Abstract

Atmospheric lidar is difficult in daylight because of sunlight scattered into the receiver field of view. In this research methods for the design and performance analysis of Fabry–Perot etalons as solar background filters are presented. The factor by which the signal to background ratio is enhanced is defined as a measure of the performance of the etalon as a filter. Equations for evaluating this parameter are presented for single-, double-, and triple-etalon filter systems. The role of reflective coupling between etalons is examined and shown to substantially reduce the contributions of the second and third etalons to the filter performance. Attenuators placed between the etalons can improve the filter performance, at modest cost to the signal transmittance. The principal parameter governing the performance of the etalon filters is the etalon defect finesse. Practical limitations on etalon plate smoothness and parallelism cause the defect finesse to be relatively low, especially in the ultraviolet, and this sets upper limits to the capability of tandem etalon filters to suppress the solar background at tolerable cost to the signal.

© 1999 Optical Society of America

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References

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  1. D. M. Rust, “Etalon filters,” Opt. Eng. 33, 3342–3348 (1994).
    [CrossRef]
  2. K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
    [CrossRef]
  3. W. R. Skinner, P. B. Hays, “Incoherent Doppler lidar for measurement of atmospheric winds,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, 383–394 (1994).
    [CrossRef]
  4. M. J. McGill, W. R. Skinner, “Multiple Fabry-Perot interferometers in an incoherent Doppler lidar,” Opt. Eng. 36, 139–145 (1997).
    [CrossRef]
  5. D. Rees, I. McWhirter, P. B. Hays, T. Dines, “A stable, rugged, capacitance-stabilised piezoelectric scanned Fabry–Perot etalon,” J. Phys. E 14, 1320–1325 (1981).
    [CrossRef]
  6. P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
    [CrossRef]
  7. J. E. Mack, D. P. McNutt, F. L. Roesler, R. Chabbal, “The PEPSIOS purely interferometric high resolution scanning spectrometer,” Appl. Opt. 2, 873–885 (1963).
  8. D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of atmospheric absorption lines from a stabilised balloon platform and measurements of stratospheric winds,” J. Phys. E 15, 191–206 (1982).
    [CrossRef]
  9. W. R. Skinner, P. B. Hays, V. J. Abreu, “Optimization of a triple etalon interferometer,” Appl. Opt. 26, 2817–2827 (1987).
    [CrossRef] [PubMed]
  10. W. R. Skinner, P. B. Hays, H. J. Grassl, D. A. Gell, M. D. Burrage, A. R. Marshall, J. Kafkalidis, “The High Resolution Doppler Imager: instrument performance in orbit since late 1991,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, P. B. Hays, J. Wang, eds., Proc. SPIE2830, 202–214 (1996).
    [CrossRef]
  11. G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, UK, 1988), Sect. 2.3.
  12. F. L. Roesler, “Effects of plate defects in a polyetalon Fabry-Perot spectrometer,” Appl. Opt. 8, 829–831 (1969).
    [CrossRef] [PubMed]
  13. P. A. Greet, “Coating stress in Fabry–Perot etalons,” Appl. Opt. 25, 3328–3330 (1986).
    [CrossRef] [PubMed]
  14. C. Korendyke, D. G. Socker, “Measured optical performance of three Fabry–Perot interferometers for use in a tunable ultraviolet filter,” Opt. Eng. 32, 2281–2285 (1993).
    [CrossRef]
  15. R. Chabbal, “Recherches expérimentales et théoriques sur la généralisation de l’emploi du spectromètre Fabry–Perot aux divers domaines de la spectroscopie,” Rev. Opt. 37, 49–104 (1958).
  16. P. B. Hays, V. J. Abreu, M. E. Dobbs, D. A. Gell, H. J. Grassl, W. R. Skinner, “The High-Resolution Doppler Imager on the Upper Atmosphere Research Satellite,” J. Geophys. Res. 98, 10,713–10,723 (1993).
    [CrossRef]
  17. W. Skinner, University of Michigan, Ann Arbor, Mich. 48109-2143 (e-mail communication, 7December1998).

