Abstract

The properties of a Fabry-Perot etalon, with surface defects compensated by irradiating a silicon oxide film, are computed for the case in which the initial surface defects function is rectangular. As a result of absorption, the compensating layer of silicon oxide must be deposited before the reflecting coating if the etalon is to be used at uv wavelengths. For visible wavelengths, the compensating layer may be a half-wave silicon oxide film deposited over the reflecting coating. An example is discussed in which the rms deviation from the mean thickness of an etalon is reduced from 2.37 nm to 0.80 nm. An automatic self-compensating process is proposed in which the radiation transmitted by an etalon may be used to produce an appropriate change in the thickness profile of a silicon oxide film.

© 1972 Optical Society of America

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References

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  1. E. Pelletier, R. Chabbal, P. Giacomo, J. Phys. 25, 275 (1964).
    [CrossRef]
  2. G. Koppelmann, K. Schreck, Optik 29, 549 (1969).
  3. I. J. Hodgkinson, Appl. Opt. 10, 396 (1971).
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. I. J. Hodgkinson, Appl. Opt. 9, 1577 (1970).
    [CrossRef] [PubMed]
  7. R. Chabbal, J. Rech. Centre Natl. Rech. Sci. 24, 138 (1953) [translation by R. B. Jacobi, A.E.R.E. (1958)].
  8. G. D. Dew, J. Sci. Instrum. 43, 409 (1966).
    [CrossRef] [PubMed]
  9. G. Schulz, J. Schwider, App. Opt. 6, 1077 (1967).
    [CrossRef]
  10. M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1959).
  11. I. J. Hodgkinson, Appl. Opt. 8, 1373 (1969).
    [CrossRef] [PubMed]

1971

1970

1969

G. Koppelmann, K. Schreck, Optik 29, 549 (1969).

I. J. Hodgkinson, Appl. Opt. 8, 1373 (1969).
[CrossRef] [PubMed]

1967

G. Schulz, J. Schwider, App. Opt. 6, 1077 (1967).
[CrossRef]

1966

1965

1964

E. Pelletier, R. Chabbal, P. Giacomo, J. Phys. 25, 275 (1964).
[CrossRef]

1953

R. Chabbal, J. Rech. Centre Natl. Rech. Sci. 24, 138 (1953) [translation by R. B. Jacobi, A.E.R.E. (1958)].

Bashkin, S.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1959).

Bradford, A. P.

Chabbal, R.

E. Pelletier, R. Chabbal, P. Giacomo, J. Phys. 25, 275 (1964).
[CrossRef]

R. Chabbal, J. Rech. Centre Natl. Rech. Sci. 24, 138 (1953) [translation by R. B. Jacobi, A.E.R.E. (1958)].

Dew, G. D.

G. D. Dew, J. Sci. Instrum. 43, 409 (1966).
[CrossRef] [PubMed]

Giacomo, P.

E. Pelletier, R. Chabbal, P. Giacomo, J. Phys. 25, 275 (1964).
[CrossRef]

Hass, G.

Hodgkinson, I. J.

Koppelmann, G.

G. Koppelmann, K. Schreck, Optik 29, 549 (1969).

McFarland, M.

Nester, J. F.

Pelletier, E.

E. Pelletier, R. Chabbal, P. Giacomo, J. Phys. 25, 275 (1964).
[CrossRef]

Ritter, E.

Schreck, K.

G. Koppelmann, K. Schreck, Optik 29, 549 (1969).

Schroeder, J. B.

Schulz, G.

G. Schulz, J. Schwider, App. Opt. 6, 1077 (1967).
[CrossRef]

Schwider, J.

G. Schulz, J. Schwider, App. Opt. 6, 1077 (1967).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1959).

App. Opt.

G. Schulz, J. Schwider, App. Opt. 6, 1077 (1967).
[CrossRef]

Appl. Opt.

