Abstract

This study describes a technique and apparatus for converting the circular fringes of a Fabry-Perot interferometer into a linear pattern which can be detected with a conventional linear detector. The conversion from a circular ring pattern at the focus of the objective lens of the interferometer is accomplished using a segment of an internally reflecting cone to direct the light from a sector of the ring pattern onto the linear detector. Light is concentrated into a single sector by the use of a kaleidoscopic mirror system. The aberrations associated with the transformation are shown to be small for high resolution devices which have large F numbers. A laboratory demonstration of a linearly scanned Fabry-Perot interferometer with a 0.7 cm. spacing illustrates a spectrum taken over ten orders with very small aperture defects. These results imply that a high resolution interferometer using five orders and a CCD detector would have a sensitivity 87.5 × greater than is presently achieved with those used to observe the winds in the upper atmosphere.

© 1990 Optical Society of America

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References

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  1. C. Fabry, A. Perot, “Sur les Franges de Lames Minces Argentees et Leur Application a la Mesure de Petites Epasseurs d’Air,” Ann. Chim Phys. 12, 459–501 (1897).
  2. P. Jacquinot, C. Dufour, “Conditions Optiques d’Emploi des Cellules PhotoElectriques dans les Spectrographes et les Interferometres,” J. Res. CNRS. 6, 91–103 (1948).
  3. D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Minature Imaging Photon Detectors,” J. Phys. E. 13, 763–770 (1980).
    [CrossRef]
  4. C. Martin, P. Jeliniki, M. Lampton, R. F. Malina, H. O. Anger, “Wedge-and Strip Anodes for Centroid-Finding Position-Sensitive Photon and Particle Detectors,” Rev. Sci. Instrum. 52, 1067–1074 (1981).
    [CrossRef]
  5. G. G. Sivjee, T. J. Hallinan, G. R. Swenson, “Fabry-Perot Interferometer Imaging System for Thermospheric Temperature and Wind Measurements,” Appl. Opt. 19, 2206–2209 (1980).
    [CrossRef] [PubMed]
  6. P. B. Hays, T. L. Killeen, B. C. Kennedy, “The Fabry-Perot Interferometer on Dynamics Explorer,” Space Sci. Instrum. 5, 395–416 (1981).
  7. T. L. Killeen, B. C. Kennedy, P. B. Hays, D. A. Synamow, D. H. Ceckowski, “Image Plane Detector for the Dynamics Explorer Fabry-Perot Interferometer,” Appl. Opt. 22, 3503–3513 (1983).
    [CrossRef] [PubMed]
  8. G. Hernandez, “Fabry-Perot Interferometers,” Cambridge Studies in Modern Optics, Vol. 3 (Cambridge U.P., New York, 1987).
  9. E. Scott Barr, “Sir David Brewster (1781–1868),” Optics News 14(4), 8–12 (1988).
  10. J. W. Meriwether, C. A. Tepley, S. A. Price, P. B. Hays, L. L. Cogger, “Remote Ground-Based Observations of Terrestrial Airglow Emissions and Thermospheric Dynamics at Calgary, Alberta, Canada,” Opt. Eng. 22, 128–131 (1983).

1988

E. Scott Barr, “Sir David Brewster (1781–1868),” Optics News 14(4), 8–12 (1988).

1983

J. W. Meriwether, C. A. Tepley, S. A. Price, P. B. Hays, L. L. Cogger, “Remote Ground-Based Observations of Terrestrial Airglow Emissions and Thermospheric Dynamics at Calgary, Alberta, Canada,” Opt. Eng. 22, 128–131 (1983).

T. L. Killeen, B. C. Kennedy, P. B. Hays, D. A. Synamow, D. H. Ceckowski, “Image Plane Detector for the Dynamics Explorer Fabry-Perot Interferometer,” Appl. Opt. 22, 3503–3513 (1983).
[CrossRef] [PubMed]

1981

C. Martin, P. Jeliniki, M. Lampton, R. F. Malina, H. O. Anger, “Wedge-and Strip Anodes for Centroid-Finding Position-Sensitive Photon and Particle Detectors,” Rev. Sci. Instrum. 52, 1067–1074 (1981).
[CrossRef]

P. B. Hays, T. L. Killeen, B. C. Kennedy, “The Fabry-Perot Interferometer on Dynamics Explorer,” Space Sci. Instrum. 5, 395–416 (1981).

