J. A. Rayas

Interferometric measurement of a diffusion coefficient: comparison of two methods and uncertainty analysis

Two methods to measure the diffusion coefficient of a species in a liquid by optical interferometry were compared. The methods were tested on a 1.75 M NaCl aqueous solution diffusing into water at 26 °C. Results were D = 1.587 × 10−9 m2 s−1 with the first method and D = 1.602 × 10−9 m2 s−1 with the second method. Monte Carlo simulation was used to assess the possible dispersion of these results. The standard uncertainties were found to be of the order of 0.05 × 10−9 m2 s−1 with both methods. We found that the value of the diffusion coefficient obtained by either method is very sensitive to the magnification of the optical system, and that if diffusion is slow the measurement of time does not need to be very accurate.

Three-dimensional deformation measurement from the combination of in-plane and out-of-plane electronic speckle pattern interferometers

An optical setup that can be switched to produce in-plane and out-of-plane sensitivity interferometers was designed for three-dimensional deformation measuring by electronic speckle pattern interferometry. Divergent illumination is considered in the evaluation of sensitivity vectors to measure both in-plane and out-of-plane displacement components. The combination of these interferometers presents the advantage of greater sensitivity in directions u, v, and w than a typical interferometer with three illumination beams provides. The system and its basic operation are described, and results with an elastic target that is exposed to a mechanical load are reported.

Fracture detection by grating moiré and in-plane ESPI techniques

Abstract Optical interferometry techniques have been used for high-precision displacement measuring. Commonly, in-plane sensitive arrangements use two symmetrical collimated wavefronts for object surface illumination. However, this is a limitation when large object surface, has to be analyzed. In this case spherical illumination is needed. As a consequence of using non-collimated symmetrical dual-beams the sensitivity vector varies with the local position on the surface target. Then, this kind of illumination is also capable of detecting a lightly and systematic out-of-plane component of deformation. In this paper a theoretical analysis of the sensitivity vector components behavior is made. Each component of the sensitivity vector to minimize the required displacement component uncertainty is calculated. This study is important in the stage of planning any interferometric measurement experiment, particularly, for moire grating interferometric technique, which has been used only in collimated illumination. By using a spherical dual-beam optical setup, the present work shows results of fracture measuring by using moire and speckle interferometric methods. As a result, advantages and disadvantages of both techniques are discussed and an accuracy study is reported.

Error in the measurement due to the divergence of the object illumination wavefront for in-plane interferometers

Commonly, in-plane sensitive interferometric optical arrangements use two symmetrical collimated wavefronts for object surface illumination. However, this is a limitation when large objects have to be analyzed. In this case spherical illumination is needed. Non-collimated symmetrical dual-beam techniques have been performed. This kind of illumination produces a sensitivity vector varying with the position. Then errors in the measurements are introduced when collimated illumination is supposed especially in extended target objects. In the present work, an in-plane configuration for electronic speckle pattern interferometer (ESPI) is used. During the design stage of an interferometer should be useful to know the components of sensitivity vector in order to minimize the un-required displacement components. This is main task of this paper. We present theoretical analysis and experimental results for object divergent and collimated illumination. The errors are obtained by comparing the in-plane displacement calculated supposing constant sensitivity vector and spatial variation of sensitivity vector for object divergent illumination. This analysis is made for a flat and cylindrical object surface target.

High topographical accuracy by optical shot noise reduction in digital holographic microscopy

In this work, we present a new method to reduce the shot noise in phase imaging of digital holograms. A spatial averaging process of phase images reconstructed at different reconstruction distances is performed, with the reconstruction distance range being specified by the numerical focus depth of the optical system. An improved phase image is attained with a 50% shot noise reduction. We use the integral of the angular spectrum as a reconstruction method to obtain a single-object complex amplitude that is needed to perform our proposal. We also show the corresponding simulations and experimental results. The topography of a homemade TiO2 stepwise of 100 nm high was measured and compared with the atomic force microscope results.

