Abstract

The design, calibration, and performance of the Mars Orbiter Laser Altimeter (MOLA) receiver are described. The MOLA measurements include the range to the surface, which is determined by the laser-pulse time of flight; the height variability within the footprint determined by the laser echo pulse width; and the apparent surface reflectivity determined by the ratio of the echo to transmitted pulse energies.

© 2000 Optical Society of America

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  1. M. T. Zuber, D. E. Smith, S. C. Soloman, D. O. Muhleman, J. W. Head, J. B. Garvin, J. B. Abshire, J. L. Bufton, “Mars Observer Laser Altimeter investigation,” J. Geophys. Res. 97, 7781–7797 (1992).
    [CrossRef]
  2. D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
    [CrossRef] [PubMed]
  3. M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
    [CrossRef] [PubMed]
  4. A. A. Albee, F. D. Palluconi, R. E. Arvidson, “Mars Global Surveyor Mission: overview and status,” Science 279, 1671–1672 (1998).
    [CrossRef] [PubMed]
  5. E. R. Cohen, B. N. Taylor, “The fundamental physical constants,” Phys. Today 50, Part 2, BG7–BG11 (1997).
  6. F. G. Lemoine, D. D. Rowlands, D. E. Smith, D. S. Chinn, D. E. Pavlis, S. B. Luthcke, G. A. Neumann, M. T. Zuber, “Orbit determination for Mars Global Surveyor during mapping,” paper AAS99–328 presented at the AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, 16–19 August 1999 (American Astronautical Society, Springfield, Va., 1999).
  7. D. D. Rowlands, D. E. Pavlis, F. G. Lemoine, G. A. Neumann, S. B. Luthcke, “The use of laser altimetry in the orbit and attitude determination of Mars Global Surveyor,” Geophys. Res. Lett. 26, 1191–1194 (1999).
    [CrossRef]
  8. C. S. Gardner, “Target signatures for laser altimeters: an analysis,” Appl. Opt. 21, 448–453 (1982).
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    [CrossRef] [PubMed]
  13. X. Sun, F. M. Davidson, L. Boutsikais, J. B. Abshire, “Receiver characteristics of laser altimeters with avalanche photodiode,” IEEE Trans. Aerosp. Electron. Syst. 28, 268–274 (1992).
    [CrossRef]
  14. J. B. Abshire, S. S. Manizade, W. H. Schaefer, R. K. Zimmerman, J. S. Citwood, J. C. Caldwell, “Design and performance of the receiver for the Mars Observer Laser Altimeter,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CF14.
  15. J. F. McGarry, L. K. Pacini, J. B. Abshire, J. B. Blair, “Design and performance of an autonomous tracking system for the Mars Observer Laser Altimeter receiver,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CThR27.
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1999 (1)

D. D. Rowlands, D. E. Pavlis, F. G. Lemoine, G. A. Neumann, S. B. Luthcke, “The use of laser altimetry in the orbit and attitude determination of Mars Global Surveyor,” Geophys. Res. Lett. 26, 1191–1194 (1999).
[CrossRef]

1998 (3)

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

A. A. Albee, F. D. Palluconi, R. E. Arvidson, “Mars Global Surveyor Mission: overview and status,” Science 279, 1671–1672 (1998).
[CrossRef] [PubMed]

1997 (1)

E. R. Cohen, B. N. Taylor, “The fundamental physical constants,” Phys. Today 50, Part 2, BG7–BG11 (1997).

1994 (2)

1992 (3)

M. T. Zuber, D. E. Smith, S. C. Soloman, D. O. Muhleman, J. W. Head, J. B. Garvin, J. B. Abshire, J. L. Bufton, “Mars Observer Laser Altimeter investigation,” J. Geophys. Res. 97, 7781–7797 (1992).
[CrossRef]

C. S. Gardner, “Ranging performance of satellite laser altimeters,” IEEE Trans. Geosci. Remote Sens. 30, 1061–1072 (1992).
[CrossRef]

