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Chapter 8:
Microprismatic Arrays

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 Kx1, Ky1, Kz1 is incident and refracted at planar surface 1. The refraction matrix R1 is derived from Eq. (1.75), where the surface normals are kx1 = 0, ky1 = 0, and kz1 = -1, referenced to the coordinate system shown, where


The direction cosines of the surface normals for surface 2 are kx2 = 0, ky2 = cos[(180 deg − φ) = 2], kz2 = -cos[(180 deg − φ) = 2], and for surface 3 are kx3 = 0, ky3 = -cos[(180 deg − φ) = 2], kz3 = -cos[(180 deg − φ) = 2].

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