David Mas

Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm

A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFTs in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from -1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT are discussed.

Fractional wavelet transform

The wavelet transform, which has had a growing importance in signal and image processing, has been generalized by association with both the wavelet transform and the fractional Fourier transform. Possible implementations of the new transformation are in image compression, image transmission, transient signal processing, etc. Computer simulations demonstrate the abilities of the novel transform. Optical implementation of this transform is briefly discussed.

Three-dimensional object recognition by Fourier transform profilometry

An automatic method for three-dimensional (3-D) shape recognition is proposed. It combines the Fourier transform profilometry technique with a real-time recognition setup such as the joint transform correlator (JTC). A grating is projected onto the object surface resulting in a distorted grating pattern. Since this pattern carries information about the depth and the shape of the object, their comparison provides a method for recognizing 3-D objects in real time. A two-cycle JTC is used for this purpose. Experimental results demonstrate the theory and show the utility of the new proposed method.

Nonlinear morphological correlation: optoelectronic implementation

An optoelectronic implementation of the nonlinear morphological correlation by use of a threshold-decomposition technique and a joint transform correlator architecture is presented. This nonlinear morphological correlation provides improved image detection compared with standard linear optical pattern-recognition correlation methods. It also offers a more robust detection of low-intensity images in the presence of high-intensity patterns to be rejected.

Wavelength-multiplexing system for single-mode image transmission.

The expanding use of optical communication by means of optical fibers and the situation of drastically increasing amounts of data to be transmitted urge the exploration of novel systems permitting the transmission of large amounts of spatial information by fiber with smaller spatial resolution. An optical encoding and decoding system is suggested for transmitting one- or two-dimensional images by means of a single-mode fiber. The superresolving system is based on wavelength multiplexing of the input spatial information, which is achieved with diffractive optical elements. Preliminary experimental results demonstrate the capabilities of the suggested method for the one- and two-dimensional cases.

Vibration frequency measurement using a local multithreshold technique

In this paper, we demonstrate the use of a video camera for measuring the frequency of small-amplitude vibration movements. The method is based on image acquisition and multilevel thresholding and it only requires a video camera with high enough acquisition rate, not being necessary the use of targets or auxiliary laser beams. Our proposal is accurate and robust. We demonstrate the technique with a pocket camera recording low-resolution videos with AVI-JPEG compression and measuring different objects that vibrate in parallel or perpendicular direction to the optical sensor. Despite the low resolution and the noise, we are able to measure the main vibration modes of a tuning fork, a loudspeaker and a bridge. Results are successfully compared with design parameters and measurements with alternative devices.

Fractional triple correlation and its applications

Higher-order correlations are well known for their use in noise removal, image enhancement, and signal identification. They are generalizations of the well-known second-order correlation. The fractionalization of the second-order correlation provides some interesting features that are related to the shift-variance property of the fractional-Fourier-transform operation. This project proposes the fractionalization of the triple-correlation operation (as well as other higher-order correlations). A suggested definition as well as some applications are given. Computer simulations demonstrate some of the features this operation offers.

Optoelectronic implementation of the triple correlation

The auto triple correlation has several fundamental advantages over the ordinary autocorrelation of second order. We present an optoelectronic processor for the computation of the auto triple correlation.

Fresnel diffraction calculation through the fast fractional Fourier transform

A new method for the calculation of the Fresnel diffraction patterns through a fast fractional Fourier transform (FRT) is presented. The FRT can be efficiently calculated for any order by using the fast-Fourier transform algorithm. The resemblances between the FRT and the Fresnel integrals allow the use of that algorithm to calculate efficiently the Fresnel integral of any object, with independence of its shape.