Dynamics of coexisting rotating waves in unidirectional rings of bistable Duffing oscillators.

We study the dynamics of multistable coexisting rotating waves that propagate along a unidirectional ring consisting of coupled double-well Duffing oscillators with different numbers of oscillators. By employing time series analysis, phase portraits, bifurcation diagrams, and basins of attraction, we provide evidence of multistability on the route from coexisting stable equilibria to hyperchaos via a sequence of bifurcations, including the Hopf bifurcation, torus bifurcations, and crisis bifurcations, as the coupling strength is increased. The specific bifurcation route depends on whether the ring comprises an even or odd number of oscillators.

Steps length error detector algorithm in phase-shifting interferometry using Radon transform as a profile measurement.

Phase-shifting is one of the most useful methods of phase recovery in digital interferometry in the estimation of small displacements, but miscalibration errors of the phase shifters are very common. In practice, the main problem associated with such errors is related to the response of the phase shifter devices, since they are dependent on mechanical and/or electrical parts. In this work, a novel technique to detect and measure calibration errors in phase-shifting interferometry, when an unexpected phase shift arises, is proposed.

Phase recovery from interferograms under high amplitude vibrations.

A phase recovery procedure using interferograms acquired in highly noisy environments as severe vibrations is described. This method may be implemented when disturbances do not allow obtaining equidistant phase shifts between consecutive interferograms due to tilt-shift and nonlinearity errors introduced by the vibrating conditions. If the amount of the tilt-shift is greater than π radians, it will lead a sign change in the phase estimation.

Measurement of the refractive index by using a rectangular cell with a fs-laser engraved diffraction grating inner wall.

A very simple method to obtain the refractive index of liquids by using a rectangular glass cell and a diffraction grating engraved by fs laser ablation on the inner face of one of the walls of the cell is presented. When a laser beam impinges normally on the diffraction grating, the diffraction orders are deviated when they pass through the cell filled with the liquid to be measured. By measuring the deviation of the diffraction orders, we can determine the refractive index of the liquid.

Phase recovery from a single interferogram with closed fringes by phase unwrapping.

We describe a new algorithm for phase determination from a single interferogram with closed fringes based on an unwrapping procedure. Here we use bandpass filtering in the Fourier domain, obtaining two wrapped phases with sign changes corresponding to the orientation of the applied filters. An unwrapping scheme that corrects the sign ambiguities by comparing the local derivatives is then proposed.