Abstract

Interferometers of the Michelson or Mach–Zehnder type are designed as array interferometers. The number of array channels is equal to the number of points needed for an interferogram for Fourier transformation. Similarly one may use an array of step gratings with each grating having a different step height and producing one point of the interferogram. These interferometers, which do not have moving parts, use all the incident light, and the interferogram is instantly produced for real-time spectroscopy.

© 1995 Optical Society of America

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References

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  1. K. D. Möller, W. G. Rothschild, Far Infrared Spectroscopy (Wiley, New York, 1971).
  2. J. Linkemann, F. Romero-Borja, H. O. Tittel, “FT spectrometer with fixed mirrors using Fizeau fringes,” in Eighth International Conference on Fourier Transform Spectroscopy, H. M. Heise, E. H. Korte, H. W. Seisler, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1575, pp. 184–187.
  3. K. D. Möller, D. P. Siddons, C. J. Hirschmugl, D. Scardino, P. Petrone, D. Carlson, G. P. Williams, “Two-mirror wave-front-dividing interferometer for infrared synchrotron radiation,” Appl. Opt. 30, 4297–4301 (1991).
    [CrossRef] [PubMed]
  4. K. D. Möller, V. P. Tomaselli, J. Colosi, R. G. Zoeller, “Capacitive-grid beam splitter for far infrared and millimeter wave interferometers,” Appl. Opt. 23, 3075–3078 (1984).
    [CrossRef] [PubMed]
  5. J. Strong, Concepts of Optics (Freeman, San Francisco, Calif., 1958).
  6. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972).
  7. K. D. Moller, “Wave-front-dividing interferometers,” Infrared Phys. 32, 321–331 (1991).
    [CrossRef]
  8. R. Ruprecht, W. Bacher, “Untersuchungen an mikrostructurierten Bandpassfiltern fur das Ferne Infrarot und ihre Herstellung durch Röntgentiefenlithographie und Mikrogalvanoformung,” Rep. IMT-Bericht 110/16 (Kernforschungszentrum Karlsruhe GmBH, Karlsruhe, Germany, 1991).
  9. W. R. Muller, H. Burkhard, P. Grosse, “Comparison measurements of very similar spectra in Fourier–transform spectroscopy,” Infrared Phys. 16, 279–284 (1976).
    [CrossRef]

1991 (2)

1984 (1)

1976 (1)

W. R. Muller, H. Burkhard, P. Grosse, “Comparison measurements of very similar spectra in Fourier–transform spectroscopy,” Infrared Phys. 16, 279–284 (1976).
[CrossRef]

Bacher, W.

R. Ruprecht, W. Bacher, “Untersuchungen an mikrostructurierten Bandpassfiltern fur das Ferne Infrarot und ihre Herstellung durch Röntgentiefenlithographie und Mikrogalvanoformung,” Rep. IMT-Bericht 110/16 (Kernforschungszentrum Karlsruhe GmBH, Karlsruhe, Germany, 1991).

Bell, R. J.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972).

Burkhard, H.

W. R. Muller, H. Burkhard, P. Grosse, “Comparison measurements of very similar spectra in Fourier–transform spectroscopy,” Infrared Phys. 16, 279–284 (1976).
[CrossRef]

Carlson, D.

Colosi, J.

Grosse, P.

W. R. Muller, H. Burkhard, P. Grosse, “Comparison measurements of very similar spectra in Fourier–transform spectroscopy,” Infrared Phys. 16, 279–284 (1976).
[CrossRef]

Hirschmugl, C. J.

Linkemann, J.

J. Linkemann, F. Romero-Borja, H. O. Tittel, “FT spectrometer with fixed mirrors using Fizeau fringes,” in Eighth International Conference on Fourier Transform Spectroscopy, H. M. Heise, E. H. Korte, H. W. Seisler, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1575, pp. 184–187.

Moller, K. D.

