Convex protrusions in TIR-based image displays

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.

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.