J. Phys.

E. Pelletier, R. Chabbal, P. Giacomo, J. Phys. 25, 275 (1964).
[CrossRef]

J. Rech. Centre Natl. Rech. Sci.

R. Chabbal, J. Rech. Centre Natl. Rech. Sci. 24, 138 (1953) [translation by R. B. Jacobi, A.E.R.E. (1958)].

J. Sci. Instrum.

G. D. Dew, J. Sci. Instrum. 43, 409 (1966).
[CrossRef] [PubMed]

Optik

G. Koppelmann, K. Schreck, Optik 29, 549 (1969).

Other

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1959).

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Figures (8)

Fig. 1
Fig. 1

Transmission factor of a symmetric Fabry-Perot interferometer compensated with half-wavelength silicon oxide films deposited over ideal HLH dielectric multilayer reflecting coatings. Each silicon oxide film has an initial refractive index of 1.64. ND is the initial surface defects finesse, and the defects function is assumed to be rectangular. (Note that the vertical scale is logarithmic.)

Fig. 2
Fig. 2

Transmission factor and finesse of a symmetric etalon compensated by silicon oxide films deposited over ideal HLH dielectric multilayer reflecting coatings. The initial refractive index of the silicon oxide is chosen to minimize the effects of absorption. The curves are plotted for an initial surface defects finesse of 20 at wavelength λ, and the initial defects function is assumed to be rectangular. A*F is plotted for comparison (broken lines).

Fig. 3
Fig. 3

Transmission factor τE of an etalon compensated with silicon oxide films deposited before the deposition of ideal HLH dielectric multilayer reflecting coatings. The initial refractive index of the silicon oxide is 1.64, and ND is the initial finesse of a rectangular defects function, for wavelength λ.

Fig. 4
Fig. 4

Self-correction of Fabry-Perot plate surface defects. The separation of the plates is adjusted to maintain maximum transmission of the uv incident radiation, at the region of the aperture where surface defects cause the separation to be greatest.

Fig. 5
Fig. 5

Change of Fabry-Perot surface defects with time in a self-correcting process. The surface defect decreases rapidly and then slowly approaches its initial value. The surface defect is expressed as a fraction of the wavelength of the uv incident radiation.

Fig. 6
Fig. 6

Self-correction of surface defects. The graph represents the relationship that exists between the various parameters. The maximum surface defect is reduced from an initial value of λuv to a minimum value of rλuv; λuv is the wavelength of the uv radiation. NR is the reflecting finesse, and hm is the maximum thickness change available from the silicon oxide film.

Fig. 7
Fig. 7

Compensation of the surface defects of Fabry-Perot plates by irradiating a silicon oxide film. The surface defects may be observed visually as the compensation process proceeds.

Fig. 8
Fig. 8

Surface defects distribution of a 1.5-cm diam Fabry-Perot etalon before compensation (solid line) and after compensation by an irradiated silicon oxide film (broken line). (The thickness of the etalon increases right to left.)

Tables (1)

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Table I Constants in Empirical Formula for Absorption Constant

Equations (13)

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p ( z , z ) = z + z c + ( ρ c λ / 2 π )
E ( z ) = A [ R ( z ) , T ( z ) , p ( z , z ) ] D ( z ) d z S .
p = z + z c + ( ρ c λ / 2 π )
θ = r 0 / b = ( λ / z N F ) 1 2 ,
( 2 j - 1 ) θ z = ( 2 j - 1 ) ( λ z / N F ) 1 2 .
M 2 N + 1 = ( 0 - i / c - i c 0 ) ,
c = [ n 0 n s ( 1 - R 1 2 ) / ( 1 + R 1 2 ) ] 1 2 ,
R = 1 + [ π 2 - π ( 4 N R 2 + π 2 ) 1 2 ] / 2 N R 2 .
h = h m [ 1 - exp ( - γ E ) ] ,
h 0 = h m { 1 - exp [ - γ A ( z 0 ) t ] } ,
h = h m { 1 - exp [ - γ 0 t A ( z 0 + h 0 - h - λ uv ) d t ] }
h ( t + d t ) = h ( t ) + d h ,
d h = γ ( h m - h ) d E = γ ( h m - h ) A ( z 0 + h 0 - h - λ uv ) d t .

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