Francisco G. Peña-Lecona

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.

Measurement of the refractive index by using a rectangular cell with a fs-laser engraved diffraction grating inner wall

A very simple method to obtain the refractive index of liquids by using a rectangular glass cell and a diffraction grating engraved by fs laser ablation on the inner face of one of the walls of the cell is presented. When a laser beam impinges normally on the diffraction grating, the diffraction orders are deviated when they pass through the cell filled with the liquid to be measured. By measuring the deviation of the diffraction orders, we can determine the refractive index of the liquid.

The Ronchi test using a liquid crystal display as a phase grating

The Ronchi test with a Liquid Crystal Display (LCD) phase grating is used for testing convergent optical systems. The rulings are computer-generated and displayed on the LCD. We prove that it is possible to make a variable electronically phase grating by using an LCD. By displaying various phase-shifted rulings and capturing the corresponding ronchigrams, the phase is obtained with the conventional phase-shifting algorithms. Experimental results are shown.

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.

Discretization of quasi-sinusoidal diffraction gratings printed on acetates

The aim of this work is to propose the use of printed acetate sheets as quasi-sinusoidal diffraction gratings, as low-cost alternative gratings for application in non-invasive optical tests. Gratings were generated with Matlab® software and made with various models of laser printers. A study of the discretization effects that depend on the symmetry in the sample was included, gratings were placed in the entrance pupil of a positive lens (illuminated by a collimated plane wave) to observe their Fourier transforms. It was found that diffraction patterns of various types of semi-sinusoidal profiles were very close to that of sinusoidal gratings. Gradual change in the size of printed ink spots was observed in more detail through a magnification of 40x. Additionally, an atomic force microscope was used to measure the roughness average of the impressions as to observe the behavior of the ink on the acetate.

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.

Comparison between quasi-sinusoidal and quasi-triangular profiles for diffraction gratings printed on acetates

The aim of this work is to propose the use of printed acetate sheets as quasi-sinusoidal and quasi-triangular diffraction gratings, as low-cost alternative gratings for application in non-invasive optical tests. Gratings were generated with Matlab® software and made with various models of laser and inkjet printers. A study of the profile gratings that depend on the symmetry in the sample was included, gratings were placed in the entrance pupil of a positive lens (illuminated by a collimated plane wave) to observe their Fourier transforms. It was found that diffraction patterns of various types of quasi-sinusoidal and quasi-triangular profiles were very close to that of sinusoidal gratings. Gradual change in the size of printed ink spots was observed in more detail through a magnification of 40x. Additionally, an atomic force microscope was used to measure the average superficial roughness of the impressions as to observe the behavior of the ink on the acetate.