K. D. Moller, “Wave-front-dividing interferometers,” Infrared Phys. 32, 321–331 (1991).
[CrossRef]

Möller, K. D.

Muller, W. R.

W. R. Muller, H. Burkhard, P. Grosse, “Comparison measurements of very similar spectra in Fourier–transform spectroscopy,” Infrared Phys. 16, 279–284 (1976).
[CrossRef]

Petrone, P.

Romero-Borja, F.

J. Linkemann, F. Romero-Borja, H. O. Tittel, “FT spectrometer with fixed mirrors using Fizeau fringes,” in Eighth International Conference on Fourier Transform Spectroscopy, H. M. Heise, E. H. Korte, H. W. Seisler, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1575, pp. 184–187.

Rothschild, W. G.

K. D. Möller, W. G. Rothschild, Far Infrared Spectroscopy (Wiley, New York, 1971).

Ruprecht, R.

R. Ruprecht, W. Bacher, “Untersuchungen an mikrostructurierten Bandpassfiltern fur das Ferne Infrarot und ihre Herstellung durch Röntgentiefenlithographie und Mikrogalvanoformung,” Rep. IMT-Bericht 110/16 (Kernforschungszentrum Karlsruhe GmBH, Karlsruhe, Germany, 1991).

Scardino, D.

Siddons, D. P.

Strong, J.

J. Strong, Concepts of Optics (Freeman, San Francisco, Calif., 1958).

Tittel, H. O.

J. Linkemann, F. Romero-Borja, H. O. Tittel, “FT spectrometer with fixed mirrors using Fizeau fringes,” in Eighth International Conference on Fourier Transform Spectroscopy, H. M. Heise, E. H. Korte, H. W. Seisler, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1575, pp. 184–187.

Tomaselli, V. P.

Williams, G. P.

Zoeller, R. G.

Appl. Opt. (2)

Infrared Phys. (2)

K. D. Moller, “Wave-front-dividing interferometers,” Infrared Phys. 32, 321–331 (1991).
[CrossRef]

W. R. Muller, H. Burkhard, P. Grosse, “Comparison measurements of very similar spectra in Fourier–transform spectroscopy,” Infrared Phys. 16, 279–284 (1976).
[CrossRef]

Other (5)

R. Ruprecht, W. Bacher, “Untersuchungen an mikrostructurierten Bandpassfiltern fur das Ferne Infrarot und ihre Herstellung durch Röntgentiefenlithographie und Mikrogalvanoformung,” Rep. IMT-Bericht 110/16 (Kernforschungszentrum Karlsruhe GmBH, Karlsruhe, Germany, 1991).

K. D. Möller, W. G. Rothschild, Far Infrared Spectroscopy (Wiley, New York, 1971).

J. Linkemann, F. Romero-Borja, H. O. Tittel, “FT spectrometer with fixed mirrors using Fizeau fringes,” in Eighth International Conference on Fourier Transform Spectroscopy, H. M. Heise, E. H. Korte, H. W. Seisler, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1575, pp. 184–187.

J. Strong, Concepts of Optics (Freeman, San Francisco, Calif., 1958).

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972).

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Figures (17)

Fig. 1
Fig. 1

Michelson interferometer for Fourier–transform spectroscopy.

Fig. 2
Fig. 2

Beam-recombination process: The superposition of the two amplitudes is spread over an interval in space, which also depends on the optical path difference between the rays in each beam. Point 1 is the center and points 1′ and 1″ have zero optical path difference. Points 2 and 3 have specific optical path differences with respect to the center that are equal but have opposite signs.

Fig. 3
Fig. 3

Mach–Zehnder interferometers without moving parts: (a) Mirrors M1 and M2 are divided horizontally into two sections, which are represented by the solid and dashed lines. The solid and dotted lines represent the optical paths that result from the separations in M1 and M2. (b) Mirrors M1 and M2 are divided vertically into two sections. Here, the solid and dotted lines represent the mirror sections, and the solid and dashed lines represent the optical paths. (c) If mirrors M1 and M2 in (b) were to replace M3 and M4 in the interferometer shown in (a), the light leaving the interferometer would be divided into four sections, shown as 1, 2, 3, and 4.

