Sergio Granieri

Fractional Fourier transform applied to spatial filtering in the Fresnel domain

The fractional Fourier transform can be optically defined through a phase-space coordinate rotation of the Wigner distribution function associated with the input signal. This operation can be achieved by performing three successive shearing processes, which are reduced to a free-space Fresnel diffraction originated by a scaled version of the input object illuminated with a spherical wave. This result is applied to describe the behavior of spatial filtering devices based on the self-imaging phenomenon (Fresnel spatial filters).

Radon–Wigner display: a compact optical implementation with a single varifocal lens

A new optical implementation of the Radon-Wigner display for one-dimensional objects is presented, making use of the fractional Fourier transform approach. The proposed setup makes use of only two conventional refractive elements: a cylindrical lens and a varifocal lens. Although the exact magnifications cannot be achieved simultaneously for all the fractional transforms, an optimum design can be obtained through balancing the conflicting magnification requirements. Experimental results are obtained with a commercially available progressive addition lens. For comparison, computer simulations are also provided.

Analysis of the Strehl ratio using the Wigner distribution function

Abstract The on-axis intensity distribution, or the Strehl ratio versus defocus, is described in a phase-space domain in terms of the Wigner distribution function. A coordinate transformation that is defined for a general annular aperture is employed to convert the pupil amplitude transmittance into a one-dimensional function. We show that the single display of the Wigner distribution function associated with this modified pupil contains all the values of the Strehl ratio along the optical axis. The analysis is performed for two primary aberrations: coma and astigmatism.

Optical propagation of fractal fields. Experimental analysis in a single display

Abstract An experimental device to show in a single display all the diffraction patterns generated by a 1D fractal structure is proposed. It is found that in addition to being the optimum display to see the evolution of the diffracted field through free space, some interesting features, such as continuous evaluation of self-similarity from the object to the far field, can be obtained experimentally.

Optical correlation based on the fractional Fourier transform

Some properties of optical correlation based on the fractional Fourier transform are analyzed. For a particular set of fractional orders, a filter is obtained that becomes insensitive to scale variations of the object. An optical configuration is also proposed to carry out the fractional correlation in a flexible way, and some experimental results are shown.

Multiple-beam fiber-optic beamformer with binary array of delay lines

A multibeam optical beamformer capable of controlling a phased-array antenna in receive/transmit mode is proposed. The processor can be programmed to sweep the antenna aperture following an independent angular sequence for each radio-frequency (RF) beam. A two-beam two-channel 3-bit version of the beamformer has been experimentally demonstrated. The optical beamformer processes two independent RF beams, for eight different angular directions, and it is based on a binary array of three delay lines. Each delay line is composed of four fiber Bragg gratings whose center wavelengths are channels 30 to 33 of the International Telecommunications Union (ITU) grid. Measurements are performed for both receive and transmit modes and for RF values between 0.5 and 1.5 GHz. We present beam-pattern results showing the squint-free performance of the beamformer within this frequency range. In the transmit mode, two RF beams are steered and characterized for a broadside target position. In the receive mode, the beamformer performance is characterized by detecting two simultaneous RF beams.

Space and spectral behaviour of optical systems under broadband illumination by using a Wigner distribution function approach

The on-axis image irradiance obtained from a radially symmetric optical system under broadband illumination is analysed in the phase-space domain of the Wigner distribution function associated with a modified one-dimensional pupil aperture. To this end, a coordinate transformation is employed in such a way that the varying on-axis irradiance can be derived from different slices of a two-dimensional Wigner distribution function, which involve both the defocus distance and the dispersion properties of the optical system. The method is illustrated by comparing the imaging performance of four different pupil apertures, when the system is illuminated with a light beam having a gaussian spectral content.

Optical beamforming in receive mode of two independent simultaneous RF beams

We propose and demonstrate a novel architecture for a programmable dispersion matrix (PDM) able to process two simultaneous independent RF beams with a resolution of 3 bits. The processor takes advantage of wavelength division multiplexing (WDM) encoding. In our two-channel approach, four adjacent ITU optical WDM channels are used as optical carriers. The odd and even optical carriers are independently modulated with each received RF-beam using electro-optic modulators. Thus, each pair of optical carriers directs RF information of one beam. The PDM is programmed to introduce independent true-time delays for even and odd optical channels. The PDM is based on three optical delay lines, arranged in a binary configuration. Each delay line consists of four fiber-Bragg gratings (FBG), with each FBG having a center-wavelength at one of the optical WDM channels. Beampatterns are characterized in receive mode for RF signals in 0.5-1.5 GHz frequency range obtained for target angles of 0° to 70°. The measurement results demonstrate the simultaneous processing of two received RF-beams and the squint free nature of the beamformer.

OPTICAL BISTABILITY IN A NONLINEAR SOA-BASED FIBER RING RESONATOR

A novel optical inverted bistable switch based on a nonlinear fiber ring resonator (FRR) containing a semiconductor optical amplifier (SOA) has been analyzed and experimentally demonstrated. Optical bistability is obtained due to the transmission characteristics of the resonator and the SOAs gain characteristics. A complete theoretical analysis and supporting simulations are presented. A prototype is demonstrated using commercial optical components. Experimental results show switching performance with falling times lower than 10 ns.

Rethinking Optical Engineering Capstone Design Experience

We developed a three quarter capstone project course sequence for our ABET accredited optical engineering program. In the first course of the sequence we teach design methodology based on a mini-project done concurrently with lectures outlining the product development process. The mini-project is centered on the design of an imaging system. The kit used for this design project consists of a webcam, 20 lenses, and a collection of lens tubes and adaptors. Over the next two quarters the students choose from a selection of client-based projects, where the focus is on team work that culminates in a functional prototype.