Diffraction enhanced imaging (DEI) is an analyzer-based X-ray phase-contrast imaging method that measures the absorption and refractive properties of an object. A well-known limitation of DEI is that it does not account for ultra-small-angle X-ray scattering (USAXS), which is produced commonly by biological tissue. In this work, an extended DEI (E-DEI) imaging method is described that attempts to circumvent this limitation. The E-DEI method concurrently reconstructs three images that depict an object's projected absorption, refraction, and USAXS properties, and can be viewed as an implementation of the multiple-image radiography (MIR) paradigm. Planar and computed tomography (CT) implementations of E-DEI and an existing MIR method are compared by use of computer-simulation studies that employ statistical models to describe USAXS effects.