1997 (1)

M. J. McGill, W. R. Skinner, “Multiple Fabry-Perot interferometers in an incoherent Doppler lidar,” Opt. Eng. 36, 139–145 (1997).
[CrossRef]

1995 (1)

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[CrossRef]

1994 (1)

D. M. Rust, “Etalon filters,” Opt. Eng. 33, 3342–3348 (1994).
[CrossRef]

1993 (2)

C. Korendyke, D. G. Socker, “Measured optical performance of three Fabry–Perot interferometers for use in a tunable ultraviolet filter,” Opt. Eng. 32, 2281–2285 (1993).
[CrossRef]

P. B. Hays, V. J. Abreu, M. E. Dobbs, D. A. Gell, H. J. Grassl, W. R. Skinner, “The High-Resolution Doppler Imager on the Upper Atmosphere Research Satellite,” J. Geophys. Res. 98, 10,713–10,723 (1993).
[CrossRef]

1987 (1)

1986 (1)

1982 (1)

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of atmospheric absorption lines from a stabilised balloon platform and measurements of stratospheric winds,” J. Phys. E 15, 191–206 (1982).
[CrossRef]

1981 (2)

D. Rees, I. McWhirter, P. B. Hays, T. Dines, “A stable, rugged, capacitance-stabilised piezoelectric scanned Fabry–Perot etalon,” J. Phys. E 14, 1320–1325 (1981).
[CrossRef]

P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
[CrossRef]

1969 (1)

1963 (1)

1958 (1)

R. Chabbal, “Recherches expérimentales et théoriques sur la généralisation de l’emploi du spectromètre Fabry–Perot aux divers domaines de la spectroscopie,” Rev. Opt. 37, 49–104 (1958).

Abreu, V. J.

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[CrossRef]

P. B. Hays, V. J. Abreu, M. E. Dobbs, D. A. Gell, H. J. Grassl, W. R. Skinner, “The High-Resolution Doppler Imager on the Upper Atmosphere Research Satellite,” J. Geophys. Res. 98, 10,713–10,723 (1993).
[CrossRef]

W. R. Skinner, P. B. Hays, V. J. Abreu, “Optimization of a triple etalon interferometer,” Appl. Opt. 26, 2817–2827 (1987).
[CrossRef] [PubMed]

Atherton, P. D.

P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
[CrossRef]

Barnes, J. E.

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[CrossRef]

Burrage, M. D.

W. R. Skinner, P. B. Hays, H. J. Grassl, D. A. Gell, M. D. Burrage, A. R. Marshall, J. Kafkalidis, “The High Resolution Doppler Imager: instrument performance in orbit since late 1991,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, P. B. Hays, J. Wang, eds., Proc. SPIE2830, 202–214 (1996).
[CrossRef]

Chabbal, R.

J. E. Mack, D. P. McNutt, F. L. Roesler, R. Chabbal, “The PEPSIOS purely interferometric high resolution scanning spectrometer,” Appl. Opt. 2, 873–885 (1963).

R. Chabbal, “Recherches expérimentales et théoriques sur la généralisation de l’emploi du spectromètre Fabry–Perot aux divers domaines de la spectroscopie,” Rev. Opt. 37, 49–104 (1958).

Dines, T.

D. Rees, I. McWhirter, P. B. Hays, T. Dines, “A stable, rugged, capacitance-stabilised piezoelectric scanned Fabry–Perot etalon,” J. Phys. E 14, 1320–1325 (1981).
[CrossRef]

Dobbs, M. E.

P. B. Hays, V. J. Abreu, M. E. Dobbs, D. A. Gell, H. J. Grassl, W. R. Skinner, “The High-Resolution Doppler Imager on the Upper Atmosphere Research Satellite,” J. Geophys. Res. 98, 10,713–10,723 (1993).
[CrossRef]

Fischer, K. F.

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[CrossRef]

Gell, D. A.

P. B. Hays, V. J. Abreu, M. E. Dobbs, D. A. Gell, H. J. Grassl, W. R. Skinner, “The High-Resolution Doppler Imager on the Upper Atmosphere Research Satellite,” J. Geophys. Res. 98, 10,713–10,723 (1993).
[CrossRef]

W. R. Skinner, P. B. Hays, H. J. Grassl, D. A. Gell, M. D. Burrage, A. R. Marshall, J. Kafkalidis, “The High Resolution Doppler Imager: instrument performance in orbit since late 1991,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, P. B. Hays, J. Wang, eds., Proc. SPIE2830, 202–214 (1996).
[CrossRef]

Grassl, H. J.

