Abstract

We present the problem of generating a computer simulation for optical interferometers. Of the several methods in use to simulate optical systems, none seems adequate to describe the image formed by interference between beams encountering a real system of lenses, mirrors, and gratings. We have developed a ray-tracing software package that can be applied to complex systems and used to generate realistic interference patterns, even from extended sources, without simplifying assumptions. We present results of a simulated nonscanning interferometer with coherent summation at a discrete-element detector. No coherence theory is added a priori; instead, the major results are shown to be verified numerically.

© 1995 Optical Society of America

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References

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  1. K. Taylor, P. D. Atherton, “Seeing-limited radial velocity field mapping of extended emission line sources using a new imaging Fabry–Perot system,” Mon. Not. R. Astron. Soc. 191, 675–684 (1980).
  2. T. H. Barnes, “Photodiode array Fourier transform spectrometer with improved dynamic range,” Appl. Opt. 24, 3702–3706 (1985).
    [Crossref] [PubMed]
  3. N. G. Douglas, H. R. Butcher, W. A. Melis, “Heterodyned, holographic spectroscopy—first results with the FRINGHE spectrometer,” Astrophys. Space Sci. 171, 307–318 (1990).
    [Crossref]
  4. W. H. Smith, N. V. Schempp, “Digital array scanned interferometers for astronomy,” Exp. Astron. 1, 389–405 (1991).
    [Crossref]
  5. J. Harlander, R. J. Reynolds, F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
    [Crossref]
  6. S. Frandsen, N. G. Douglas, H. R. Butcher, “An astronomical spectrometer,” Astron. Astrophys. 279, 310–321 (1993).
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975), pp. 508ff.
  8. N. G. Douglas, F. J. van Hoesel, “A non-scanning interferometer with postdisperser,” in Proceedings of the ESO Workshop on High Resolution Spectroscopy with the VLT (European Southern Observatory, Munich, 1992), pp. 289–292.
  9. G. W. Stroke, “Diffraction gratings,” in Encyclopedia of Physics, S. Flügge, ed. (Springer-Verlag, Berlin, 1967), Vol. XXXIX, Chap. 14.
  10. J. M. Vaughan, The Fabry–Perot Interferometer (Adam Hilger, Bristol, UK, 1989), Appendix 8.

1993 (1)

S. Frandsen, N. G. Douglas, H. R. Butcher, “An astronomical spectrometer,” Astron. Astrophys. 279, 310–321 (1993).

1992 (1)

J. Harlander, R. J. Reynolds, F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[Crossref]

1991 (1)

W. H. Smith, N. V. Schempp, “Digital array scanned interferometers for astronomy,” Exp. Astron. 1, 389–405 (1991).
[Crossref]

1990 (1)

N. G. Douglas, H. R. Butcher, W. A. Melis, “Heterodyned, holographic spectroscopy—first results with the FRINGHE spectrometer,” Astrophys. Space Sci. 171, 307–318 (1990).
[Crossref]

1985 (1)

1980 (1)

K. Taylor, P. D. Atherton, “Seeing-limited radial velocity field mapping of extended emission line sources using a new imaging Fabry–Perot system,” Mon. Not. R. Astron. Soc. 191, 675–684 (1980).

Atherton, P. D.

K. Taylor, P. D. Atherton, “Seeing-limited radial velocity field mapping of extended emission line sources using a new imaging Fabry–Perot system,” Mon. Not. R. Astron. Soc. 191, 675–684 (1980).

Barnes, T. H.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975), pp. 508ff.

Butcher, H. R.

S. Frandsen, N. G. Douglas, H. R. Butcher, “An astronomical spectrometer,” Astron. Astrophys. 279, 310–321 (1993).

N. G. Douglas, H. R. Butcher, W. A. Melis, “Heterodyned, holographic spectroscopy—first results with the FRINGHE spectrometer,” Astrophys. Space Sci. 171, 307–318 (1990).
[Crossref]

Douglas, N. G.

S. Frandsen, N. G. Douglas, H. R. Butcher, “An astronomical spectrometer,” Astron. Astrophys. 279, 310–321 (1993).

N. G. Douglas, H. R. Butcher, W. A. Melis, “Heterodyned, holographic spectroscopy—first results with the FRINGHE spectrometer,” Astrophys. Space Sci. 171, 307–318 (1990).
[Crossref]

N. G. Douglas, F. J. van Hoesel, “A non-scanning interferometer with postdisperser,” in Proceedings of the ESO Workshop on High Resolution Spectroscopy with the VLT (European Southern Observatory, Munich, 1992), pp. 289–292.

Frandsen, S.

S. Frandsen, N. G. Douglas, H. R. Butcher, “An astronomical spectrometer,” Astron. Astrophys. 279, 310–321 (1993).

Harlander, J.

J. Harlander, R. J. Reynolds, F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[Crossref]

Melis, W. A.

N. G. Douglas, H. R. Butcher, W. A. Melis, “Heterodyned, holographic spectroscopy—first results with the FRINGHE spectrometer,” Astrophys. Space Sci. 171, 307–318 (1990).
[Crossref]

Reynolds, R. J.

J. Harlander, R. J. Reynolds, F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[Crossref]

Roesler, F. L.

J. Harlander, R. J. Reynolds, F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[Crossref]

Schempp, N. V.

W. H. Smith, N. V. Schempp, “Digital array scanned interferometers for astronomy,” Exp. Astron. 1, 389–405 (1991).
[Crossref]

Smith, W. H.

W. H. Smith, N. V. Schempp, “Digital array scanned interferometers for astronomy,” Exp. Astron. 1, 389–405 (1991).
[Crossref]

Stroke, G. W.

