Journal ArticleDOI
Matrix formulation of the reconstruction of phase values from phase differences
TLDR
The phase reconstruction problem is formulated in terms of a vector-matrix multiplication and it is shown that previous solution methods are equivalent to this general description, and the errors in reconstruction are analyzed.Abstract:
Methods in speckle imaging and adapative optics, as well as a new technique in digital image restoration, require the calculation of the Fourier phase spectrum from measurements of the differences on a two-dimensional grid of the phase spectrum. The calculation of phases from phase differences has been analyzed in the literature and relaxation mechanisms for computing the phase have been derived by least-squares analysis. In the following paper we formulate the phase reconstruction problem in terms of a vector-matrix multiplication, and we then show that previous solution methods are equivalent to this general description. We also analyze the errors in reconstruction and reconcile previously published error results based on simulations with an analytical error expression derived from Parseval’s theorem. Finally, we comment upon the rate of convergence of phase reconstructions, and discuss numerical analysis literature which indicates that the methods previously published for phase reconstruction can be made to converge much faster.read more
Citations
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Journal ArticleDOI
Synthetic aperture radar interferometry
Richard Bamler,Philipp Hartl +1 more
TL;DR: In this article, a review of the technology and signal theoretical aspects of InSAR is presented, where the phase differences of at least two complex-valued SAR images acquired from different orbit positions and/or at different times are exploited to measure several geophysical quantities, such as topography, deformations, glacier flows, ocean currents, vegetation properties, etc.
Journal ArticleDOI
A novel phase unwrapping method based on network programming
TL;DR: A new phase unwrapping method is described and tested, which starts from the fact that the phase differences of neighboring pixels can be estimated with a potential error that is an integer multiple of 2/spl pi/.
Journal ArticleDOI
Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods
TL;DR: In this article, a robust method for 2D phase principal values (in a least-squares sense) by using fast cosine transforms was developed, which can be used to isolate inconsistent regions (i.e., phase shear).
Journal ArticleDOI
Wave-front estimation from wave-front slope measurements
TL;DR: In this paper, the problem of wavefront estimation from wave-front slope measurements has been examined from a least-squares curve fitting model point of view, and a new zonal phase gradient model is introduced and its error propagator, which relates the mean square wavefront error to the noisy slope measurements, has been compared with two previously used models.
Journal ArticleDOI
Phase retrieval in crystallography and optics
TL;DR: In this paper, the principles of phase retrieval in crystallography are outlined and compared and contrasted with phase retrieval for general imaging, and the emphasis is on phase-retrieval algorithms and areas in which results in one discipline have, and may, contribute to the other.
References
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Journal ArticleDOI
Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements
TL;DR: In this article, the problem of fitting a wavefront distortion estimate to a (single-instant) set of phase-difference measurements has been formulated as an unweighted least-square problem.
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Wave-front reconstruction for compensated imaging
TL;DR: In this paper, the authors analyzed the conversion from phase differences to phases and derived the optimal linear estimator in terms of least noise propagation for a compensated imaging (CI) system.
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Real-time atmospheric compensation
TL;DR: In this paper, an active optical imaging system capable of correcting optical wave-front errors in real time at frequencies in the kilohertz range was developed, which can be applied to apertures of any size; experimental results were shown for a system with 21 correction zones.
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Image retrieval from astronomical speckle patterns
TL;DR: In this paper, a technique for processing astronomical photographs to remove the effects of turbulence has been proposed, which involves averaging over many short-exposure photographs of an object to reconstruct a diffraction-limited image of the object.