P. B. Hays, V. J. Abreu, M. E. Dobbs, D. A. Gell, H. J. Grassl, W. R. Skinner, “The High-Resolution Doppler Imager on the Upper Atmosphere Research Satellite,” J. Geophys. Res. 98, 10,713–10,723 (1993).
[CrossRef]

W. R. Skinner, P. B. Hays, H. J. Grassl, D. A. Gell, M. D. Burrage, A. R. Marshall, J. Kafkalidis, “The High Resolution Doppler Imager: instrument performance in orbit since late 1991,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, P. B. Hays, J. Wang, eds., Proc. SPIE2830, 202–214 (1996).
[CrossRef]

Greenaway, A. H.

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of atmospheric absorption lines from a stabilised balloon platform and measurements of stratospheric winds,” J. Phys. E 15, 191–206 (1982).
[CrossRef]

Greet, P. A.

Hays, P. B.

P. B. Hays, V. J. Abreu, M. E. Dobbs, D. A. Gell, H. J. Grassl, W. R. Skinner, “The High-Resolution Doppler Imager on the Upper Atmosphere Research Satellite,” J. Geophys. Res. 98, 10,713–10,723 (1993).
[CrossRef]

W. R. Skinner, P. B. Hays, V. J. Abreu, “Optimization of a triple etalon interferometer,” Appl. Opt. 26, 2817–2827 (1987).
[CrossRef] [PubMed]

D. Rees, I. McWhirter, P. B. Hays, T. Dines, “A stable, rugged, capacitance-stabilised piezoelectric scanned Fabry–Perot etalon,” J. Phys. E 14, 1320–1325 (1981).
[CrossRef]

W. R. Skinner, P. B. Hays, “Incoherent Doppler lidar for measurement of atmospheric winds,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, 383–394 (1994).
[CrossRef]

W. R. Skinner, P. B. Hays, H. J. Grassl, D. A. Gell, M. D. Burrage, A. R. Marshall, J. Kafkalidis, “The High Resolution Doppler Imager: instrument performance in orbit since late 1991,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, P. B. Hays, J. Wang, eds., Proc. SPIE2830, 202–214 (1996).
[CrossRef]

Hernandez, G.

G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, UK, 1988), Sect. 2.3.

Hicks, T. R.

P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
[CrossRef]

Irgang, T. D.

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[CrossRef]

Kafkalidis, J.

W. R. Skinner, P. B. Hays, H. J. Grassl, D. A. Gell, M. D. Burrage, A. R. Marshall, J. Kafkalidis, “The High Resolution Doppler Imager: instrument performance in orbit since late 1991,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, P. B. Hays, J. Wang, eds., Proc. SPIE2830, 202–214 (1996).
[CrossRef]

Korendyke, C.

C. Korendyke, D. G. Socker, “Measured optical performance of three Fabry–Perot interferometers for use in a tunable ultraviolet filter,” Opt. Eng. 32, 2281–2285 (1993).
[CrossRef]

Mack, J. E.

Marshall, A. R.

W. R. Skinner, P. B. Hays, H. J. Grassl, D. A. Gell, M. D. Burrage, A. R. Marshall, J. Kafkalidis, “The High Resolution Doppler Imager: instrument performance in orbit since late 1991,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, P. B. Hays, J. Wang, eds., Proc. SPIE2830, 202–214 (1996).
[CrossRef]

McGill, M. J.

M. J. McGill, W. R. Skinner, “Multiple Fabry-Perot interferometers in an incoherent Doppler lidar,” Opt. Eng. 36, 139–145 (1997).
[CrossRef]

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[CrossRef]

McNutt, D. P.

McWhirter, I.

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of atmospheric absorption lines from a stabilised balloon platform and measurements of stratospheric winds,” J. Phys. E 15, 191–206 (1982).
[CrossRef]

D. Rees, I. McWhirter, P. B. Hays, T. Dines, “A stable, rugged, capacitance-stabilised piezoelectric scanned Fabry–Perot etalon,” J. Phys. E 14, 1320–1325 (1981).
[CrossRef]

Reay, N. K.

