Abstract

Theoretical performance limits of stationary Fourier spectrometers without mechanical scanning are analyzed and compared with the performance of a scanning Fourier spectrometer. Spectrometers employing uncollimated light are most favorable. In amplitude-splitting interferometers the reduction in fringe visibility brought about by the extended source can be avoided and leads to high optical throughput in the corresponding spectrometer. In a stationary wave-front-splittirig interferometer, realized without a beam splitter, the fringe contrast depends on the size of the source. The use of a slit source increases the optical throughput of source-size-limited spectrometers.

© 1991 Optical Society of America

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References

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  1. G. J. Swanson, “Broad-source fringes in grating and conventional interferometers,” J. Opt. Soc. Am. A 1, 1147–1153 (1984).
    [CrossRef]
  2. T. Okamoto, S. Kawata, S. Minami, “Fourier transform spectrometer with a self-scanning photodiode array,” Appl. Opt. 23, 269–273 (1984).
    [CrossRef] [PubMed]
  3. T. H. Barnes, “Photodiode array Fourier transform spectrometer with improved dynamic range,” Appl. Opt. 24, 3702–3706 (1985).
    [CrossRef] [PubMed]
  4. S. C. Leon, “Broad source fringe formation with a Fresnel biprism and a Mach–Zehnder interferometer,” Appl. Opt. 26, 5259–5265 (1987).
    [CrossRef] [PubMed]
  5. E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987).
  6. J. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, New York, 1979).
  7. Presented in most textbooks of optics, for instance, Ref. 5.
  8. K. Yoshihara, K. Nakashima, M. Higuchi, “Holographic spectroscopy using a Mach–Zehnder interferometer,” Jpn. J. Appl. Phys. 15, 1169–1170 (1976).
    [CrossRef]

1987

1985

1984

1976

K. Yoshihara, K. Nakashima, M. Higuchi, “Holographic spectroscopy using a Mach–Zehnder interferometer,” Jpn. J. Appl. Phys. 15, 1169–1170 (1976).
[CrossRef]

Barnes, T. H.

Chamberlain, J.

J. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, New York, 1979).

Hecht, E.

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987).

Higuchi, M.

K. Yoshihara, K. Nakashima, M. Higuchi, “Holographic spectroscopy using a Mach–Zehnder interferometer,” Jpn. J. Appl. Phys. 15, 1169–1170 (1976).
[CrossRef]

Kawata, S.

Leon, S. C.

Minami, S.

Nakashima, K.

K. Yoshihara, K. Nakashima, M. Higuchi, “Holographic spectroscopy using a Mach–Zehnder interferometer,” Jpn. J. Appl. Phys. 15, 1169–1170 (1976).
[CrossRef]

Okamoto, T.

Swanson, G. J.

Yoshihara, K.

K. Yoshihara, K. Nakashima, M. Higuchi, “Holographic spectroscopy using a Mach–Zehnder interferometer,” Jpn. J. Appl. Phys. 15, 1169–1170 (1976).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

K. Yoshihara, K. Nakashima, M. Higuchi, “Holographic spectroscopy using a Mach–Zehnder interferometer,” Jpn. J. Appl. Phys. 15, 1169–1170 (1976).
[CrossRef]

Other

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987).

J. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, New York, 1979).

Presented in most textbooks of optics, for instance, Ref. 5.

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Figures (6)

Fig. 1
Fig. 1

(a) Stationary Michelson interferometer with extended source (S, source; L, lens; BS, beam splitter; M’s, mirrors; P, detection plane); (b) virtual source diagram of the stationary Michelson interferometer; (c) nomenclature for the circular source.

Fig. 2
Fig. 2

(a) Modified Mach–Zehnder interferometer with extended source; (b) virtual source drawing of the modified Mach– Zehnder interferometer (notation as for Fig. 1).

Fig. 3
Fig. 3

(a) Triangle interferometer with extended source; (b) virtual source diagram of the triangle interferometer (notation as for Fig. 1).

Fig. 4
Fig. 4

(a) Double-mirror interferometer with extended source; (b) virtual source drawing of the double-mirror interferometer (notation as for Fig. 1).

Fig. 5
Fig. 5

Modified Mach–Zehnder interferometer with uncollimated light.

Fig. 6
Fig. 6

Throughputs of the spectrometers compared with those of the scanning Michelson spectrometer: UN, uncollimated light.

Tables (1)

Tables Icon

Table 1 Equations of Resolving Powers and Throughputs of the Spectrometers and Comparison of the Throughputsa

Equations (17)

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D ( x ) 2 x α .
T ( λ ) B ( λ ) Ω A c ( d A s / A s ) = I 0 ( d A s / A s ) ,
I = I 0 + I 0 π r s 2 0 π cos [ 2 π λ 2 α ( x + L r s cos φ f ) ] 2 r s 2 sin 2 φ d φ = I 0 + I 0 2 J 1 ( z ) z cos ( 2 π λ 2 x α ) ,
I 0 2 J 1 ( z ) z = T ( λ ) B ( λ ) λ 2 A c 8 π D max 2 z J 1 ( z ) .
R = λ / Δ λ = z opt / 2.4 ( Ω π ) 1 / 2 .
I = I 0 + I 0 π r s 2 0 π cos [ 2 π λ 2 x α ( 1 r s 2 cos 2 φ 2 f 2 ) ] 2 r s 2 sin 2 φ d φ = I 0 + I 0 [ J 0 ( z ) cos ( z 0 ) J 1 ( z ) sin ( z 0 ) ] ,
S ( ϑ ) = S ( ϑ ) + S ( ϑ ) ,
S ( ϑ ) = { [ Ω ϑ 0 / 2 π ( ϑ 0 ϑ ) 1 ] 1 / 2 ϑ 0 ( 1 Ω / 2 π ) < ϑ ϑ 0 0 otherwise .
R = 2 π / Ω .
D ( x ) = l x / f ,
I = I 0 + I 0 cos [ ( 2 π / λ ) l x / f ] .
R = l r c / 0.6 λ f
D ( x ) l β = 4 h α x / f ,
I = I 0 + I 0 π r s 2 0 π cos [ 2 π λ ( l x / f + 4 α r s cos φ ) ] 2 r s 2 sin 2 φ d φ = I 0 + I 0 2 J 1 ( z ) z cos ( 2 π λ l x / f ) ,
R = ( r c h z opt ) / 1.2 f 2 ( Ω π ) 1 / 2 .
I = I 0 + I 0 sinc ( D Ω / 2 λ ) cos ( z 0 ) ,
R = 2 π / Ω .

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