X. Sun, F. M. Davidson, L. Boutsikais, J. B. Abshire, “Receiver characteristics of laser altimeters with avalanche photodiode,” IEEE Trans. Aerosp. Electron. Syst. 28, 268–274 (1992).
[CrossRef]

1989 (1)

F. M. Davidson, X. Sun, “Slot clock recovery in optical PPM communication systems with avalanche photodiode photodetectors,” IEEE Trans. Commun. 37, 1164–1172 (1989).
[CrossRef]

1982 (1)

1974 (1)

P. P. Webb, R. J. McIntyre, J. Conradi, “Properties of avalanche photodiodes,” RCA Rev. 35, 234–278 (1974).

Abshire, J. B.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Soloman, D. O. Muhleman, J. W. Head, J. B. Garvin, J. B. Abshire, J. L. Bufton, “Mars Observer Laser Altimeter investigation,” J. Geophys. Res. 97, 7781–7797 (1992).
[CrossRef]

X. Sun, F. M. Davidson, L. Boutsikais, J. B. Abshire, “Receiver characteristics of laser altimeters with avalanche photodiode,” IEEE Trans. Aerosp. Electron. Syst. 28, 268–274 (1992).
[CrossRef]

J. B. Abshire, S. S. Manizade, W. H. Schaefer, R. K. Zimmerman, J. S. Citwood, J. C. Caldwell, “Design and performance of the receiver for the Mars Observer Laser Altimeter,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CF14.

J. F. McGarry, L. K. Pacini, J. B. Abshire, J. B. Blair, “Design and performance of an autonomous tracking system for the Mars Observer Laser Altimeter receiver,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CThR27.

Afzal, R. S.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

R. S. Afzal, “The Mars Observer Laser Altimeter: laser transmitter,” Appl. Opt. 33, 3184–3188 (1994).
[CrossRef] [PubMed]

R. S. Afzal, “MOLA-2 laser transmitter calibration and performance,” (Laser Remote Sensing Branch, NASA Goddard Space Flight Center, Greenbelt, Md., 1997).

Aharonson, O.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

Albee, A. A.

A. A. Albee, F. D. Palluconi, R. E. Arvidson, “Mars Global Surveyor Mission: overview and status,” Science 279, 1671–1672 (1998).
[CrossRef] [PubMed]

Arvidson, R. E.

A. A. Albee, F. D. Palluconi, R. E. Arvidson, “Mars Global Surveyor Mission: overview and status,” Science 279, 1671–1672 (1998).
[CrossRef] [PubMed]

Banerdt, W. B.

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

Blair, J. B.

J. F. McGarry, L. K. Pacini, J. B. Abshire, J. B. Blair, “Design and performance of an autonomous tracking system for the Mars Observer Laser Altimeter receiver,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CThR27.

Boutsikais, L.

X. Sun, F. M. Davidson, L. Boutsikais, J. B. Abshire, “Receiver characteristics of laser altimeters with avalanche photodiode,” IEEE Trans. Aerosp. Electron. Syst. 28, 268–274 (1992).
[CrossRef]

Bufton, J. L.

L. Ramos-Izquierdo, J. L. Bufton, P. Hayes, “Optical system design and integration of the Mars Observer Laser Altimeter,” Appl. Opt. 33, 307–322 (1994).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Soloman, D. O. Muhleman, J. W. Head, J. B. Garvin, J. B. Abshire, J. L. Bufton, “Mars Observer Laser Altimeter investigation,” J. Geophys. Res. 97, 7781–7797 (1992).
[CrossRef]

Caldwell, J. C.

J. B. Abshire, S. S. Manizade, W. H. Schaefer, R. K. Zimmerman, J. S. Citwood, J. C. Caldwell, “Design and performance of the receiver for the Mars Observer Laser Altimeter,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CF14.

Chinn, D. S.

F. G. Lemoine, D. D. Rowlands, D. E. Smith, D. S. Chinn, D. E. Pavlis, S. B. Luthcke, G. A. Neumann, M. T. Zuber, “Orbit determination for Mars Global Surveyor during mapping,” paper AAS99–328 presented at the AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, 16–19 August 1999 (American Astronautical Society, Springfield, Va., 1999).

