Robust phase demodulation of interferograms with open or closed fringes

We present two robust algorithms for fringe pattern analysis with partial-field and closed fringes. The algorithm for partial-field fringe patterns is presented as a refinement method for precomputed coarse phases. Such an algorithm consists of the minimization of a regularized cost function that incorporates an outlier rejection strategy, which causes the algorithm to become robust. On the basis of the phase refinement method, we propose a propagative scheme for phase retrieval from closed-fringe interferograms. The algorithm performance is demonstrated by demodulating closed-fringe interferograms with complex spatial distribution of stationary points and gradients in the illumination components.     

Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier

We present an optical phase measurement method based on the Hilbert transform for the analysis of a time series of speckle interferograms modulated by a temporal carrier. We discuss the influence of nonmodulating pixels, modulation loss, and noise that affect the bias and modulation intensities of the interferometric signal and propose the application of the empirical mode decomposition method for its minimization. We also show the equivalence between the phase recovery approaches that are based on the Hilbert and the Fourier transforms. Finally, we present a numerical comparison between these methods using computer-simulated speckle interferograms modulated with a temporal carrier.     

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.     

Generation of carrier fringes in holography and shearography

Double-exposure holography and double-exposure shearography are often used together with the carrier fringe technique, which requires additional shifting of the light source in a prescribed manner between exposures. In the holographic carrier fringe technique, difficulty in prescribing a suitable movement of the light source may be alleviated through visualization of the moiré fringes that are reconstructed by slight displacement of two overlaid families of ellipsoids in a holodiagram. Because shearography is the first differential of holography, it is often impractical to perform two successive optical differentiations on the ellipsoids to visualize the shearographic carrier fringes. A simple method of discerning holographic and shearographic carrier fringes is described. The method is based on the hyperboloids in a holodiagram that represent Young's (interference) fringes produced by the interference of two point sources. The hyperboloids are analogous to holographic carrier fringes, whereas the moiré patterns reconstructed from two overlaid hyperboloids are analogous to shearographic carrier fringes. Use of this method for explaining the formation of deformation fringes in plate bending, as well as the effect of light-source movement on the deformation fringes, is also illustrated.     

Phase reconstruction and unwrapping from holographic interferograms of partially absorbent phase objects

A method for automated phase reconstruction from holographic interferograms of nonideal phase objects based on a two-dimensional Fourier transform is described. In particular, the problem of phase unwrapping is solved because earlier techniques are inappropriate for the phase unwrapping from interferograms of partially absorbent objects. A noise-level-dependent criterion for the binary mask that defines the unwrapping path for the flood algorithm is derived. The method shows high noise immunity, and the result is reliable provided that the true phase is free of discontinuities. The phase distribution in the outmasked regions is estimated by a linear least-squares fit to the surrounding unwrapped pixels.     

Recording double-exposure interferograms on a photothermoplastic carrier in photoinduced and photothermoplastic regimes

Technical Physics Letters - It is suggested to record double-exposure holographic interferograms on a photothermoplastic carrier based on chalcogenide glassy semiconductors (CGSs), with the first...     

Real-time holographic vibrometry with a ferroelectric liquid-crystal spatial light modulator

A fast ferroelectric liquid-crystal spatial light modulator, originally developed for optical computing, has found a new application in vibrometry. A new scheme of vibration-synchronized double-exposure holographic interferometry is proposed that makes full use of the speed of the ferroelectric liquid-crystal spatial light modulator. Preliminary experiments were performed that demonstrate virtually continuous real-time vibrometric data acquisition.     

Analysis of interferograms from a diffractive-lens-based common-path interferometer

We present a method of numerical analysis of interferograms for a diffractive-lens-based common-path interferometer recently introduced by Elfstr?m et al. [Opt. Express 14, 3847 (2006)OPEXFF1094-408710.1364/OE.14.003847]. Practical aspects such as the effect of higher diffraction orders upon the interferograms are considered. We show that this method can be used to solve the phase function of the inspected lens. In addition, we show that by using this method it is possible to estimate the focal length and imaging properties of the inspected lens.     

Temperature field measurements of small,nonpremixed flames with use of an Abel inversion of holographic interferograms

Interferometry has been used for many years as a semi-quantitative image-based diagnostic for combustion research. In this paper, we use image-plane, double-pulse holographic interferograms of axisymmetric flames to infer their radial temperature distribution. An Abel inversion is performed on the fringe data to account for line-of-sight integration through the flame. The sensitivity of nonresonant refractive diagnostics decreases inversely with temperature, and the accuracy of the technique is discussed in this context. A small, nonpremixed capillary flame is investigated, and the temperatures inferred from interferometry are compared with those obtained with N2 coherent anti-Stokes Raman spectroscopy thermometry. Additionally, the thermal field of a burning monodisperse methanol droplet stream is investigated interferometrically. Because of their small size, both of these flames challenge the performance limit of temperature interferometery.     

Real-time vibration measurement by a spatial phase-shifting technique with a tilted holographic interferogram

Real-time vibration measurement by a tilted holographic interferogram is presented that utilizes the real-time digital fringe processor of a video signal. Three intensity data sampled at every one-third of the fringe spacing of the tilted fringes are used to calculate the modulation term of the fringe that is a function of a vibration amplitude. A three-dimensional lookup table performs the calculation in a TV repetition rate to give a new fringe profile that contours the vibration amplitude. Vibration modes at the resonant frequencies of a flat speaker were displayed on a monitor as changing the exciting frequency of vibration.     

