Abstract: 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.