Phase unwrapping is an intermediate step for interferogram analysis. A smooth phase associated with an
interferogram can be estimated using a curve mesh of functions. Each of these functions can be approximated
by a linear combination of basis functions. In some cases constraints are needed to solve the phase unwrapping
problem, for example, when estimated values never can be negative. In this work it is proposed a method for
phase unwrapping using a set of functions in a mesh which are lineal combinations of Chebyshev polynomials.
Results show good performance when applied to noisy and noiseless synthetic images.
The large number of projections needed for tomographic reconstruction makes prohibitive the use of algebraic methods for fast phase object reconstruction. However, for smooth and continuous phase objects, the reconstruction can be performed with few projections by using an algorithm that approximates the phase as a linear combination of gaussian basis functions. This work presents an accurate algebraic reconstruction of a flame temperature from two independent interferometers using a He-Ne laser (623.8nm).
Refractive index, temperature, pressure, velocity and many other physical magnitudes of phase objects in the refraction less limit are of great interest in engineering and science. Optical tomography is a technique used to estimate these magnitudes. For axially symmetrical phase objects the tomographic reconstruction can be carried out from just one projection when using Abel transform. However, for noisy projections the reconstruction shows low quality. This quality can be improved when using the Kalman filter to compute the inverse Abel Transform. In this paper a tomographic reconstruction method for syntectic axially symmetrical phase objects using Kalman filter is presented.
Phase unwrapping is an intermediate step for interferogram analysis. The phase associated with an interferogram can be estimated using a curve mesh of functions. Each of these functions can be approximated by a linear combination of basis functions. Chebyshev polynomials in addition to being a family of orthogonal polynomials can be defined recursively. In this work a method for phase unwrapping using Chebyshev polynomials is proposed. Results show good performance when applied to synthetic images without noise and also to synthetic images with noise.
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