Abstract

Astrometric measurements using stellar interferometry rely on precise measurement of the central white light fringe to accurately obtain the optical pathlength difference of incoming starlight to the two arms of the interferometer. One standard approach to stellar interferometry uses a channeled spectrum to determine phases at a number of different wavelengths that are then converted to the pathlength delay. When throughput is low these channels are broadened to improve the signal-to-noise ratio. Ultimately the ability to use monochromatic models and algorithms in each of the channels to extract phase becomes problematic and knowledge of the spectrum must be incorporated to achieve the accuracies required of the astrometric measurements. To accomplish this an optimization problem is posed to estimate simultaneously the pathlength delay and spectrum of the source. Moreover, the nature of the parameterization of the spectrum that is introduced circumvents the need to solve directly for these parameters so that the optimization problem reduces to a scalar problem in just the pathlength delay variable. A number of examples are given to show the robustness of the approach.

© 2005 Optical Society of America

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2003 (1)

2002 (1)

2000 (1)

1999 (1)

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

1998 (2)

1996 (1)

1995 (2)

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. 273, L53–L58 (1995).

P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
[CrossRef]

1994 (1)

A. Quirrenbach, D. Mozurkewich, D. F. Buscher, C. A. Hummel, J. T. Armstrong, “Phase-referenced visibility averaging in optical long-baseline interferometry,” Astron. Astrophys. 286, 1019–1027 (1994).

1991 (1)

1990 (1)

1988 (1)

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

1984 (1)

J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. (Bellingham) 23, 350–352 (1984).
[CrossRef]

1973 (1)

G. H. Golub, V. Peryera, “The differentiation of pseudo-inverses and nonlinear least squares problems whose variables are separate,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 10, 413–432 (1973).
[CrossRef]

Armstrong, J. T.

A. Quirrenbach, D. Mozurkewich, D. F. Buscher, C. A. Hummel, J. T. Armstrong, “Phase-referenced visibility averaging in optical long-baseline interferometry,” Astron. Astrophys. 286, 1019–1027 (1994).

Baldwin, J. E.

J. E. Baldwin, R. C. Boysen, G. C. Cox, C. A. Haniff, J. Rogers, P. J. Warner, D. M.A. Wilson, C. D. Mackay, “Design and performance of COAST,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 118–124. (1994).

Benson, K. A.

K. A. Benson, D. Mozurkewich, S. M. Jefferies, “Active optical fringe tracking at the NPOI,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 493–496 (1998).

Boden, A. F.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

A. F. Boden, “Elementary theory of interferometry,” in Principles of Long Baseline Stellar Interferometry, P. R. Lawson, ed., Course Notes from the 1999 Michelson Interferometry Summer School, Jet Propulsion Laboratory Pasadena, Calif., August 15–19, 1999.

Booth, A. J.

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. 273, L53–L58 (1995).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon1989).

Boysen, R. C.

J. E. Baldwin, R. C. Boysen, G. C. Cox, C. A. Haniff, J. Rogers, P. J. Warner, D. M.A. Wilson, C. D. Mackay, “Design and performance of COAST,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 118–124. (1994).

Bronowicki, A. J.

A. J. Bronowicki, R. MacDonald, Y. Gursel, R. Goullioud, T. Neville, “Dual-stage passive vibration isolation for optical interferometer missions,” in Interferometry in Space, M. Shao, ed., Proc. SPIE4852, 753–763 (2003).

Buscher, D. F.

A. Quirrenbach, D. Mozurkewich, D. F. Buscher, C. A. Hummel, J. T. Armstrong, “Phase-referenced visibility averaging in optical long-baseline interferometry,” Astron. Astrophys. 286, 1019–1027 (1994).

Catanzarite, J.

Chim, S. S.C.

Colavita, M. M.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

P. R. Lawson, M. M. Colavita, P. J. Dumont, B. F. Lane, “Least squares estimation and group delay in astrometric interferometers,” in Interferometry in Optical Astronomy, P. J. Lena and A. Quirrenbach, eds., Proc. SPIE4006, 397–406 (2000).

M. M. Colavita, P. L. Wizinowich, “Keck Interferometer: Progress report,” in Interferometry in Optical Astronomy, P. J. Lena and A. Quirrenbach, eds., Proc. SPIE4006, 310–320 (2000).

Cox, G. C.

J. E. Baldwin, R. C. Boysen, G. C. Cox, C. A. Haniff, J. Rogers, P. J. Warner, D. M.A. Wilson, C. D. Mackay, “Design and performance of COAST,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 118–124. (1994).

