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Image formation with partially coherent radiation is evaluated with the Hopkins formula and then applied to x-ray microscopy. Image characteristics expected from instruments with circular and annular pupils in partially coherent conditions are considered for two-point objects and a knife-edge object. The theoretically expected values for image characteristics that are easy accessible by an experiment, such as the width of a knife edge, are given for various x-ray microscopes.

The conceptual design of the Gran Telescopio Canarias (GTC) has been completed. One of the challenges facing the GTC Project is to obtain excellent image quality using a segmented primary mirror. The segmentation will introduce a physical effect that contributes to significant degradation of image quality.The image quality requirement imposes the use of an active optical system to correct figure instabilities of the optical surfaces and part of the unavoidable fabrication figure errors. The active correction includes the capability of 5-axis motion of the secondary mirror, 3-axis motion of each primary mirror segment, and 6 active degrees of freedom to deform each segment. A mixed strategy of closed-and open-loop control of the active correction will be implemented. This paper discusses the expected wavefront errors of the GTC, how they are corrected by active optics, and the expected image quality performance in FWHM, 080 and Central Intensity ratio.

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