Abstract

The theory of certain errors involved in interferometric frequency calibration is developed. The origins of these errors are (1) the effective slit width of the monochromator and (2) the height of the slit. For uncoated, low reflecting interferometer plates a complete theory is given. For higher reflecting plates the effect of the slit height has been calculated in detail for one definite choice of reflection coefficient. The results of this calculation are thought to be representative also for other cases.

The main effect both of the slit width and the slit height is a blurring of the interference pattern. But moreover the maxima are displaced on account of the slit height effect. This may cause serious errors in calibrations. Curves are presented, giving the “fractional order” of the maxima for different cases.

© 1956 Optical Society of America

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References

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  1. J. H. Jaffe, J. Opt. Soc. Am. 43, 1170 (1953).
    [CrossRef]
  2. H. D. Polster, J. Opt. Soc. Am. 44, 503 (1954).
    [CrossRef]
  3. D. H. Rank and J. M. Bennett, J. Opt. Soc. Am. 45, 46 (1955).
    [CrossRef]
  4. D. H. Rank and H. E. Bennett, J. Opt. Soc. Am. 45, 69 (1955).
    [CrossRef]
  5. S. Brodersen, J. Opt. Soc. Am. 44, 22 (1954).
    [CrossRef]
  6. Rank, Shull, Bennett, and Wiggins, J. Opt. Soc. Am. 43, 952 (1953).
    [CrossRef]

1955 (2)

1954 (2)

1953 (2)

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Figures (6)

Fig. 1
Fig. 1

Optical arrangement.

Fig. 2
Fig. 2

Interference fringes in first approximation for different values of F.

Fig. 3
Fig. 3

Slit width effect on amplitude for F≤0.2.

Fig. 4
Fig. 4

Slit height effect on amplitude for F≤0.2.

Fig. 5
Fig. 5

Fractional order corrections.

Fig. 6
Fig. 6

Interference fringes for F=10 (R=53.7%) for different values of NΦ2/2.

Equations (15)

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1 / [ 1 + F sin 2 ( 2 π t ν cos φ ) ] ,
I = I 0 / [ 1 + F sin 2 ( 2 π t ν ) ] .
I = I 0 Φ 0 Φ 1 1 + F sin 2 ( 2 π t ν cos φ ) d φ .
I = I 0 s g 2 Φ s ν - s ν + s ( 1 - ν 1 - ν s ) × 0 Φ 1 1 + F sin 2 ( 2 π t ν 1 cos φ ) d φ d ν 1 ,
I I 0 s g 2 = 1 s 2 Φ 0 Φ ν - s ν + s ( s - ν 1 - ν ) × [ 1 - F 2 + F 2 cos ( 4 π t ν 1 cos φ ) ] d ν 1 d φ
I I 0 s g 2 = 1 - F 2 + F 2 1 Φ × 0 Φ ( sin ( 2 π t s cos φ ) 2 π t s cos φ ) 2 cos ( 4 π t ν cos φ ) d φ .
I I 0 s g 2 = 1 - F 2 + F 2 ( sin ( 2 π t s ) 2 π t s ) 2 1 Φ × 0 Φ cos ( 4 π t ν cos φ ) d φ .
[ sin ( 2 π t s ) / 2 π t s ] 2 .
y = ( 1 / Φ ) 0 Φ cos ( 4 π t ν cos φ ) d φ .
2 t ν = N = N 0 + δ ,
y = ( 1 / Φ ) 0 Φ cos 2 π ( δ - N φ 2 / 2 ) d φ .
y = ( u N Φ 2 / 2 ) - 1 2 n = m - 1 m - u N Φ 2 / 2 × [ ( m - n ) 1 2 - ( m - n - 1 ) 1 2 cos [ 2 π ( n + 1 2 ) / u ] ,
y / δ = ( - 2 π / Φ ) 0 Φ sin 2 π ( δ - N Φ 2 / 2 ) d φ = 0 ,
y max = 1 - ( 16 π 2 / 45 ) ( N Φ 2 / 2 ) ,
I I 0 = 1 Φ 0 Φ 1 / [ 1 + F 2 - F 2 cos 2 π ( δ - N φ 2 2 ) ] d φ .