and |f x /(f u2 *cos θ u2 )| is within 1/12 of (m 2 /3+1/6); or

|tan θ u2 | is within the range of 0.52 to 0.56, and |f x /(f u2 *cos θ u2 )| is within 1/12 of (m 2 /2−1/4); or

|tan θ u2 | is within the range of 0.59 to 0.62, and |f x /(f u2 *cos θ u2 )| is within 1/12 of (m 2 /3−1/4); or

|tan θ u2 | is within the range of 0.7 to 0.8, and |f x /(f u2 *cos θ u2 )| is within 1/12 of (m 2 /3−1/12); and

wherein the parameter set {θ v2 , f y , f v2 } satisfies the following criteria:

|tan θ v2 | is within the range of 0.26 to 0.28, and |f y 1/12 of (n 2 /3−1/6), where n 2 is a positive integer; or

|tan θ v2 | is within the range of 0.38 to 0.48, and |f y /(f 2 *cos θ v2 )| is within 1/12 of (n 2 /3+1/6); or

|tan θ v2 | is within the range of 0.52 to 0.56, and |f y /(f v2 *cos θ v2 )| is within 1/12 of (n 2 /2−1/4); or

|tan θ v2 | is within the range of 0.59 to 0.62, and |f y /(f v2 *cos θ v2 )| is within 1/12 of (n 2 /3−1/4); or

|tan θ v2 | is within the range of 0.7 to 0.8, and |f y /(f v2 *cos θ v2 )| is within 1/12 of (n 2 /3−1/12).

20. The display device of claim 19 , wherein each display pixel comprises three primary-colored subpixels;

f x =f y =f;

each of |tan θ u1 | and |tan θ v1 | lies within one of the following ranges: 0.26-0.28, 0.38-0.48, 0.52-0.56, 0.59-0.62, 0.7-0.8;

[f/(f u1 *cos θ u1 )] lies within one of the following ranges, where n is a positive integer:

a. (n/3−1/4)-(n/3−1/12), if ltan within 0.26-0.28;

b. (n/3+1/12)-(n/3+1/4), if |tan θ u1 | lies within 0.38-0.48;

c. (n/2−1/3)-(n/2−1/6), if |tan θ u1 | lies within 0.52-0.56;

d. (n/3−1/3)-(n/3−1/6), if |tan θ u1 | lies within 0.59-0.62;

e. (n/3−1/6)-(n/3), if |tan θ u1 | lies within 0.7-0.8; and

[f/(f v1 *cos θ v1 )] lies within one of the following ranges, where n is a positive integer:

f. (n/3−1/4)-(n/3−1/12), if |tan θ v1 | lies within 0.26-0.28;

g. (n/3+1/12)-(n/3+1/4), if |tan θ v1 | lies within 0.38-0.48;

h. (n/2−1/3)-(n/2−1/6), if |tan θ v1 | lies within 0.52-0.56;

i. (n/3−1/3)-(n/3−1/6), if |tan θ v1 | lies within 0.59-0.62;

j. (n/3−1/6)-(n/3), if |tan θ v1 | lies within 0.7-0.8; and

each of |tan θ u2 | and |tan θ v2 | lies within one of the following ranges: 0.26-0.28, 0.38-0.48, 0.52-0.56, 0.59-0.62, 0.7-0.8;

[f/(f u2 *cos θ u2 )] lies within one of the following ranges, where n is a positive integer:

k. (n/3−1/4)-(n/3−1/12), if |tan θ u2 | lies within 0.26-0.28;

l. (n/3+1/12)-(n/3+1/4), if |tan θ u2 | lies within 0.38-0.48;

m. (n/2−1/3)-(n/2−1/6), if |tan θ u2 | lies within 0.52-0.56;

n. (n/3−1/3)-(n/3−1/6), if |tan θ u2 | lies within 0.59-0.62;

o. (n/3−1/6)-(n/3), if |tan θ u2 | lies within 0.7-0.8; and

[f/(f v2 *cos θ v2 )] lies within one of the following ranges, where n is a positive integer:

p. (n/3−1/4)-(n/3−1/12), if |tan θ v2 | lies within 0.26-0.28;

q. (n/3+1/12)-(n/3+1/4), if |tan θ v2 | lies within 0.38-0.48;

r. (n/2−1/3)-(n/2−1/6), if |tan θ v2 | lies within 0.52-0.56;

s. (n/3−1/3)-(n/3−1/6), if |tan θ v2 | lies within 0.59-0.62; and

t. (n/3−1/6)-(n/3), if |tan θ v2 | lies within 0.7-0.8.