Abstract

Methods are described for investigating the dimensional stability of passive Fabry-Perot etalons with spacers made of low expansion materials. The measurements are made in terms of the Krypton 86 primary length standard which is reproducible to 1 part in 108. The precision of the measurements defined as LL when ΔL is the smallest detectable change in the optical length L is also of this order.

© 1970 Optical Society of America

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References

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  1. J. H. Jaffe, J. Phys. Radium 19, 273 (1958).
    [CrossRef]
  2. G. R. Hanes, Can. J. Phys. 37, 1283 (1959).
    [CrossRef]
  3. R. M. Hill, C. F. Bruce, Australian J. Phys. 15, 194 (1962).
    [CrossRef]
  4. C. F. Bruce, R. M. Hill, Australian J. Phys. 14, 64 (1961).
    [CrossRef]
  5. P. E. Ciddor, National Standards Laboratory, csiro, Sydney, private communication.
  6. P. Connes, Rev. Opt. Theor. Instrum. 35, 37 (1956).
  7. P. Connes, J. Phys. Radium 19, 262 (1958).
    [CrossRef]
  8. D. A. Jackson, Proc. Roy. Soc. London A263, 289 (1961).
  9. D. J. Bradley, Nature 215, 499 (1967).
    [CrossRef]
  10. M. Herscher, Appl. Opt. 7, 951 (1968).
    [CrossRef]
  11. J. R. Johnson, Appl. Opt. 7, 1061 (1968).
    [CrossRef] [PubMed]
  12. D. J. Bradley, C. J. Mitchell, Phil. Trans. Roy. Soc. A263, 209 (1968).

1968 (3)

D. J. Bradley, C. J. Mitchell, Phil. Trans. Roy. Soc. A263, 209 (1968).

M. Herscher, Appl. Opt. 7, 951 (1968).
[CrossRef]

J. R. Johnson, Appl. Opt. 7, 1061 (1968).
[CrossRef] [PubMed]

1967 (1)

D. J. Bradley, Nature 215, 499 (1967).
[CrossRef]

1962 (1)

R. M. Hill, C. F. Bruce, Australian J. Phys. 15, 194 (1962).
[CrossRef]

1961 (2)

C. F. Bruce, R. M. Hill, Australian J. Phys. 14, 64 (1961).
[CrossRef]

D. A. Jackson, Proc. Roy. Soc. London A263, 289 (1961).

1959 (1)

G. R. Hanes, Can. J. Phys. 37, 1283 (1959).
[CrossRef]

1958 (2)

J. H. Jaffe, J. Phys. Radium 19, 273 (1958).
[CrossRef]

P. Connes, J. Phys. Radium 19, 262 (1958).
[CrossRef]

1956 (1)

P. Connes, Rev. Opt. Theor. Instrum. 35, 37 (1956).

Bradley, D. J.

D. J. Bradley, C. J. Mitchell, Phil. Trans. Roy. Soc. A263, 209 (1968).

D. J. Bradley, Nature 215, 499 (1967).
[CrossRef]

Bruce, C. F.

R. M. Hill, C. F. Bruce, Australian J. Phys. 15, 194 (1962).
[CrossRef]

C. F. Bruce, R. M. Hill, Australian J. Phys. 14, 64 (1961).
[CrossRef]

Ciddor, P. E.

P. E. Ciddor, National Standards Laboratory, csiro, Sydney, private communication.

Connes, P.

P. Connes, J. Phys. Radium 19, 262 (1958).
[CrossRef]

P. Connes, Rev. Opt. Theor. Instrum. 35, 37 (1956).

Hanes, G. R.

G. R. Hanes, Can. J. Phys. 37, 1283 (1959).
[CrossRef]

Herscher, M.

Hill, R. M.

R. M. Hill, C. F. Bruce, Australian J. Phys. 15, 194 (1962).
[CrossRef]

C. F. Bruce, R. M. Hill, Australian J. Phys. 14, 64 (1961).
[CrossRef]

Jackson, D. A.

D. A. Jackson, Proc. Roy. Soc. London A263, 289 (1961).

Jaffe, J. H.

J. H. Jaffe, J. Phys. Radium 19, 273 (1958).
[CrossRef]

Johnson, J. R.

