Papers by Gustavo Rodriguez-Zurita
Optics Communications, 1999
. It is well known that the integral of a tomographic projection zero-order moment represents the... more . It is well known that the integral of a tomographic projection zero-order moment represents the total irradiance absorption of an object. Therefore, it must be rotational invariant. In this paper it is shown that the filtered projections must obey the same condition. Numerical examples are presented to illustrate the usefulness of the invariance property to judge the filtering process performance. Furthermore, the possibility to inspect the fulfilment of the invariance with experimental data is discussed, and the development of a rejection criterion for projection data in experimental tomography is suggested. q
Measurement Science & Technology, 2009
A grating interferometer to produce n lateral-sheared phase-shifted interferograms simultaneously... more A grating interferometer to produce n lateral-sheared phase-shifted interferograms simultaneously in collimated light and with adjustable shear is proposed. It consists of a variable lateral-shear interferometer in conjunction with a grating interferometer. This combination enables the use of phase-shifting techniques for measuring moving wavefront slopes. Several shifted interferograms can be achieved with a single shot using two mutually crossed phase gratings of equal frequency, while the required phase shifts can be performed with modulation of polarization. Results of the proposed method for cases of n = 4, 5 and 7 interferograms are reported.
Experimental results for the cases of n = 4,5,7 shearograms for one lateral shearing interferomet... more Experimental results for the cases of n = 4,5,7 shearograms for one lateral shearing interferometer and for one rotational shearing interferometer are shown. These results are obtained choosing one from several possible configurations of each system in only one-shot.
A method to obtain spiral fringes and embedded vortices is presented. Both beam Bessel obstructio... more A method to obtain spiral fringes and embedded vortices is presented. Both beam Bessel obstruction and interference with a reference wave are involved. Corresponding phase reconstruction is achieved with single shot phase-shifting interferometry.
It has been shown that edge-enhanced images by using optical spatial filtering system of double F... more It has been shown that edge-enhanced images by using optical spatial filtering system of double Fourier-transform can be successfully obtained by implemented the optical Hilbert-transform . This implementation can be obtained by placing a phase step filter of ¿ radians at the frequency plane. Under this background, in this paper, we show how the edge-enhanced of a phase object slice using optical tomography and optical spatial filtering could be obtained. This procedure is principally based by obtaining sequentially the Hilbert-transform of each projection and by applying the filtered back-projection algorithm to obtain the image reconstruction. In this paper, both theoretical analysis and numerical simulations are shown.
Journal of Optics A: Pure and Applied Optics, 2009
A new technique to measure oscillation frequencies and modal shapes of an Euler-Bernoulli cantile... more A new technique to measure oscillation frequencies and modal shapes of an Euler-Bernoulli cantilever beam using dynamic profilometry and phase extraction techniques is presented. The proposed technique does not require a fixed reference or out-of-plane conversion, and works on nonstop vibration. A binary pattern is projected on the cantilever beam surface mechanically forced to vibrate harmonically in a natural mode. The Fourier transform method is employed to obtain the phase difference between two consecutive frames, in particular it is applied to four consecutive frames so that three consecutive phase differences are available. Finally, the three-step temporal phase-shifting technique is applied to measure the vibration's eigenvalues and eigenfunctions. This paper presents the analysis of the underlying theory and the experimental results obtained.
Optics Communications, 2007
A novel phase extraction method for fringe patterns with carrier frequency and with slow variatio... more A novel phase extraction method for fringe patterns with carrier frequency and with slow variation with time is presented. It is based on the Fourier-transform method and on the quotient of the two adjacent frame fringe patterns. The fringe patterns are obtained by fringe projection on a fixed end of a homogenous cantilever undergoing harmonic vibration. Contours of different vibrating modes of the cantilever for frequencies less than that of the camera frame rate (33.3 ms) may be obtained with this method. Results are shown for the theoretical analysis and the experimental mode contours.
Heterodyne holographic interferometry allows high accuracy for phase-difference extraction betwee... more Heterodyne holographic interferometry allows high accuracy for phase-difference extraction between two wave fronts, especially when they are previously recorded in the same recording medium. In part, this is because the wave fronts can be affected by the recording process in a very similar way. The double reconstruction of a doubleexposure hologram with two independent references results in a two-beam holographic interferometer with an arm conveying a wave modulated in frequency when using heterodyne techniques. The heterodyne frequency has been usually introduced with a plane mirror attached to a piezo-electric stack driven with a suitable variable power supply. For holographic interferometry, however, less attention has been devoted to alternative phase retrieval variants as, for example, phase-shifting with modulation of polarization or Fourier methods. In this work, we propose and demonstrate the basic capabilities of modulation of polarization performing as a phase-shifting technique for holographic interferometry with two references in a phase-stepping scheme. Experimental results are provided.
