Abstract

A Michelson interferometer of fixed-path difference, capable of scanning over only one fringe, has been shown to be useful for the measurement of Doppler shifts from isolated emission lines. It is straightforward to field widen this type of configuration, but if different wavelengths are to be selected, the field widening must be achromatic. Further, for Doppler shift measurement, one requires a path difference that is highly stable with respect to temperature. The generalized requirements for meeting all these conditions are set out and a configuration that satisfies them is described. Sample characteristics are given for a number of different systems.

© 1985 Optical Society of America

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References

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  1. R. L. Hilliard, G. G. Shepherd, “Wide-Angle Michelson Interferometer for Measuring Doppler Line Widths,” J. Opt. Soc. Am. 56, 362 (1966).
    [CrossRef]
  2. A. M. Title, H. E. Ramsey, “Improvements in Birefringent Filters. 6: Analog Birefringent Elements,” Appl. Opt. 19, 2046 (1980).
    [CrossRef] [PubMed]
  3. G. G. Shepherd et al., “WAMDII: Wide Angle Michelson Doppler Imaging Interferometer for Spacelab,” Appl. Opt. 24, 1571 (1985).
    [CrossRef] [PubMed]

1985 (1)

G. G. Shepherd et al., “WAMDII: Wide Angle Michelson Doppler Imaging Interferometer for Spacelab,” Appl. Opt. 24, 1571 (1985).
[CrossRef] [PubMed]

1980 (1)

A. M. Title, H. E. Ramsey, “Improvements in Birefringent Filters. 6: Analog Birefringent Elements,” Appl. Opt. 19, 2046 (1980).
[CrossRef] [PubMed]

1966 (1)

R. L. Hilliard, G. G. Shepherd, “Wide-Angle Michelson Interferometer for Measuring Doppler Line Widths,” J. Opt. Soc. Am. 56, 362 (1966).
[CrossRef]

Hilliard, R. L.

R. L. Hilliard, G. G. Shepherd, “Wide-Angle Michelson Interferometer for Measuring Doppler Line Widths,” J. Opt. Soc. Am. 56, 362 (1966).
[CrossRef]

Ramsey, H. E.

A. M. Title, H. E. Ramsey, “Improvements in Birefringent Filters. 6: Analog Birefringent Elements,” Appl. Opt. 19, 2046 (1980).
[CrossRef] [PubMed]

Shepherd, G. G.

G. G. Shepherd et al., “WAMDII: Wide Angle Michelson Doppler Imaging Interferometer for Spacelab,” Appl. Opt. 24, 1571 (1985).
[CrossRef] [PubMed]

R. L. Hilliard, G. G. Shepherd, “Wide-Angle Michelson Interferometer for Measuring Doppler Line Widths,” J. Opt. Soc. Am. 56, 362 (1966).
[CrossRef]

Title, A. M.

A. M. Title, H. E. Ramsey, “Improvements in Birefringent Filters. 6: Analog Birefringent Elements,” Appl. Opt. 19, 2046 (1980).
[CrossRef] [PubMed]

Appl. Opt. (2)

A. M. Title, H. E. Ramsey, “Improvements in Birefringent Filters. 6: Analog Birefringent Elements,” Appl. Opt. 19, 2046 (1980).
[CrossRef] [PubMed]

G. G. Shepherd et al., “WAMDII: Wide Angle Michelson Doppler Imaging Interferometer for Spacelab,” Appl. Opt. 24, 1571 (1985).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

R. L. Hilliard, G. G. Shepherd, “Wide-Angle Michelson Interferometer for Measuring Doppler Line Widths,” J. Opt. Soc. Am. 56, 362 (1966).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Field-widened Michelson interferometer having a refractive medium of thickness d1 and some air in one arm and air only in the other arm.

Fig. 2
Fig. 2

Field-widened Michelson interferometer as in Fig. 1 but with a thermal compensation mirror of thickness E and linear expansion coefficient γ.

Fig. 3
Fig. 3

Compensated field-widened Michelson interferometer as in Fig. 2 but with the addition of a slightly wedged prism 2, of thickness d2, that is translated to effect small changes in the optical path difference.

Fig. 4
Fig. 4

(a) Schematic drawing of the compensated field-widened Michelson interferometer of Shepherd et al.3 but with a 45° beam splitter for direct comparison with Fig. 3 (b). A fully compensated version of the configuration of (a).

Fig. 5
Fig. 5

Calculated field-widening characteristics for the configuration of Fig. 4(b).

Tables (1)

Tables Icon

Table I Characteristics of Various Michelson Interferometer Configurations

Equations (19)

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Δ 0 = 2 [ ( n 1 1 ) d 1 ( n 2 1 ) d 2 E ( h 2 h 1 ) ] .
ω = ( 1 1 n 1 ) d 1 ( 1 1 n 2 ) d 2 + E + ( h 2 h 1 ) .
d ω d λ = d 1 n 1 2 d n 1 d λ d 2 n 2 2 d n 2 d λ .
( Δ 0 T ) λ = 2 { [ β 1 + α 1 ( n 1 1 ) ] d 1 [ β 2 + α 2 ( n 2 1 ) ] d 2 γ E α 1 ( h 2 h 2 ) } ,
2 Δ 0 λ T = 2 [ ( β 1 λ ) T + ( n 1 λ ) T ] d 1 2 [ ( β 2 λ ) T + α 2 ( n 2 λ ) T ] d 2 .
d 1 ( 1 n 1 2 d n 1 d λ ) = d 2 ( 1 n 2 2 d n 2 d λ ) ,
d 1 ( β 1 λ + α 1 n 1 λ ) = d 2 ( β 2 λ + α 2 n 2 λ ) .
n 1 2 ( α 1 + β 1 / λ n 1 / λ ) = n 2 2 ( α 2 + β 2 / λ n 2 / λ ) .
d 2 = R 1 d 1 .
[ β 1 + α 1 ( n 1 1 ) ] d 1 [ β 2 + α 2 ( n 2 1 ) ] R 1 d 1 = γ E + α 1 ( h 2 h 1 ) ,
R 2 d 1 = E + ( α 1 / γ ) ( h 2 h 1 ) ,
d 1 [ ( 1 1 n 1 ) R 1 ( 1 1 n 2 ) + R 2 ] = ( h 2 h 1 ) ( 1 α 1 / γ ) ,
[equation omitted on the printed page]
Δ 0 = 2 d 1 [ ( n 1 1 ) R 1 ( n 2 1 ) R 2 + R 3 ( α 1 / γ ) ] ,
d 1 = 2.2107 cm , E = 1.3220 , d 2 = 3.5614 , F = 1.9167 .
( Δ T ) λ mm K 1
( ω T ) λ mm K 1
( ω λ ) T mm μ m 1
2 Δ λ T mm μ m 1 K 1

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