Direct unwrapped phase estimation in phase shifting interferometry using Levenberg-Marquardt algorithm

An algorithm for the direct unwrapped phase estimation from the linearly phase shifted interferograms is presented. The temporal fringe intensity along each pixel is represented as a function of fringe amplitude, phase step and the searched phase. These parameters are estimated in the nonlinear least squares sense using the Levenberg-Marquardt algorithm. The proposed method allows the masked interferograms to be handled using a pixel selection approach to provide the appropriate initial conditions at a given pixel utilizing the estimated parameters at one of its neighboring pixels, which results in direct unwrapped phase estimation. Simulation results are provided to evaluate the performance of the proposed method as a function of noise power, spatially varying phase step, number of interferograms and phase step detuning error. The experimental results are also provided in the case of a holographic interferometry setup.

Phase estimation from noisy phase fringe patterns using linearly independent basis functions

Rishikesh Dilip Kulkarni, Pramod Rastogi

A novel technique is proposed for obtaining unwrapped phase estimation from a highly noisy exponential phase field. In this technique, the interference phase is represented as a linear combination of linearly independent and pre-defined basis functions along each row/column of the phase field at a time. Consequently, the problem of phase estimation is converted into the problem of the estimation of the weights of the basis functions. The extended Kalman filter formulation allows for the accurate estimation of these weights. The simulation results indicate that the formulation offers a strong noise robustness in the phase estimation. Experimental results obtained using digital holographic interferometry and digital speckle pattern interferometry setups are provided to demonstrate the practical applicability of the proposed method.

Iop Publishing Ltd2015

Spatial Fringe Analysis Methods and their Application to Holographic Interferometry and Fringe Projection Techniques

Sai Siva Gorthi

To date, no fringe analysis technique has the capability to provide simultaneous and direct estimation of the continuous distributions corresponding to the interference phase and its first and second-order derivatives within the framework of a single interferometric configuration. Achieving this task would provide a significant advancement in the field of optical metrology as it allows for the measurement of displacement, strain, and curvature of a deformed object and avoids the necessity of using filtering and unwrapping procedures, multiple analysis techniques, and multiple interferometric configurations. Developing such a spatial fringe analysis method with the added advantage of having less computational complexity would open up avenues for making real-time measurements such as in the study of temporal evolution of deformation and/or strain. This thesis presents a novel approach based on piecewise polynomial phase approximation as an elegant all-in-one solution to the problems mentioned above. This approach has given birth to several advanced fringe analysis methods such as discrete-chirp-Fourier transform method, high-order instantaneous moments method, and cubic-phase function method. Significant advancements brought in the field by these methods are made evident by both theoretical analysis (simulation results) and by experimental demonstrations such as the measurement of displacement, strain and curvature in digital holographic interferometry and the measurement of 3D shape, temporal evolution of deformation and/or strain in fringe projection techniques.

EPFL2010

Numerical simulation of a sailing boat

Matteo Lombardi

In this work, various aspects concerning the numerical simulation of a sailing boat are investigated. The attention is focused on simulation of the free-surface, the fluid-structure interaction (FSI) between wind and sails, and the dynamics of the whole boat. Some preliminary work on shape optimization is also presented. Free-surface simulations are carried out both on classical academic benchmark problems and for the prediction of the wave pattern around racing yachts. The comparison with experimental results and numerical data obtained with other CFD codes has proven the validity of the proposed set-up. In this framework, the Level Set method has been implemented and validated as a possible solution to the problem of interface diffusion arising in planing conditions with the standard Volume of Fluid approach. The FSI problem governing the interaction between wind and sails is solved via a strongly coupled segregated approach based on the standard Dirichlet-Neumann coupling. The structural solution is based on a MITC4 finite-element shell code. The fluid and structural meshes are non-conforming and the exchange of information at the interface is obtained via radial basis functions (RBF) interpolation. The fluid mesh motion is accomplished either through the mapping generated using the radial basis functions or via a method based on the inverse distance weighting (IDW) interpolations. The attention is paid to the methodological aspects of this complex problem and to the analysis of the numerical results. The fluid-structure interaction simulations of one and two sail configurations, with different trimmings, are presented; both steady and transient simulations are performed. The results obtained are very encouraging and show the potential of the proposed model. The dynamic motion of the Series 60 hull and the Alinghi’s AC 32 monohull complete of bulb, keel and sails have also been investigated. For the latter in particular, the free sink, trim and roll case has proven to be particularly interesting, with the boat rolling considerably on the side due to the aerodynamic loads exerted by the wind on the sails. Here, the whole boat has been considered as a rigid body but the integration of the FSI module for the sails into the full boat dynamic system is already under development. Finally, a preliminary analysis of shape optimization techniques applied to sailing boat elements have been investigated: in particular the attention has been focused on the drag minimization of (pseudo) bulb geometries under the constraint of fixed volume/fixed righting moment. The shape parametrization have been achieved either using directly the surface element nodes or via the Free Form Deformation (FFD) technique while the optimization algorithm has been based either on the solution of the adjoint Navier-Stokes equations or via pseudo finite-difference algorithms. The algorithm and developments mentioned have been implemented in a common open-source framework, the library OpenFOAM®.

EPFL2012

Numerical simulation of a sailing boat

Matteo Lombardi

EPFL2012