A system for forming an image (110) of a substantially translucent specimen (102) has an illuminator (108) configured to variably illuminate the specimen from a plurality of angles of illumination such that (a) when each angle (495) at a given point on the specimen is mapped to a point (445) on a plane (420) perpendicular to an
optical axis (490), the points on the plane have an increasing density (e.g. FIGS. 4, 11C, 11E, 12C, 12E, 13A, 14A, 14C, 14E, 15A, 15C, 15E) towards an axial position on the plane; or (b) the illumination angles are arranged with a substantially
regular pattern in a polar coordinate
system (FIG. 13A,13B) defined by a
radial coordinate that depends on the magnitude of the distance from an
optical axis and an angular coordinate corresponding to the orientation of the angle relative to the
optical axis. A
detector is configured to acquire a plurality of variably illuminated, relatively lower-resolution intensity images (104) of the specimen based on light emitted from the illuminator according to variable illumination and filtered by an optical element (109). A processor is arranged to computationally reconstruct a relatively higher-resolution image of the specimen by iteratively updating overlapping regions (1005) of the relatively higher-resolution image in Fourier space (FIG. 10B) with the variably-illuminated, lower-resolution intensity images.