Diffractive (Lensless) Imaging

Diffractive (or lensless) imaging refers to the use of theoretical methods and computer algorithms to solve the phase problem for scattering by a nonperiodic object. The name coherent X-ray diffractive imaging (CXDI) is used in the X-ray community, which we could generalize to CDI. Additional information about the object, such as the sign of the scattering potential and the approximate boundary of the object, may be combined with the measured scattered intensity to solve for the phases of the scattered amplitudes. In this way, under conditions of single scattering (and other approximations that often apply in optics and in electron, X-ray, and neutron diffraction) it may be possible to reconstruct a real-space image of an object by Fourier transform of the complex scattering distribution, or Fraunhoffer diffraction pattern. (Applications to Fresnel near-field imaging are also possible. In this geometry, resolution is, however, limited by detector pixel size, since the magnification is unity if lenses are not used.) In this review we will not discuss the recently developed and powerful transport of intensity method, which is also applicable to the near field (Paganin and Nugent, 1998). By avoiding the need for a lens, the aberrations and resolution limits introduced by lenses are thus avoided. Within the past decade this process has been demonstrated experimentally for neutron, X-ray, and electron scattering, so that the field has reached an exciting point. The electron work has produced atomic-resolution images, while experiments with soft X-rays have finally produced three-dimensional (tomographic) reconstructions. It now offers the real possibility of diffraction- limited imaging with any radiation for which lenses do not exist. Since each radiation interacts differently with matter, the method can be expected to provide us with new information on matter in fields as diverse as biology, materials science, and astronomy.