Fig. 4
Fig. 4

Schematic diagram of a Mach–Zehnder interferometer for a 16 point × 16 point interferogram (256-point). Mirrors M1 and M2 each have 16 steps equal to 2d and are vertically stepped; mirrors M3 and M4 each have 16 steps equal to d and are horizontally stepped. The positions of a baffle or an array of lenses, a detector array, and the beam splitters (B1 and B2) are indicated as well.

Fig. 5
Fig. 5

(a) Schematic diagram of a Michelson interferometer with a lens or baffle array and a detector array. Profiles of the vertical grooves of two Michelson mirrors with (b) a sequence of small steps and (c) a sequence of large steps.

Fig. 6
Fig. 6

Schematic diagram of a lamellar grating with four reflectors [two sets of two reflectors (1 and 2) each].

Fig. 7
Fig. 7

Fraunhofer interference–diffraction pattern depending on the displacement h and the diffraction angle θ for a minigrating with four reflectors: (a) schematic diagram of the grating showing incident and reflected light; (b) normalized intensity plotted versus the diffraction angle and showing constructive interference (solid curve) with a path difference of nλ and destructive interference (dotted curve) with a path difference of nλ/2; and (c) other path differences, λ/6, 2λ/6, 4λ/6, and 5λ/6 (curves not labeled).

Fig. 8
Fig. 8

Interference–diffraction patterns for point and extended light sources: Patterns for light of two wavelengths [(a) λ and (b) λ/2] from one point of a source, and patterns in the focal plane of the concentration optic for light of one wavelength (λ) from (c) one point and (d) two points of an extended source.

Fig. 9
Fig. 9

Mach–Zehnder interferometer with two beam splitters, each with two reflective and two transmissive areas. The broken lines delineate the openings of the beam splitters. The striped paths represent light guided by the reflective strips; the open paths represent light guided by the transmissive strips.

Fig. 10
Fig. 10

Beam splitter with a two-dimensional rectangular pattern (periodic structure).

Fig. 11
Fig. 11

Beam splitter with a random pattern (random structure).

Fig. 12
Fig. 12

A grating with open and reflecting strips of width d used as beam splitter. For destructive interference, the reflected and the transmitted beams have a phase difference of λ/2. If no light travels in the direction of the detector, the light is diffracted into an angle α, given by d sin α = λ/2, with respect to the zero order.

Fig. 13
Fig. 13

Lens and cone arrays with zero- and first-order light. The solid lines represent the zero-order light; the dashed lines represent the first-order light. Together, these lines represent the limits of the beam. (a) For the lens, the aperture prevents the first-order light from arriving at the detector. (b) For the cone, the aperture is less effective.

Fig. 14
Fig. 14

Incident light is diffracted by 2 n gratings (6 are shown). The profile of each successive grating has an increasing distance between the tops and bottoms of the grooves (shown for gratings 1 through 4).

Fig. 15
Fig. 15

Lenses (right-hand side) concentrate the light of each part of the array interferometer on the focal plane (not shown), and then apertures are used to prevent the first-order light from arriving at the detector. Cones or an array of lenses or baffles (left-hand side) may be used to direct light from an extended source.

Fig. 16
Fig. 16

Design of an array interferometer for the visible and the IR regions.

Fig. 17
Fig. 17

One interferometer is used to obtain interferograms for two different wavelength regions. Array 1 is sensitive to the wavelength produced by source 1, and likewise for source and array 2. M1–M4, mirrors; B1 and B2, beam splitters.

Equations (1)

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u 2 u 0 2 = [ sin ( π d λ sin θ ) π d λ sin θ ] 2 × [ cos 2 ( 2 π d λ sin θ ) cos 2 ( π d λ sin θ + φ 2 ) ] ,

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