Out-of-plane displacement measurement by electronic speckle pattern interferometry in presence of large in-plane displacement

We measured out-of-plane displacement in presence of large in-plane displacements and deformations by electronic speckle pattern interferometry (ESPI). By means of digital speckle photography (DSP) the large in-plane displacement is measured and then compensated by software from interferometric images, before calculating the phase distribution related to the out-of-plane deformation. This means that decorrelation effects are not present and that the use of intermediate images is not necessary. The optical phase was extracted by spatial phase shifting, which enables the study of rapid transient events. The proposed method was applied to different combinations of out-of-plane deformation and large in-plane displacement. The compensation of large in-plane displacement allows us to maintain the contrast of ESPI fringes.

Influence of object roughness on specimen gratings for moire´ interferometry

Moireinterferometry is a high-sensitivity method for whole- field, in-plane displacement measuring. This technique requires the sur- face under test to be mirror-like and prepared with a fine diffraction grat- ing (typically ;1200 lines/mm). Gratings are commonly made of photoresist. However, if we want to analyze engineering structures, to have a surface without preparation under polishing, the surface rough- ness is an important parameter to be characterized. We analyze the fringe visibility of moireduring the fabrication of specimen gratings in function of the surface object roughness. The surface object target is impregnated with photoresist Shipley S1822. Two beams from a He-Cd laser illuminating the surface target are used to record the specimen grating. With a similar optical system we use a He-Ne laser to obtain a virtual grating and consequently the interferometric moirefringes. Through the correlation length and basic statistical the surface rough- ness is characterized.

Uncertainty analysis of displacements measured by in-plane electronic speckle-pattern interferometry with spherical wave fronts

Displacement measurements by optical interferometry depend on the induced phase difference and on the interferometers sensitivity vector; the latter depends in turn on the illuminating sources and on the geometry of the optical arrangement. We have performed an uncertainty analysis of the in-plane displacements measured by electronic speckle-pattern interferometry with spherical incident wave fronts. We induced the displacements by applying a uniaxial tensile load on a nominally flat elastic sample. We approached the displacement uncertainty by propagating the uncertainties that we considered reasonable to assign to the measured phase difference and to the characteristic parameters of the interferometers sensitivity vector. Special attention was paid to evaluating contributions to the displacement uncertainty. Moreover, we observed that the uncertainty decreases if the angles of incidence and the source-target distances are increased.

Half-quadratic cost function for computing arbitrary phase shifts and phase: Adaptive out of step phase shifting

We present a phase shifting robust method for irregular and unknown phase steps. The method is formulated as the minimization of a half-quadratic (robust) regularized cost function for simultaneously computing phase maps and arbitrary phase shifts. The convergence to, at least, a local minimum is guaranteed. The algorithm can be understood as a phase refinement strategy that uses as initial guess a coarsely computed phase and coarsely estimated phase shifts. Such a coarse phase is assumed to be corrupted with artifacts produced by the use of a phase shifting algorithm but with imprecise phase steps. The refinement is achieved by iterating alternated minimization of the cost function for computing the phase map correction, an outliers rejection map and the phase shifts correction, respectively. The method performance is demonstrated by comparison with standard filtering and arbitrary phase steps detecting algorithms.

Measuring object shape by using in-plane electronic speckle pattern interferometry with divergent illumination

Electronic speckle pattern interferometry is a useful technique for displacement, deformation and contouring measurements. Traditionally, for contouring measurements, collimated illumination with a constant sensitivity vector is used, and the surface area analysis is limited to the illuminated area. In some industrial applications, large surfaces require to be analyzed in restricted space conditions. Considering this situation, an optical system with divergent illumination for whole-field measurements can be used. It is known that displacement fields and the optical phase are related by the sensitivity vector. Therefore, to compute the sensitivity vector, illumination position and superficial shape need to be considered, a condition that becomes an impediment for surface contouring if the superficial shape is unknown. In this work, a simple iterative algorithm based on the Gauss–Seidel technique is presented to compute contouring measurements. Contouring measurements from both ESPI and a coordinate-measuring machine (CMM) are compared. In addition, a measurement comparison considering supposed collimated and divergent illumination is presented.