Evaluation of the Field on a Uniform Array of Knife Edges Using Edge Reflection

Physical optics and a self-consistency argument are used to derive an approximate simple expression for the wave field for plane-wave incidence on a uniform infinite array of knife edges. An array of knife edges is regarded both as a reflecting surface and as a combined reflecting-surface and knife-edge diffraction problem. The reflection coefficient and field are obtained by requiring the two points of view to yield the same result. When one knife edge is used in the diffraction part of the calculation, the field can be expressed as a simple function of the angle of incidence involving the Fresnel integral. Field amplitudes obtained from this function differ by at most 14% from those obtained using an infinite series. Agreement can be improved further by using more than one knife edge in the diffraction part of the calculation, requiring a numerical evaluation.