9.1 Basic Refractive Fresnel Lens Design
The refractive Fresnel lens consists of a series of adjacent microprisms designed to provide a varying deviation angle over the lens area. These angles are programmed to focus or collimate incident light. The most common Fresnel lens consists of a series of concentric grooves replicated in optical plastic, with grooves on one side and a planar surface on the other, and having positive power. It is often referred to as a positive aspheric Fresnel lens. Figure 9.1 shows how a continuous aspheric lens can be collapsed to a Fresnel lens surface, eliminating much of the bulk material. The profile of the continuous aspheric surface can be described by the standard equation of an aspheric surface, axially symmetric about the z axis:
where z and x are the coordinates of the surface, c is the vertex curvature, k is the conic constant, and a1, a2, a3, and a4 are the aspheric coefficients.
The basic geometry for ray tracing through a positive aspheric Fresnel lens is shown in Fig. 9.2(a), and the refractive geometry at a single echelon is shown in Fig. 9.2(b).1 Here, θ1 and θ2 are the incident and exit-ray angles, θ2′ is the angle of incidence at the exit surface, t is the lens thickness, and n is the refractive index of the lens material. From this geometry and the application of Snell's law, the groove angle can be calculated from the equation