Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography

We compare two methods of reconstructing the complex index-of-refraction distribution of a scattering object from optical scattering data obtained in a set of scattering experiments employing incident monochromatic plane waves. The first method generates an approximate reconstruction directly from the far-field intensity, which is measured as a function of scattering angle for each incident plane wave. The second method uses an iterative phase-retrieval algorithm to extract the phase of the scattered field over any given plane from the measurement of the intensity of the total field over that plane and from a priori object-support information. The reconstruction is then performed from the scattered field that is so determined by using the filtered backpropagation algorithm of diffraction tomography. We compare the performance of the two procedures on computer-simulated and experimental scattering data.

[1]  A. Walther.  The Question of Phase Retrieval in Optics , 1963 .

[2]  E. Wolf,et al.  Inverse Diffraction and a New Reciprocity Theorem , 1968 .

[3]  George C. Sherman,et al.  Diffracted Wave Fields Expressible by Plane-Wave Expansions Containing Only Homogeneous Waves , 1968 .

[4]  E. Wolf.  Determination of the Amplitude and the Phase of Scattered Fields by Holography , 1970 .

[5]  R. Gerchberg.  A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[6]  D. L. Misell.  Comment onA method for the solution of the phase problem in electron microscopy , 1973 .

[7]  Michael A. Fiddy,et al.  LETTER TO THE EDITOR: The application of dispersion relations (Hilbert transforms) to phase retrieval , 1974 .

[8]  J R Fienup,et al.  Reconstruction of an object from the modulus of its Fourier transform. , 1978, Optics letters.

[9]  H. Ferwerda,et al.  The Phase Reconstruction Problem for Wave Amplitudes and Coherence Functions , 1978 .

[10]  Monson H. Hayes,et al.  Iterative Procedures For Signal Reconstruction From Phase , 1980, Other Conferences.

[11]  L. Taylor.  The phase retrieval problem , 1981 .

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

[13]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[14]  A. J. Devaney,et al.  A Computer Simulation Study of Diffraction Tomography , 1983, IEEE Transactions on Biomedical Engineering.

[15]  M. NietoVesperinas.  Inverse scattering problems: A study in terms of the zeros of entire functions , 1984 .

[16]  Aharon Levi,et al.  Image restoration by the method of generalized projections with application to restoration from magnitude , 1984 .

[17]  L Hesselink,et al.  High speed optical tomography for flow visualization. , 1985, Applied optics.

[18]  M A Fiddy,et al.  Inversion of optical scattered field data , 1986 .

[19]  A J Devaney,et al.  Reconstructive tomography with diffracting wavefields , 1986 .

[20]  N George,et al.  Image reconstruction from partial Fresnel zone information. , 1986, Applied optics.

[21]  P. Scott,et al.  Phase retrieval and twin-image elimination for in-line Fresnel holograms , 1987 .

[22]  C. Pichot,et al.  Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics , 1988 .

[23]  R. Pratt,et al.  The application of diffraction tomography to cross-hole seismic data , 1988 .

[24]  B Dong,et al.  Phase retrieval from two intensity measurements in an optical system involving nonunitary transformation. , 1990, Applied optics.

[25]  Anthony J. Devaney,et al.  Initial Testing of a Clinical Ultrasound Mammograph , 1991 .

[26]  Anthony J. Devaney,et al.  Tomographic reconstruction from optical scattered intensities , 1992 .