Citwood, J. S.

J. B. Abshire, S. S. Manizade, W. H. Schaefer, R. K. Zimmerman, J. S. Citwood, J. C. Caldwell, “Design and performance of the receiver for the Mars Observer Laser Altimeter,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CF14.

Cohen, E. R.

E. R. Cohen, B. N. Taylor, “The fundamental physical constants,” Phys. Today 50, Part 2, BG7–BG11 (1997).

Conradi, J.

P. P. Webb, R. J. McIntyre, J. Conradi, “Properties of avalanche photodiodes,” RCA Rev. 35, 234–278 (1974).

Davidson, F. M.

X. Sun, F. M. Davidson, L. Boutsikais, J. B. Abshire, “Receiver characteristics of laser altimeters with avalanche photodiode,” IEEE Trans. Aerosp. Electron. Syst. 28, 268–274 (1992).
[CrossRef]

F. M. Davidson, X. Sun, “Slot clock recovery in optical PPM communication systems with avalanche photodiode photodetectors,” IEEE Trans. Commun. 37, 1164–1172 (1989).
[CrossRef]

Duxbury, T. C.

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

Fishbaugh, K.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

Ford, P. G.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

Frey, H. V.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

Gardner, C. S.

C. S. Gardner, “Ranging performance of satellite laser altimeters,” IEEE Trans. Geosci. Remote Sens. 30, 1061–1072 (1992).
[CrossRef]

C. S. Gardner, “Target signatures for laser altimeters: an analysis,” Appl. Opt. 21, 448–453 (1982).
[CrossRef] [PubMed]

Garvin, J. B.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Soloman, D. O. Muhleman, J. W. Head, J. B. Garvin, J. B. Abshire, J. L. Bufton, “Mars Observer Laser Altimeter investigation,” J. Geophys. Res. 97, 7781–7797 (1992).
[CrossRef]

Hayes, P.

Head, J. W.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Soloman, D. O. Muhleman, J. W. Head, J. B. Garvin, J. B. Abshire, J. L. Bufton, “Mars Observer Laser Altimeter investigation,” J. Geophys. Res. 97, 7781–7797 (1992).
[CrossRef]

Ivanov, A. B.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

Johnson, C. L.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

Lemoine, F. G.

D. D. Rowlands, D. E. Pavlis, F. G. Lemoine, G. A. Neumann, S. B. Luthcke, “The use of laser altimetry in the orbit and attitude determination of Mars Global Surveyor,” Geophys. Res. Lett. 26, 1191–1194 (1999).
[CrossRef]

F. G. Lemoine, D. D. Rowlands, D. E. Smith, D. S. Chinn, D. E. Pavlis, S. B. Luthcke, G. A. Neumann, M. T. Zuber, “Orbit determination for Mars Global Surveyor during mapping,” paper AAS99–328 presented at the AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, 16–19 August 1999 (American Astronautical Society, Springfield, Va., 1999).

Luthcke, S. B.

D. D. Rowlands, D. E. Pavlis, F. G. Lemoine, G. A. Neumann, S. B. Luthcke, “The use of laser altimetry in the orbit and attitude determination of Mars Global Surveyor,” Geophys. Res. Lett. 26, 1191–1194 (1999).
[CrossRef]

F. G. Lemoine, D. D. Rowlands, D. E. Smith, D. S. Chinn, D. E. Pavlis, S. B. Luthcke, G. A. Neumann, M. T. Zuber, “Orbit determination for Mars Global Surveyor during mapping,” paper AAS99–328 presented at the AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, 16–19 August 1999 (American Astronautical Society, Springfield, Va., 1999).

Manizade, S. S.

J. B. Abshire, S. S. Manizade, W. H. Schaefer, R. K. Zimmerman, J. S. Citwood, J. C. Caldwell, “Design and performance of the receiver for the Mars Observer Laser Altimeter,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CF14.

McGarry, J. F.

J. F. McGarry, L. K. Pacini, J. B. Abshire, J. B. Blair, “Design and performance of an autonomous tracking system for the Mars Observer Laser Altimeter receiver,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CThR27.