P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
[CrossRef]

Rees, D.

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of atmospheric absorption lines from a stabilised balloon platform and measurements of stratospheric winds,” J. Phys. E 15, 191–206 (1982).
[CrossRef]

D. Rees, I. McWhirter, P. B. Hays, T. Dines, “A stable, rugged, capacitance-stabilised piezoelectric scanned Fabry–Perot etalon,” J. Phys. E 14, 1320–1325 (1981).
[CrossRef]

Ring, J.

P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
[CrossRef]

Roesler, F. L.

Rounce, P. A.

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of atmospheric absorption lines from a stabilised balloon platform and measurements of stratospheric winds,” J. Phys. E 15, 191–206 (1982).
[CrossRef]

Rust, D. M.

D. M. Rust, “Etalon filters,” Opt. Eng. 33, 3342–3348 (1994).
[CrossRef]

Scott, A. F. D.

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of atmospheric absorption lines from a stabilised balloon platform and measurements of stratospheric winds,” J. Phys. E 15, 191–206 (1982).
[CrossRef]

Skinner, W.

W. Skinner, University of Michigan, Ann Arbor, Mich. 48109-2143 (e-mail communication, 7December1998).

Skinner, W. R.

M. J. McGill, W. R. Skinner, “Multiple Fabry-Perot interferometers in an incoherent Doppler lidar,” Opt. Eng. 36, 139–145 (1997).
[CrossRef]

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[CrossRef]

P. B. Hays, V. J. Abreu, M. E. Dobbs, D. A. Gell, H. J. Grassl, W. R. Skinner, “The High-Resolution Doppler Imager on the Upper Atmosphere Research Satellite,” J. Geophys. Res. 98, 10,713–10,723 (1993).
[CrossRef]

W. R. Skinner, P. B. Hays, V. J. Abreu, “Optimization of a triple etalon interferometer,” Appl. Opt. 26, 2817–2827 (1987).
[CrossRef] [PubMed]

W. R. Skinner, P. B. Hays, H. J. Grassl, D. A. Gell, M. D. Burrage, A. R. Marshall, J. Kafkalidis, “The High Resolution Doppler Imager: instrument performance in orbit since late 1991,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, P. B. Hays, J. Wang, eds., Proc. SPIE2830, 202–214 (1996).
[CrossRef]

W. R. Skinner, P. B. Hays, “Incoherent Doppler lidar for measurement of atmospheric winds,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, 383–394 (1994).
[CrossRef]

Socker, D. G.

C. Korendyke, D. G. Socker, “Measured optical performance of three Fabry–Perot interferometers for use in a tunable ultraviolet filter,” Opt. Eng. 32, 2281–2285 (1993).
[CrossRef]

Towlson, W.

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of atmospheric absorption lines from a stabilised balloon platform and measurements of stratospheric winds,” J. Phys. E 15, 191–206 (1982).
[CrossRef]

Appl. Opt. (4)

J. Geophys. Res. (1)

P. B. Hays, V. J. Abreu, M. E. Dobbs, D. A. Gell, H. J. Grassl, W. R. Skinner, “The High-Resolution Doppler Imager on the Upper Atmosphere Research Satellite,” J. Geophys. Res. 98, 10,713–10,723 (1993).
[CrossRef]

J. Phys. E (2)

D. Rees, P. A. Rounce, I. McWhirter, A. F. D. Scott, A. H. Greenaway, W. Towlson, “Observations of atmospheric absorption lines from a stabilised balloon platform and measurements of stratospheric winds,” J. Phys. E 15, 191–206 (1982).
[CrossRef]

D. Rees, I. McWhirter, P. B. Hays, T. Dines, “A stable, rugged, capacitance-stabilised piezoelectric scanned Fabry–Perot etalon,” J. Phys. E 14, 1320–1325 (1981).
[CrossRef]

Opt. Eng. (5)

P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
[CrossRef]

