Abstract
This paper addresses the problem of phase reconstruction from amplitude for a diffracted wave. We utilize the Rytov transformation of the Helmholtz wave equation to relate the phase and amplitude functions; this results in two partial differential equations. We show that each of these PDEs yields a perturbation scheme to reconstruct the phase from amplitude. We also examine issues involved with the implementation of these methods in practice.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Soumekh, “Phase reconstruction/unwrapping from amplitude for diffracted waves using a perturbation solution of the wave equation,” IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 36, no. 7, July 1988.
S.M. Rytov, “Diffraction of light by ultrasonic waves,” Izv. Akad. Nauk SSSR, Ser. Fiz. 2, p. 223, 1937.
E. Wolf, “Is a complete determination of the energy spectrum of light possible from measurements of the degree of coherence,” Proc. Phys. Soc. 80, 1269–1272, 1962.
G. Ramachandran and R. Srinivasan, Fourier Methods in Crystallography, Wiley, New York, 1970.
H.A. Ferwerda, “The phase reconstruction problem for wave amplitudes and coherence functions,” in Inverse Source Problems in Optics, H.P. Baltes, Ed., Spring-Verlag, Berlin, 1978.
R. Lemons and C. Quate, “Acoustic microscope: Scanning version,” Appl. Phys. Lett. 24 (4), 163–165, 1974.
V.I. Tatarski, Wave Propagation in a Turbulent Medium, McGraw Hill, New York, 1961.
L.A. Chernov,Wave Propagation in a Random Medium, McGraw Hill, New York, 1968.
A. Ishimaru, Wave Propagation and Scattering in Random Media, Academic Press, 1978.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Plenum Press, New York
About this chapter
Cite this chapter
Soumekh, M. (1989). Phase Reconstruction from Amplitude Based on the Rytov Transformation of the Wave Equation. In: Shimizu, H., Chubachi, N., Kushibiki, Ji. (eds) Acoustical Imaging. Acoustical Imaging, vol 17. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0791-4_33
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0791-4_33
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-8084-2
Online ISBN: 978-1-4613-0791-4
eBook Packages: Springer Book Archive