An error bound for the Born approximation

We derive an explicit error bound for the Born approximation for the inverse scattering problem of the Helmholtz equation at fixed frequency.

[1]  A. Devaney.  A filtered backpropagation algorithm for diffraction tomography. , 1982, Ultrasonic imaging.

[2]  B. Chen,et al.  Validity of diffraction tomography based on the first born and the first rytov approximations. , 1998, Applied optics.

[3]  S. Silver.  Scattering and diffraction , 1984 .

[4]  Barry Simon,et al.  Methods of modern mathematical physics. III. Scattering theory , 1979 .

[5]  Shmuel Agmon,et al.  Spectral properties of Schrödinger operators and scattering theory , 1975 .

[6]  T. Habashy,et al.  Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering , 1993 .

[7]  Margaret Cheney,et al.  Three-dimensional inverse scattering for the wave equation: weak scattering approximations with error estimates , 1988 .

[8]  L. E. Larsen,et al.  Limitations of Imaging with First-Order Diffraction Tomography , 1984 .

[9]  Manuel Nieto Vesperinas,et al.  Scattering And Diffraction In Physical Optics , 2006 .

[10]  Mark S. C. Reed,et al.  Method of Modern Mathematical Physics , 1972 .

[11]  広 久保田,et al.  Principle of Optics , 1960 .

[12]  M. Oristaglio,et al.  Accuracy of the Born and Rytov approximations for reflection and refraction at a plane interface , 1985 .

[13]  Joseph B. Keller,et al.  Accuracy and Validity of the Born and Rytov Approximations , 1969 .

[14]  THEORY OF ELECTRON INTERFERENCE EXPERIMENTS , 1956 .

[15]  Frank Natterer,et al.  Mathematical methods in image reconstruction , 2001, SIAM monographs on mathematical modeling and computation.