Abstract

A new method for analytically obtaining the form of an interferogram is proposed. The method permits simple implementation for a computerized treatment. We can use it to determine easily the thickness of a thin film.

© 1993 Optical Society of America

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References

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  1. D. C. Flanders, T. M. Lyszczarz, “A precision wide-range optical gap measurement technique,” J. Vac. Sci. Technol. B 1, 1195–1199 (1983).
    [CrossRef]
  2. M. Martínez-Risco, Oeuvres Scientifiques (Presses Universitaires de France, Paris, 1976), pp. 73–79.
  3. A good estimate of the inaccuracy of the model is the size of the real source that appears instead of the point source. With a thickness of tenths of micrometers and an usual He–Ne laser beam, the source diameter can be of the order of 0.02d. If the source is not a point, a decrease of the fringe contrast appears, which is not really significant, as we have experimentally observed. The successive reflections produce an increase in the source size, but the beams that have been reflected many times are also less important for the interferogram. A more complete and detailed study of the model will soon be published by the authors.

1983 (1)

D. C. Flanders, T. M. Lyszczarz, “A precision wide-range optical gap measurement technique,” J. Vac. Sci. Technol. B 1, 1195–1199 (1983).
[CrossRef]

Flanders, D. C.

D. C. Flanders, T. M. Lyszczarz, “A precision wide-range optical gap measurement technique,” J. Vac. Sci. Technol. B 1, 1195–1199 (1983).
[CrossRef]

Lyszczarz, T. M.

D. C. Flanders, T. M. Lyszczarz, “A precision wide-range optical gap measurement technique,” J. Vac. Sci. Technol. B 1, 1195–1199 (1983).
[CrossRef]

Martínez-Risco, M.

M. Martínez-Risco, Oeuvres Scientifiques (Presses Universitaires de France, Paris, 1976), pp. 73–79.

J. Vac. Sci. Technol. B (1)

D. C. Flanders, T. M. Lyszczarz, “A precision wide-range optical gap measurement technique,” J. Vac. Sci. Technol. B 1, 1195–1199 (1983).
[CrossRef]

Other (2)

M. Martínez-Risco, Oeuvres Scientifiques (Presses Universitaires de France, Paris, 1976), pp. 73–79.

A good estimate of the inaccuracy of the model is the size of the real source that appears instead of the point source. With a thickness of tenths of micrometers and an usual He–Ne laser beam, the source diameter can be of the order of 0.02d. If the source is not a point, a decrease of the fringe contrast appears, which is not really significant, as we have experimentally observed. The successive reflections produce an increase in the source size, but the beams that have been reflected many times are also less important for the interferogram. A more complete and detailed study of the model will soon be published by the authors.

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Figures (3)

Fig. 1
Fig. 1

Operating conditions. A laser beam is focused on the film by a microscope objective, and the interference produced by its multiple internal reflections is observed on a plane at a distance l, where a CCD linear array is placed. The incidence angle is designated as 45°.

Fig. 2
Fig. 2

Virtual source model. We consider the emerging beam as coming from a virtual point at a distance Epl from the incidence point. We have represented only one internal reflection to make the figure simpler.

Fig. 3
Fig. 3

Cylindrical film. The angle between normals is α. Again, we have limited the number of considered beams to only two to keep the drawing clear.

Equations (6)

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I ( y ) = a 2 | r 1 exp ( i k R 0 ) R 0 + N = 1 r 1 N 1 r 2 N t 2 exp ( i k R N ) R N | 2 ,
R N = [ l 2 + y 2 + N 2 E 2 + 2 N E ( l + y ) ] 1 / 2 ,
E pl = 2 d ( 2 n 2 1 ) 1 / 2 ,
α = sin 1 ( q sin 1 2 n ) 1 2 n ,
E cyl = ρ sin 2 α + cos 2 α × { sin 2 α [ 2 ( n 2 1 ) sin α q ( 2 n 2 1 ) 1 / 2 ] + cos 2 α [ 2 sin α ( 2 n 2 1 ) 1 / 2 ] } .
d e ( ρ ) = E cyl ( ρ ) E pl d ,

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