Optical generation of the Wigner distribution of 2-D real signals

Redundancy of phase-space distribution functions in complex field recovery problems

Shows that the amplitude and phase of an optical field can be recovered from only a section of phase-space distribution functions, the information contained in other sections being redundant. Experimental implications of this result are discussed, and a physical interpretation of it is offered. In particular the sampling problem in tomography is solved for any field distribution.

One-step measurement of optical fields in multimode circular fibers

We propose to determine the optical field in multimode circular fibers by using a one-step method that measures the Wigner distribution function of a section of the field in the fiber. This method allows an estimation not only of the power carried by each mode but also of the relative phases of different modes in the fiber. An additional measurement with the same setup can even determine the propagation constants of different modes. An example is provided, and the connection of this method of field recovery to the coupling coefficient between fibers and light sources is also discussed.

Optical realization of the ambiguity function of real two-dimensional light sources

We propose a setup that can generate the sectional ambiguity function of a two-dimensional real light source. The setup is easy to implement; the theoretical analysis and experimental results are given.

Can the Wigner transform of a two-dimensional rotationally symmetric beam be fully recovered from the Wigner transform of its one-dimensional approximation?

It is shown that the full four-dimensional Wigner transform of a coherent, rotationally symmetric light beam can be completely recovered by measurement, in one step, of the Wigner transform of an equivalent one-dimensional light beam. The method of generating this equivalent light beam from a two-dimensional circular light beam is presented.

Phase-space measurements of micro-optical objects

The phase-space measurement of micro-optical objects with submillimeter dimensions is reported for the first time to our knowledge. The experimental data were compared with simulated results from interferometric measurements and were found to be in good agreement.

Recovery of the refractive-index profile from the wigner distribution of an optical waveguide

We propose a new method for the recovery of the refractive-index profile of a single-mode or multimode optical guided structure. We solve the inverse problem using the Wigner distribution and reduce it to the solution of a linear system of equations.

Wigner-transform implementation in the time-frequency domain

An analogy between two-dimensional space and time optics is presented. A setup that performs the time-frequency Wigner transform is proposed, and as an example the propagation of a Gaussian pulse in such a setup is analyzed.

Real time self-pumped optical phase-conjugator based igner distribution processor for complex signals

Based on a combination of linear shift-invariant optical elements and a nonlinear photorefractive crystal serving as a self-pumped optical phase-conjugator, the real time optical generation of an auto- and cross- Wigner distribution for complex signals is demonstrated.

Optical digital implementation of the Wigner distribution function: use in space variant filtering of real images

An optical digital processor based on the Wigner distribution function (WDF) has been implemented, permitting space variant filtering of 2-D real images. The processor sequentially generates all space samples of the distribution; thus, each sample can be modified by a different filter. The filtered Wigner distribution function is optically inverted, and a digital image processor selects the information associated with each sample of the image. Compared to a digital implementation, the required computer time has been reduced to the point where future practical use of Wigner filtering can be expected.

Space-variant filtering through the Wigner distribution function

Space-invariant and space-variant filtering of discrete images with unidimensional variation is performed in this paper through the Wigner distribution function (WDF). Low-pass, bandpass, and high-pass filtering is used in the Fourier domain and in the Wigner distribution, to compare their different behavior in both cases. A space-variant filter is generated to modify the WDF of an object to obtain, after inversion, a spatially variant filtered image. Finally, spatially variant defocused images generated through the Wigner distribution are restored by Wiener based filters applied in the Wigner domain. The method applied to recover the filtered images can easily be generalized to bidimensional images.

Image analysis through the Wigner distribution function

The Wigner distribution (WD) for discrete images is computed and applied for texture analysis. First, the WD for different test images with spatial frequency and gray level information content is computed, and the most important features of the WD are outlined. Likewise, the original image with 1-D variation is recovered from the discrete WD; local filtering operations have been performed on the distribution, and a filtered version of the original image is then obtained. Since the WD entails simultaneous representation of the intensity distribution and of the spatial interdependence, it seems specially adequate for processing of textured information. In this way, texture recognition is performed through the extraction of features from the WD, and the results are compared with other methods. Finally, to avoid the great computational effort that requires this kind of representation, a hybrid optical-digital processing system is proposed for the texture recognition process.