1980

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Minature Imaging Photon Detectors,” J. Phys. E. 13, 763–770 (1980).
[CrossRef]

G. G. Sivjee, T. J. Hallinan, G. R. Swenson, “Fabry-Perot Interferometer Imaging System for Thermospheric Temperature and Wind Measurements,” Appl. Opt. 19, 2206–2209 (1980).
[CrossRef] [PubMed]

1948

P. Jacquinot, C. Dufour, “Conditions Optiques d’Emploi des Cellules PhotoElectriques dans les Spectrographes et les Interferometres,” J. Res. CNRS. 6, 91–103 (1948).

1897

C. Fabry, A. Perot, “Sur les Franges de Lames Minces Argentees et Leur Application a la Mesure de Petites Epasseurs d’Air,” Ann. Chim Phys. 12, 459–501 (1897).

Anger, H. O.

C. Martin, P. Jeliniki, M. Lampton, R. F. Malina, H. O. Anger, “Wedge-and Strip Anodes for Centroid-Finding Position-Sensitive Photon and Particle Detectors,” Rev. Sci. Instrum. 52, 1067–1074 (1981).
[CrossRef]

Barlow, F. E.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Minature Imaging Photon Detectors,” J. Phys. E. 13, 763–770 (1980).
[CrossRef]

Ceckowski, D. H.

Cogger, L. L.

J. W. Meriwether, C. A. Tepley, S. A. Price, P. B. Hays, L. L. Cogger, “Remote Ground-Based Observations of Terrestrial Airglow Emissions and Thermospheric Dynamics at Calgary, Alberta, Canada,” Opt. Eng. 22, 128–131 (1983).

Dufour, C.

P. Jacquinot, C. Dufour, “Conditions Optiques d’Emploi des Cellules PhotoElectriques dans les Spectrographes et les Interferometres,” J. Res. CNRS. 6, 91–103 (1948).

Fabry, C.

C. Fabry, A. Perot, “Sur les Franges de Lames Minces Argentees et Leur Application a la Mesure de Petites Epasseurs d’Air,” Ann. Chim Phys. 12, 459–501 (1897).

Hallinan, T. J.

Hays, P. B.

J. W. Meriwether, C. A. Tepley, S. A. Price, P. B. Hays, L. L. Cogger, “Remote Ground-Based Observations of Terrestrial Airglow Emissions and Thermospheric Dynamics at Calgary, Alberta, Canada,” Opt. Eng. 22, 128–131 (1983).

T. L. Killeen, B. C. Kennedy, P. B. Hays, D. A. Synamow, D. H. Ceckowski, “Image Plane Detector for the Dynamics Explorer Fabry-Perot Interferometer,” Appl. Opt. 22, 3503–3513 (1983).
[CrossRef] [PubMed]

P. B. Hays, T. L. Killeen, B. C. Kennedy, “The Fabry-Perot Interferometer on Dynamics Explorer,” Space Sci. Instrum. 5, 395–416 (1981).

Hernandez, G.

G. Hernandez, “Fabry-Perot Interferometers,” Cambridge Studies in Modern Optics, Vol. 3 (Cambridge U.P., New York, 1987).

Jacquinot, P.

P. Jacquinot, C. Dufour, “Conditions Optiques d’Emploi des Cellules PhotoElectriques dans les Spectrographes et les Interferometres,” J. Res. CNRS. 6, 91–103 (1948).

Jeliniki, P.

C. Martin, P. Jeliniki, M. Lampton, R. F. Malina, H. O. Anger, “Wedge-and Strip Anodes for Centroid-Finding Position-Sensitive Photon and Particle Detectors,” Rev. Sci. Instrum. 52, 1067–1074 (1981).
[CrossRef]

Kellock, S. J.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Minature Imaging Photon Detectors,” J. Phys. E. 13, 763–770 (1980).
[CrossRef]

Kennedy, B. C.

T. L. Killeen, B. C. Kennedy, P. B. Hays, D. A. Synamow, D. H. Ceckowski, “Image Plane Detector for the Dynamics Explorer Fabry-Perot Interferometer,” Appl. Opt. 22, 3503–3513 (1983).
[CrossRef] [PubMed]

P. B. Hays, T. L. Killeen, B. C. Kennedy, “The Fabry-Perot Interferometer on Dynamics Explorer,” Space Sci. Instrum. 5, 395–416 (1981).

Killeen, T. L.

