Noé Alcalá Ochoa

Convenient method for calibrating nonlinear phase modulators for use in phase- shifting interferometry

A method to calibrate a nonlinear phase modulator is de- scribed that is based on the minimization of a function obtained from a sequence of interferometric images. The method is equally applicable to smooth wavefront and speckled wavefront interferometry, allowing con- venient in situ calibration for a wide range of interferometer configura- tions. The main advantage over previous calibration methods is that both the linear and quadratic phase variation terms are measured. The per- formance of the proposed method is verified by experiments in which the phase shift is determined independently by a Fourier transform method.

Contrast enhancement of electronic speckle pattern interferometry addition fringes.

The electronic speckle pattern interferometer in the double-pulse addition mode can be used to measure physical parameters in unstable environmental conditions. Owing to additive optical noise, however, the fringe patterns obtained have poor contrast. Some methods that use subtraction of addition double-pulsed fringe patterns improve fringe visibility but impose a limitation in measurement time ranges. To increase this range, to be limited by only the pulse separation, the contrast enhancement of double-pulsed addition-fringe patterns with a spatial filter based on local-standard-deviation measurements is investigated. Computer simulations and experimental results are presented.

The Ronchi test with an LCD grating

A low cost liquid crystal display (LCD) is used to perform the optical test of polished mirrors. The method is based on a typical Ronchi test configuration where the LCD acts like a grating and a phase shifting device.

Sinusoidal liquid crystal display grating in the Ronchi test

The Ronchi test with a LCD amplitude sinusoidal grating is used for testing convergent optical systems. The rulings are computer- generated and displayed on the LCD. By displaying various phase- shifted rulings and capturing the corresponding images, the phase is obtained with the conventional phase-shifting algorithms. For reference, experimental results are compared with those on a commercial Fizeau interferometer.

Flatness measurement by a grazing Ronchi test

The Ronchi test with a LCD amplitude sinusoidal grating is used for testing nominally flat surfaces. We prove that it is possible to measure flat surfaces without using a reference element by modifying the common optical Ronchi set up. The Ronchi rulings are computer generated and displayed on the LCD. By displaying various phase-shifted rulings and capturing the corresponding images, the phase is obtained with the conventional phase-shifting algorithms. Theoretical and experimental results are shown.

Noise reduction in twin-pulsed addition electronic speckle pattern interferometry fringe patterns

Addition fringe patterns are obtained in real time with electronic speckle pattern interferometry (ESPI) when two pulses are fired within a single field of a COD camera, i.e., within 1/50 s. The ability to use ESPI in this manner means that target deformation can be studied in very severe environments. A major drawback is that the addition fringes are intrinsically noisy and of very low contrast, impeding a full analysis of the deformation. Experimental results are presented for two methods of reducing noise in addition fringe patterns: subtraction of a reference frame and subtraction of addition fringe patterns. The subtraction procedure leads to high-contrast fringes, which can contain information of both target deformation and rigid body motion. An analytical representation of this behavior is presented.

Super-resolution with complex masks using a phase-only LCD.

Two methods to achieve super-resolution with complex masks displayed in one-phase-only liquid crystal display (LCD) are described. The first method decomposes the complex mask into two phase-only elements with a posterior recombination using an interferometer, and the second method simultaneously encodes the amplitude and the phase by modulating the amplitude of the carrier phase. Experimental results are presented using a liquid crystal on silicon spatial light modulator under reflection.

Non-iterative method for designing super-resolving pupil filters

We propose a method of designing pupil filters for transverse super-resolution without making use of recursive algorithms or the parabolic approximation for the point spread function (PSF). We represent the amplitude of the PSF as an expansion of orthogonal functions from the Fourier-Bessel transform of a Dini series. Their coefficients are related with desired features of the PSF, such as the transversal super-resolution gain and the intensity of the secondary maxima. We show the possibility to derive closed formulas to obtain large super-resolution gains with tolerable side-lobe intensities, at the expense of increasing the intensity of a chosen secondary lobe.

Multiplicative electronic speckle-pattern interferometry fringes

A theoretical analysis of fringe patterns and its experimental corroboration obtained by multiplication of two speckled images with electronic speckle-pattern interferometry (ESPI) are reported. A specifically designed digital filter is used to enhance the contrast and visibility of the inherently noisy multiplication fringes. Phase retrieval is achieved by a phase-stepping technique. Experimental results are presented for the in-plane-sensitive optical ESPI setup; however, out-of-plane and shearing setups may be used as well. The method represents an alternative to the subtraction and addition techniques in ESPI.

Normalization and smoothing algorithm for electronic speckle-pattern interferometry fringes

This work points out that a modification of the fringe analysis method proposed by Kreis may serve as a normalization and filtering method for electronic speckle-pattern interferometry (ESPI) fringes. By rotating a half-plane in the frequency space, a fringe pattern may be normalized without being distorted significantly. If a passband filter is used during the rotation, a smoothed fringe pattern is obtained. Experimental verification is presented using images obtained from ESPI.