G. Moliere, Z. Naturforsch. 2, 133 (1947).
I. I. Gol'dman and A. B. Midgal, JETP 1, 304 (1955).
L. I. Schiff, Phys. Rev. 103, 443 (1956).
R. J. Glauber, in Lectures in Theoretical Physics, edited by W. E. Britten and L. G. Dunham (Wiley–Interscience, New York, 1959).
The WKB approximation is ψ~ψW=exp[i∫(k2-U2)½ds], with the integration along the classical trajectory.
Schiff3 has extended the Moliere approximation for use in large-angle scattering.
The WKB approximation is ψW=exp(ik∫nds), with the integration along the ray path.
It will be assumed that the mean value of n1 satisfies 〈n1〉 = 0, and that 〈n12〉 is constant.
The use of the Fresnel or stationary-phase approximation to evaluate the Rytov integral was introduced by A. M. Obukhov, Izv. Akad. Nauk SSSR, Ser. Geograf. Geofiz., No. 2, 155 (1959).
L. A. Chernov, Wave Propagation in a Random Medium McGraw-Hill, New York, 1960), especially p. 66 and Appendix I.
V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), especially p. 127.
Although several aspects of the Rytov approximation have undergone considerable investigation in recent years, the use the Fresnel stationary-phase approximation for its evaluation continues to be widely accepted. See, for example, V. I. Tatarski, Propagation of Waves in a Turbulent Atmosphere (Nauka, Moscow, 1967), especially pp. 283–7 (in Russian).
Yu. N. Barabanekov, Yu. A. Kravtsov, S. M. Rytov, and V. I. Tatarski, Usp. Fiz. Nauk 102, 3 (1970), especially p. 9.
More precisely, the Fresnel paraboloid of revolution (the region of stationary phase). See Ref. 3 and the discussion by C. Eckhart, Rev. Mod. Phys. 20, 399 (1948).
The separation of the scattered field into refractive and diffractive parts is discussed by H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 103. The distinction between coherent and incoherent scattering in random media is discussed by M. Lax, Rev. Mod. Phys. 23, 287 (1951), especially p. 290.
G. Modesitt, On the Upper and Lower Limits to the Rytov Approximation (The Rand Corporation, Santa Monica, Calif., 1969), RM-6090.
This condition is neither necessary nor sufficient for the validity of the Rytov equation; it has been derived many times with various approaches, some of which are discussed in Ref. 16.
A closely related inconsistency is that which arises from the assertion (see, for example, Ref. 12, p. 127) that, for z small compared to ka2, the Rytov equation may be further approximated and render valid the equations of linear (in n1) geometric optics. This view, when combined with the widely adopted upper limit given above (γz <ka2) implies, inconsistently, the existence when γ > 1 of an interval γ-1 <z/ka2 < 1 in which the Rytov equation is invalid and the less general geometric equation is valid.