T. L. Killeen, B. C. Kennedy, P. B. Hays, D. A. Synamow, D. H. Ceckowski, “Image Plane Detector for the Dynamics Explorer Fabry-Perot Interferometer,” Appl. Opt. 22, 3503–3513 (1983).
[CrossRef] [PubMed]

P. B. Hays, T. L. Killeen, B. C. Kennedy, “The Fabry-Perot Interferometer on Dynamics Explorer,” Space Sci. Instrum. 5, 395–416 (1981).

Lampton, M.

C. Martin, P. Jeliniki, M. Lampton, R. F. Malina, H. O. Anger, “Wedge-and Strip Anodes for Centroid-Finding Position-Sensitive Photon and Particle Detectors,” Rev. Sci. Instrum. 52, 1067–1074 (1981).
[CrossRef]

Malina, R. F.

C. Martin, P. Jeliniki, M. Lampton, R. F. Malina, H. O. Anger, “Wedge-and Strip Anodes for Centroid-Finding Position-Sensitive Photon and Particle Detectors,” Rev. Sci. Instrum. 52, 1067–1074 (1981).
[CrossRef]

Martin, C.

C. Martin, P. Jeliniki, M. Lampton, R. F. Malina, H. O. Anger, “Wedge-and Strip Anodes for Centroid-Finding Position-Sensitive Photon and Particle Detectors,” Rev. Sci. Instrum. 52, 1067–1074 (1981).
[CrossRef]

McWhirter, I.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Minature Imaging Photon Detectors,” J. Phys. E. 13, 763–770 (1980).
[CrossRef]

Meriwether, J. W.

J. W. Meriwether, C. A. Tepley, S. A. Price, P. B. Hays, L. L. Cogger, “Remote Ground-Based Observations of Terrestrial Airglow Emissions and Thermospheric Dynamics at Calgary, Alberta, Canada,” Opt. Eng. 22, 128–131 (1983).

Perot, A.

C. Fabry, A. Perot, “Sur les Franges de Lames Minces Argentees et Leur Application a la Mesure de Petites Epasseurs d’Air,” Ann. Chim Phys. 12, 459–501 (1897).

Price, S. A.

J. W. Meriwether, C. A. Tepley, S. A. Price, P. B. Hays, L. L. Cogger, “Remote Ground-Based Observations of Terrestrial Airglow Emissions and Thermospheric Dynamics at Calgary, Alberta, Canada,” Opt. Eng. 22, 128–131 (1983).

Rees, D.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Minature Imaging Photon Detectors,” J. Phys. E. 13, 763–770 (1980).
[CrossRef]

Rounce, P. A.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Minature Imaging Photon Detectors,” J. Phys. E. 13, 763–770 (1980).
[CrossRef]

Scott Barr, E.

E. Scott Barr, “Sir David Brewster (1781–1868),” Optics News 14(4), 8–12 (1988).

Sivjee, G. G.

Swenson, G. R.

Synamow, D. A.

Tepley, C. A.

J. W. Meriwether, C. A. Tepley, S. A. Price, P. B. Hays, L. L. Cogger, “Remote Ground-Based Observations of Terrestrial Airglow Emissions and Thermospheric Dynamics at Calgary, Alberta, Canada,” Opt. Eng. 22, 128–131 (1983).

Ann. Chim Phys.

C. Fabry, A. Perot, “Sur les Franges de Lames Minces Argentees et Leur Application a la Mesure de Petites Epasseurs d’Air,” Ann. Chim Phys. 12, 459–501 (1897).

Appl. Opt.

J. Phys. E.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Minature Imaging Photon Detectors,” J. Phys. E. 13, 763–770 (1980).
[CrossRef]

J. Res. CNRS.

P. Jacquinot, C. Dufour, “Conditions Optiques d’Emploi des Cellules PhotoElectriques dans les Spectrographes et les Interferometres,” J. Res. CNRS. 6, 91–103 (1948).

Opt. Eng.

J. W. Meriwether, C. A. Tepley, S. A. Price, P. B. Hays, L. L. Cogger, “Remote Ground-Based Observations of Terrestrial Airglow Emissions and Thermospheric Dynamics at Calgary, Alberta, Canada,” Opt. Eng. 22, 128–131 (1983).

Optics News

E. Scott Barr, “Sir David Brewster (1781–1868),” Optics News 14(4), 8–12 (1988).

Rev. Sci. Instrum.

