Abstract

An electronic fringe counter for use with optical interferometers is described. Provision is made for automatic counting of integral fringes, interpolation to within 1/200 wavelength or approximately 10−7 inch, and indication of the direction of motion of the interferometer plates. Automatic interpolation is achieved by vibrating one plate of the interferometer and analyzing the resulting ac signals from a photomultiplier exposed to a portion of the fringes in the image plane of the optical system. The use of an ac analyzer eliminates troublesome dc drifts associated with photoelectronic circuits and provides an oscilloscope display of the phase progression from fringe to fringe.

© 1954 Optical Society of America

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References

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  1. A somewhat similar nonvibrating system using two separate photomultiplier channels has been developed by E. Root (private communication). See also Harrison, Jacobsen, and Camus, J. Opt. Soc. Am. 40, 800 (1950).
    [Crossref]
  2. C. Pulfrich, Z. Instrumentenk. 28, 261 (1898).
  3. See, for example, S. Tolansky, Multiple-Beam Interferometry (Oxford University Press, London, 1948), Chapter II.
  4. H. Osterberg, J. Opt. Soc. Am. 22, 19 (1932).
    [Crossref]
  5. See also F. H. Branin, J. Opt. Soc. Am. 43, 839 (1953).
    [Crossref]
  6. R. Feldt, A. B. Du Mont Laboratories (private communication).
  7. G. R. Harrison and J. E. Archer, J. Opt. Soc. Am. 41, 495 (1951).
    [Crossref]

1953 (1)

1951 (1)

1932 (1)

1898 (1)

C. Pulfrich, Z. Instrumentenk. 28, 261 (1898).

Archer, J. E.

Branin, F. H.

Feldt, R.

R. Feldt, A. B. Du Mont Laboratories (private communication).

Harrison, G. R.

Osterberg, H.

Pulfrich, C.

C. Pulfrich, Z. Instrumentenk. 28, 261 (1898).

Root, E.

A somewhat similar nonvibrating system using two separate photomultiplier channels has been developed by E. Root (private communication). See also Harrison, Jacobsen, and Camus, J. Opt. Soc. Am. 40, 800 (1950).
[Crossref]

Tolansky, S.

See, for example, S. Tolansky, Multiple-Beam Interferometry (Oxford University Press, London, 1948), Chapter II.

J. Opt. Soc. Am. (3)

Z. Instrumentenk. (1)

C. Pulfrich, Z. Instrumentenk. 28, 261 (1898).

Other (3)

See, for example, S. Tolansky, Multiple-Beam Interferometry (Oxford University Press, London, 1948), Chapter II.

R. Feldt, A. B. Du Mont Laboratories (private communication).

A somewhat similar nonvibrating system using two separate photomultiplier channels has been developed by E. Root (private communication). See also Harrison, Jacobsen, and Camus, J. Opt. Soc. Am. 40, 800 (1950).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Block diagram of an electronic fringe interpolator for an optical interferometer.

Fig. 2
Fig. 2

Interference fringes in the image plane of the interferometer.

Fig. 3
Fig. 3

Measured amplitudes of Vω and V2ω (plotted points) versus plate vibration amplitude d1. Normalized curves of J1 and J2 (smooth curves) are shown for comparison.

Fig. 4
Fig. 4

Rectified wave for integral fringe counting.

Fig. 5
Fig. 5

Oscilloscope pattern used in fringe interpolation.

Equations (14)

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E ( x ) = E 0 + E 1 [ 1 + cos ( 2 π x s + ϕ ) ] ,
ϕ = ( 4 π d / λ ) + ,
F ( ϕ ) = S { E 0 + E 1 [ 1 + β cos ( ϕ + δ ) ] } ,
V ( ϕ ) = K S [ E 0 + E 1 ( 1 + β cos ϕ ) ] ,
V ( ϕ ) = V d c + V 1 cos ϕ ,
d ( t ) = d 0 ( t ) + d 1 cos ( ω t + b ) ,
ϕ 0 = 4 π d 0 λ +             and             ϕ 1 = 4 π d 1 λ .
V 1 cos ϕ = V 1 [ cos ϕ 0 cos ( ϕ 1 cos ω t ) - sin ϕ 0 sin ( ϕ 1 cos ω t ) ] ,
V 1 cos ϕ = V 1 { cos ϕ 0 [ J 0 ( ϕ 1 ) - 2 J 2 ( ϕ 1 ) cos 2 ω t + 2 J 4 ( ϕ 1 ) cos 4 ω t - ] - sin ϕ 0 [ 2 J 1 ( ϕ 1 ) cos ω t - 2 J 3 ( ϕ 1 )     cos 3 ω t + ] } .
V 0 = V 1 J 0 ( ϕ 1 ) cos ϕ 0 + V d c V ω = - 2 V 1 J 1 ( ϕ 1 ) sin ϕ 0 cos ω t V 2 ω = - 2 V 1 J 2 ( ϕ 1 )     cos ϕ 0 cos 2 ω t } .
and V ω = - 2 V 1 A α ω J 1 ( ϕ 1 ) sin ϕ 0 cos ( ω t + θ ω ) V 2 ω = - 2 V 1 A α 2 ω J 2 ( ϕ 1 ) cos ϕ 0 cos ( 2 ω t + θ 2 ω ) } ,
V 0 = V d c - 0.1 V 1 cos ϕ 0 V ω = - V 1 A α ω sin ϕ 0 cos ( ω t + θ ω ) V 2 ω = - V 1 A α 2 ω cos ϕ 0 cos ( 2 ω t + θ 2 ω ) } .
( V 2 ω ) det = V 1 A α ω | cos ( 4 π d 0 ( t ) λ + ) | ,
and V v = V 1 A α ω sin ( 4 π d 0 λ + ) V h = V 1 A α 2 ω cos ( 4 π d 0 λ + ) } .