McIntyre, R. J.

P. P. Webb, R. J. McIntyre, J. Conradi, “Properties of avalanche photodiodes,” RCA Rev. 35, 234–278 (1974).

Muhleman, D. O.

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Soloman, D. O. Muhleman, J. W. Head, J. B. Garvin, J. B. Abshire, J. L. Bufton, “Mars Observer Laser Altimeter investigation,” J. Geophys. Res. 97, 7781–7797 (1992).
[CrossRef]

Neumann, G. A.

D. D. Rowlands, D. E. Pavlis, F. G. Lemoine, G. A. Neumann, S. B. Luthcke, “The use of laser altimetry in the orbit and attitude determination of Mars Global Surveyor,” Geophys. Res. Lett. 26, 1191–1194 (1999).
[CrossRef]

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

F. G. Lemoine, D. D. Rowlands, D. E. Smith, D. S. Chinn, D. E. Pavlis, S. B. Luthcke, G. A. Neumann, M. T. Zuber, “Orbit determination for Mars Global Surveyor during mapping,” paper AAS99–328 presented at the AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, 16–19 August 1999 (American Astronautical Society, Springfield, Va., 1999).

Pacini, L. K.

J. F. McGarry, L. K. Pacini, J. B. Abshire, J. B. Blair, “Design and performance of an autonomous tracking system for the Mars Observer Laser Altimeter receiver,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CThR27.

Palluconi, F. D.

A. A. Albee, F. D. Palluconi, R. E. Arvidson, “Mars Global Surveyor Mission: overview and status,” Science 279, 1671–1672 (1998).
[CrossRef] [PubMed]

Pavlis, D. E.

D. D. Rowlands, D. E. Pavlis, F. G. Lemoine, G. A. Neumann, S. B. Luthcke, “The use of laser altimetry in the orbit and attitude determination of Mars Global Surveyor,” Geophys. Res. Lett. 26, 1191–1194 (1999).
[CrossRef]

F. G. Lemoine, D. D. Rowlands, D. E. Smith, D. S. Chinn, D. E. Pavlis, S. B. Luthcke, G. A. Neumann, M. T. Zuber, “Orbit determination for Mars Global Surveyor during mapping,” paper AAS99–328 presented at the AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, 16–19 August 1999 (American Astronautical Society, Springfield, Va., 1999).

Personick, S. D.

R. G. Smith, S. D. Personick, “Receiver design for optical fiber communications,” in Semiconductor Devices for Optical Communication, H. Kressel, ed. (Springer-Verlag, New York, 1980), Chap. 4.
[CrossRef]

Pettengill, G. H.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

Phillips, R. J.

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

Ramos-Izquierdo, L.

Rowlands, D. D.

D. D. Rowlands, D. E. Pavlis, F. G. Lemoine, G. A. Neumann, S. B. Luthcke, “The use of laser altimetry in the orbit and attitude determination of Mars Global Surveyor,” Geophys. Res. Lett. 26, 1191–1194 (1999).
[CrossRef]

F. G. Lemoine, D. D. Rowlands, D. E. Smith, D. S. Chinn, D. E. Pavlis, S. B. Luthcke, G. A. Neumann, M. T. Zuber, “Orbit determination for Mars Global Surveyor during mapping,” paper AAS99–328 presented at the AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, 16–19 August 1999 (American Astronautical Society, Springfield, Va., 1999).

Schaefer, W. H.

J. B. Abshire, S. S. Manizade, W. H. Schaefer, R. K. Zimmerman, J. S. Citwood, J. C. Caldwell, “Design and performance of the receiver for the Mars Observer Laser Altimeter,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CF14.

Smith, D. E.

