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  1. J. J. Snyder, in Laser Spectroscopy III, J. L. Hall, J. L. Carlsten, Eds. (Springer, Berlin, 1977), pp. 419–420.
  2. P. L. Jackson, J. Geophys. Res. 72, 1400 (1967).
    [CrossRef]
  3. W. Y. Chen, G. R. Stegen, J. Geophys. Res. 79, 3019 (1971).
    [CrossRef]
  4. We consider only a linear slope for simplicity. A more complete analysis shows that our result for the optimum value of b is exact through order α2 and is only slightly modified for higher orders.
  5. For data with only a small number of extrema, it is better to fit the maxima and minima separately and use the mean values of the two slopes and two intercepts. This procedure eliminates bias due to there being an unequal number of maxima and minima.

1971 (1)

W. Y. Chen, G. R. Stegen, J. Geophys. Res. 79, 3019 (1971).
[CrossRef]

1967 (1)

P. L. Jackson, J. Geophys. Res. 72, 1400 (1967).
[CrossRef]

Chen, W. Y.

W. Y. Chen, G. R. Stegen, J. Geophys. Res. 79, 3019 (1971).
[CrossRef]

Jackson, P. L.

P. L. Jackson, J. Geophys. Res. 72, 1400 (1967).
[CrossRef]

Snyder, J. J.

J. J. Snyder, in Laser Spectroscopy III, J. L. Hall, J. L. Carlsten, Eds. (Springer, Berlin, 1977), pp. 419–420.

Stegen, G. R.

W. Y. Chen, G. R. Stegen, J. Geophys. Res. 79, 3019 (1971).
[CrossRef]

J. Geophys. Res. (2)

P. L. Jackson, J. Geophys. Res. 72, 1400 (1967).
[CrossRef]

W. Y. Chen, G. R. Stegen, J. Geophys. Res. 79, 3019 (1971).
[CrossRef]

Other (3)

We consider only a linear slope for simplicity. A more complete analysis shows that our result for the optimum value of b is exact through order α2 and is only slightly modified for higher orders.

For data with only a small number of extrema, it is better to fit the maxima and minima separately and use the mean values of the two slopes and two intercepts. This procedure eliminates bias due to there being an unequal number of maxima and minima.

J. J. Snyder, in Laser Spectroscopy III, J. L. Hall, J. L. Carlsten, Eds. (Springer, Berlin, 1977), pp. 419–420.

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Figures (2)

Fig. 1
Fig. 1

fortran subroutine for locating the symmetry points of a fringe pattern.

Fig. 2
Fig. 2

Computer-generated fringe pattern. 1024 points with values between 0 and 255. Fringe period is 33.456 points. Gaussian envelope has (1/e) width of 600 and is centered at point number 400.

Tables (1)

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Table I Errors in Analysis of Computer-Generated Fringesa

Equations (15)

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f ( x , ϕ ) = I ϕ ( 1 + α x ) [ 1 + cos ( x + ϕ ) ] = I ϕ [ 1 + α x + cos ϕ cos x sin ϕ sin x + α ( cos ϕ ) x ( cos x ) α ( sin ϕ ) x ( sin x ) ] ,
g ( b , ϕ ) = b 0 f ( x , ϕ ) d x b 0 f ( x , ϕ ) d x = { α [ b 2 + 2 cos ϕ ( 1 cos b b sin b ) ] + 2 α sin ϕ ( 1 cos b ) } I ϕ .
g 0 ( b ) { α [ b 2 + 2 ( 1 cos b b sin b ) ] + 2 δ ϕ 0 ( 1 cos b ) } I 2 n π ,
g π ( b ) { α [ b 2 2 ( 1 cos b b sin b ) ] 2 δ ϕ π ( 1 cos b ) } I ( 2 n + 1 ) π .
δ ϕ 0 α [ b 2 + 2 ( 1 cos b b sin b ) ] 2 ( 1 cos b ) δ ϕ π + α [ b 2 2 ( 1 cos b b sin b ) ] 2 ( 1 cos b ) } .
δ ϕ 0 α ( 1 π 2 4 ) δ ϕ π = α ( 1 + π 2 4 ) b = π } .
1 cos b b sin b = 0
δ ϕ 0 + α b 2 2 ( 1 cos b ) δ ϕ π α b 2 2 ( 1 cos b ) } .
b 0.742 π ,
δ ϕ 0 = δ ϕ π + 1.6 α .
ϕ 0 = π ( a 0 a 1 ) ϕ 0 = π ( a 0 a 1 + 1 ) } ,
Δ λ ¯ / λ
σ ( Δ λ λ )
Δ ϕ ¯ / 2 π
σ ( Δ ϕ 2 π )

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