Abstract

The consequences of causality and analyticity are commonly invoked in procedures for determining optical constants from reflectance data using the Kramers—Kronig relation. Here an entirely elementary argument is advanced, which exploits only the parity of Fourier transforms and the vanishing of the impulse response for negative times, and which avoids the concept of analyticity. This leads to a simply understood algorithm for such computations. The new procedure shows large gains of computational efficiency over the classical Kramers—Kronig approach. The method is applied first to model data and compared with exact results; it is then applied to real data and compared with the result obtained by the standard method. Excellent agreement is obtained in all cases.

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  1. T. S. Robinson, Proc. Phys. Soc. Lond. B 65, 910 (1952); J. S. Toll, Phys. Rcv. 104, 1760 (1956); F. C. Jahoda, Phys. Rev. 107, 1261 (1957); M. Gottlieb, J. Opt. Soc. Am. 50, 343 (1960); H. Philipp and E. Taft, Phys. Rev. 136, A1445 (1964).
  2. R. de L. Kronig, Physica (Utr.) 3, 1009 (1936); H. A. Kramers, Atti Congr. Intern. Fisici, Como 2, 545 (1927).
  3. B. G. Anex and W. T. Simpson, Rev. Mod. Phys. 32, 466 (1960); B. Franconi, G. A. Gerhold, and W. T. Simpson, Mol. Cryst. Liq. Cryst. 6, 41 (1969).
  4. C. W. Peterson (private communication, 1970).
  5. J. W. Cooley and J. W. Tukey, Math. Comput. 19, 297 (1965).
  6. See, e.g., J. D. Jackson, in Dispersion Relations, edited by G. R. Screaton (Wiley—Interscience, New York, 1961), p. 1.
  7. O. A. Ershov and V. M. Burtseva, Opt. Spektrosk. 27, 167 (1970) [Opt. Spectrosc. 27, 84 (1970)].

Anex, B. G.

B. G. Anex and W. T. Simpson, Rev. Mod. Phys. 32, 466 (1960); B. Franconi, G. A. Gerhold, and W. T. Simpson, Mol. Cryst. Liq. Cryst. 6, 41 (1969).

Burtseva, V. M.

O. A. Ershov and V. M. Burtseva, Opt. Spektrosk. 27, 167 (1970) [Opt. Spectrosc. 27, 84 (1970)].

Cooley, J. W.

J. W. Cooley and J. W. Tukey, Math. Comput. 19, 297 (1965).

de L. Kronig, R.

R. de L. Kronig, Physica (Utr.) 3, 1009 (1936); H. A. Kramers, Atti Congr. Intern. Fisici, Como 2, 545 (1927).

Ershov, O. A.

O. A. Ershov and V. M. Burtseva, Opt. Spektrosk. 27, 167 (1970) [Opt. Spectrosc. 27, 84 (1970)].

Jackson, J. D.

See, e.g., J. D. Jackson, in Dispersion Relations, edited by G. R. Screaton (Wiley—Interscience, New York, 1961), p. 1.

Peterson, C. W.

C. W. Peterson (private communication, 1970).

Robinson, T. S.

T. S. Robinson, Proc. Phys. Soc. Lond. B 65, 910 (1952); J. S. Toll, Phys. Rcv. 104, 1760 (1956); F. C. Jahoda, Phys. Rev. 107, 1261 (1957); M. Gottlieb, J. Opt. Soc. Am. 50, 343 (1960); H. Philipp and E. Taft, Phys. Rev. 136, A1445 (1964).

Simpson, W. T.

B. G. Anex and W. T. Simpson, Rev. Mod. Phys. 32, 466 (1960); B. Franconi, G. A. Gerhold, and W. T. Simpson, Mol. Cryst. Liq. Cryst. 6, 41 (1969).

Tukey, J. W.

J. W. Cooley and J. W. Tukey, Math. Comput. 19, 297 (1965).

Other

T. S. Robinson, Proc. Phys. Soc. Lond. B 65, 910 (1952); J. S. Toll, Phys. Rcv. 104, 1760 (1956); F. C. Jahoda, Phys. Rev. 107, 1261 (1957); M. Gottlieb, J. Opt. Soc. Am. 50, 343 (1960); H. Philipp and E. Taft, Phys. Rev. 136, A1445 (1964).

R. de L. Kronig, Physica (Utr.) 3, 1009 (1936); H. A. Kramers, Atti Congr. Intern. Fisici, Como 2, 545 (1927).

B. G. Anex and W. T. Simpson, Rev. Mod. Phys. 32, 466 (1960); B. Franconi, G. A. Gerhold, and W. T. Simpson, Mol. Cryst. Liq. Cryst. 6, 41 (1969).

C. W. Peterson (private communication, 1970).

J. W. Cooley and J. W. Tukey, Math. Comput. 19, 297 (1965).

See, e.g., J. D. Jackson, in Dispersion Relations, edited by G. R. Screaton (Wiley—Interscience, New York, 1961), p. 1.

O. A. Ershov and V. M. Burtseva, Opt. Spektrosk. 27, 167 (1970) [Opt. Spectrosc. 27, 84 (1970)].

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