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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 54, Iss. 5 — May. 1, 1964
  • pp: 612–622

Precise Method for Measuring the Absolute Phase Change on Reflection

JEAN M. BENNETT  »View Author Affiliations

JOSA, Vol. 54, Issue 5, pp. 612-622 (1964)

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A method is described for measuring the absolute phase change on reflection of semitransparent films which is both precise and accurate. The films are deposited on portions of two fuzed-quartz optical flats and the shift in the fringes of equal chromatic order between the coated and uncoated portions of the interferometer is measured. Since the phase change is very sensitive to small changes in the optical constants, this method is useful for studying the effects of aging, applied electromagnetic fields, oxide growth, and other factors. Also, since areas of the order of 1.3 by 0.0033 mm are sufficient for each measurement, the phase change can be used to study possible variations in the film structure over the interferometer surface. Measured values of phase change on reflection versus wavelength are smooth to ±0.1°. When systematic errors have been taken into account, the measurements are still accurate to about ±1°.

JEAN M. BENNETT, "Precise Method for Measuring the Absolute Phase Change on Reflection," J. Opt. Soc. Am. 54, 612-622 (1964)

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  1. O. S. Heavens, Optical Properties of Thin Solid Filmns (Butterworths Scientific Publications Ltd., London, 1955), p. 174.
  2. O. Wiener, Ann. Physik 31, 629 (1887).
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  18. Four other forms of the complex refractive index are in current use in the literature: n+i (Ref. 4), n(1-ik) (Ref. 19), n(l+ik) (Ref. 20) and n(l-ik) (Ref. 21), where k represents the attenuation of the wave per vacuum wavelength and 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.
  19. See Ref. 1, p. 49.
  20. See Ref. 17, p. 610.
  21. R. W. Ditchburn, Light (Blackie & Son Ltd., London, 1952), p. 441.
  22. 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."
  23. See Ref. 1, pp. 55–88.
  24. 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 Δ.
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  29. 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.
  30. The minus sign in Eq. (10) is absolutely necessary to le 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.
  31. This apparent paradox was first noted and explained by D. H. Rank and H. E. Bennett, J. Opt. Soc. Am. 45, 69 (1955).
  32. See Ref. 26, p. 83.
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  36. See Ref. 25, p. 97.
  37. 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.
  38. See Ref. 26, p. 101.
  39. It is assumed that the wavelengths of the two-beam reflection minima are identical to the wavelengths of the maxima in transmission.
  40. 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.
  41. 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 elilflinated. 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.
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  46. 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.
  47. Johnson Matthey JM 50 silver rod obtained from Jarrell-Ash Company.
  48. Obtained from the Aluminum Company of America.
  49. W. F. Koehler, J. Opt. Soc. Am. 43, 743 (1953); 45, 1015 (1955).
  50. H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961).
  51. H. E. Bennett, J. M. Bennett, and E. J. Ashley, J. Opt. Soc. Am. 52, 1245 (1962).
  52. Vickers projection microscope manufactured by Cooke, Troughton, and Simms, Ltd., York, England.
  53. Model BK 3643 direct reading spectrograph manufactured by Bausch & Lomb Optical Company, Rochester, New York.
  54. Very fast Type C panchromatic antihalation plates obtained from Eastman Kodak Company, Rochester, New York.
  55. Corning filter No. 2404 is used in photographing the neon spectrum to eliminate the lines which obscure some of the interference fringes.
  56. A commercial model is available from the David W. Mann Company, Lincoln, Massachussetts.
  57. J. M. Bennett and W. F. Koehler, J. Opt. Soc. Am. 49, 466 (1959).
  58. W. F. Koehler and F. K. Odencrantz, J. Opt. Soc. Am. 47, 862 (1957).
  59. A. G. Worthing and J. Geffner, Treatment of Experimental Data (John Wiley & Sons, Inc., New York, 1943), p. 207.
  60. B. O. Seraphin, J. Opt. Soc. Am. 52, 912 (1962).
  61. Note the typesetter's errors on p. 1246 of Faust's paper (Ref. 3) which give ΔV = ½d.
  62. J. Holden, Proc. Phys. Soc. (London) 62, 405 (1949).
  63. 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~β2π~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."
  64. T. M. Donovan, E. J. Ashley, and H. E. Bennett, J. Opt. Soc. Am. 53, 1403 (1963).

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