Performance of Apodized Apertures under Partially Coherent Illumination

The performance characteristics of optical systems having apodized apertures and employing partially coherent illumination have been investigated. The pupil function has been taken to be of the form f(x y) = 1 m g (x 2 + y 2), where g is the amplitude shading parameter of the filter. The generalized cross-transfer functions for the system have been calculated for different values of the coherence parameter which is the ratio of the numerical aperture of the condenser to that of the objective. The modulations of periodic targets commonly employed, namely, the sine wave, square wave and triangular wave objects, have also been investigated. It has been shown that for the partially coherent and the incoherent illuminations ( S 1) the apodization improves the low frequency response at a cost of the high frequency response of the system. However, for coherent and near coherent illuminations (