Image data compression based on non-negative incoherent imaging systems.

Channel and memory capacities are limited and expensive resources in optical communication. In this work we propose several approaches to reduce the required capacity by using the a priori knowledge about the optical system used to capture the spatial information. The a priori knowledge is related to the triangularlike shape of the optical transfer function and to its spectral symmetry. In our work we will demonstrate a reduction in memory capacity required for the same image quality or a resolution enhancement for the same physical memory capacity. We will also present a nearly all-optical implementation of these techniques.

Optical wave fields with lateral and longitudinal periodicity.

The propagation of stationary wave fields that exhibit simultaneously lateral and longitudinal periodicity is investigated. As a model, we use a Fabry-Perot resonator with periodically structured mirrors under monochromatic plane wave illumination. The resonator leads to a longitudinal periodicity, the grating mirrors to a lateral periodicity. The angular spectrum of the transmitted wave field is given as the product of two terms, one related to the lateral, the other to the longitudinal properties. Its modal structure can vary significantly depending on the ratio of the lateral and longitudinal periods and the reflectivity of the resonator's mirrors. For example, it is possible to generate bandgap behavior despite the fact that the periods may be significantly larger than the wavelength. The results of this investigation apply to the design of phase-coupled array resonators and multiplexers.

Holography in phase space.

Holography is reformulated by using the framework of phase-space optics. The Leith-Upatnieks off-axis reference hologram is compared with precursors, namely, single-sideband holography. The phase-space representation of complex amplitudes focuses on similarities between different holographic recording schemes and is particularly useful for investigating the degree of freedom and the space-bandwidth product of optical signals and systems. This allows one to include computer-generated holography and recent developments in digital holography in the discussion.

Bow-tie effect: differential operator.

We propose to use a differential operator for representing the influence of phase-only filters on the defocused modulation transfer function of the clear pupil aperture. We present a phase-only filter that implements optically Taylor's theorem in phase space. We show numerical simulations of the modulation transfer functions and the images that can be obtained by using the proposed filter.

Fractional Montgomery effect: a self-imaging phenomenon.

Self-imaging means image formation without the help of a lens or any other device between object and image. There are three versions of self-imaging: the classical Talbot effect (1836), the fractional Talbot effect, and the Montgomery effect (1967). Talbot required the object to be periodic; Montgomery realized that quasiperiodic suffices. Classical means that the distance from object to image is an integer multiple of the Talbot distance Z(T) = 2p2/lambda, where p is the grating period. Fractional implies a distance that is a simple fraction of Z(T): say, Z(T)/2, Z(T)/4, 3Z(T)/2.... We explore the most general case of the fractional Montgomery effect.

Temporal filtering by double diffraction.

We present a theoretical analysis of the temporal behavior of double-diffraction setups. It applies, in particular, to Talbot and Montgomery interferometers, whose operation is based on the self-imaging effect. The use of both types of interferometer as temporal filters for optical and terahertz applications was recently suggested. We show that double-diffraction setups can be modeled as communications channels with dispersive behavior caused by diffraction. We develop mathematical expressions for the phase delay, the group velocity, and the group-velocity dispersion for both quasi-monochromatic and polychromatic case. Based on these results, the temporal impulse response of a double-diffraction setup is derived. Finally, a general description of its practical implementation are presented.