ABSTRACT
Coherent X-ray diffractive imaging (CXDI) is a relatively new imaging method that can produce an image of a sample without using optics between the sample and detector (see Fig. 12.1). This differs from conventional microscopy schemes that use objective lenses to produce an image of an object. Taking into account the difficulties of producing lenses at hard X-ray energies that are both highly resolving and efficient, we see clearly the advantages of the so-called “lensless” microscopy techniques. After its first demonstration [1-4], CXDI was successfully applied at third-generation synchrotron sources for imaging micron-and nanometer-size samples (see Refs. [5-10] for recent reviews). The conventional CXDI experiment is performed with an isolated sample illuminated by a coherent, plane wave (Fig. 12.1). The
incident wave may be described by a complex field (with a real and an imaginary part) of uniform magnitude and phase. The radiation interacts with the sample, which affects both the amplitude and phase of this field. The scattered radiation from the sample propagates to a two-dimensional (2D) detector in the far-field, and the diffracted intensities are measured. The detector can be positioned either in the forward direction, or in the case of a crystalline sample at the Bragg angle positions (Fig. 12.1). It will be shown in the following sections that in the limit of kinematical scattering, which is a good approximation for scattering on nanostructures, the amplitude of the scattered field can be expressed as the Fourier transform (FT) of the electron density of a sample (see also Chapter1). However, the measurement of diffracted intensities exclusively is insufficient to unambiguously determine the electron density of a sample, as the phase information is lost during the measurement process (the measured quantity is the intensity and not the complex amplitude). Fortunately, with some additional knowledge of constraints on the sample in object space, the structure of the sample can be reconstructed using phase retrieval algorithms based on an iterative approach [11-13] (see also Ref. [14] for a review of iterative methods).
