Convex protrusions in TIR-based image displays
Total internal reflection (TIR) based image displays comprise at least one high refractive index (>˜1.5) convex protrusion interfaced with a low refractive index (<˜1.5) medium. Total internal reflection of light is frustrated at this interface by movement of electrophoretically mobile particles into and out of the evanescent wave region. The size, shape and arrangement of the convex protrusions, typically in the shape of lenses, affects TIR at the interface and ultimately the brightness of the display. The brightness is a critical aspect of reflective displays. The degree of brightness determines what applications the displays may be used for and their ultimate acceptance by consumers. For example, high brightness displays allow for the use of color filter arrays for applications requiring color. The shape of the convex protrusions may be described by a polar coordinate system.
1. A totally internally reflective (TIR) image display, comprising:
a front assembly having a light guide, a front sheet, a front electrode and a plurality of convex protrusions, each of the plurality of convex protrusions having a respective dark pupil area, the front assembly forming a side edge;
a light source to emit light through an edge of the light guide;
a back assembly forming a gap with the front assembly, the back assembly having a back plane and a rear electrode; and
a medium disposed in the gap, the medium including a plurality of electrophoretic particles movable to one of the front electrode or the rear electrode responsive to an applied bias;
wherein at least one of the plurality of convex protrusions is configured to minimize the dark pupil area,
wherein each convex protrusion of the plurality of convex protrusions includes a first side and a second side, the first side being in contact with the front sheet and the second side comprises a surface profile defined by the equation: Y(x)=0.123*cosh(3.1*x)−1.373, in which x represents a width of a base of the convex protrusion,
wherein the each convex protrusion of the plurality of convex protrusions is configured to totally internally reflect a ray of light entering the each convex protrusion from the first side,
wherein a refractive index of the each convex protrusion is greater than 1.4.
2. The display of claim 1 , wherein at least one convex protrusion is defined by a height (h) and a width (w) and wherein the ratio of the height to the width is in the range of about 0.3-0.7.
3. The display of claim 1 , wherein at least one convex protrusion comprises a surface profile defined by the equation: Y(x)=Y 0 +a 2 x 2 +a 4 x 4 +a 6 x 6 +a 8 x 8 ; in which Y 0 , a 1 , a 4 , a 6 and a 8 are constants.
4. The display of claim 1 , wherein at least one convex protrusion comprises a surface profile defined by the equation
Y
(
x
)
=
C
x
2
1
+
1
-
(
1
+
k
)
C
2
x
2
+
a
2
x
2
+
a
4
x
4
+
a
6
x
6
+
Y
0
in which a 1 , k, C, a 4 , a 6 and as are constants.
5. A totally internally reflective (TIR) image display, comprising:
a front assembly having a front sheet, a front electrode and a dielectric layer, the front electrode interposed between the front sheet and the dielectric layer, the front sheet further including a plurality of convex protrusions, each of the plurality of convex protrusions having a respective dark pupil area; and
a back assembly forming a gap with the front assembly, the back assembly having a back plane and a rear electrode, the rear electrode positioned opposite the dielectric layer;
wherein at least one of the plurality of convex protrusions is configured to minimize the dark pupil area,
wherein each convex protrusion of the plurality of convex protrusions includes a first side and a second side, the first side being in contact with the front sheet and the second side comprises a surface profile defined by the equation: Y(x)=0.123*cosh(3.1*x)−1.373, in which x represents a width of a base of the convex protrusion,
wherein the each convex protrusion of the plurality of convex protrusions is configured to totally internally reflect a ray of light entering the each convex protrusion from the first side,
wherein a refractive index of the each convex protrusion is greater than 1.4.
6. The display of claim 5 , further comprising a low refractive index medium having a plurality of electrophoretically mobile particles is disposed in the gap.
7. The display of claim 5 , wherein the plurality of convex protrusions are positioned one of symmetrically or asymmetrically with respect to one another.
8. The display of claim 5 , wherein the plurality of convex protrusions overlap.
9. The display of claim 5 , wherein the plurality of convex protrusions have substantially the same shape.
10. The display of claim 5 , wherein the plurality of convex protrusions have different shapes.
11. The display of claim 5 , wherein at least one convex protrusion is defined by a height (h) and a width (w) and wherein the ratio of the height to the width is in the range of about 0.3-0.7.
12. The display of claim 5 , wherein at least one convex protrusion comprises a surface profile defined by the equation: Y(x)=Y 0 +a 2 x 2 +a 4 x 4 +a 6 x 6 +a 8 x 8 ; in which Y 0 , a 1 , a 4 , a 6 and ag are constants.
13. The display of claim 5 , wherein at least one convex protrusion comprises a surface profile defined by the equation
Y
(
x
)
=
C
x
2
1
+
1
-
(
1
+
k
)
C
2
x
2
+
a
2
x
2
+
a
4
x
4
+
a
6
x
6
+
Y
0
in which a 1 , k, C, a 4 , a 6 and as are constants.
14. A method to form a totally internally reflective (TIR) image display, the method comprising:
forming a front assembly having a light guide, a front sheet, a front electrode and a plurality of convex protrusions, each of the plurality of convex protrusions having a respective dark pupil area, the front assembly forming a side edge;
placing a light source to emit light through an edge of the light guide;
placing a back assembly across the front assembly to form a gap with the front assembly, the back assembly having a back plane and a rear electrode; and
disposing a medium in the gap, the medium including a plurality of electrophoretic particles movable to one of the front electrode or the rear electrode responsive to an applied bias;
wherein at least one of the plurality of convex protrusions is shaped to minimize the dark pupil area,
wherein each convex protrusion of the plurality of convex protrusions includes a first side and a second side, the first side being in contact with the front sheet and the second side comprises a surface profile defined by the equation: Y(x)=0.123*cosh (3.1*x)−1.373, in which x represents a width of a base of the convex protrusion,
wherein the each convex protrusion of the plurality of convex protrusions is configured to totally internally reflect a ray of light entering the each convex protrusion from the first side,
wherein a refractive index of the each convex protrusion is greater than 1.4.
15. The method of claim 14 , wherein the plurality of convex protrusions overlap.
16. The method of claim 14 , wherein a pair of adjacent protrusions are separated by a spacing(s) and wherein the distance between the pair of adjacent protrusions (p) such that s is a fraction of p.
17. The method of claim 14 , wherein at least one convex protrusion is defined by a height (h) and a width (w) and wherein the ratio of the height to the width is in the range of about 0.3-0.7.
18. The method of claim 14 , wherein at least one convex protrusion comprises a surface profile defined by the equation: Y(x)=0.123*cosh (3.1*x)−1.373, in which x represents a width of a base of the convex protrusion.
19. The method of claim 14 , wherein at least one convex protrusion comprises a surface profile defined by the equation: Y(x)=Y 0 +a 2 x 2 +a 4 x 4 +a 6 x 6 +a 8 x 8 ; in which Y 0 , a 1 , a 4 , a 6 and ag are constants.
20. The method of claim 14 , wherein at least one convex protrusion comprises a surface profile defined by the equation
Y
(
x
)
=
C
x
2
1
+
1
-
(
1
+
k
)
C
2
x
2
+
a
2
x
2
+
a
4
x
4
+
a
6
x
6
+
Y
0
in which a 1 , k, C, a 4 , a 6 and as are constants.