G. W. Stroke, “Diffraction gratings,” in Encyclopedia of Physics, S. Flügge, ed. (Springer-Verlag, Berlin, 1967), Vol. XXXIX, Chap. 14.

Taylor, K.

K. Taylor, P. D. Atherton, “Seeing-limited radial velocity field mapping of extended emission line sources using a new imaging Fabry–Perot system,” Mon. Not. R. Astron. Soc. 191, 675–684 (1980).

van Hoesel, F. J.

N. G. Douglas, F. J. van Hoesel, “A non-scanning interferometer with postdisperser,” in Proceedings of the ESO Workshop on High Resolution Spectroscopy with the VLT (European Southern Observatory, Munich, 1992), pp. 289–292.

Vaughan, J. M.

J. M. Vaughan, The Fabry–Perot Interferometer (Adam Hilger, Bristol, UK, 1989), Appendix 8.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975), pp. 508ff.

Appl. Opt. (1)

Astron. Astrophys. (1)

S. Frandsen, N. G. Douglas, H. R. Butcher, “An astronomical spectrometer,” Astron. Astrophys. 279, 310–321 (1993).

Astrophys. J. (1)

J. Harlander, R. J. Reynolds, F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[Crossref]

Astrophys. Space Sci. (1)

N. G. Douglas, H. R. Butcher, W. A. Melis, “Heterodyned, holographic spectroscopy—first results with the FRINGHE spectrometer,” Astrophys. Space Sci. 171, 307–318 (1990).
[Crossref]

Exp. Astron. (1)

W. H. Smith, N. V. Schempp, “Digital array scanned interferometers for astronomy,” Exp. Astron. 1, 389–405 (1991).
[Crossref]

Mon. Not. R. Astron. Soc. (1)

K. Taylor, P. D. Atherton, “Seeing-limited radial velocity field mapping of extended emission line sources using a new imaging Fabry–Perot system,” Mon. Not. R. Astron. Soc. 191, 675–684 (1980).

Other (4)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975), pp. 508ff.

N. G. Douglas, F. J. van Hoesel, “A non-scanning interferometer with postdisperser,” in Proceedings of the ESO Workshop on High Resolution Spectroscopy with the VLT (European Southern Observatory, Munich, 1992), pp. 289–292.

G. W. Stroke, “Diffraction gratings,” in Encyclopedia of Physics, S. Flügge, ed. (Springer-Verlag, Berlin, 1967), Vol. XXXIX, Chap. 14.

J. M. Vaughan, The Fabry–Perot Interferometer (Adam Hilger, Bristol, UK, 1989), Appendix 8.

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Figures (13)

Fig. 1
Fig. 1

Schematic of a nonscanning interferometer.

Fig. 2
Fig. 2

Equivalent layout of the grating arm (upper) and the mirror arm (lower) of the interferometer shown in Fig. 1.

Fig. 3
Fig. 3

Wave-front summing for linear wavefronts.

Fig. 4
Fig. 4

Part of a discrete detector such as a CCD, showing various incident rays.

Fig. 5
Fig. 5

Ray tracing at a grating. Two rays with equal path lengths are shown. Although they are initially in phase, a correction must be applied to keep them in phase after they intersect the grating.

Fig. 6
Fig. 6

Grating geometry, in which Y is the grating normal and Z is the axis parallel to the grooves. The figure is incorrect in the reference.

Fig. 7
Fig. 7

Simulation of two-beam interferometer output with the following parameters: wavelength, 589.5 nm; Littrow wavelength, 589 nm; m = 5 grating (θ = 68.5°); fiber diameter 750 μm; and 25.9-mm-diameter beam imaged with magnification 0.5 onto 22-μm pixels. (a) Mirror/grating configuration, (b) two-grating configuration. Superimposed are fits (see the text).

Fig. 8
Fig. 8

Real interferogram with the use of a postdispersed non-scanning interferometer. The dispersion axis is from left to right, and the source used was a Th–Ar emission lamp.

Fig. 9
Fig. 9

Simulated interferogram with four input wavelengths (delta functions) at 588.263, 588.570, 588.859, and 588.145 nm and relative strengths of 7, 14, 13, and 8, respectively.

Fig. 10
Fig. 10

Real interferogram; continuous spectrum with absorption lines.

Fig. 11
Fig. 11

Simulated interferograms. For these simulations the input spectrum was generated over 0.005-nm steps. (a) Point source, (b) 100-μm-diameter fiber, (c) 200-μm-diameter fiber.

Fig. 12
Fig. 12

Overview of the ray-tracing software.

Fig. 13
Fig. 13

Overview of rt.c.

Equations (13)

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μ 12 = 2 J 1 ( v ) v ,
v = 2 π ρ ξ f λ .
I ( y , z ) = - I ( σ ) ( 1 + μ cos α ) d σ ,
α ( r ) = ( k 1 - k 2 ) · ( r - r 0 ) + k 1 · ( r 0 - r 1 ) - k 2 · ( r 0 - r 2 ) + ϕ 1 - ϕ 2 ,
a j = n j ( sin ϕ j + i cos ϕ j ) ,
I ( x p , y p ) = ( j = 1 , 2 n j sin ϕ j ) 2 + ( j = 1 , 2 n j cos ϕ j ) 2 ,
γ = - γ ,
α = m λ n d - α ,
β = + ( 1 - α 2 - γ 2 ) 1 / 2 ,
α = cos θ cos ϕ ,
β = sin θ ,
γ = cos θ sin ϕ
Δ ϕ = 2 π x ( α - α ) n λ ,

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