D. M. Rust, “Etalon filters,” Opt. Eng. 33, 3342–3348 (1994).
[CrossRef]

K. F. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J. McGill, T. D. Irgang, “Visible wavelength Doppler lidar for measurement of wind and aerosol profiles during day and night,” Opt. Eng. 34, 499–511 (1995).
[CrossRef]

M. J. McGill, W. R. Skinner, “Multiple Fabry-Perot interferometers in an incoherent Doppler lidar,” Opt. Eng. 36, 139–145 (1997).
[CrossRef]

C. Korendyke, D. G. Socker, “Measured optical performance of three Fabry–Perot interferometers for use in a tunable ultraviolet filter,” Opt. Eng. 32, 2281–2285 (1993).
[CrossRef]

Rev. Opt. (1)

R. Chabbal, “Recherches expérimentales et théoriques sur la généralisation de l’emploi du spectromètre Fabry–Perot aux divers domaines de la spectroscopie,” Rev. Opt. 37, 49–104 (1958).

Other (4)

W. Skinner, University of Michigan, Ann Arbor, Mich. 48109-2143 (e-mail communication, 7December1998).

W. R. Skinner, P. B. Hays, “Incoherent Doppler lidar for measurement of atmospheric winds,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, 383–394 (1994).
[CrossRef]

W. R. Skinner, P. B. Hays, H. J. Grassl, D. A. Gell, M. D. Burrage, A. R. Marshall, J. Kafkalidis, “The High Resolution Doppler Imager: instrument performance in orbit since late 1991,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, P. B. Hays, J. Wang, eds., Proc. SPIE2830, 202–214 (1996).
[CrossRef]

G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, UK, 1988), Sect. 2.3.

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Figures (6)

Fig. 1
Fig. 1

SBR enhancement that is due to a single filter etalon. The “perfect etalon” curve is for infinite defect finesse. The solid curves are the approximation obtained with an ideal dielectric filter for etalon illumination, for the indicated values of defect finesse. The points are obtained by integration with a real dielectric filter function.

Fig. 2
Fig. 2

Etalon peak transmittance versus reflectance finesse for several values of defect finesse, to be correlated with Fig. 1. For lidar, this is also the signal transmittance, so values much less than unity are seldom tolerable, forcing operation in the regime of low reflectance finesse values.

Fig. 3
Fig. 3

Transmittance functions for the dual-etalon solar filter. The transmittances of the dielectric filter and the LRE define the envelope. Three MRE curves are shown. If one neglects the interetalon reflections, the bottom curve is obtained, showing deep minima. Allowing for reflections, with no attenuation between etalons, sharply reduces the depth of the minima. A 5% attenuation inserted between etalons recovers a substantial portion of the MRE contrast.

Fig. 4
Fig. 4

SBR enhancement factor that is due to the insertion of a second etalon, with (solid curves) and without (dashed curves) consideration of the reflective coupling between the two etalons and with no absorptive losses between etalons. Absent the reflections, the result is as for a single etalon. The reflections sharply decrease the SBR enhancement factor.

Fig. 5
Fig. 5

SBR enhancement factor for the dual-etalon filter, now with a 5% absorber between the etalons. The background rejection is significantly improved, at modest cost to signal transmittance.

Fig. 6
Fig. 6

SBR enhancement that is due to a third Fabry–Perot etalon. Solid curves are the calculation according to Eq. (11), including the HRE–LRE reflective coupling term. Dashed curves are the calculation omitting this term. The HRE–LRE coupling term is small, but not insignificant, despite 5% attenuators between both etalon pairs.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

GTpk Sλdλ SλTλdλ.
Tλ=Tpk1-RE21+RE2-2RE cos2πm,
Tpk=1-A1-R21-R1+R1+RE1-RE,
FE=πRE1-RE,
FE=FR-2+FD-2-1/2.
FD=λ4δs2+22δrms2+3δp21/2,
Tmean=1-A1-R21-R1+R.
Gideal=1+RE1-RE=1+2FEπ21/22π FE.
T12λ=τ12T1T21+τ122R1R2+τ122R1R22+,
T12λ=τ12T1λT2λ1-τ122R1λR2λ.
T123λ=τ12τ23T1λT2λT3λ1-τ122R1λR2λ1-τ232R2λR3λ-τ122τ232R1λT22λR3λ,

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