Abstract

This paper describes a CO2 laser interferometer allowing absolute distance measurements using a set of CO2 lines. The method relies on the so-called fractional fringe technique. First, we introduce some theoretical topics related to this application of CO2 spectroscopy. The second part of the paper is a description of the instrument.

© 1979 Optical Society of America

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References

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  1. F. R. Petersen et al., Phys. Rev. Lett. 31, 573 (1973).
    [CrossRef]
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

1973 (1)

F. R. Petersen et al., Phys. Rev. Lett. 31, 573 (1973).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

Petersen, F. R.

F. R. Petersen et al., Phys. Rev. Lett. 31, 573 (1973).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

Phys. Rev. Lett. (1)

F. R. Petersen et al., Phys. Rev. Lett. 31, 573 (1973).
[CrossRef]

Other (1)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

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Tables (1)

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Table I Solution for Six Wavelengths Showing the Single Coincidence Within SE = ±0.1 μm Between 0–1 m.

Equations (13)

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L = k i [ ( λ i ) / 2 ] + i .
Γ N - 1 = k 1 [ ( λ 1 ) / 2 ] = k n [ ( λ N ) / 2 ] ,
Γ i j k = Γ i j - Γ j k = 2 ( σ i - 2 σ j + σ k ) .
Γ N = Γ i w = 2 [ C N - 1 0 σ i - C N - 1 1 σ j + ( - 1 ) N - 1 C N - 1 N - 1 σ w ] ,
T ( v , J ) = G ( v ) + B v J ( J + 1 ) - D v J 2 ( J + 1 ) 2 + H v J 3 ( J + 1 ) 3 - L v J 4 ( J + 1 ) 4 + ,
m = - J m = J + 1 for the P branch ( Δ J = - 1 ) , for the R branch ( Δ J = + 1 ) .
σ ( m ) = σ 0 + m ( B v + B v ) + m 2 [ ( B v - B v ) - ( D v - D v ) ] - m 3 [ 2 ( D v + D v ) - ( H v + H v ) ] - m 4 [ ( D v - D v ) - 3 ( H v - H v ) ] + ,
Γ i w = 2 { [ C N - 1 0 m i ( - 1 ) N - 1 C N - 1 N - 1 m w ] α 1 + [ C N - 1 0 m i 2 ( - 1 ) N - 1 C N - 1 N - 1 m w 2 ] α 2 + }
C N - 1 0 m q - C N - 1 1 ( m + 2 p ) q + ( - 1 ) N - 1 C N - 1 N - 1 [ m + 2 ( N - 1 ) p ] q = 0
α 1 ~ 0.78 cm - 1 , α 2 ~ 0.30 × 10 - 2 cm - 1 , α 3 ~ 0.13 10 - 6 , α 4 ~ 0.18 × 10 - 7 cm - 1 ,
Γ 12 - 1 ~ [ ( 0.34 ) / p ] cm ;             Γ 123 - 1 ~ [ ( 21 ) / ( p 2 ) ] cm ;             Γ 1234 - 1 ~ [ ( 10 4 ) / ( p 3 ) ] cm .
δ L = [ 2 E ( δ Δ λ / 2 ) ] · λ 1 + λ 2 4             if [ λ 1 - λ 2 ] = Δ λ < δ ,
K = 2 E [ ( δ ) / ( Δ λ / 2 ) ] + 1.

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