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Soloman, D. O. Muhleman, J. W. Head, J. B. Garvin, J. B. Abshire, J. L. Bufton, “Mars Observer Laser Altimeter investigation,” J. Geophys. Res. 97, 7781–7797 (1992).
[CrossRef]

F. G. Lemoine, D. D. Rowlands, D. E. Smith, D. S. Chinn, D. E. Pavlis, S. B. Luthcke, G. A. Neumann, M. T. Zuber, “Orbit determination for Mars Global Surveyor during mapping,” paper AAS99–328 presented at the AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, 16–19 August 1999 (American Astronautical Society, Springfield, Va., 1999).

Smith, R. G.

R. G. Smith, S. D. Personick, “Receiver design for optical fiber communications,” in Semiconductor Devices for Optical Communication, H. Kressel, ed. (Springer-Verlag, New York, 1980), Chap. 4.
[CrossRef]

Snyder, D. L.

D. L. Snyder, Random Point Process (Wiley, New York, 1975).

Soloman, S. C.

M. T. Zuber, D. E. Smith, S. C. Soloman, D. O. Muhleman, J. W. Head, J. B. Garvin, J. B. Abshire, J. L. Bufton, “Mars Observer Laser Altimeter investigation,” J. Geophys. Res. 97, 7781–7797 (1992).
[CrossRef]

Solomon, S. C.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

Sun, X.

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

X. Sun, F. M. Davidson, L. Boutsikais, J. B. Abshire, “Receiver characteristics of laser altimeters with avalanche photodiode,” IEEE Trans. Aerosp. Electron. Syst. 28, 268–274 (1992).
[CrossRef]

F. M. Davidson, X. Sun, “Slot clock recovery in optical PPM communication systems with avalanche photodiode photodetectors,” IEEE Trans. Commun. 37, 1164–1172 (1989).
[CrossRef]

Taylor, B. N.

E. R. Cohen, B. N. Taylor, “The fundamental physical constants,” Phys. Today 50, Part 2, BG7–BG11 (1997).

Vig, J. R.

J. R. Vig, Introduction of Quartz Frequency Standards, Research and Development Technical Report, (Research, Development and Engineering Center, U.S. Army Communications-Electronics Command, Fort Monmouth, N.J., 1997).

Webb, P. P.

P. P. Webb, R. J. McIntyre, J. Conradi, “Properties of avalanche photodiodes,” RCA Rev. 35, 234–278 (1974).

Zimmerman, R. K.

J. B. Abshire, S. S. Manizade, W. H. Schaefer, R. K. Zimmerman, J. S. Citwood, J. C. Caldwell, “Design and performance of the receiver for the Mars Observer Laser Altimeter,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CF14.

Zuber, M. T.

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Soloman, D. O. Muhleman, J. W. Head, J. B. Garvin, J. B. Abshire, J. L. Bufton, “Mars Observer Laser Altimeter investigation,” J. Geophys. Res. 97, 7781–7797 (1992).
[CrossRef]

F. G. Lemoine, D. D. Rowlands, D. E. Smith, D. S. Chinn, D. E. Pavlis, S. B. Luthcke, G. A. Neumann, M. T. Zuber, “Orbit determination for Mars Global Surveyor during mapping,” paper AAS99–328 presented at the AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, 16–19 August 1999 (American Astronautical Society, Springfield, Va., 1999).

Zwally, H. J.

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

Appl. Opt. (3)

Geophys. Res. Lett. (1)

D. D. Rowlands, D. E. Pavlis, F. G. Lemoine, G. A. Neumann, S. B. Luthcke, “The use of laser altimetry in the orbit and attitude determination of Mars Global Surveyor,” Geophys. Res. Lett. 26, 1191–1194 (1999).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (1)

X. Sun, F. M. Davidson, L. Boutsikais, J. B. Abshire, “Receiver characteristics of laser altimeters with avalanche photodiode,” IEEE Trans. Aerosp. Electron. Syst. 28, 268–274 (1992).
[CrossRef]

IEEE Trans. Commun. (1)

F. M. Davidson, X. Sun, “Slot clock recovery in optical PPM communication systems with avalanche photodiode photodetectors,” IEEE Trans. Commun. 37, 1164–1172 (1989).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

C. S. Gardner, “Ranging performance of satellite laser altimeters,” IEEE Trans. Geosci. Remote Sens. 30, 1061–1072 (1992).
[CrossRef]

