Literature Cited
M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, Wave Theory [in Russian], Nauka, Moscow (1979).
Yu. E. Anikonov and A. G. Marchuk, “On the inverse diffraction problem,” in: Mathematical Problems of Geophysics [in Russian], No. 6 (4.2), VTs SO AN SSSR, Novosibirsk (1975), pp. 54–62.
A. G. Marchuk, “Restoration of total field from its amplitude,” in: Some Mathematical Tasks and Problems of Geophysics [in Russian], VTs SO AN SSSR, Novosibirsk (1976), pp. 130–134.
A. Majda, “High frequency asymptotic for the scattering matrix and the inverse problem for acoustical scattering,” Commun. Pure Appl. Math.,29, No. 3, 261–291 (1976).
A. G. Sveshnikov, Yu. A. Eremin, and A. V. Chivilev, “Study of uniqueness of inverse diffraction problem,” Differents. Uravn.,15, No. 12, 2205–2209 (1979).
A. L. Bukhgeim, Volterra Equations and Inverse Problems [in Russian], Nauka, Novosibirsk (1983).
V. N. Stepanov, “Geometric topics in inverse scattering problem,” Sib. Mat. Zh.,25, No. 1, 133–145 (1984).
E. Wolf, “Is a complete determination of energy spectrum of the degree of coherence?” Proc. Phys. Soc. London,80, Pt. 6, No. 518, 1269–1272 (1962).
A. J. J. Drenth, A. M. J. Huiser, and H. A. Ferwerda, “The problem of phase retrieval in light and electron microscopy of strong objects,” Opt. Acta,22, No. 7, 615–628 (1975).
A. J. M. Huiser, A. J. J. Drenth, and H. A. Ferwerda, “On phase retrieval in electron microscopy from image and diffraction pattern,” Optik,45, No. 4, 303–316 (1976).
B. J. Hoenders, “On the solution of the phase retrieval problem,” J. Math. Phys.,16, No. 9, 1719–1725 (1975).
A. M. J. Huiser and H. A. Ferwerda, “On the problem of phase retrieval in electron microscopy from image and diffraction pattern. II. On the uniqueness and stability,” Optik,46, No. 4, 407–420 (1976).
A. M. J. Huiser and H. A. Ferwerda, “The problem of phase retrieval in light and electron microscopy of strong objects. II. On the uniqueness and stability of object reconstruction procedures using two defocused images,” Optika Acta,23, No. 6, 445–456 (1976).
G. Ross, M. A. Fiddy, and M. Nieto-Vesperinas, “The inverse scattering problems in structural determinations,” in: Inverse Scattering Problems in Optics, Springer-Verlag, New York (1980).
V. K. Ablekov et al., “On the uniqueness of the relation between phase and amplitude distributions of diffraction field,” Dokl. Akad. Nauk SSSR,271, No. 1, 1377–1380 (1983).
H. A. Ferwerda, “Problem of restoration of phase of wave front from amplitude distribution and coherence functions,” in: Inverse Problems in Optics [in Russian], Mashinostroenie, Moscow (1984).
M. V. Klibanov, V. G. Volostnikov, and V. V. Kotlyar, “On uniqueness theorems of phase problem in optics,” Dokl. Akad. Nauk SSSR,279, No. 6, 1348–1351 (1984).
S. A. Akhmanov, Yu. E. D'yakov, and A. S. Chirkin, Introduction to Statistical Radiophysics and Optics [in Russian], Nauka, Moscow (1981).
S. N. Rytov, Yu. A. Kravtsov, and V. N. Tatarskii, Introduction to Statistical Radiophysics [in Russian], Part 2, Nauka, Moscow (1978).
E. Titchmarsh, Theory of Functions, Oxford Univ. Press (1939).
M. V. Klibanov, “On uniqueness of determination of finite function from the modulus of its Fourier transform,” Dokl. Akad. Nauk SSSR, No. 2, 278–280 (1985).
Additional information
Kuibyshev. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 27, No. 5, pp. 95–109, September–October, 1986.
Rights and permissions
About this article
Cite this article
Klibanov, M.V. Inverse scattering problems and restoration of a function from the modulus of its Fourier transform. Sib Math J 27, 708–719 (1986). https://doi.org/10.1007/BF00969199
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00969199