C. Martin, P. Jeliniki, M. Lampton, R. F. Malina, H. O. Anger, “Wedge-and Strip Anodes for Centroid-Finding Position-Sensitive Photon and Particle Detectors,” Rev. Sci. Instrum. 52, 1067–1074 (1981).
[CrossRef]

Space Sci. Instrum.

P. B. Hays, T. L. Killeen, B. C. Kennedy, “The Fabry-Perot Interferometer on Dynamics Explorer,” Space Sci. Instrum. 5, 395–416 (1981).

Other

G. Hernandez, “Fabry-Perot Interferometers,” Cambridge Studies in Modern Optics, Vol. 3 (Cambridge U.P., New York, 1987).

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Figures (8)

Fig. 1
Fig. 1

Conceptual diagram of the optical principle used to convert the circular Fabry-Perot fringe pattern into a linear spectrum along the axis of the transforming 45° cone.

Fig. 2
Fig. 2

Geometry used in the raytrace algorithm developed to determine the distribution of fringe light in the detector plane.

Fig. 3
Fig. 3

Spot diagrams for rings in the fringe plane as transformed into the detector plane by a 45° cone, for several ray bundle divergence angles. Ray bundle half angle cone are: a) 1.5°, b) 3.5°, c) 5.5°, and d) 7.5°. Here the cone segment has an azimuthal extent of 90°.

Fig. 4
Fig. 4

Distribution function of rays as transformed into the detector plane by a 45° cone, for several ray bundle divergence angles. Ray bundle half angle cone are: a) 1.5°, b) 3.5°, c) 5.5°, and d) 7.5°. Here the cone segment has an azimuthal extent of 90°.

Fig. 5
Fig. 5

Kaleidoscopic Fabry-Perot optics with conical circle to line interferometric optics (CLIO) system. a) Basic optical layout showing objective, kaleidoscope, telecentric lens, transforming cone, and detector. b) Perspective illustration of a complete interferometer utilizing the CLIO system.

Fig. 6
Fig. 6

Signal from several Fabry-Perot interferometers using the CLIO system and incorporating a 500-element CCD detector. Here the interferometer has a gap of 1.0 cm and plate area of 78.5 cm2. Focal length of the main objective varied to image a) one order, b) five orders, and c) ten orders on the detector.

Fig. 7
Fig. 7

Perspective illustration of the laboratory test model of the CLIO system.

Fig. 8
Fig. 8

Comparison of observations of ten orders of an interferogram generated by the laboratory test model of the CLIO system with the theoretical model for the same instrument parameters.

Tables (1)

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Table I Comparison of Michigan Airglow Observatory Interferometer with the new Circle to Line Optical Design

Equations (14)

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f / # = ( 2 tan Δ ϕ ) - 1 .
I ( r , λ ) = I 0 ( λ ) ( 1 - R ) 2 1 - 2 R cos ( Φ ) + R 2
Φ = 4 π μ t λ cos ( θ ) , where θ = tan - 1 ( r f 0 ) .
r m 2 = f 0 2 λ m μ t ,
f 0 = μ t λ L d ( 1 + N - 1 )
X = ( X 0 + Z tan Φ cos θ ) , Y = ( Y 0 + Z tan Φ sin θ )
X 0 = r 0 cos θ 0 and Y 0 = r 0 sin θ 0
ρ c 2 = Z 2 tan 2 Ψ c = X 2 + Y 2 = ( r 0 cos θ 0 + Z tan Φ cos θ ) 2 + ( r 0 sin θ 0 + Z tan Φ sin θ ) 2 .
Z c = r 0 tan Φ cos ( θ - θ 0 ) + r 0 2 tan 2 Φ cos 2 ( θ - θ 0 ) - r 0 2 ( tan 2 Φ - tan 2 Ψ c ) ( tan 2 Ψ c - tan 2 Φ )
X c = ( r 0 cos θ 0 + Z c tan Φ cos θ ) and Y c = ( r 0 sin θ 0 + Z c tan Φ sin θ ) ,
I = I - 2 ( n · I ) n ,
I x = - sin Φ cos θ I y = - sin Φ sin θ I z = - cos Φ
n x = cos Ψ c X c X c 2 + Y c 2 n y = cos Ψ c Y c X c 2 + Y c 2 n z = - sin Ψ c .
Y p = Δ = Y c + I y S S = - ( Y c - Δ ) I y such that X p = X c + I x S = X c - I x ( Y c - Δ ) I y Z p = Z c + I Z S = Z c - I Z ( Y c - Δ ) I y .

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