Francisco J. Casillas-Rodríguez

Phase recovery from a single interferogram with closed fringes by phase unwrapping

We describe a new algorithm for phase determination from a single interferogram with closed fringes based on an unwrapping procedure. Here we use bandpass filtering in the Fourier domain, obtaining two wrapped phases with sign changes corresponding to the orientation of the applied filters. An unwrapping scheme that corrects the sign ambiguities by comparing the local derivatives is then proposed. This can be done, assuming that the phase derivatives do not change abruptly among adjacent areas as occurs with smooth continuous phase maps. The proposed algorithm works fast and is robust against noise, as demonstrated in experimental and simulated data.

Steps length error detector algorithm in phase-shifting interferometry using Radon transform as a profile measurement

Phase-shifting is one of the most useful methods of phase recovery in digital interferometry in the estimation of small displacements, but miscalibration errors of the phase shifters are very common. In practice, the main problem associated with such errors is related to the response of the phase shifter devices, since they are dependent on mechanical and/or electrical parts. In this work, a novel technique to detect and measure calibration errors in phase-shifting interferometry, when an unexpected phase shift arises, is proposed. The described method uses the Radon transform, first as an automatic-calibrating technique, and then as a profile measuring procedure when analyzing a specific zone of an interferogram. After, once maximum and minimum value parameters have been registered, these can be used to measure calibration errors. Synthetic and real interferograms are included in the testing, which has thrown good approximations for both cases, notwithstanding the interferogram fringe distribution or its phase-shifting steps. Tests have shown that this algorithm is able to measure the deviations of the steps in phase-shifting interferometry. The developed algorithm can also be used as an alternative in the calibration of phase shifter devices.

Phase recovery from interferograms under high amplitude vibrations

A phase recovery procedure using interferograms acquired in highly noisy environments as severe vibrations is described. This method may be implemented when disturbances do not allow obtaining equidistant phase shifts between consecutive interferograms due to tilt-shift and nonlinearity errors introduced by the vibrating conditions. If the amount of the tilt-shift is greater than π radians, it will lead a sign change in the phase estimation. This situation cannot be handled correctly by algorithms that consider small errors or non-equidistant phase shifts during the phase shifting process under moderate disturbances. In experimental applications, it is observed that the tilt-shift is often the most dominant error in phase differences that one must deal with. In this work, a Fourier technique is used for the processing and recovering of the cosine of the phase differences. Once the phase differences are obtained, the phase encoded in the interferograms is determined. The proposed algorithm is tested in two sets of interferograms obtained from the analysis of an optical component, finding an rms error in the phase reconstructions of 0.1388 rad.

Phase tracking with a spatial synchronous method.

A modified form of a phase tracking method to demodulate a single fringe pattern is presented. Phase values from local areas of the interferogram are recovered by means of a spatial synchronous technique instead of solving the set of nonlinear equations obtained from the implementation of the ordinary algorithm. This results in a significant speed improvement of the method. Additionally, the robustness against noise is maintained, and the sensitivity to contrast variations is decremented with respect to the phase tracking technique.

Artificial Visual System Used for Dental Fluorosis Discrimination

A new technique for the estimation of the degree of fluorosis based on Dean Index and artificial vision system to improve the diagnostic of dental fluorosis is proposed. A group of 15 people diagnosed with dental fluorosis according with the Dean Index was studied. The images were digitally processed in order to discern and estimate the dental fluorosis using a discrimination algorithm based on one layer of Artificial Neural Networks and statistics criterion. A vision system and the implemented algorithm showed the ability to detect the different degrees of dental fluorosis in accordance with the diagnosis. Additionally, with this technique it was possible to identify the different affectation degrees of fluorosis by dental piece. The inclusion of a vision system and an algorithm for the estimation of dental fluorosis in this technique contributes as an alternative tool for an objective diagnostic by specialists.

Fourier analysis of quadratic phase interferograms

A phase demodulation method from a single interferogram with a quadratic phase term is developed. The fringe pattern being analysed may contain circular, elliptic or astigmatic fringes. The Fourier transform of such interferograms is seen to be also a sine or a cosine of a second order polynomial in both the real and imaginary parts. In this work we take a discrete Fourier transform of the fringe patterns and then we take separate inverse discrete transforms of the real and imaginary parts of the frequency spectrum. This results in two new interferograms corresponding to the sine and cosine of the quadratic term of the phase modulated by the sine and cosine of the linear term. The linear term of these interferograms may be recovered with similar procedures of fringe analysis from open fringe interferograms. Once the linear term is retrieved the quadratic phase of the interferogram being analysed can also be calculated. The present approach is also being investigated for interferograms with nearly circularly symmetry given that the phase contains some tilt. The described procedure of Fourier analysis from quadratic phase interferograms of nearly symmetric interferograms could be used instead of complex and time consuming algorithms for phase recovery from fringe patterns with closed fringes. Finally, the method is tested in simulated and real data.

Method for measuring the refractive index of liquids using a cylindrical cell

Abstract. A new and simple method for measuring the refractive index of liquid substances is presented. In this method, a laser beam impinges transversely on a glass tube (cylindrical cell) filled with the liquid to be measured. The laser beam incident on the cylindrical cell is deviated when it propagates through the wall of the cell and the liquid contained in it. By measuring the deviation of the principal ray of the laser beam when it emerges from the cylindrical cell, we can determine the refractive index of the liquid. To show the feasibility of the method, we measured the refractive index of pure water with a He-Ne laser.

Phase recovery from interferograms under severe vibrations

A phase recovery procedure from several interferograms acquired in highly noisy environments as severe vibrations is described. This procedure may be implemented when phase shifting techniques may not be applicable due to the high error in the phase shift due to the vibrations. The phase differences among successive interferograms may contain nonlinear terms that could lead a sign changes in the supposed constants shift terms among acquired images. This can not be handled correctly with algorithms that corrects small nonlinearities in the phase shifts due to moderate disturbances during the phase shifting process. In most interferometric configurations for phase measurements the main effect of vibrations is to introduce a misalignment in the interferometric setup. Then, the phase differences between each interferogram may contain piston, tilt, and defocus errors. We observed that the tilt term is often the most dominant of the phase differences terms. In such cases, cosine of the phase differences among interferograms may be recovered. This cosine may be processed with Fourier methods in order to recover the phase differences. Once the phase differences are available the phase encoded in the interferograms may be determined. The proposed algorithm is tested in real interferograms.

Scattering light measurement of optical surfaces using a new dynamic angle limited integrated scattering method

The dynamic angle limited integrated scattering (DALIS) method has been developed to examine optically smooth reflective surfaces with well-defined form. The DALIS system shows advantages over the conventional angle-resolved scattering. We propose a new configuration and results in the DALIS method by using a spherical mirror as a collecting element of the scattered light from the surface of a sample under test. Furthermore, the proposed method improves the detection of the scattered light and is suitable to be applied in workshop inspection during optical polishing processes.