A light ray in space is characterized by two vectors: (i) a transverse spatial vector associated with the point where intersects given spherical cap; (ii) an angular-frequency which defines direction of propagation. Given propagating from emitter to receiver, linear equation established that links its representative vectors on and receiver. The link expressed means matrix not homogeneous, since...

We have developed a novel experimental technique for tracking small particles in three dimensions with nanometer accuracy. The longitudinal positioning of a micrometer-sized particle is determined by using the Fresnel approximation to describe the transverse distribution of the wavefront that originated in the particle. The method utilizes the high-sensitivity quantitative phase imaging capabil...

A mathematical model that describes the behavior of low-resolution Fresnel lenses encoded in any low-resolution device (e.g., a spatial light modulator) is developed. The effects of low-resolution codification, such the appearance of new secondary lenses, are studied for a general case. General expressions for the phase of these lenses are developed, showing that each lens behaves as if it were...

The impact of decreased zone height on the focal properties of hard X-ray Bragg-Fresnel zone plates has been studied by numerical simulation. Decreased zone height allows for smaller zone widths and, although the efficiency of the lens is decreased, the signal-to-background ratio in the focal plane of the lens remains at a comparatively high level. This is distinct from an analogous case of ord...

A mathematical model describing the behavior of low-resolution Fresnel encoded lenses (LRFEL's) encoded in any low-resolution device (e.g., a spatial light modulator) has recently been developed. From this model, an LRFEL with a short focal length was optimized by our imposing the maximum intensity of light onto the optical axis. With this model, analytical expressions for the light-amplitude d...

A photon echo experiment in Tm(3+):YAG is reported that shows, for the first time to the authors' knowledge, the time-domain equivalent of the transition from near- to far-field diffraction, including Talbot self-imaging effects. The experiment demonstrates the huge dispersion capability of photon echoes and opens the way to further exploration of space-time duality.

A technique is proposed for computing the field radiated from a rectangular aperture. This technique, based on the discrete fractional Fourier transform, avoids the complexities of computing the diffraction pattern by the direct evaluation of the Fresnel integral. The advocated approach provides a fast and accurate computational tool, especially in the case of evaluating pulsed fields radiated ...