G. N. Balanis, “Inverse Scattering: determination of inhomogeneities in sound speed,” J. Math. Phys. 23, 2362–2568 (1982).

[CrossRef]

H. N. Kritikos, D. L. Jaggard, D. B. Ge, “Numerical reconstruction of smooth dielectric profiles,” Proc. IEEE 70, 295–297 (1982).

[CrossRef]

P. B. Abraham, H. E. Moses, “Exact solutions of the one-dimensional acoustic wave equations for several new velocity profiles: transmission and reflection coefficients,” J. Acoust. Soc. Am. 71, 1391–1399 (1982).

[CrossRef]

S. Coen, “Inverse scattering of a layered and dispersionless dielectric half-space, part I: reflection data from plane waves at normal incidence,” IEEE Trans. Antennas Propag. AP–29, 726–732 (1981).

[CrossRef]

K. R. Pechenick, J. M. Cohen, “Inverse scattering—exact solution of the Gel’fand–Levitan equation,” J. Math. Phys. 22, 1513–1516 (1981).

[CrossRef]

O. Hald, “Numerical solution of the Gel’fand–Levitan equation,” Linear Alg. Its Appl. 28, 99–111 (1979).

[CrossRef]

J. A. Ware, K. Aki, “Continuous and discrete inverse scattering problems in a stratified elastic medium: I—plane waves at normal incidence,” J. Acoust. Soc. Am. 45, 911–921 (1969).

[CrossRef]

I. M. Gel’fand, B. M. Levitan, “On the determination of a differential equation by its spectral function,” Am. Math. Soc. Transl. 1, 253–304 (1955).

V. A. Marchenko, “Reconstruction of the potential energy from the phase of scattered waves,” Dokl. Akad. Nauk SSR 104, 695–698 (1955).

P. B. Abraham, H. E. Moses, “Exact solutions of the one-dimensional acoustic wave equations for several new velocity profiles: transmission and reflection coefficients,” J. Acoust. Soc. Am. 71, 1391–1399 (1982).

[CrossRef]

J. A. Ware, K. Aki, “Continuous and discrete inverse scattering problems in a stratified elastic medium: I—plane waves at normal incidence,” J. Acoust. Soc. Am. 45, 911–921 (1969).

[CrossRef]

G. N. Balanis, “Inverse Scattering: determination of inhomogeneities in sound speed,” J. Math. Phys. 23, 2362–2568 (1982).

[CrossRef]

S. Coen, “Inverse scattering of a layered and dispersionless dielectric half-space, part I: reflection data from plane waves at normal incidence,” IEEE Trans. Antennas Propag. AP–29, 726–732 (1981).

[CrossRef]

K. R. Pechenick, J. M. Cohen, “Inverse scattering—exact solution of the Gel’fand–Levitan equation,” J. Math. Phys. 22, 1513–1516 (1981).

[CrossRef]

H. E. Moses, C. M. deRidder, “Properties of dielectrics from reflection coefficients,” Tech. Rep. 322 (MIT Lincoln Laboratory, Lexington, Mass., 1963).

D. L. Jaggard, P. Frangos, “The inverse scattering problem for layered dispersionless media with incomplete and imprecise data,” submitted to IEEE Trans. Antennas Propag.

H. N. Kritikos, D. L. Jaggard, D. B. Ge, “Numerical reconstruction of smooth dielectric profiles,” Proc. IEEE 70, 295–297 (1982).

[CrossRef]

I. M. Gel’fand, B. M. Levitan, “On the determination of a differential equation by its spectral function,” Am. Math. Soc. Transl. 1, 253–304 (1955).

O. Hald, “Numerical solution of the Gel’fand–Levitan equation,” Linear Alg. Its Appl. 28, 99–111 (1979).

[CrossRef]

H. N. Kritikos, D. L. Jaggard, D. B. Ge, “Numerical reconstruction of smooth dielectric profiles,” Proc. IEEE 70, 295–297 (1982).

[CrossRef]

D. L. Jaggard, P. Frangos, “The inverse scattering problem for layered dispersionless media with incomplete and imprecise data,” submitted to IEEE Trans. Antennas Propag.

A. K. Jordan, “Applications of the Gel’fand–Levitan theory to profiles with bandpass characteristics,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1972).

