A microprismatic array is a series of prismatic elements that are positioned next to each other in a 2D pattern or, in some cases, a 3D pattern. These prismatic elements can be identical or vary in geometry and have smaller dimensions than conventional single prisms. They are often replicated in optical plastic and can be a rigid sheet or a flexible film, with the sheet area much greater than the thickness. These prismatic sheets or films can subsequently be shaped into other forms, such as a rectangle or cylinder, for specialty applications.

8.1 Roof Prism Linear Array

The linear array in Fig. 8.1 consists of a flat sheet of repeating isosceles roof prisms, having a vertex angle φ. The prismatic array has a refractive index n, surrounded by air with refractive index n₀. For an individual prism, an incident light-ray vector with direction cosines K_x1, K_y1, K_z1 is incident and refracted at planar surface 1. The refraction matrix R₁ is derived from Eq. (1.75), where the surface normals are k_x1 = 0, k_y1 = 0, and k_z1 = -1, referenced to the coordinate system shown, where

(8.1)

The direction cosines of the surface normals for surface 2 are k_x2 = 0, k_y2 = cos[(180 deg − φ) = 2], k_z2 = -cos[(180 deg − φ) = 2], and for surface 3 are k_x3 = 0, k_y3 = -cos[(180 deg − φ) = 2], k_z3 = -cos[(180 deg − φ) = 2].