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This restriction comes from both the perturbation used in Eq. (6b) and the approximation ln(φ/ φ0)≃δφ/φ0. Instead of it, another form of restriction equivalent to that of the usual Rytov approximation can be used and given in such a way that, after introducing the Rytov transform in Eq. (4), we obtain the equation of Riccati type and solve it by means of the method of smooth perturbations.1 To avoid a long procedure for that method, the present deduction was used, which leads to this restriction.
For instance, see Ref.2, p.83.9. See Ref. 1, p.186.
W. P. Brown, J. Opt. Soc. Am. 56, 1045 (1966).
L. S. Taylor, Radio Science 2, 437 (1967).
D. L. Fried, J. Opt. Soc. Am. 57, 268 (1967).
D. A. deWolf, J. Opt. Soc. Am. 57, 1057 (1967).