I. Kay, “The inverse scattering problem,” Res. Rep. No. EM–74 (New York University, New York, N.Y., 1955).

H. N. Kritikos, D. L. Jaggard, D. B. Ge, “Numerical reconstruction of smooth dielectric profiles,” Proc. IEEE 70, 295–297 (1982).

[CrossRef]

I. M. Gel’fand, B. M. Levitan, “On the determination of a differential equation by its spectral function,” Am. Math. Soc. Transl. 1, 253–304 (1955).

V. A. Marchenko, “Reconstruction of the potential energy from the phase of scattered waves,” Dokl. Akad. Nauk SSR 104, 695–698 (1955).

P. B. Abraham, H. E. Moses, “Exact solutions of the one-dimensional acoustic wave equations for several new velocity profiles: transmission and reflection coefficients,” J. Acoust. Soc. Am. 71, 1391–1399 (1982).

[CrossRef]

H. E. Moses, C. M. deRidder, “Properties of dielectrics from reflection coefficients,” Tech. Rep. 322 (MIT Lincoln Laboratory, Lexington, Mass., 1963).

K. R. Pechenick, J. M. Cohen, “Inverse scattering—exact solution of the Gel’fand–Levitan equation,” J. Math. Phys. 22, 1513–1516 (1981).

[CrossRef]

J. A. Ware, K. Aki, “Continuous and discrete inverse scattering problems in a stratified elastic medium: I—plane waves at normal incidence,” J. Acoust. Soc. Am. 45, 911–921 (1969).

[CrossRef]

I. M. Gel’fand, B. M. Levitan, “On the determination of a differential equation by its spectral function,” Am. Math. Soc. Transl. 1, 253–304 (1955).

V. A. Marchenko, “Reconstruction of the potential energy from the phase of scattered waves,” Dokl. Akad. Nauk SSR 104, 695–698 (1955).

S. Coen, “Inverse scattering of a layered and dispersionless dielectric half-space, part I: reflection data from plane waves at normal incidence,” IEEE Trans. Antennas Propag. AP–29, 726–732 (1981).

[CrossRef]

J. A. Ware, K. Aki, “Continuous and discrete inverse scattering problems in a stratified elastic medium: I—plane waves at normal incidence,” J. Acoust. Soc. Am. 45, 911–921 (1969).

[CrossRef]

P. B. Abraham, H. E. Moses, “Exact solutions of the one-dimensional acoustic wave equations for several new velocity profiles: transmission and reflection coefficients,” J. Acoust. Soc. Am. 71, 1391–1399 (1982).

[CrossRef]

K. R. Pechenick, J. M. Cohen, “Inverse scattering—exact solution of the Gel’fand–Levitan equation,” J. Math. Phys. 22, 1513–1516 (1981).

[CrossRef]

G. N. Balanis, “Inverse Scattering: determination of inhomogeneities in sound speed,” J. Math. Phys. 23, 2362–2568 (1982).

[CrossRef]

O. Hald, “Numerical solution of the Gel’fand–Levitan equation,” Linear Alg. Its Appl. 28, 99–111 (1979).

[CrossRef]

H. N. Kritikos, D. L. Jaggard, D. B. Ge, “Numerical reconstruction of smooth dielectric profiles,” Proc. IEEE 70, 295–297 (1982).

[CrossRef]

A. K. Jordan, “Applications of the Gel’fand–Levitan theory to profiles with bandpass characteristics,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1972).

D. L. Jaggard, P. Frangos, “The inverse scattering problem for layered dispersionless media with incomplete and imprecise data,” submitted to IEEE Trans. Antennas Propag.

This is obtained from Eq. (2.8) of Ref. 8 with a change of variables and subsequent reordering.

This is found by combining Eqs. (3.5) and (3.8) of Ref. 8.

Here ΔK indicates the difference between the kernel function at any point and its value at an adjacent lattice point.

I. Kay, “The inverse scattering problem,” Res. Rep. No. EM–74 (New York University, New York, N.Y., 1955).

H. E. Moses, C. M. deRidder, “Properties of dielectrics from reflection coefficients,” Tech. Rep. 322 (MIT Lincoln Laboratory, Lexington, Mass., 1963).