Francisco E. Veiras

Phase shift formulas in uniaxial media: an application to waveplates

The calculation of phase shift and optical path difference in birefringent media is related to a wide range of applications and devices. We obtain an explicit formula for the phase shift introduced by an anisotropic uniaxial plane-parallel plate with arbitrary orientation of the optical axis when the incident wave has an arbitrary direction. This allows us to calculate the phase shift introduced by waveplates when considering oblique incidence as well as optical axis misalignments. The expressions were obtained by using Maxwells equations and boundary conditions without any approximation. They can be applied both to single plane wave and space-limited beams.

Wide angle conoscopic interference patterns in uniaxial crystals

The fringe pattern obtained when a divergent (or convergent) beam goes through a sample of birefringent crystal between two crossed polarizers contains information that is inherent to the crystalline sample under study. The formation of fringe patterns is analyzed from distinct approaches and with different degrees of approximation considering cones of light of large numerical aperture. We obtain analytic explicit formulas of the phase shift on the screen and compare them with the exact numerical solution. The results obtained are valid for arbitrary orientation of the optical axis and are not restricted either to low birefringence or to small angles of incidence. Moreover, they enable the extraction of the main features related to the characterization of uniaxial crystal slabs, such as the optical axis tilt angle and the principal refractive indices.

Characterization of uniaxial crystals through the study of fringe patterns

The fringe pattern obtained when a divergent (or convergent) beam goes through a sample of birefringent crystal between two polarizers contains information which is inherent of the crystalline sample under study. On the other hand, by considering the design details of the experience and the parameters that are characteristic of the uniaxial plate, it is possible to theoretically obtain the luminous intensity corresponding to each point on a screen or CCD. Thus, this theoretical model allows us to obtain, from images experimentally obtained and theoretical expressions, the parameters that are characteristic of the plates. The results obtained proved the concordance between theory and experience while endorsing this technique for the characterization of birrefringent crystals and devices based on this type of materials.

Amplitude and phase retrieval in simultaneous π/2 phase-shifting heterodyne interferometry using the synchrosqueezing transform

This paper presents a method for amplitude and phase retrieval in simultaneous π/2 phase-shifting heterodyne interferometry. The used optical setup admits the introduction of a temporal carrier and simultaneously verifies the two-beam interferometry equation for each intensity signal, which are π/2  rad out of phase (quadrature). The spatiotemporal recovering process is obtained by isolating the object amplitude and phase using wavelet transform analysis of the temporal series composed by the difference between the measured pixel intensities corresponding to each quadrature signal. This process is subsequently improved by introducing a framework based on the synchrosqueezing transform, which recovers the data of interest with higher accuracy when very low scattering amplitudes and phase excursions must be determined in noisy working conditions. The advantages and limitations of the presented method are analyzed and discussed using numerical simulations and also experimental data obtained from temporal speckle pattern interferometry.

Comparison of real-time phase-reconstruction methods in temporal speckle-pattern interferometry.

Three real-time methods for object-phase recovery are implemented and compared in temporal speckle-pattern interferometry. Empirical mode and intrinsic time-scale decompositions are used and compared as real-time nonstationary and nonlinear filtering techniques for the extraction of the spatio-temporal evolution of the object phase. The proposed real-time methods avoid the application of the Hilbert transform and improve the accuracy of the measurement by filtering under-modulated pixels using Delaunay triangulation. The performance of the proposed methods is evaluated by comparing phase-recovery accuracy and computation time by means of numerical simulations and experimental data obtained from common and simultaneous π/2 phase-shifting heterodyne interferometry.

Birefringent phase demodulator: application to wave plate characterization

The scope of this work is to present a phase demodulator that enables the recovery of temporal phase information contained in the phase difference between two signals with different polarizations. This demodulator is a polarization interferometer that may consist only of a uniaxial crystal slab and a polarizer sheet. The phase shift between two orthogonal components of the electric field is translated into space by means of birefringent crystals, which act as demodulators or phase analyzers with great robustness. The experimental scheme utilized is based on a simple conoscopic interference setup. Each portion of the space in which the interference pattern is projected contains not only the unknown temporal phase we want to recover, but also a phase shift due to the uniaxial crystal itself. The underlying idea is developing simultaneous phase shifting with uniaxial crystals. Thus, different phase recovery techniques can be applied in order to maximize their ability to track high-speed signals. Depending on the characteristics of the fringe pattern, it will permit phase recovery via different classical procedures. In order to prove the demodulator under different experimental and signal processing schemes, we employed it for wave plate characterization. The results obtained not only allow some wave plate features such as axes determination and retardance to be characterized, but also prove the working principle and capabilities of the demodulator.

Novel achromatic single reflection quarter-wave retarder: Design and measurement

In this work, we present an achromatic quarter-wave retarder whose design is based upon the reflection properties of an isotropic-anisotropic interface. In theory, it is possible to obtain a π/2 phase shift by means of a total internal reflection at an isotropic-isotropic interface. However, in order to achieve such a phase shift, it is necessary to use a medium with a particularly high refractive index. We have previously shown that these phase shifts can be achieved by means of a total internal reflection in an isotropic-uniaxial interface, which allows the use of smaller refractive index media. By means of this property, we designed, built, and characterized a novel quarter-wave retarder that makes it possible to obtain circularly polarized light from a linear polarization state. We developed some guidelines that allowed us to obtain a device of competitive performance, low cost, and manageable manufacture.

Wideband quad optical sensor for high-speed sub-nanometer interferometry

This paper describes the design and performance of a low-noise and high-speed optical sensor that provides two output signals in quadrature from the simultaneous detection of four phase-shifted interferograms. The sensor employs four high-speed photodiodes and high-speed, low-noise transimpedance amplifiers. The optical and electronic design was optimized for high-speed displacement measurement interferometry, over a broad range of operating frequencies. Compared to other experimental schemes, the sensor is simpler and of lower cost. The performance of the sensor is demonstrated by characterizing a piezoelectric transducer for ultrasonic applications. We measured displacements between 38 pm and 32 nm with 6% relative uncertainty, in the frequency range from 1 to 2 MHz.

Comparative analysis of nanometric inspection methods in fringeless speckle pattern interferometry

In digital speckle pattern interferometry, fringeless speckle pattern interferograms are obtained when the object field deformation is insufficient to produce local phase variations higher than 2π. Therefore, the use of the well-known phase recovery algorithms based on fringe processing is not adequate. In this work, distinct algorithms based on the application of a straightforward arccosine function to a filtered interferogram and the correlation of intensity images and implicit smoothing splines are proposed, analyzed, and compared for the fast inspection of nanometric displacement fields, avoiding the acquisition of several images. In addition, three different methods for the normalization of fringeless speckle pattern interferograms are proposed. The Structural Similarity Index is used to assess the performance of the tested methods by means of numerical simulations under different illuminations, signal-to-noise ratios, phase excursions, and mean speckle size conditions. The analysis shows that the phase recovered by the methods based on the arccosine function and correlation are appropriate for a fast inspection solution. The implicit smoothing spline outperforms other methods in almost all conditions.

Interferometría óptica dinámica para la determinación del coeficiente piezoeléctrico en polímeros

Piezoelectric polymers are of great interest due to their physical properties that allow their use in many applications. Their are particularly important for biomedical applications. Moreover, broadband sensor development requires a reliable system to measure the piezoelectric coefficient of these materials. In this work, we propose an interferometric scheme to measure this coefficient on a polyvinylidene fluoride sample in the frequency range between 100 Hz and 10 kHz using a Michelson interferometer with quadrature detection. The results were compared with an indirect method based on dielectric spectroscopy.