F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill Book Company, Inc., New York, 1957), 3rd ed., p. 273.
By one reflecting surface is meant the inner-coated surface of one interferometer plate. The light lost by reflection from the outer surfaces of the plates is ignored since it only decreases the total intensity, and the change in the shape of the transmitted energy curves is negligible. It is also assumed that the two inner-coated surfaces have nearly the same values of T and R.
The minus sign in Eq. (10) is absolutely necessary to be consistent with the previous definition of β as a positive angle. Since the optical path is shorter than the geometrical path, this is equivalent to having the wave reflected from a fictitious surface in front of the actual surface.
See Ref. 27, p. 423.
M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 279.
Four other forms of the complex refractive index are in current use in the literature: n+ik (Ref. 4), n(1−ik) (Ref. 19), n(1+iκ) (Ref. 20) and n(1−iκ) (Ref. 21), where k represents the attenuation of the wave per vacuum wavelength and κ is related in the same way to the attenuation per wavelength in the medium. Hence the expressions for r in various references may actually be identical although they appear to be different. Care should be taken to determine which form of the complex refractive index is used when applying equations for the reflectance and the phase change on reflection.
See Ref. 1, p. 49.
See Ref. 17, p. 610.
R. W. Ditchburn, Light (Blackie & Son Ltd., London, 1952), p. 441.
Care should be taken not to confuse this positive β with Heavens’ “phase advance” (Ref. 1, p. 171). His “phase advance” and “phase retard” are measured relative to the negative real axis so that values of Er in the second quadrant are called “retard” and those in the third quadrant “advance.”
See Ref. 1, pp. 55–88.
This expression may be obtained from the relations given on p. 91 of Ref. 1. However, there is a typographical error in Eq. 4(140). The correct expression should read Δ0=arc tan(BC−AD)/(AC+BD) where Δ0 is identical to β.
S. Tolansky, Multiple-Beam Inlerferometry of Surfaces and Films (Clarendon Press, Oxford, England, 1948), p. 9.
W. E. Williams, Applications of Inlerferometry (Methuen and Company Ltd., London, 1930), p. 77.
O. S. Heavens, Optical Properties of Thin Solid Films (Butter-worths Scientific Publications Ltd., London, 1955), p. 174.
S. Nawata, Sci. Rep. Res. Inst. Tohoku Univ. Ser. A3, 740 (1951).
See Ref. 25, p. 97.
These fringes are similar to channelled spectra (Ref. 38), Edser–Butler fringes, or white light Fabry–Perot fringes (Ref. 36) except that an image of the interferometer (rather than the light source) is focused on the slit of the spectrograph.
See Ref. 26, p.101.
It is assumed that the wavelengths of the two-beam reflection minima are identical to the wavelengths of the maxima in transmission.
Equation (13) is strictly correct for an air–dielectric reflection. It also holds approximately for interferometers coated with some metal films. However, it does not hold for all metal films or for dielectric coatings.
This method is similar to that used by Shklyarevskii (Ref. 42) except that the integers he used for his Mλ products were one less than those used here. Both Koehler (Ref. 43) and Koester (Ref. 44) have shown that τ may be determined exactly regardless of the choice of the integer if the phase change is properly eliminated. Furthermore, Koester proves that by using a graphical method similar to the one described here (his integers differ from the ones in the present paper by an arbitrary integer N), “the difference between the two curves is a constant. Regardless of the selection of N and the variation of phase shift with wavelength the difference between the curves is twice the step height ….” The integers M used in this paper are purposely chosen to give the most nearly constant Mλ product so that the graphical method will have the most accuracy.
This shift of approximately one order toward the blue (higher orders of interference) in the multiple-beam fringe system in reflection relative to the two-beam fringe system is observed when the reflecting film on the side of the incident beam is a metal. This same effect has also been observed by Faust (Ref. 3) for silver and aluminum but is not completely understood.
Johnson Matthey JM 50 silver rod obtained from Jarrell-Ash Company.
Obtained from the Aluminum Company of America.
See Ref. 26, p. 83.
Vickers projection microscope manufactured by Cooke, Troughton, and Simms, Ltd., York, England.
Model BK 3643 direct reading spectrograph manufactured by Bausch & Lomb Optical Company, Rochester, New York.
Very fast Type C panchromatic antihalation plates obtained from Eastman Kodak Company, Rochester, New York.
Corning filter No. 2404 is used in photographing the neon spectrum to eliminate the lines which obscure some of the interference fringes.
A commercial model is available from the David W. Mann Company, Lincoln, Massachusetts.
Note the typesetter’s errors on p. 1246 of Faust’s paper (Ref. 3) which give Δν=12d.
I. N. Shklyarevskii (Ref. 42) goes through a similar type of derivation to obtain his Eq. (1) [our Eq. (15)]. However, he makes the approximation that β1/π∼β2/π∼1 (our notation) which is a much more drastic assumption than is necessary. Furthermore, he apparently was not successful with the simple formula since he states “It is easy to see that if the dispersion of the phase change is neglected, the thin film thicknesses cannot be measured with a high degree of accuracy.”
A. G. Worthing and J. Geffner, Treatment of Experimental Data (John Wiley & Sons, Inc., New York, 1943), p. 207.