Coded-aperture systems have been proposed for use in nuclear-medicine imaging. Computer simulations of orthogonal-view coded-aperture systems in conjunction with reconstruction algorithms have produced promising tomographic images. Furthermore, it is anticipated that reconstructions can be improved by optimizing the coded aperture. A strategy is given for the design of coded apertures with respect to a given class of objects that are to be imaged. It is assumed that the first and second order statistics of the object class are known. The Karhunen-Loeve eigenvectors and eigenvalues are used to define two subspaces within the space of all possile objects. 'Interest Space' is the subspace of all objects that one is interested in measuring. 'Indifference Space' is the subspace orthogonal to interest space and contains only objects in which we have no interest. An alternative characterisation of object space utilizes the singular value decomposition of the system to form orthogonal subspaces called 'measurement space' and 'null space'. Measurement space contains objects measured well by the system while null space contains objects about which the system will record little or no information at all. The author describes the concept of 'alignment' in which the aperture parameters are adjusted until the system is tuned to measure the given object class well.