Jesus Blanco-Garcia

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.

Comparison of carrier removal methods in the analysis of TV holography fringes by the Fourier transform method

Carrier removal is a key step in the Fourier transform method (FTM) of fringe pattern analysis because it can give rise to significant errors in the recovered phase. The existing methods of fringe carrier removal in the FTM are reviewed and a comparison of three different methods, translation of the sidelobe to the frequency origin, leastsquares fit and subtraction of the phase of the undeformed carrier fringes, are presented. Computer-generated fringe patterns are used to determine the differences between the original and the retrieved phase distributions. Several figures of merit are proposed to assess the performance of the mentioned methods. Experimental fringe patterns, obtained by double-pulsed-subtraction TV holography, are analyzed by the methods considered here, and the retrieved phase distributions are also compared.

Transient deformation measurement by double-pulsed-subtraction TV holography and the Fourier transform method

We report the measurement of transient bending waves with double-pulsed-subtraction TV holography. The correlation fringe patterns are automatically quantitatively analyzed by the application of Fourier methods. A novel optical setup with two different object-beam optical paths is demonstrated for the generation of carrier fringes. The proposed system is highly immune to environmental disturbances because the optical setup imposes no lower limit on the time separation between laser pulses. One removes the linear phase distribution due to the spatial carrier in the spatial domain by subtracting the phase of the undeformed carrier fringes from the phase of the modulated fringes. Experimental results obtained with an aluminum plate excited by the impact of a piezoelectric translator are presented.

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.

Double-pulsed-carrier speckle-shearing pattern interferometry for transient deformation analysis

We report on a novel technique for the evaluation of transient phase in double-pulsed electronic speckle-shearing pattern interferometry. Our technique requires the acquisition of just two speckle-shear interferograms which are correlated by subtraction to obtain a fringe pattern. A spatial carrier is generated by means of an original optical setup based on the separation and later recombination of the two beams produced by a Nd:YAG twin pulsed laser. One introduces an optical path difference in the curvature radii of the illumination beams by mismatching the distances from two diverging lenses to a beam combiner. This procedure gives rise to a linear phase term in the second speckle- shear interferogram that plays the role of a spatial carrier and allows the use of spatial phase measurement methods to analyze the fringe pattern. We present the theoretical aspects of the technique as well as its experimental implementation.

An ESPI system for determining in-plane deformations. Three-dimensional analysis of the carrier fringes and a proposal for analysis of transient in-plane deformations

In this work we report results on analysis of in-plane deformation using the symmetrical illumination technique. A single illumination source is doubled by means of a mirror placed perpendicular to the object being tested. Carrier fringes are introduced by displacing the symmetrical sources (one of which is virtual), a technique often used in contouring. We present a three-dimensional theoretical model for the generation of the carrier fringes and analyse the basic concepts of this model. Experimental results obtained using a cw laser are also presented. These results and the ones obtained by applying this technique to out-of-plane and shearing systems are the basis for proposing the application of the concept to analysis of in-plane transient deformation using a double cavity Nd:YAG laser. A convenient set-up for that purpose is described.

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.

Multiplicative moiré two-beam phase-stepping and Fourier-transform methods for the evaluation of multiple-beam Fizeau patterns: a comparison

A phase-evaluation method of multiple-beam Fizeau patterns that combines two-beam phase-stepping algorithms with the moiré effect was previously reported [Appl. Opt. 34, 3639-3643(1995)]. The method is based on a multiplicative moiréimage-formation process obtained by the direct superposition of high-frequency multiple-beam Fizeau carrier fringes upon a transmission grating (working as a phase modulator). We present a comparison between this multiplicative moiré two-beam phase-stepping method and the well-known Fourier-transform method for the topographic measurement of an undoped silicon wafer. The discrepancy between the two methods yields a rms phase-difference value of the order of(~2pi/90).

Design of a New Microcontroller-Based Vernier Fringe Counter for Interferometric Measurement of Laser Wavelength

This paper presents a new electronic Vernier fringe counter for the wavelength measurement of a diode laser in a scanning interferometer. The system is intended to be a low cost alternative to commercial systems used for gauge block calibration. The counter stage and phase coincidence detector are made with a microcontroller and high-speed CMOS logic to achieve the required resolution. The microcontroller also can synchronize with other elements to make a fully automated measurement system. This electronic design improves the resolution of the electronic counters in the previous designs.

Study of plate vibrations by moire holography

Advantages of moire holography with single illumination beam as a real-time method to detect vibrational modes of diffusing objects have been already experimentally demonstrated by several authors. The main obstacle to automatizing the analysis of the moire pattern is the difficulty in filtering the carrier pattern. At the present, it seems affordable to realize filtering in quasi-real time by means of a digital image-processing system. However, several problems arise in this operation, for example, the spread of the spatial frequency spectrum of the carrier fringes. Different filtering algorithms, with and without FFT, are compared. Different ways to combine both carriers are examined.