Optics Communications, 2006
An experimental setup for phase extraction of 2D phase distributions is presented. The system use... more An experimental setup for phase extraction of 2D phase distributions is presented. The system uses a common-path interferometer consisting of two windows in the input plane and a translating grating as spatial filter. In the output, interference of the fields associated with replicated images of the input windows is achieved by a proper choice of the windows spacing with respect to the grating period, the focal length of the transforming lens and the wavelength of the coherent illumination employed. Because in this type of grating interferometer a grating is placed as a spatial filter, the phase changes which are needed for phase-shifting interferometry can be easily performed with translations of the grating driven by a linear actuator. Some experimental results are shown.
In this paper, a method for phase retrieval by using Fourier analysis and techniques to solve dif... more In this paper, a method for phase retrieval by using Fourier analysis and techniques to solve differential equations is presented. From the technique proposed by Takeda et al., the function y x, φ ∇
Optics Express, 2008
Among several techniques, phase shifting interferometry can be implemented with a grating used as... more Among several techniques, phase shifting interferometry can be implemented with a grating used as a beam divider to attain several interference patterns around each diffraction order. Because each pattern has to show a different phase-shift, a suitable shifting technique must be employed. Phase gratings are attractive to perform the former task due to their higher diffraction efficiencies. But as is very well known, the Fourier coefficients of only-phase gratings are integer order Bessel functions of the first kind. The values of these real-valued functions oscillate around zero, so they can adopt negative values, thereby introducing phase shifts of pi at certain diffraction orders. Because this almost trivial fact seems to have been overlooked in the literature regarding its practical implications, in this communication such phase shifts are stressed in the description of interference patterns obtained with grating interferometers. These patterns are obtained by placing two windows in the object plane of a 4f system with a sinusoidal grating/grid in the Fourier plane. It is shown that the corresponding experimental observations of the fringe modulation, as well as the corresponding phase measurements, are all in agreement with the proposed description. A one-shot phase shifting interferometer is finally proposed taking into account these properties after proper incorporation of modulation of polarization.
Recibido el 7 de abril de 1992; aceptado el 19 de noviembre de 1992 RESUMEN. Se plantea una práct... more Recibido el 7 de abril de 1992; aceptado el 19 de noviembre de 1992 RESUMEN. Se plantea una práctica de laboratorio para medir los parámetros de Stokes de los haces reflejados y transmitidos por una frontera interdieléctrica cuando el medio de incidencia se caracterice por un Índice refractivo mayor que el medio de transmisión. Se muestran los resultados preliminares de un arreglo experimental según el método propuesto y se comparan los resultados con la teoría.
Journal of Optics, 2012
Some equations were incorrect. Corrected equations are presented in this paper.
Optics Letters, 2008
To extract phase distributions, which evolve in time using phase-shifting interferometry, the sim... more To extract phase distributions, which evolve in time using phase-shifting interferometry, the simultaneous capture of several interferograms with a prescribed shift has to be done. Previous interferometric systems aimed to fulfill such a task were reported to get only four interferograms. It is pointed out that more than four suitable interferograms can be obtained with an interferometer that uses two windows in the object plane, a phase grid as a pupil, and modulation of polarization for each diffraction orders in the image plane. Experimental results for five, seven, and nine interferograms are given.
Optical tomography ofphase objects could be carried out with optical derivatives at the phase det... more Optical tomography ofphase objects could be carried out with optical derivatives at the phase detecting stage. A particularly convenient related technique is the use of a fractional derivative of fractional order 1/2, which consists of a spatial filter with square-root amplitude transmittance. An advantage of this type of filter is that it can be implemented as a real filter when dealing with phase objects. Irradiance is proportional to the phase derivative of order one, and it can be obtained. If a tomographic detection system is equiped with such a filter, phase gradient of projections can be determined, and directional derivatives of phase slices can be displayed. Slice images resulting from an experimental tomographic system for parallel projections includes a spatial filter. with square-root amplitude transmittance made from a liquid crystal display operating in amplitude modulation are shown.
Optics Express, 2011
In this paper, we make a proposal to obtain the Hilbert-transform for each entry of the projectio... more In this paper, we make a proposal to obtain the Hilbert-transform for each entry of the projection data leaving the slice of a thin phase object. These modified projections are stacked in such a way that they form a modified sinogram called Hilbert-sinogram. We prove that the inverse Radon-transform of this sinogram is the directional Hilbert-transform of the slice function, and the reconstructed image is the directional edge enhancement of the distribution function on the slice. The Hilbert-transform is implemented by a 4f optical Fourier-transform correlator and a spatial filter consisting of a phase step of π radians. One important feature of this proposal is to perform a turn of 180° in the spatial filter at a certain value of the projection angle within the range 0 , 360 . The desired direction of enhancement can be chosen by the proper selection of such turning angle. We present both the mathematical modeling and numerical results.
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Papers by Gustavo Rodriguez-Zurita