Mitchell, C. J.

D. J. Bradley, C. J. Mitchell, Phil. Trans. Roy. Soc. A263, 209 (1968).

Appl. Opt. (2)

Australian J. Phys. (2)

R. M. Hill, C. F. Bruce, Australian J. Phys. 15, 194 (1962).
[CrossRef]

C. F. Bruce, R. M. Hill, Australian J. Phys. 14, 64 (1961).
[CrossRef]

Can. J. Phys. (1)

G. R. Hanes, Can. J. Phys. 37, 1283 (1959).
[CrossRef]

J. Phys. Radium (2)

J. H. Jaffe, J. Phys. Radium 19, 273 (1958).
[CrossRef]

P. Connes, J. Phys. Radium 19, 262 (1958).
[CrossRef]

Nature (1)

D. J. Bradley, Nature 215, 499 (1967).
[CrossRef]

Phil. Trans. Roy. Soc. (1)

D. J. Bradley, C. J. Mitchell, Phil. Trans. Roy. Soc. A263, 209 (1968).

Proc. Roy. Soc. London (1)

D. A. Jackson, Proc. Roy. Soc. London A263, 289 (1961).

Rev. Opt. Theor. Instrum. (1)

P. Connes, Rev. Opt. Theor. Instrum. 35, 37 (1956).

Other (1)

P. E. Ciddor, National Standards Laboratory, csiro, Sydney, private communication.

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Figures (7)

Fig. 1
Fig. 1

(Top) Experimental arrangement for measurement of etalon stability. S, light source; L1, illuminating lens; E, etalon; V, etalon mounting; L2, projection lens; A, aperture, P, photomultiplier. (Bottom) Schematic view of etalon mounting.

Fig. 2
Fig. 2

Experimental relation between changes in order of interference ΔN and ratio of harmonic components in detected current signal i1/i2. R(reflectance) = 0.83; a(scan amplitude) = 0.1; b(aperture radius/2) = 0.05.

Fig. 3
Fig. 3

Experimental relations between ΔN and i1/i2 for different values of the parameters R, a, b, and ϕ(angle between plats.)

Curve 1 R = 0.89 (multilayer)a ≈ 0.05, b = 0.05, ϕ = 0,
Curve 2 R = 0.89a ≈ 0.10, b = 0.05, ϕ = 0,
Curve 3 R = 0.89a ≈ 0.15, b = 0.05, ϕ = 0,
Curve 4 R = 0.89a ≈ 0.10, b = 0.05, ϕ = 5
× 10−6 rad,
Curve 5 R = 0.83 (silver)a ≈ 0.10, b = 0.05, ϕ = 0.
Fig. 4
Fig. 4

Theoretical relations between ΔN and i1/i2 for R = 0.89 (multilayer); a = 0.05, 0.10, 0.15; b ≈ 0.05; ϕ = 0.

Fig. 5
Fig. 5

Intensity distribution curve for spherical Fabry-Perot for different values of order N = M + f at center. M, integer; f, fraction.

Fig. 6
Fig. 6

Changes in interference ring radius δρ for a change in order ΔN = 0.01 for various values of the initial ring radius ρ.

Fig. 7
Fig. 7

Calibration graph showing changes in measured radius of interference ring with changes in order of interference ΔN at N = 3.3 × 105.

Equations (6)

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i 0 = 2 p b [ 1 + 2 Σ k ( G k J 0 ( 2 π k a ) sin 2 π k b × cos 2 π k N ) / 2 π k b ] ( θ e / h c σ ) ,
i 1 = 4 p [ Σ G k J 1 ( 2 π k a ) sin 2 π k b sin 2 π k N / π k ] ( θ e / h c σ ) ,
i 2 = 4 p [ Σ G k J 2 ( 2 π k a ) sin 2 π k b cos 2 π k N / π k ] ( θ e / h c σ ) ,
p = ( π 2 D 2 / 4 t σ ) p ,
I 1 1 + [ 2 R / ( 1 R 2 ) ] 2 sin 2 δ / 2 ,
δ m = ( 4 ρ 3 / r 3 λ + 8 e ρ / r 2 λ ) δ ρ .

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