Multiresolution phase retrieval in the fresnel region by use of wavelet transform.

@article{Souvorov2006MultiresolutionPR,
  title={Multiresolution phase retrieval in the fresnel region by use of wavelet transform.},
  author={A. Souvorov and Tetsuya Ishikawa and A. Kuyumchyan},
  journal={Journal of the Optical Society of America. A, Optics, image science, and vision},
  year={2006},
  volume={23 2},
  pages={
          279-87
        }
}
A multiresolution (multiscale) analysis based on wavelet transform is applied to the problem of optical phase retrieval from the intensity measured in the in-line geometry (lens-free). The transport-of-intensity equation and the Fresnel diffraction integral are approximated in terms of a wavelet basis. A solution to the phase retrieval problem can be efficiently found in both cases using the multiresolution concept. Due to the hierarchical nature of wavelet spaces, wavelets are well suited to… 
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References

SHOWING 1-10 OF 28 REFERENCES
Linear algorithms for phase retrieval in the Fresnel region
Composite techniques for phase retrieval in the Fresnel region
Phase retrieval with the transport-of-intensity equation: matrix solution with use of Zernike polynomials
A new technique is proposed for the recovery of optical phase from intensity information. The method is based on the decomposition of the transport-of-intensity equation into a series of Zernike…
Optical phase retrieval by use of first Born- and Rytov-type approximations.
TLDR
It is shown theoretically and by numerical simulations that, despite the differences in their formulation, the two algorithms for phase retrieval deliver fairly similar results when used for optical phase retrieval in the near and intermediate fields.
Phase-retrieval stagnation problems and solutions
The iterative Fourier-transform algorithm has been demonstrated to be a practical method for reconstructing an object from the modulus of its Fourier transform (i.e., solving the problem of…
Phase retrieval algorithms: a comparison.
TLDR
Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods and it is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm forThe problem of two intensity measurements converge.
Fresnelets: new multiresolution wavelet bases for digital holography
TLDR
A Heisenberg-like uncertainty relation is derived that relates the localization of Fresnelets with that of their associated wavelet basis and, according to this criterion, the optimal functions for digital hologram processing turn out to be Gabor functions, bringing together two separate aspects of the holography inventor's work.
Phase retrieval in crystallography and optics
TLDR
The principles of phase retrieval in crystallography are outlined and are compared and contrasted withphase retrieval in general imaging, and areas in which results in one discipline have, and may, contribute to the other are discussed.
Deterministic phase retrieval: a Green’s function solution
Equations for the propagation of phase and irradiance are derived, and a Green’s function solution for the phase in terms of irradiance and perimeter phase values is given. A measurement scheme is…
Contrast and resolution in imaging with a microfocus x-ray source
A simple general treatment of x-ray image formation by Fresnel diffraction is presented; the image can alternatively be considered as an in-line hologram. Particular consideration is given to…
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