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Different spatial distributions of optical vortices have been generated and characterized by implementing arrays of devil’s vortex lenses in a reconfigurable spatial light modulator. A simple design procedure assigns the preferred position and topological charge value to each vortex in the structure, tuning the desired angular momentum. Distributions with charges and momenta of the opposite sign have been experimentally demonstrated. The angular velocity exhibited by the phase distribution around the focal plane has been visualized, showing an excellent agreement with the simulations. The practical limits of the method, with interest for applications involving particle transfer and manipulation, have been evaluated.

The construction of fractal generalized zone plates from a set of periodic diffractive optical elements with circular symmetry is proposed. This allows us, for instance, to increase the number of foci of a conventional fractal zone plate while keeping the self-similarity property within the axial irradiance. The focusing properties of these fractal diffractive optical elements for points not only along but also in the close vicinity of the optical axis are investigated. In both cases analytical expressions for the irradiance are derived. Numerical simulations of the energetic efficiency of fractal generalized zone plates under plane wave illumination are carried out. In addition, some effects on the axial irradiance caused by variations in the area of their transparent rings are shown.

We describe two different scale-tunable optical correlators working under totally incoherent light. They behave as spatially incoherent wavelength-independent imaging systems with an achromatic point-spread function (PSF). In both cases it is possible to adapt the scale of the achromatic PSF, i.e., to modify the scaling factor of the PSF and preserve the chromatic compensation, by one’s shifting the input along the optical axis. The remarkable properties of these systems allow us to carry out a scale-tunable color pattern-recognition experiment with natural light.

The strong chromatic distortion associated with diffractive optical elements is fully exploited to achieve an achromatic optical Fourier transformation under broadband point-source illumination by means of an air-spaced diffractive lens doublet. An analysis of the system is carried out by use of the Fresnel diffraction theory, and the residual secondary spectrum (both axial and transversal) is evaluated. We recognize that the proposed optical architecture allows us to tune the scale factor of the achromatic Fraunhofer diffraction pattern of the input by simply moving the diffracting screen along the optical axis of the system. The performance of our proposed optical setup is verified by several laboratory results.

A method of visualization of phase changes in two-dimensional pure-phase objects by use of two orthogonal Fourier plane filters that realize the half-order differentiation is presented. Real semiderivative filters used in two dimensions and in sequence yield output-image intensity signals proportional to the first derivatives of the input-object phase that appear on a constant background. This nonlinear filtration of spatial frequencies permits the alleviation of the consequences of square-law detection and makes phase changes visible. Phase changes in gradient-index phosphate glass are calculated experimentally. We discuss the accuracy of the proposed method.

Fractional derivatives of two-dimensional images have been discussed theoretically in terms of Fourier optics and computer simulated. Filters that realize the half-order differentiation can be either complex or real. We prove, in terms of fractional calculus, that the semiderivative filter is useful for the visualization of phase changes in a phase object in such a way that the output-image intensity is directly proportional to the first derivative of the input object. We give computer-simulated results of one-dimensional semidifferentiating.

We present an optical system that performs Stokes polarimetric imaging with a single-pixel detector. This fact is possible by applying the theory of compressive sampling to the data acquired by a commercial polarimeter without spatial resolution. The measurement process is governed by a spatial light modulator, which sequentially generates a set of preprogrammed light intensity patterns. Experimental results are presented and discussed for an object that provides an inhomogeneous polarization distribution.

The duality between the axial irradiance distribution originated by any circularly symmetric diffracting aperture under monochromatic illumination and its diffracted spectral intensity at a fixed on-axis point under broadband illumination is highlighted and experimentally investigated. Two applications are derived from this basic result. On the one hand, we suggest the use of a broadband source and a spectrometer for a single-shot measurement of the axial response of pupil filters. Second, we implement a spectral filter having a transmission spectrum with a fractal structure of frequencies. Experimental results and potential applications in synthetic spectra designs are provided.