Partial spatial coherence effects in digital holographic microscopy with a laser source

We investigate a digital holographic microscope that permits us to modify the spatial coherence state of the sample illumination by changing the spot size of a laser beam on a rotating ground glass. Out-of-focus planes are refocused by digital holographic reconstruction with numerical implementation of the Kirchhoff-Fresnel integral. The partial coherence nature of the illumination reduces the coherent artifact noise with respect to fully coherent illumination. The investigated configuration allows the spatial coherence state to be changed without modifying the illumination level of the sample. The effect of the coherence state on the digital holographic reconstruction is theoretically and experimentally evaluated. We also show how multiple reflection interferences are limited by the use of reduced spatial coherent illumination.     

Estimation of insertion loss of a holographic switch with an optically addressed spatial light modulator

We investigate the cause of the insertion loss of our holographic switch by determining the relation between the diffraction efficiency and the hologram patterns generated by the control beams. According to the calculation the theoretical insertion loss is 7.4 dB with loss distribution of 0.03 dB under the conditions of a previous experiment. We find that incomplete storage of the interference pattern on the optically addressed spatial light modulator is the strongest factor determining the insertion loss.     

Local frequency estimation for the fringe pattern with a spatial carrier: principle and applications

A local frequency estimation approach for the fringe pattern with a spatial carrier by which the 2D spatial frequencies at a certain pixel are estimated from its neighborhood is presented. The applications of this approach in the fringe pattern analyses are also introduced. First, a 2D spatial carrier phase-shifting algorithm is derived. With it the detuning errors induced by frequency mismatching are avoided, and the stronger phase deformations can be successfully coped with. Second, a novel aperture extrapolation method is developed by which the phase accuracies of the Fourier-transform method at the aperture boundaries are effectively improved.     

Analysis of color distortions in a transmission-type holographic screen

Full-color transmission-type holographic screens for displaying stereoscopic and multiview images suffer color distortions, especially at their edges. These distortions arise because the reconstructed image of the diffuser appears not at a specified location at different locations for different parts of the screen. Analysis shows that the diffuser strip, which is an object that records the screen, should be extended further in the photoplate direction than in the conventional position to remove the distortions and that use of a short-wavelength laser in the blue spectral region, along with extending the diffuser, is recommended for recording large-sized screens. The analysis also allows the largest sizes of screens that can be recorded for a given set of parameters to be calculated. A comparison of the quality of the images displayed on the screens recorded in the conventional position and in the newly developed position has shown distinctive improvements for the new position.     

Transient deformation measurement with electronic speckle pattern interferometry by use of a holographic optical element for spatial phase stepping

We have used a computer-generated holographic optical element (HOE) with electronic speckle pattern interferometry to calculate the interference phase corresponding to the deformation of a test object from a single TV frame. The HOE is a modified crossed phase grating that introduces a known phase change between the +/-1 diffracted orders, without being translated. The progressive propagation of transient mechanical waves was measured with an rms precision of 2pi/30.     

Temporal phase evaluation by fourier analysis of fringe patterns with spatial carrier

Abstract

A new method is presented for the temporal evaluation of fringe patterns with spatial carrier. The proposed technique involves recording the irradiance fluctuations obtained when a linear variation of the set-up sensitivity is introduced. In this condition, the use of a spatial carrier introduces a linear temporal carrier frequency. In this way, Fourier analysis can be performed to obtain the phase and, finally, the quantity to be measured. The optimum conditions for the sensitivity variation have been studied in order to minimize the errors associated with the Fourier analysis. The technique has been applied to measure the distribution of ray deflections on the surface of two ophthalmic lenses using a deflectometric set-up.     

Conductive properties of foam materials with open or closed cells

The work is devoted to computer simulations of the effective conductive properties of open and closed-cell foam materials. The conductivity of the solid phase of the foam is assumed to be much larger than the one of the filler. For the calculation of the effective conductivity, a complex cell element of the foam that consists of a typical cell and its nearest neighbors is introduced. This element is embedded in the medium with the conductivity of the solid phase. For the calculation of the field and field flux in the complex cell, 3D-integral equations for the fields in heterogenous media are used. The effective conductivity is the coefficient that relates the average field and the field flux in the central part of the complex cell. The method is applied to the calculation of the effective conductivity of open cell foams with various shapes of ligaments. Transition from open to closed-cell foams is considered. Predictions of the method are compared with the experimental data available in the literature.     

Catalogue of photoelastic fringes for a biaxially loaded infinite plate with a hole

This paper presents a typical catalogue of "virtual" photoelastic isochromatic fringes around the hole of a biaxially loaded infinite plate for two problems. Problem 1 relates to an infinite plate in which the circular hole is drilled first and then the loads are applied. Problem 2 is the residual stress problem in which the hole is drilled after the biaxial load is applied to the infinite plate. Use of this catalogue allows visualisation of the stress distribution around the hole, and a first approximation to the solution of the inverse problem using photoelasticity.