Phase estimation using a state-space approach based method

Gannavarpu, Rajshekhar; Rastogi, Pramod K.

doi:10.1016/j.optlaseng.2013.02.022

Cited by 37 publications

(19 citation statements)

References 16 publications

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“…Different phase unwrapping algorithms have been proposed based on segmentwise [31][32][33] or blockwise [34][35][36] polynomial phase approximation. Although these methods provide satisfactory results in some cases, they are based on two important assumptions that require first, the true phase distribution to be spatially continuous and second, the wrapped phase measurement to be available over the entire segment or block.…”

Section: A Local Polynomial Approximation Of Phasementioning

confidence: 99%

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter

Kulkarni

Rastogi

2018

Appl. Opt.

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A noise-robust phase unwrapping algorithm is proposed based on state space analysis and polynomial phase approximation using wrapped phase measurement. The true phase is approximated as a two-dimensional first order polynomial function within a small sized window around each pixel. The estimates of polynomial coefficients provide the measurement of phase and local fringe frequencies. A state space representation of spatial phase evolution and the wrapped phase measurement is considered with the state vector consisting of polynomial coefficients as its elements. Instead of using the traditional nonlinear Kalman filter for the purpose of state estimation, we propose to use the linear Kalman filter operating directly with the wrapped phase measurement. The adaptive window width is selected at each pixel based on the local fringe density to strike a balance between the computation time and the noise robustness. In order to retrieve the unwrapped phase, either a line-scanning approach or a quality guided strategy of pixel selection is used depending on the underlying continuous or discontinuous phase distribution, respectively. Simulation and experimental results are provided to demonstrate the applicability of the proposed method.

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Section: A Local Polynomial Approximation Of Phasementioning

confidence: 99%

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter

Kulkarni

Rastogi

2018

Appl. Opt.

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“…As discussed earlier in Section 1, we can take this to be about ± W 0 2 /λ, where W 0 is the equivalent waist size for the beam. This focal spread can be re-expressed in terms of the more convenient 1/e 2 semiopening angle in intensity for the far-field pattern of the horn θ 0 , given by λ/πW 0 [19], so that the range over which there is excellent coupling is given alternatively by ± 332 × λ/(θ 0,deg ) 2 , where θ 0,deg is the 1/e 2 semi-opening angle expressed in degrees. The uncertainty in the curvature difference term Δ(1/R) should therefore satisfy the inequality…”

Section: Tolerancing Issuesmentioning

confidence: 99%

“…For non-standard millimeter-wave horn designs, and other feed structures, the phase center may be difficult to reliably predict by simulation, in which case, an experimental determination is necessary. Although the phase center can be deduced from direct phase measurements, using expensive instrumentation such as a vector network analyzer, it is also possible to recover phase information employing other methods that rely on measuring the intensity only, especially those that have been developed at other wavelengths, for example [1][2][3][4][5]. One such method, presented in this paper, makes use of a relatively inexpensive quasi-optical phase retrieval approach based on interference of the horn under test (HUT) with a well-understood reference beam, as in a holographic recording setup [6,7].…”

Section: Introductionmentioning

confidence: 99%

Determination of the Phase Centers of Millimeter-Wave Horn Antennas Using a Holographic Interference Technique

McAuley

Murphy

McCarthy

et al. 2016

J Infrared Milli Terahz Waves

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In this paper, we discuss how a holographic interference technique can be applied in the experimental determination of the phase centers of non-standard horn antennas in the millimeter-waveband. The phase center is the point inside the horn from which the radiation appears to emanate when viewed from the far-field, and knowing its location is necessary for optimizing coupling efficiencies to quasi-optical systems. For non-standard horn designs, and other feed structures, the phase center may be difficult to reliably predict by simulation, in which case, before committing to antenna manufacture, there is a requirement for it to be determined experimentally. Although the phase center can be recovered by direct phase measurement of the far-field beam pattern, this usually involves expensive instrumentation such as a vector network analyzer for millimeter wave horn antennas. In this paper, we describe one inexpensive alternative, which is based on measuring the interference pattern in intensity between the radiation from the horn of interest and a reference beam derived from the same coherent source in an off-axis holography setup. The accuracy of the approach is improved by comparison with the interference pattern of a well-understood standard horn (such as a corrugated conical horn) in the same experimental setup. We present an example of the technique applied to a profiled smooth-walled horn antenna, which has been especially designed for cosmic microwave background (CMB) polarization experiments.

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“…All the unwrapping methods available in the literature don't consider the effect of noise in the wrapped phase and result in noisy phase maps and frequently employ ad-hoc heuristic techniques such as median filtering to remove noise. The piecewise polynomial approximation approach [12] and signal tracking approach [15], [16] provides unwrapped phase directly, but the non-linear measurement model limits the performance of those methods. In this paper we propose a mathematically sound and more reliable restoration approach for the estimation of accurate phase map by exploiting the properties of Taylor series expansion with Kalman filter framework.…”

Section: Introductionmentioning

confidence: 99%

Phase unwrapping with Kalman filter based denoising in digital holographic interferometry

Sukumar

Waghmare

Singh

et al. 2015

2015 International Conference on Advances in Computing, Communications and Informatics (ICACCI)

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Phase information recovered through interferometric techniques is mathematically wrapped in the interval (−π, π]. Obtaining the original unwrapped phase is very important in numerous number of applications. This paper discusses a Fourier transform based phase unwrapping method. Kalman filter is proposed for denoising in post processing step to restore the unwrapped phase without any noise. The proposed method is highly robust to noise and performs better even at lower SNR values (5-10dB) with a very less value of RMS error. Also, the time taken for execution is very less compared to the many available methods in the literature.

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Phase estimation using a state-space approach based method

Cited by 37 publications

References 16 publications

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter

Determination of the Phase Centers of Millimeter-Wave Horn Antennas Using a Holographic Interference Technique

Phase unwrapping with Kalman filter based denoising in digital holographic interferometry

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