Abstract

We have derived an expression for the combined effects of a converging beam of light and mirror misalignment on the interferograms obtained with a Michelson interferometer. Each effect has been considered separately by others and leads to symmetric interferograms whose modulation is less than 100%. The combined effect produces an asymmetry in the interferogram as well as a decrease in the modulation. The magnitude of the asymmetric term is given in terms of the optical parameters of the interferometer.

© 1974 Optical Society of America

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References

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  1. A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, 1927), p. 35.
  2. G. W. Stroke, J. Opt. Soc. Am. 47, 1097 (1957).
    [CrossRef]
  3. C. S. Williams, Appl. Opt. 5, 1084 (1966).
    [CrossRef] [PubMed]

1966

1957

Michelson, A. A.

A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, 1927), p. 35.

Stroke, G. W.

Williams, C. S.

Appl. Opt.

J. Opt. Soc. Am.

Other

A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, 1927), p. 35.

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Figures (2)

Fig. 1
Fig. 1

Geometry for the problem of a converging beam of light of half-angle θ and mirror misalignment α. M1 is the fixed mirror, M2 is the image of the moving mirror misaligned by an angle α from the position M2′ parallel to M1. D is the distance from M1 to the focus, d is the distance of M2 from the position of zero path difference, ρ and ϕ are the polar coordinates of the intersection of the incoming ray of light with M2′, and r is the distance of the incoming ray from the optic axis to the intersection with M1.

Fig. 2
Fig. 2

The ratio of the amplitude of F(Ω,σd) to its value at d = 0 as a function of |σd/(σd)max|. The curves for f/2 through f/20 lie on essentially the same curve. F(Ω,0) = −1/32(f/)2 and σdmax = 4(f/)2.

Equations (18)

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P ( d ) = 2 π R 2 I 0 ( 1 + cos 4 π σ d )
P ( d ) = 2 π R 2 I 0 [ 1 + sin ( Ω σ d ) Ω σ d cos 4 π σ d ( 1 - Ω 4 π ) ] .
P ( d ) = 2 π R 2 I 0 [ 1 + 2 J 1 ( 4 π σ R α ) 4 π σ R α cos 4 π σ d ] ,
d P = 2 I 0 d A ( 1 + cos 2 π σ δ ) ,
d = d + α ρ sin ϕ = d + α ( D - d ) tan θ sin ϕ .
δ = 2 d cos θ .
δ = 2 [ d + α ( D - d ) tan θ sin ϕ ] cos θ .
P = 2 I 0 0 R r d r 0 2 π [ 1 + cos ( a cos θ + b sin θ sin ϕ ) ] d ϕ ,
P = 2 π R 2 I 0 [ 1 + ( 2 / R 2 ) I R ] ,
I R = 0 R r J 0 ( b sin θ ) cos ( a cos θ ) d r .
I R = 0 R r J 0 ( b r D ) cos ( a - a r 2 2 D 2 ) d r .
I R = 0 R r ( 1 - b 2 r 2 4 D 2 ) cos ( a - a r 2 2 D 2 ) d r .
P ( d ) = 2 π R 2 I 0 [ 1 + sin ( Ω σ d ) Ω σ d cos 4 π σ d ( 1 - Ω 4 π ) + α 2 [ β ( d ) ] 2 F ( Ω , σ d ) ] ,
F ( Ω , σ d ) = 1 2 { ( 1 - Ω 2 π ) sin 4 π σ d [ 1 - ( Ω / 2 π ) ] 4 π σ d [ 1 - ( Ω / 2 π ) ] - [ 1 - ( Ω / 4 π ) ] sin ( Ω σ d ) Ω σ d sin 4 π σ d [ 1 - ( Ω / 4 π ) ] 4 π σ d [ 1 - ( Ω / 4 π ) ] }
β ( d ) = 4 π σ ( D - d )
Ω = π / [ 4 ( f / ) 2 ] .
α 2 β 0 2 F ( Ω , 0 ) = - π 2 2 ( α σ D f / ) 2 = - 2 π 2 ( α R λ ) 2
α ( 2 A ) 1 / 2 ( f / ) / π σ D .

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