Fractal zone plates (FZPs), i.e., zone plates with a fractal structure, are described. The focusing properties of this new type of zone plate are compared with those of conventional Fresnel zone plates. It is shown that the axial irradiance exhibited by the FZP has self-similarity properties that can be correlated to those of the diffracting aperture.

This Roadmap article on digital holography provides an overview of a vast array of research activities in the field of digital holography. The paper consists of a series of 25 sections from the prominent experts in digital holography presenting various aspects of the field on sensing, 3D imaging and displays, virtual and augmented reality, microscopy, cell identification, tomography, label-free live cell imaging, and other applications. Each section represents the vision of its author to describe the significant progress, potential impact, important developments, and challenging issues in the field of digital holography.

The utilization of microscope objectives (MOs) in digital holographic microscopy (DHM) has associated effects that are not present in conventional optical microscopy. The remaining phase curvature, which can ruin the quantitative phase imaging, is the most evident and analyzed. As phase imaging is considered, this interest has made possible the development of different methods of overcoming its undesired consequences. Additionally to the effects in phase imaging, there exist a set of less obvious conditions that have to be accounted for as MOs are utilized in DHM to achieve diffraction-limit operation. These conditions have to be considered even in the case in which only amplitude or intensity imaging is of interest. In this paper, a thorough analysis of the physical parameters that control the appropriate utilization of MOs in DHM is presented. A regular DHM system is theoretically modeled on the basis of the imaging theory. The Fourier spectrum of the recorded hologram is analyzed to evaluate the performance of the DHM. A set of the criteria that consider the microscope features and the recording parameters to achieve DHM operation at the diffraction limit is derived. Numerical modeling and experimental results are shown to validate our findings.

One of the main challenges in three-dimensional integral imaging is its limited depth of field. Such a limitation is imposed by diffraction, among other factors. The easiest way to improve the depth of field is by reducing the numerical aperture of the microlenses. However, such an improvement is obtained at the expense of an important deterioration in the spatial resolution. We propose a technique, which is novel in the context of integral imaging, for improving the depth of field with no deterioration of the spatial resolution. The technique, based on amplitude modulation of the array of phase elements, can substantially improve the figure of merit of the product of depth of the focus and the squared resolution.

The focusing properties of diffractive lenses designed using the Fibonacci sequence are studied. It is demonstrated that these lenses present two equal intensity foci and that the ratio of the two focal distances approaches the golden mean. This distinctive optical characteristic is experimentally confirmed. It is suggested that the versatility and potential scalability of these lenses may allow for new applications ranging from X-ray microscopy to THz imaging.