A second optimum value of ψ0=62.63°was inadvertently missed in Eq. (26a) of Ref. 16.

Since the determinant of the instrument matrix appears in the denominator of various condition numbers, it is not surprising that the criterion of the maximum determinant approximately corresponds to the minimum condition number.

A. De, R. M. A. Azzam, “Optimal coated silicon membrane beam splitters for the division-of-amplitude photopolarimeter (DOAP),” presented at the Annual Meeting of the Optical Society of America, Orlando, Florida, September 29–October 3, 2002, paper WZ3.

R. M. A. Azzam, “Ellipsometry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, Chap. 27.

R. A. Chipman, “Polarimetry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, Chap. 22.

R. M. A. Azzam, “Mueller-matrix ellipsometry: a review,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 396–405 (1997).

[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

For a thick uncoated dielectric slab BS, Δrand Δtassume the trivial values of 0 or ±π, and condition (6c) is violated; hence detA=0.Therefore thin-film coatings are required for the BS of DOAP.

According to Eq. (4), a given error δIin the measured signal vector Iresults in a corresponding error δSof the derived Stokes vector S, which is given by δS=A-1δI.Because A-1is proportional to 1/detA,maximization of |detA|is consistent with reduction of the error δS.

Equation (13a) has an infinite number of solutions, and it is by convention11that the ellipsometric angle ψ is confined to the first quadrant, 0≤ψ≤π/2.