UKF based multi-component phase estimation in digital holographic Moiré
01 Dec 2013-pp 1-4
TL;DR: A novel method, based on Unscented Kalman Filter (UKF), is introduced for the estimation of multiple phase maps from a complex multi-component signal encountered in digital holographic moiré.
Abstract: Simultaneous measurement of multi-dimensional deformations can be done in digital holographic Moire by illuminating the object with multiple beams from different angles and recording the interference pattern due to multiple beams. This technique involves reliable estimation of resultant multiple phase maps from a one record of the reconstructed interference moire field. In this paper, we introduce a novel method, based on Unscented Kalman Filter (UKF), for the estimation of multiple phase maps from a complex multi-component signal encountered in digital holographic moire. The State space model used in this method is determined by Taylor series expansion of phase component as process model and polar to Cartesian conversion as measurement model.
Citations
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28 Feb 2017
TL;DR: A new method to reconstruct surface of a 3D object by processing its 2D holographic signal, based on Extended Kalman Filter (EKF), which has good performance on removing noise and has been successfully used in recovering topography in InSAR.
Abstract: Holographic [1] signals are one of the visual signals which are important and popular, because after proper processing they enable viewers to watch 3D scenes without wearing any external equipment. Holographic technology, though not mature yet, is thus believed to be the ultimate way of 3D display. However, current optical viewing methods are not mature in accuracy. Under this circumstance, research on holographic signal processing is mostly carried out in computers. A complete system can be set up in computers to simulate the whole procedure. However, in such a system, there is a major problem. That is how to view reconstructed 3D objects on a 2D computer screen so that the output of the system can be evaluated. One commonly-used method is to obtain 2D projection images at different distances from hologram plane. However, this method can only show the front views of reconstructed 3D objects, thus is not suitable for comprehensively evaluation. Another method is to solve the problem by surface reconstruction, which can view the reconstructed 3D objects from different angle of view. Surface reconstruction can be done by estimating phase in light field [3]. There are several methods dealing with it. For example, there are norm based methods like least-squares, path-following methods like branch-cut, Fourier method, and energy minimization method. However, most of them don’t perform very well because their anti-noise characteristics are not so good. In [4], authors use Unscented Kalman Filter (UKF) to solve noise problem and prove that UKF is effective in removing AWGN noise. But they don’t give demonstration about its specific application in holographic signal reconstruction. In this paper, we propose a new method to reconstruct surface of a 3D object by processing its 2D holographic signal. The method is based on Extended Kalman Filter (EKF). EKF has good performance on removing noise [2], and has been successfully used in recovering topography in InSAR [5]. The anti-noise characteristics of EKF will extend our method to various scenes. Our method involves pre-filtering, EKF, and self-adaptive weighting. With our method, the reconstructed 3D object can be viewed on a 2D screen. This will certainly facilitate future research on signal processing of 3D holograms.
Cites methods from "UKF based multi-component phase est..."
...In [4], authors use Unscented Kalman Filter (UKF) to solve noise problem and prove that UKF is effective in removing AWGN noise....
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...[4] RG Waghmare, "UKF based multi-component phase estimation in digital holographic Moiré", NCVPRIPG, 2013 [5] B Osmanoğlu, "InSAR phase unwrapping based on extended Kalman filtering", Radar Conference, 2009....
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References
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08 Nov 2004
TL;DR: The motivation, development, use, and implications of the UT are reviewed, which show it to be more accurate, easier to implement, and uses the same order of calculations as linearization.
Abstract: The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT.
6,098 citations
TL;DR: The principles and major applications of digital recording and numerical reconstruction of holograms (digital holography) are described, which are applied to measure shape and surface deformation of opaque bodies and refractive index fields within transparent media.
Abstract: This article describes the principles and major applications of digital recording and numerical reconstruction of holograms (digital holography). Digital holography became feasible since charged coupled devices (CCDs) with suitable numbers and sizes of pixels and computers with sufficient speed became available. The Fresnel or Fourier holograms are recorded directly by the CCD and stored digitally. No film material involving wet-chemical or other processing is necessary. The reconstruction of the wavefield, which is done optically by illumination of a hologram, is performed by numerical methods. The numerical reconstruction process is based on the Fresnel–Kirchhoff integral, which describes the diffraction of the reconstructing wave at the micro-structure of the hologram. In the numerical reconstruction process not only the intensity, but also the phase distribution of the stored wavefield can be computed from the digital hologram. This offers new possibilities for a variety of applications. Digital holography is applied to measure shape and surface deformation of opaque bodies and refractive index fields within transparent media. Further applications are imaging and microscopy, where it is advantageous to refocus the area under investigation by numerical methods.
1,171 citations
"UKF based multi-component phase est..." refers methods in this paper
...The reconstructed interference field can be given as Γ(x, y) = a1e iϕ1 + a2e iϕ2 (1) In digital holographic interferometry, two holograms are recorded corresponding before and after the deformation....
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TL;DR: The paper demonstrates a phase estimation method in fringe analysis that relies on local polynomial phase approximation and subsequent state-space formulation and the application of Kalman filter to estimate parameters.
30 citations
TL;DR: An elegant technique for the simultaneous measurement of in-plane and out-of-plane displacements of a deformed object in digital holographic interferometry using sensitivity vectors of the optical configuration is proposed.
Abstract: This paper proposes an elegant technique for the simultaneous measurement of in-plane and out-of-plane displacements of a deformed object in digital holographic interferometry. The measurement relies on simultaneously illuminating the object from multiple directions and using a single reference beam to interfere with the scattered object beams on the CCD plane. Numerical reconstruction provides the complex object wave-fields or complex amplitudes corresponding to prior and postdeformation states of the object. These complex amplitudes are used to generate the complex reconstructed interference field whose real part constitutes a moire interference fringe pattern. Moire fringes encode information about multiple phases which are extracted by introducing a spatial carrier in one of the object beams and subsequently using a Fourier transform operation. The information about the in-plane and out-of-plane displacements is then ascertained from the estimated multiple phases using sensitivity vectors of the optical configuration.
23 citations
"UKF based multi-component phase est..." refers background in this paper
...These multiple phase maps and application of sensitivity vector to there maps enables the in-plane and out-of-plane measurement [3]....
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TL;DR: An elegant method to simultaneously estimate the desired multiple phases from a single fringe pattern by modeling the reconstructed interference field as a piecewise multicomponent polynomial phase signal.
Abstract: Simultaneous measurement of multidimensional displacements using digital holographic interferometry involves multi-directional illumination of the deformed object and requires the reliable estimation of the resulting multiple interference phase distributions. The paper introduces an elegant method to simultaneously estimate the desired multiple phases from a single fringe pattern. The proposed method relies on modeling the reconstructed interference field as a piecewise multicomponent polynomial phase signal. Effectively, in a given region or segment, the reconstructed interference field is represented as the sum of different components i.e. complex signals with polynomial phases. The corresponding polynomial coefficients are estimated using the product high-order ambiguity function. To ensure proper matching of the estimated coefficients with the corresponding components, an amplitude based discrimination criterion is used. The main advantage of the proposed method is direct retrieval of multiple phases without the application of spatial carrier based filtering operations.
23 citations
"UKF based multi-component phase est..." refers background in this paper
...The reconstructed interference moiré field of DHMo with variable amplitude embedded in noise can be expressed by equation (5) is [7] Γ(x, y) = α1(x, y)e iφ1(x,y) + α2(x, y)e iφ2(x,y) + η(x, y) (6) where alphai(x, y) are the real valued amplitude and φi(x, y) are the real valued interference phase…...
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