Combined effects of amplitude and phase variations on the irradiance in the image of a periodic complex object, which has amplitude and phase distributions, have been investigated for an optical system with partially coherent object illumination. A general expression to obtain the illuminance in the image and the image contrast of such an object is derived by use of the concept of the effective source specifying the coherence condition. The irradiance in the image for the diffraction-limited aberration-free optical system illuminated with bounded effective sources that have uniform and nonuniform radiance, and also with annular illumination, have been calculated. Numerical calculations have been made to obtain the image, in which harmonics up to the thirteenth order are taken into account. One of the results is that abrupt amplitude and phase variations are extremely influential for the appearance of the image of a periodic, low-contrast, complex object for any mode of illumination. On the other hand, less abrupt changes of the amplitude and phase in a complex object produce less variation of the appearance and contrast of the image for any illumination mode except annular illumination. Images of pure amplitude and phase objects have also been obtained by use of the general treatment, and their characteristics are evaluated. It is suggested that a technique to manipulate the radiance distribution in the effective source is valuable in improving the fidelity of the image of a periodic complex object formed by an optical system under partially coherent illumination.
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