Ellipsometry in the Measurement of Surfaces and Thin Films, edited by E. Passaglia, R. Stromberg, and J. Kruger, Nat. Bur. Stand. (U.S.) Misc. Publ. No. 256 (U. S. Government Printing Office, Washington, D. C., 1964).

Proceedings of the Symposium on Recent Developments in Ellipsometry, edited by N. M. Bashara, A. B. Buckman, and A. C. Hall (North-Holland, Amsterdam, 1969).

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 336 (1972).

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 1521 (1972); ibid. 64, 128 (1974).

Proceedings of the Third International Conference on Ellipsometry, edited by N. M. Bashara and R. M. A. Azzam (North-Holland, Amsterdam, 1976), in press.

M. Elshazly-Zaghloul, R. M. A. Azzam, and N. M. Bashara, in Ref. 5.

P. S. Hauge, in Ref. 5.

D. J. De Smet, in Ref. 5.

A. B. Buckman and N. M. Bashara, Phys. Rev. 174, 719 (1968).

A. B. Buckman, in Ref. 2, p. 193.

B. D. Cahan, J. Horkans, and E. Yeager, Surface Sci. 37, 559 (1973).

J. Horkans, B. D. Cahan, and E. Yeager, Surface Sci. 46, 1 (1974).

W. A. Shurcliff, Polarized Light (Harvard University, Cambridge, 1962).

D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971).

If *J*_{ss} = 0, the Jones matrix [Eq. (1)] can still be normalized by factoring out another nonzero element, e. g., *J*_{pp}. The subsequent development has to be modified accordingly.

This choice of time dependence is adopted only for simplicity. The analysis is applicable to any waveform of periodic modulation *M*(*t*) impressed on the sample given that the resulting optical perturbations (δσ_{ss}, δψ_{i}, δΔ_{i}) also have the same waveform as, and are in phase with, the modulation. Thus, we may replace sinω*t* by *M*(*t*) in Eqs. (9) and (10). Furthermore, the step that leads from Eq. (14) to Eq. (16) remains valid when *M*(*t*) replaces sinω*t*. The caret over a quantity that varies as *M*(*t*) signifies the peak value of *M*(*t*).

They include the azimuth angles and optical properties of the individual elements of *P* and *A*.

A lock-in amplifier can be used for the precise measurement of the small ac signal received by the photodetector (see Fig. 2). The reference signal to the lock-in amplifier is derived from the same source of modulation *M* applied to the sample. The procedure is similar to that discussed in Refs. 9 and 10.

The determination of (δψ⌃_{t}, δΔ⌃_{t}), *i* = 1, 2, 3, (or δĴ_{n}) can be separated from the determination of δσ⌃_{ss}/σ¯_{ss} by subtracting one (e. g., the seventh) of the seven equations represented by Eq. (16) from the remaining six. This gives a matrix equation of the form δm′ = I′ δS′. δm′ is a modified 6 × 1 measurement vector with elements (δ*m*_{k} - δm_{7}) (*k* = 1, 2, …, 6); I′ is a modified 6 × 6 instrument matrix with elements [(α¯_{Ψ1k}-α_{Ψ17}),(α¯_{Δ1k}-α¯_{Δ17}),(α¯_{Ψ2k}-α_{Ψ27}),(α_{Δ2k}-α_{Δ27}),(α¯_{Ψ3k}-α_{Ψ27}),(α¯_{Δ3k}-α¯_{Δ37})] in the *k*th row (*k* = 1, 2, …, 6); and δS′ is a 6 × 1 sample-perturbation vector with elements δΨ_{1}, δΔ_{1}, δΨ_{2}, δΔ_{2}, δΨ_{3}, δΔ_{3}. δS′, and hence δĴ_{n}, can be obtained from δS′ = [I′]^{-1}δm′, where [I′]^{-1} is the inverse of I′. Once δS′ has been determined, [Equation]_{ss}/σ¯_{ss} can be calculated from any one of Eqs. (16). This procedure has the obvious advantage of requiring the inversion of a 6×6 matrix (I′) instead of a 7×7 matrix (I).

See, for example, F. L. McCrackin, J. Opt. Soc. Am. 60 57 (1970). Notice that we assume unit amplitude for the electric vibration of the light leaving the polarizer.

Extension to the general case of arbitrary values of ρ_{C} and *C* is straightforward but the results are quite complicated.

M. Cardona, Modulation Spectroscopy (Academic, New York, 1969).

R. M. A. Azzam, Opt. Commun. 16, 153 (1976).

This assumes that the principal axes of the dielectric tensors of the substrate and film have arbitrary *but known* orientation.