Benito Vasquez Dorrio

Phase error calculation in a Fizeau interferometer by Fourier expansion of the intensity profile

The spectrum of the intensity profile of multiple-beam Fizeau interferograms is presented. Knowledge of this spectrum provides valuable information about the characteristics of Fizeau interferograms, allowing one to calculate the phase error when the Fizeau profile is evaluated by means of two-beam phase-stepping algorithms, as is usual for low-reflectivity coefficients.

Fizeau phase-measuring interferometry using the moiré effect

The automation of the fringe pattern analysis in Fizeau interferometry combining the moiré effect with the phase-stepping evaluation method is presented. In this case the phase modulator is a Ronchi grid placed at the interferometer image plane yielding a moiré image, and the necessary phase steps are obtained, simply translating the grid in its own plane, perpendicular to the optical axis. A detailed description of the moiré image formation as an incoherent superposition is developed. Measurements were carried out in a Fizeau interferometer built by the authors, and rms repeatabilities of less than 3 deg in the phase-difference values were attained.

Fibreoptic reflectometric technique for the automatic detection and measurement of surface cracks

A new fibreoptic reflectometric technique for the automatic detection and measurement of surface cracks is proposed, described and analysed. A relationship between the system output image and the surface crack distribution is obtained from theory and a crack measurement principle is derived. Analysis of the experimental data obtained using a first laboratory prototype has validated the proposed measurement principle. The results of a second generation prototype confirm that the technique promises to be a valuable tool in practical inspection tasks.

A multiplicative analogical moiré phase-shifting Twyman-Green technique for Nd:YAG rod wavefront distortion measurement

Nd:YAG rod wavefront distortion has been quantified in a Twyman-Green interferometer which employs the multiplicative analogical moire phase-shifting method for demodulation. The measuring procedure is based on the superimposition of a transmission grating located outside the interferometric module with a phase modulated high-frequency Twyman-Green spatial carrier. Later, a set of fringe patterns, provided by low-pass filtering of the phase-shifted multiplicative moire patterns obtained, is combined in a generic phase-shifting algorithm (GPSA). The interesting test information is achieved once the previous procedure has been carried out with and without the transparent object located in the measuring area. The wavefront distortion (WFD) is calculated by the subtraction of these results provided by the GPSA, or directly if a differential phase-shifting algorithm (DPSA) is employed. The WFD obtained is in accordance with characteristics of the test object. The comparison of the results obtained with both families of algorithms provides information about the sensitivities to error sources of the DPSA employed. A first approximation to the analysis of significant error sources of DPSAs is presented.

Transparent object analysis in a Mach-Zehnder interferometer using the multiplicative analogical moire phase-shifting method

Transparent object Wave-Front Distortion has been measured in a Mach-Zehnder interferometer employing as evaluation tool the Multiplicative Analogical Moire Phase-Shifting Method. The measuring procedure is based on the direct superimposition of a transmission grating with a phase modulated high-frequency Mach-Zehnder spatial carrier. Latter, a set of phase-shifted fringe patterns, provided by low-pass filtering of the obtained multiplicative moire patterns, is combined in a Generic Phase-Shifting Algorithm (GPSA). The interesting information is achieved once the previous procedure is carried out with and without the transparent object located at the measuring area. The Wave- Front Distortion can be calculated by subtraction of these results provided by the GPSA or directly if a Differential PSA is employed. A comparison of the results obtained with both algorithms has been done.

The spatial resolution performance of a fibre-optic reflectometric technique for the automatic detection and measurement of surface cracks

We present an analysis of the spatial resolution achievable with a new fibre-optic reflectometric technique, contrived by the authors for the automatic detection of cracks in the inner sides of steam generator tubes of small diameter (≃20 mm). An analytical expression of the modulation transfer function (MTF) of our measurement system is obtained, from which the resolution limit of the technique is defined. Experimental values of the MTF, measured with a first laboratory prototype, are compared with the theoretical predictions and the range of validity of the theoretical expressions is discussed. Also, some of the results obtained with a second-generation prototype are presented, it being demonstrated that parallel cracks with a spacing of 50 μm between adjacent edges can be resolved in practical inspection tasks.

Transient bending wave analysis by Fourier evaluation of single-pulsed TV holography fringe patterns

In this paper we demonstrate the feasibility of impact- induced transient deformations measurement by single-pulsed subtraction TV holography an the Fourier transform method with contouring fringes as spatial carrier. Fringe formation in single-pulsed subtraction TV holography and phase demodulation by the Fourier transform method are descried. Contouring fringes are proved to be well suited for introducing spatial carrier in the correlation fringe patterns. Experimental results are presented. Finally, the degree of immunity to environmental disturbances of this technique is discussed and improvements are proposed.

Measurement range analysis in moiré evaluation Fizeau interferometry.

Fizeau interferograms are evaluated by two-beam phase-stepping algorithms. The sinusoidal intensity profile pattern needed for the application of these algorithms is obtained by low-pass filtering the moiré pattern provided by the superposition of the interferogram onto a Ronchi grid. The phase modulation is performed by the in-plane displacement of the grid by means of a motorized stage. In this research the measurement range of the evaluation method as a function of the maximum derivative of height surfaces is calculated. A spherical surface is measured in different configurations in order to verify the obtained results.

Crack detection by TV holography: continuous and pulsed techniques

Two TV-holographic techniques to detect cracks in mechanical elements are demonstrated. One of them employs continuous illumination and is based in the modal analysis of the part. The other one consists in the study by pulsed TV-holography of transient waves induced in the part.

Surface evaluation combining the moire effect and phase-stepping techniques in Fizeau interferometry

The usual phase-stepping algorithms are employed to evaluate the phase of Fizeau interferograms in topographic measurements. The superposition of the interferogram with a Ronchi grid provides a Moire pattern. The phase modulation is obtained by the in plane displacement of the grid, while a sinusoidal intensity pattern is obtained by defocusing the image acquisition system. In this work, the measurement range of the method in the function of the maximum variation of height surfaces is calculated and verified.