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).
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.
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.
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 wrapping is an intermediate step ffor interferometry analysis. When phase is smooth, its unwrapping can be carried out fitting local planes with finite extension at each point of the phase gradient. We propose a method easy to implement that spends the same computation time than those techniques based on basis functions.
A simple method for phase unwrapping is proposed. When phase is smooth, continuous and slightly noisy,
morphological processing can be used to estimate the unwrapped phase. The application of morphological processing
converts the continuous (real) range [-π, π) into a discrete (integer) range. This domain transformation
may allow an increase of speed performance in the unwrapping phase processing. Since the wrapped phase is
modulo 2π, it is possible to delimit regions with 4-connectivity that allows the proper phase map estimation.
The maximum intensity of the noise that allows a good reconstruction of the original phase map was 2.
Many problems in metrology and optical tomography have to recover information from the wrapping phase. In most of the cases, phase, that is associate to a physical magnitude, is continuous and generally, varies smoothly. Therefore, we can say that the problem in these cases is reduced to find a continuous phase. Considering this, many solutions to this kind of problems have been proposed, from the use of local planes to the implementation of most robust algorithms. However, these methods are also very slow. That is why the unwrapping problem is an open subject research in optics. We propose a phase unwrapping method based on finite differences that is fast and robust. In addition, it is easy to program.
Proc. SPIE. 6024, ICO20: Optical Devices and Instruments
KEYWORDS: Signal to noise ratio, Diffraction, Optical transfer functions, Point spread functions, Visualization, Imaging systems, Image processing, Image resolution, Wavefronts, Wigner distribution functions
The aim of this work is to propose a positiveness constraint on the Wigner Distribution Function (WDF) of the detected image of two incoherent point sources: if WDF lacks of zeroes along the frequency coordinate the object can not be resolved by imaging and detected systems; otherwise, it can. This criterion can be applied without preference for a circular clear diffraction limited aperture and for complex apertures with small aberration values; furthermore, it holds if the intensity of each source is different or even when the sources are not points.
We propose an algebraic reconstruction method (ART) based on smooth functions to obtain the refraction index distribution of a radially symmetric phase object. Recovering the refraction index of a transversal section enables us to obtain some other physical variables such as temperature, pressure, etc. Considering phase objects with a radially symmetric distribution allows the recovery of information regarding the volumetric distribution of the refraction index based on a single projection. The proposed method is accurate, faster, and somewhat easier to implement than other currently used ART methods. As a sample application, the proposed method is applied to a burning candle case.
We propose an algebraic method of tomographic reconstruction based on basis radial functions. This method minimizes the quadratic error and is aimed to be used in smooth cross sections. Unlike Kaczmarz's method, the proposed method obtains a good estimation of the cross section with an inconsistent projections diagram although its computing time is increased.