José A. Gómez-Pedrero

Algorithm for fringe pattern normalization

In this work we present a new algorithm for fringe pattern normalization, that is, background suppression and modulation normalization. Normalization is necessary for several fringe pattern processing techniques. For example, this is the case of the regularization and phase sampling methods. In general, background suppression can be accomplished by high-pass filtering, however if modulation is not constant or almost constant over the field of view, normalization is a difficult task. The solution proposed is based in the use of two orthogonal bandpass filters, from which a normalized irradiance distribution is obtained. We have applied the method to simulated as well as experimental data with good results.

Improved method for isochromatic demodulation by RGB calibration

The red-blue-green (RGB) calibration technique consists in constructing an a priori calibration table of the isochromatic retardation versus the triplet of RGB values obtained with a RGB CCD camera. In this way a lookup table (LUT) is built in which the entry is the corresponding RGB triplet and the output is the given retardation. This calibration (a radiometric quantity) depends on the geometric and chromatic parameters of the setup. Once the calibration is performed, the isochromatic retardation at a given point of the sample is computed as the one that minimizes the Euclidean distance between the measured RGB triplet and the triplets stored in the LUT. We present an enhanced RGB calibration algorithm for isochromatic fringe pattern demodulation. We have improved the standard demodulation algorithm used in RGB calibration by changing the Euclidean cost function to a regularized one in which the fidelity term corresponds to the Euclidean distance between RGB triplets; the regularizing term forces piecewise continuity for the isochromatic retardation. Additionally we have implemented a selective search in the RGB calibration LUT. We have tested the algorithm with simulated as well as real photoelastic data with good results.

Local dioptric power matrix in a progressive addition lens

In this paper we use the formalism of the Dioptric Power Matrix to visualise and characterise the properties of a Progressive Addition Lens. For progressive addition lenses, the dioptric power matrix is point‐dependent, and we have measured its elements over the lens surface by means of an automatic focimeter. We show the obtained contour plots corresponding to the matrix elements, and we compare them with the traditional sphere and cylinder graphs. Although the two representations give the same information, the advantages and disadvantages between them are analysed. The dioptric power matrix method turns out to be specially useful for the computation of prismatic effects along the lens surface.

Measurement of retardation in digital photoelasticity by load stepping using a sinusoidal least-squares fitting

The use of digital photoelasticity permits us to determine the distribution of principal stress difference by means of the analysis of a photoelastic fringe pattern using a phase measurement method. However, conventional phase measurement methods for fringe pattern analysis require the application of an unwrapping process which commonly fails in the presence of discontinuities. To alleviate this problem, load-stepping methods have been developed. We present an alternative load-stepping algorithm that is based on a nonlinear sinusoidal least-squares fitting. The description of this technique together with its verification on simulated and real experiments are presented in this work.

Measurement of surface defects on thin steel wires by atomic force microscopy

The characterisation of surface defects on thin metallic wires is very important for the industrial applications of these wires. The physical dimensions of the surface defects presented by several thin steel wires of different diameters have been measured using Atomic Force Microscopy (AFM). The measurements made show two main defects in thin steel wires: holes and scratches, but other defects like porosity or protuberances have also been observed. We have found an empirical relationship between the physical dimensions of the scratches and the wire diameter.

Wavefront measurement by solving the irradiance transport equation for multifocal systems

A method for sensing wavefronts is presented. The method is based on the resolution of the irradiance transport equation, which relates the irradiance distribution and the shape of the wavefront of a light beam propagating along a given direction. The method presents no restrictions in the locations of the measurement planes and incorporates an improved procedure to geometrically correct the acquired images to take into account the effect of ray deflection in the propagation of the irradiance distributions. With the proposed technique, we measure the wavefront at the exit pupil of a progressive addition lens and find good agreement with an alternative deflectometric method.

A generalization of Prentice's law for lenses with arbitrary refracting surfaces

A generalization of the Prentices law is presented in this paper. The idea consists of removing some (but not all) of the approximations that comprise the paraxial approach. In that way, we obtain a new formulation that permits us to compute the prismatic power of a lens made up of arbitrary refracting surfaces, and to improve the precision obtained by Prentices law when applied to monofocal lenses. The resulting formalism is simple and manageable and its derivation leads us to a precise definition of the local dioptric power matrix, introduced in a previous paper, as well as a better understanding of the same.

Steerable spatial phase shifting applied to single-image closed-fringe interferograms.

It is well known that spatial phase shifting interferometry (SPSI) may be used to demodulate two-dimensional (2D) spatial-carrier interferograms. In these cases the application of SPSI is straightforward because the modulating phase is a monotonic increasing function of space. However, this is not true when we apply SPSI to demodulate a single-image interferogram containing closed fringes. This is because using these algorithms, one would obtain a wrongly demodulated monotonic phase all over the 2D space. We present a technique to overcome this drawback and to allow any SPSI algorithm to be used as a single-image fringe pattern demodulator containing closed fringes. We make use of the 2D spatial orientation direction of the fringes to steer (orient) the one-dimensional SPSI algorithm in order to correctly demodulate the nonmonotonic 2D phase all over the interferogram.

Temporal evaluation of fringe patterns with spatial carrier with an improved asynchronous phase demodulation algorithm

Abstract A method for temporal evaluation of fringe patterns with a spatial carrier is presented. The proposed technique consists in the recording of the temporal irradiance fluctuations obtained when a linear variation of the set-up sensitivity is introduced. In this way, the use of a spatial carrier introduces a linear temporal carrier frequency. This allows the use of fast and low time consuming temporal asynchronous demodulation algorithms, similar to those employed in spatial phase shifting techniques. An existing five-step algorithm has been corrected for asynchronous demodulation. It is shown that it is possible to fix the sensitivity variation in such a way that the algorithm presents optimum behaviour against noise and nonlinearities presented by the temporal irradiance signal. Finally, the technique has been applied to measure the shape of an object, using a fringe projection set-up.

Classification of surface structures on fine metallic wires

In this report a classification of the main surface structures found on fine metallic wires is carried out (between ∼20 and 500 μm in diameter). For this, we have analyzed a series of wires of different metallic materials, diameters and production environments by scanning electron microscopy, atomic force microscopy, and confocal microscopy. A description and the images of the structures is given and, in addition, a nomenclature to be used by manufacturers, customers and researches is proposed. With this information the surface quality of fine metallic wires may be improved in a fabrication level. One of the objectives of this catalogue of defects is to serve as a basis for measuring the quality of the surface of the wires during the production process and the development of a measuring device for that purpose.