Reduction in Edge-Ringing in Aberrated Images of Coherent Edge Objects by Multishaded Aperture

The images of a straight edge in coherent illumination produced by an optical system with circular aperture and apodized with multiple filters have been studied. The most common problem encountered in the coherent-imaging techniques is the edge-ringing. To minimize the edge-ringing, multishaded aperture method has been proposed. Image intensity distribution curves are drawn and edge-ringing values are evaluated. The results are compared to that of the airy case with the use of single, double and triple filtering. 1. Introduction In order to improve the results of an optical system, there are two methods, namely, modification of the optical system and postdetection processing. The former involves choosing an optimum optical system itself and the latter involves operations on the system’s output. In many situations the first one is followed by changing the pupil function with suitable apodization. Apodization is the technique that modifies the imaging properties of an optical system such that the system impulse does not show ringing by manipulating its entrance pupil [1–3]. Parthasaradhi et al. [4] have investigated the effect of variable apodization on the diffracted field characteristics of aperture with Straubel class of pupil functions and Triangular filters. In their study, they have divided the pupil into different number of concentric annular zones and used the same set of pupil functions having different values of the apodization parameter, thus giving rise to nonuniform transmission of different zones. Ramanathan et al. [5] have investigated the coherent images of straight edges employing variable apodisation with Kaiser filters. Rao et al. [6] have studied the coherent edge imaging of straight edge objects with Straubel apodization filters. Gupta and Singh [7] have studied the frequency response of an apodized system by dividing the aperture into several rings of different areas and also investigated the performance of an optical system having linear polarization masks at different zones on the aperture with a particular reference to the two-point resolution of points having nearly equal brightness and the optical transfer function. In the previous paper we proposed the technique of “variable apodization” which involves the shading of circular aperture with two or more filters over different zones of the aperture. The present work introduces the technique “multishaded aperture.” This involves the shading of entire aperture with two or more filters simultaneously as shown in Figure 1. Figure 1: Aperture shaded with the three filters. 2. Theory