Uriel Rivera-Ortega

Phase-shifting interferometry by wave amplitude modulation.

A new method for phase-shifting interferometry based on wave amplitude modulation is proposed and discussed. This proposal is based on the interference of three waves, where two waves attend as two reference waves and the other wave attends as a probe wave. Thereby, three interference terms are obtained, but because a phase difference of π/2 between the two references is kept constant, one of the three terms will be dropped, while the two remaining will be put in quadrature. Under these conditions, the resulting pattern is mathematically modeled by an interferogram of two waves, where an additional phase is given by the amplitude variations of the reference waves. In this Letter, both a theoretical model and some numerical simulations are presented.

On–off laser diode control for phase retrieval in phase-shifting interferometry

This paper describes an alternative automated setup for phase-shifting and phase retrieval based on the wavelength tunability of a laser diode. For many industrial and scientific applications it is desirable that the laser gets stabilized. In this paper, on the contrary, the laser diode is turned on and off for a short period of time. The generated variations of voltage and temperature cause a modulation of its wavelength. This modulation is used for a simple demonstration of the phase-shifting phenomena and phase retrieval under the scheme of an unbalanced Twyman–Green interferometer and using the Carre algorithm. The on–off switching of the laser can be done manually, but for this proposal, it will be emulated by a pulse voltage signal from a data acquisition device.

Double aperture common-path phase-shifting interferometry by translating a ruling at the input plane

A method for introducing phase steps in an interferogram based on translating a ruling at the input plane of a double aperture common-path interferometer is presented. The setup is built on a 4f optical system consisting of two apertures at the input plane and a Ronchi ruling in the Fourier plane, where at each aperture a Ronchi ruling is also placed. By filtering at the Fourier plane a single diffraction order of the spectrum from the rulings in the object plane, we demonstrate that a phase step is generated when one of the rulings in the input plane is translated. The principal advantage of this proposal lies in improving the resolution in the phase step. We develop a theoretical model and show experimental results.

Wavelength estimation by using the Airy disk from a diffraction pattern with didactic purposes

In this paper a simple and easy to implement method that uses the Airy disk generated from a Fraunhofer diffraction pattern due to a circular aperture will be used to estimate the wavelength of the illuminating laser source. This estimation is based on the measurement of the Airy disk diameter, whose approximation is directly proportional to the wavelength of the light source and to the distance between the aperture and the image plane; and inversely proportional to the diameter of the aperture. Due to the characteristics and versatility of the present proposal, this is perfectly suitable for use in graduate or undergraduate physics laboratories, or even in classrooms for educational and/or demonstrative purposes.

Phase shifting and phase retrieval with a fully automated laser diode system

A low-cost and fully automated process for phase-shifting interferometry (PSI) by continuously changing the input voltage of a laser diode (LD) under the scheme of an unbalanced Twyman-Green interferometer (TGI) setup is presented. The input signal of a LD is controlled by a data acquisition (NI-DAQ) device that allows it to change its wavelength according to its tunability features. The automation and data analysis will be done using LabVIEW in combination with MATLAB. The phase map is obtained using the Carré algorithm. Measurements of visibility and phase shift to verify the PSI requirements are shown. It is demonstrated with experimental results and statistical analysis that the phase retrieval can be successfully achieved without calibration and using minimal optical devices.

Inhomogeneous phase-visibility modulating interferometry by space on-off non-quadrature amplitude modulation.

A new method in interferometry based on on-off non-quadrature amplitude modulation for object phase retrieval is presented. Although the technique introduces inhomogeneous visibility and phase variations in the interferogram, it is shown that the phase retrieval of a given object is still possible. This method is implemented by using three beams and two Mach-Zehnder interferometers in series. One of the arms of the system is used as a probe beam and the other two are used as reference beams, yielding from their sum the conventional reference beam of a two-beam interferometer. We demonstrate that, if there is a phase difference within the range of (0,π) between these two beams, the effect of modulation in both amplitude and phase is generated for the case of on-off non-quadrature amplitude modulation. An analytical discussion is provided to sustain this method. Numerical and experimental results are also shown.

Phase-Shifting Generated by Wavelength Modulation by Means of Switching On-Off a Laser Diode

It is well known that one of the features of a laser diode is its wavelength tunability which can be modulated with a variable injection current and/or temperature of its active region. For many industrial and scientific applications it is desirable that the laser gets stabilized. In this paper, on the contrary, the laser diode is turned on-off for a short period of time. The generated peak variations of voltage and temperature will cause a modulation of its wavelength. This modulation is used to add phase-shifts in an unbalanced Twyman-Green interferometer and by using Carre algorithm the phase of the resulting interference wave will be retrieved.

Low-cost automated system for phase-shifting and phase retrieval based on the tunability of a laser diode

A low-cost and fully automated process for phase-shifting interferometry by continuously changing and turning on-off the input voltage of a laser diode under the scheme of an unbalanced Twyman-Green interferometer setup is presented. The input signal of a laser diode is controlled by a Data Acquisition (NI-DAQ) device which permits to change its wavelength according to its tunability features. The automation and data analysis will be done using LabVIEW in combination with MATLAB. By using Carré algorithm the phase map is obtained. Measurements of visibility and phase-shift to verify the PSI requirements are also shown.

Computational tool for phase-shift calculation in an interference pattern by fringe displacements based on a skeletonized image

In this manuscript an algorithm based on a graphic user interface (GUI) designed in MATLAB for an automatic phase-shifting estimation between two digitalized interferograms is presented. The proposed algorithm finds the midpoint locus of the dark and bright interference fringes in two skeletonized fringe patterns and relates their displacements with the corresponding phase-shift. In order to demonstrate the usefulness of the proposed GUI, its application to simulated and experimental interference patterns will be shown. The viability of this GUI makes it a helpful and easy-to-use computational tool for educational or research purposes in optical phenomena for undergraduate or graduate studies in the field of physics.

Visualizing the phenomena of wave interference, phase-shifting and polarization by interactive computer simulations

In this manuscript a computer based simulation is proposed for teaching concepts of interference of light (under the scheme of a Michelson interferometer), phase-shifting and polarization states. The user can change some parameters of the interfering waves, such as their amplitude and phase difference in order to graphically represent the polarization state of a simulated travelling wave. Regarding to the interference simulation, the user is able to change the wavelength and type of the interfering waves by selecting combinations between planar and Gaussian profiles, as well as the optical path difference by translating or tilting one of the two mirrors in the interferometer setup, all of this via a graphical user interface (GUI) designed in MATLAB. A theoretical introduction and simulation results for each phenomenon will be shown. Due to the simulation characteristics, this GUI can be a very good non-formal learning resource.