J. Geophys. Res. (1)

M. T. Zuber, D. E. Smith, S. C. Soloman, D. O. Muhleman, J. W. Head, J. B. Garvin, J. B. Abshire, J. L. Bufton, “Mars Observer Laser Altimeter investigation,” J. Geophys. Res. 97, 7781–7797 (1992).
[CrossRef]

Phys. Today (1)

E. R. Cohen, B. N. Taylor, “The fundamental physical constants,” Phys. Today 50, Part 2, BG7–BG11 (1997).

RCA Rev. (1)

P. P. Webb, R. J. McIntyre, J. Conradi, “Properties of avalanche photodiodes,” RCA Rev. 35, 234–278 (1974).

Science (3)

D. E. Smith, M. T. Zuber, H. V. Frey, J. B. Garvin, J. W. Head, D. O. Muhleman, G. H. Pettengill, R. J. Phillips, S. C. Solomon, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter,” Science 279, 1686–1692 (1998).
[CrossRef] [PubMed]

M. T. Zuber, D. E. Smith, S. C. Solomon, J. B. Abshire, R. S. Afzal, O. Aharonson, K. Fishbaugh, P. G. Ford, H. V. Frey, J. B. Garvin, J. W. Head, A. B. Ivanov, C. L. Johnson, D. O. Muhleman, G. A. Neumann, G. H. Pettengill, R. J. Phillips, X. Sun, H. J. Zwally, W. B. Banerdt, T. C. Duxbury, “Observation of the north polar region of Mars from the Mars Orbiter Laser Altimeter,” Science 282, 2053–2060 (1998).
[CrossRef] [PubMed]

A. A. Albee, F. D. Palluconi, R. E. Arvidson, “Mars Global Surveyor Mission: overview and status,” Science 279, 1671–1672 (1998).
[CrossRef] [PubMed]

Other (7)

J. B. Abshire, S. S. Manizade, W. H. Schaefer, R. K. Zimmerman, J. S. Citwood, J. C. Caldwell, “Design and performance of the receiver for the Mars Observer Laser Altimeter,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CF14.

J. F. McGarry, L. K. Pacini, J. B. Abshire, J. B. Blair, “Design and performance of an autonomous tracking system for the Mars Observer Laser Altimeter receiver,” in Conference on Laser and Electro-Optics, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Paper CThR27.

J. R. Vig, Introduction of Quartz Frequency Standards, Research and Development Technical Report, (Research, Development and Engineering Center, U.S. Army Communications-Electronics Command, Fort Monmouth, N.J., 1997).

R. G. Smith, S. D. Personick, “Receiver design for optical fiber communications,” in Semiconductor Devices for Optical Communication, H. Kressel, ed. (Springer-Verlag, New York, 1980), Chap. 4.
[CrossRef]

R. S. Afzal, “MOLA-2 laser transmitter calibration and performance,” (Laser Remote Sensing Branch, NASA Goddard Space Flight Center, Greenbelt, Md., 1997).

F. G. Lemoine, D. D. Rowlands, D. E. Smith, D. S. Chinn, D. E. Pavlis, S. B. Luthcke, G. A. Neumann, M. T. Zuber, “Orbit determination for Mars Global Surveyor during mapping,” paper AAS99–328 presented at the AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, 16–19 August 1999 (American Astronautical Society, Springfield, Va., 1999).

D. L. Snyder, Random Point Process (Wiley, New York, 1975).

Cited By

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Figures (8)

Fig. 1
Fig. 1

MGS spacecraft and the MOLA.

Fig. 2
Fig. 2

Illustration of the MOLA measurement geometry. The drawing assumes that the pointing angle, the pointing error, and the surface normal vectors are all in the same plane.

Fig. 3
Fig. 3

Timing diagram of the MOLA optical and electrical signals.

Fig. 4
Fig. 4

Simplified MOLA receiver block diagram assuming lossless power splitter and filters and a unity scaling factor for all receiver channels. The filter characteristics are listed in Table 2.

