Abstract

This paper considers the optical design of a wide-angle fixed-path Michelson interferometer consisting of two arm glasses and an air gap. It is shown that this configuration can be optimized to give (a) extra large fringes (over 50° in diameter) over a range of wavelength, (b) a path difference nearly independent of wavelength, or (c) a path difference specified differently at two different wavelengths for observing a pair of doublets. Specific examples refer to the airglow wavelengths of 557.7, 630.0, 732.0 nm and others, and to a path difference of 4.5 cm. The properties of different glass combinations are discussed.

© 1985 Optical Society of America

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References

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  1. G. G. Shepherd et al., “WAMDII: Wide-Angle Michelson Doppler Imaging Interferometer for Spacelab,” Appl. Opt. 24, 1571 (1985).
    [Crossref] [PubMed]
  2. R. L. Hilliard, G. G. Shepherd, “Wide-Angle Michelson Interferometer for Measuring Doppler Line Widths,” J. Opt. Soc. Am. 56, 362 (1966).
    [Crossref]
  3. A. M. Title, H. E. Ramsey, “Improvements in Birefringent Filters. 6: Analog Birefringent Elements,” Appl. Opt. 19, 2046 (1980).
    [Crossref] [PubMed]
  4. G. Thuillier, G. G. Shepherd, “Fully Compensated Michelson Interferometer of Fixed-Path Difference,” Appl. Opt. 24, 1599 (1985).
    [Crossref] [PubMed]
  5. Optical Glass Catalog 3050E (Schott Optical Glass, Inc., Duryea, Pa. 18642).
  6. H. H. Zwick, G. G. Shepherd, “Defocusing a Wide-Angle Michelson Interferometer,” Appl. Opt. 10, 2569 (1971).
    [Crossref] [PubMed]

1985 (2)

1980 (1)

1971 (1)

1966 (1)

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Figures (4)

Fig. 1
Fig. 1

Field-widened Michelson with two glasses and air gap. n1 and n2 are the refractive indices of the arm glasses; S is the beam splitter surface; θ is the angle of incidence in air.

Fig. 2
Fig. 2

Change of path difference with incident angle optimized at 630 nm for a wide field: solid line, F4/LaSF5; dashed line, FK5/ SF57.

Fig. 3
Fig. 3

Change of path difference with incident angle with different degrees of defocusing; optimized for a wide field.

Fig. 4
Fig. 4

Variation of path difference with wavelength; combinations optimized to minimize this variation.

Tables (4)

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Table I Glasses Used in Searcha

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Table II Wide-Angle Combinations a

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Table III Combinations for Achromatic Δ0a

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Table IV Combinations with Δ0 Defined At Two Wavelengths

Equations (27)

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Δ = 2 ( n 3 t 3 + n 2 t 2 n 1 t 1 ) ( t 3 n 3 + t 2 n 2 t 1 n 1 ) sin 2 θ ( t 3 n 3 3 + t 2 n 2 3 t 1 n 1 3 ) sin 4 θ 4 ( t 3 n 3 5 + t 2 n 2 5 t 1 n 1 5 ) sin 6 θ 8 .
Δ 0 = 2 ( t 3 + n 2 t 2 n 1 t 1 ) .
t 3 + t 2 n 2 t 1 n 1 = 0 .
t 3 + t 2 n 2 3 t 1 n 1 3 = 0 .
t 1 = Δ 0 n 1 3 2 ( n 2 2 n 1 2 ) ( n 1 2 1 ) , t 2 = Δ 0 n 2 3 2 ( n 2 2 n 1 2 ) ( n 2 2 1 ) , t 3 = Δ 0 2 ( n 1 2 1 ) ( n 2 2 1 ) . }
t 1 t 2 = n 1 2 n 2 2 d n 2 / d λ d n 1 / d λ .
n 1 2 n 1 2 1 d n 1 d λ = n 2 2 n 2 2 1 d n 2 d λ .
n 2 n 2 1 d n d λ
Δ T and 2 Δ λ T
2 Δ λ T .
d n d λ n 2 n 2 1
t 3 + t 2 n 2 3 t 1 n 1 3 = e ,
t 1 = t 1 + n 1 3 n 2 2 e ( n 2 2 n 1 2 ) ( n 1 2 1 ) , t 2 = t 2 + n 1 2 n 2 3 e ( n 2 2 n 1 2 ) ( n 2 2 1 ) , t 3 = t 3 + n 1 2 n 2 2 e ( n 1 2 1 ) ( n 2 2 1 ) , }
t 2 n 2 λ t 1 n 1 λ = 0 .
t 2 = Δ 0 2 [ ( n 2 1 n 2 ) γ ( n 1 1 n 1 ) ] , t 1 = γ t 2 and t 3 = t 1 n 1 t 2 n 2 , }
γ = n 2 λ / n 1 λ .
2 Δ λ T .
Δ 0 2 = t 3 + n 2 t 2 n 2 t 1 .
t 3 + t 2 n 2 t 1 n 1 = 0 .
t 1 = d Δ 0 2 c Δ 0 2 bc ad , t 2 = b Δ 0 2 a Δ 0 2 bc ad , t 3 = t 1 n 1 t 2 n 2 , }
a = n 1 1 n 1 , b = n 1 1 n 1 , c = n 2 1 n 2 , d = n 2 1 n 2 .
d n d λ × 10 5 ( nm 1 )
d n d λ n 2 n 2 1 × 10 5 ( nm 1 )
2 Δ d λ T ( cm nm 1 K 1 )
Δ T ( cm K 1 )
2 Δ d λ T ( cm nm 1 K 1 )
Δ T ( cm K 1 )

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