Juan Antonio Quiroga

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.

The general theory of phase shifting algorithms.

We have been reporting several new techniques of analysis and synthesis applied to Phase Shifting Interferometry (PSI). These works are based upon the Frequency Transfer Function (FTF) and how this new tool of analysis and synthesis in PSI may be applied to obtain very general results, among them; rotational invariant spectrum; complex PSI algorithms synthesis based on simpler first and second order quadrature filters; more accurate formulae for estimating the detuning error; output-power phase noise estimation. We have made our cases exposing these aspects of PSI separately. Now in the light of a better understanding provided by our past works we present and expand in a more coherent and holistic way the general theory of PSI algorithms. We are also providing herein new material not reported before. These new results are on; a well defined way to combine PSI algorithms and recursive linear PSI algorithms to obtain resonant quadrature filters.

General n-dimensional quadrature transform and its application to interferogram demodulation

Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(phi) into -sin(phi) regardless of the frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of phi over all the domain of interest. Our quadrature operator is composed of two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal. The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward.

Phase measuring algorithm for extraction of isochromatics of photoelastic fringe patterns

In recent years phase-measuring techniques have been applied to the problem of extracting information of photoelastic data. We present a new phase-measuring algorithm for extraction of the isochromatics of photoelastic fringe patterns. The algorithm permits the extraction of the isochromatic phase with almost no influence from the isoclinics, thus avoiding the usual problems of low-modulation areas associated with isoclinics. The isochromatic phase map obtained with this algorithm is well suited for a full separation of the stress components in a sample. The algorithm can be used with any commercial diffuse-light circular polariscope.

Phase-unwrapping algorithm for noisy phase-map processing

Automated fringe-pattern processing is important in a great number of industrial applications, such as optical data testing and quality control. One of the main problems that arises with these processes is the automated phase unwrapping of the phase map associated with the fringe pattern. Usually the phase map presents problems such as noise, and low-modulation areas. A new phase-unwrapping algorithm with high noise immunity is presented. The algorithm is easily implemented and can process arbitrary shapes. The main features of this algorithm are the use of a queue for the processing of arbitrary shapes and a selection criterion that determines which pixels are going to be processed.

Phase-unwrapping algorithm based on an adaptive criterion

A new algorithm for phase unwrapping of phase maps with noise or logical inconsistencies is proposed. It is based on the use of an adaptive threshold and the second difference of the locally unwrapped phase as a selection criterion for the pixels to be processed.

FOURIER TRANSFORM METHOD FOR AUTOMATIC PROCESSING OF MOIRE DEFLECTOGRAMS

In this work, a Fourier transform technique for automatic analysis of moiredeflectograms is presented. A squared grating is used to multiplex the information of the deflection in two orthogonal directions in one image. This procedure avoids the necessity of rotating the grat- ings to obtain the complete deflection information. With this method only two fringe patterns, reference and distorted, are needed to determine the complete deflection information. To deal with irregularly shaped process- ing areas, a Gerchberg extrapolation method is used. The automatic determination of the carrier as well as the size and position of the recon- struction windows permit the complete and automatic measurement of the deflection produced by an ophthalmic lens in two orthogonal direc- tions. Afterwards, the refractive power maps can be obtained. Experi- mental results obtained with a progressive addition lens are presented and comparison with measurements obtained with a commercial focime- ter are shown showing a good agreement.

Adaptive monogenic filtering and normalization of ESPI fringe patterns

A technique is presented for filtering and normalizing noisy fringe patterns, which may include closed fringes, so that single-frame demodulation schemes may be successfully applied. It is based on the construction of an adaptive filter as a linear combination of the responses of a set of isotropic bandpass filters. The space-varying coefficients are proportional to the envelope of the response of each filter, which in turn is computed by using the corresponding monogenic image [Felsberg and Sommer, IEEE Trans. Signal Process. 49, 3136 (2001)]. Some examples of demodulation of real Electronic Speckle Pattern Interferometry (ESPI) images patterns are presented.

Fast two-dimensional simultaneous phase unwrapping and low-pass filtering.

Here, we present a fast algorithm for two-dimensional (2D) phase unwrapping which behaves as a recursive linear filter. This linear behavior allows us to easily find its frequency response and stability conditions. Previously, we published a robust to noise recursive 2D phase unwrapping system with smoothing capabilities. But our previous approach was rather heuristic in the sense that not general 2D theory was given. Here an improved and better understood version of our previous 2D recursive phase unwrapper is presented. In addition, a full characterization of it is shown in terms of its frequency response and stability. The objective here is to extend our previous unwrapping algorithm and give a more solid theoretical foundation to it.

Regularized quadrature and phase tracking from a single closed-fringe interferogram

A new sequential phase demodulator based on a regularized quadrature and phase tracker system (RQPT) is applied to demodulate two-dimensional fringe patterns. This RQPT system tracks the fringe patterns quadrature and phase in a sequential way by following the path of the fringes. To make the RQPT system more robust to noise, the modulating phase around a small neighborhood is modeled as a plane and the quadrature of the signal is estimated simultaneously with the fringes modulating phase. By sequentially calculating the quadrature of the fringe pattern, one obtains a more robust sequential demodulator than was previously possible. This system may be applied to the demodulation of a single interferogram having closed fringes.