Fig. 5
Fig. 5

Original and seventh-order polynomial fit of the inverse z function.

Fig. 6
Fig. 6

MOLA channel 1 ranging error versus received signal level for 1-, 3-, 10-, and 30-deg slope surfaces.

Fig. 7
Fig. 7

MOLA channel 1 ranging error versus threshold level normalized with respect to pulse amplitude.

Fig. 8
Fig. 8

MOLA channel 1 ranging error as a function of range.

Tables (6)

Tables Icon

Table 1 MOLA System Parameters

Tables Icon

Table 2 Low-Pass Filter Parameters

Tables Icon

Table 3 Start Interpolator Bit Pattern to Time Conversion

Tables Icon

Table 4 Stop Interpolator Bit Pattern to Time Conversion

Tables Icon

Table 5 Instrument Zero-Range Time Offsets with Leading-Edge Timinga

Tables Icon

Table 6 Pulse Width and Area Conversion Factors, Count Offsets, and the Threshold Scaling Factors

Equations (52)

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

Rm=cΔTopt2,
hs=RMGS2+Rm2-2RmRMGS cosϕ1/2-Rref,
Er=EtrτrArRm2rsπ τa2,
σr2=σx2+σf2+4Rm2c2tan4γ+tan2γtan2θ,
FWHMl=326.62El-0.95 ns,
ΔTopt=Nf+Δt0-Δt1-τle0+τf0+τlei-τfi-τdi.
τlei=Wyi2,
Wy0FWHMf02+FWHMl21/2,
Wyi=aWili-bWi, i=1, 2, 3, 4.
Ayi=aAimi-bAi,
yi=athreithi,
fit=A2πσriexp-t22σri2.
yi=fiWyi2=A2πσriexp-Wyi222σri2.
Ayi=-Wyi/2Wyi/2A2πσriexp-t22σri2dt=A erfWyi22σri,
Ayiyi=Wyiπ2erfWyi22σriWyi22σriexp-Wyi22σri2.
AyiyiWyi=zWyi22σri.
zxπ2erfxx exp-x2
σri=Wyi221z-1AyiyiWyi.
A=Ayi1erfz-1AyiyiWyi.
σopt=σr2i-σf2i1/2,
σfi=FWHMi22 ln21/2.
Er=ARdet.
RphRdethcληd,
ΔTopttr+Wy2+To+Q=tr+tf2+To+Q,
varΔTopt=vartr+tf2+varQ=14vartr+vartf+Δt0212+Δt1212+ΔW212,
xt=st+nt,
stsTr+sTrt-Tr,
xtrsTr+sTrtr-Tr+ntr.
sTrtr-Tr+ntr0.
vartr=tr-Tr2varnTrsTr2.
st=Npe- hfτpt-τdτ,
stNpet2πσopt2+σf23/2exp-t22σopt2+σf2.
Tr=-σr2 ln2πσrsthNpe1/2,
sth=yRph,
varnt=varnsigt+varnbg+varndk+varnamp.
varnsigt=FNpe- hf2τpt-τdτ,
F=keffG+2-1G1-keff,
varnbg=2F ηdλhc PbgBn,
Bn=12- hf2τdτ.
Pbg=IsΔλ θFOV24 rsArτr,
varndk=2F Idkq Bn,
varnamp=Iamp2Bnq2G2,
vartr=FNpe- hf2τpTr-τdτ+2Fηdhc/λ Pbg+IdkqBn+Iamp2q2G2 BnNpet2πσopt2+σf23/2exp-t22σopt2+σf22.
vartr=vartf.
varToptσopt2NpeF.
varWy=vartr-tf+ΔW212=vartr+vartf+ΔW212.
varσopt<2.36 varWy
hAt=1,TrtTf0,otherwise.
hfAt=- hft-uhAudu=TrTf hft-udu.
varAy=Rph2FNpe-TrTf hfτ-udu2p-τdτ+ΔA212,
varAyRph2FNpeTrTf p-τdτ+ΔA12=Rph2FNpe+ΔA12.
Ay=varAyAy2FNpe,

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