Creath, K.

K. Creath, “Phase-measurement interferometery techniques,” in Progress in Optics, Vol. XXVI, E. Wolf, ed. (Elsevier, 1988), pp. 350–393.

Danner, R.

R. Danner, S. Unwin, Space Interferometry Mission, Taking the Measure of the Universe, Jet Propulsion Laboratory Pub. 400-811, March 1999.

Davis, J.

J. Davis, W. J. Tango, E. D. Thorvaldson, “Dispersion in stellar interferometry: simultaneous optimization for delay tracking and visibility measurements,” Appl. Opt. 37, 5132–5136 (1998).
[CrossRef]

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. 273, L53–L58 (1995).

Dennis, J. E.

J. E. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations [SIAM (Soc. Ind. Appl. Math.), 1996].
[CrossRef]

Dumont, P. J.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

P. R. Lawson, M. M. Colavita, P. J. Dumont, B. F. Lane, “Least squares estimation and group delay in astrometric interferometers,” in Interferometry in Optical Astronomy, P. J. Lena and A. Quirrenbach, eds., Proc. SPIE4006, 397–406 (2000).

Golub, G. H.

G. H. Golub, V. Peryera, “The differentiation of pseudo-inverses and nonlinear least squares problems whose variables are separate,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 10, 413–432 (1973).
[CrossRef]

G. H. Golub, C. F. Van Loan, Matrix Computations, 2nd ed. (The Johns Hopkins U. Press, 1989).

Goullioud, R.

A. J. Bronowicki, R. MacDonald, Y. Gursel, R. Goullioud, T. Neville, “Dual-stage passive vibration isolation for optical interferometer missions,” in Interferometry in Space, M. Shao, ed., Proc. SPIE4852, 753–763 (2003).

R. Goullioud, T. J. Shen, “SIM astrometric demonstration at 24 picometers on the MAM testbed,” presented at the IEEE Aerospace Conference, March 6–13, 2004, Big Sky, Montana.

Greivenkamp, J. E.

J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. (Bellingham) 23, 350–352 (1984).
[CrossRef]

Gubler, J.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

Gursel, Y.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

A. J. Bronowicki, R. MacDonald, Y. Gursel, R. Goullioud, T. Neville, “Dual-stage passive vibration isolation for optical interferometer missions,” in Interferometry in Space, M. Shao, ed., Proc. SPIE4852, 753–763 (2003).

Haniff, C. A.

J. E. Baldwin, R. C. Boysen, G. C. Cox, C. A. Haniff, J. Rogers, P. J. Warner, D. M.A. Wilson, C. D. Mackay, “Design and performance of COAST,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 118–124. (1994).

Harasaki, A.

Hariharan, P.

P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
[CrossRef]

Hershey, J.

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Hines, B. E.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Hughes, J. A.

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Hummel, C. A.

A. Quirrenbach, D. Mozurkewich, D. F. Buscher, C. A. Hummel, J. T. Armstrong, “Phase-referenced visibility averaging in optical long-baseline interferometry,” Astron. Astrophys. 286, 1019–1027 (1994).

Hutter, D. J.

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Jefferies, S. M.

K. A. Benson, D. Mozurkewich, S. M. Jefferies, “Active optical fringe tracking at the NPOI,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 493–496 (1998).

Johnston, K. J.

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Kaplan, G. H.

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Kato, T.

T. Kato, Perturbation Theory for Linear Operators (Springer-Verlag, 1980).

Kino, G. S.

Koresko, C. D.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

Kulkarni, S. R.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

Lane, B. F.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

P. R. Lawson, M. M. Colavita, P. J. Dumont, B. F. Lane, “Least squares estimation and group delay in astrometric interferometers,” in Interferometry in Optical Astronomy, P. J. Lena and A. Quirrenbach, eds., Proc. SPIE4006, 397–406 (2000).

Larkin, K. G.

Laskin, R.

R. Laskin, “The Space Interferometry Mission (SIM)- technology completion and transition to flight,” in New Frontiers in Stellar Interferometry, W. Traub, ed., Proc. SPIE5491, 334–352 (2004).

Lawson, P. R.

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. 273, L53–L58 (1995).

P. R. Lawson, M. M. Colavita, P. J. Dumont, B. F. Lane, “Least squares estimation and group delay in astrometric interferometers,” in Interferometry in Optical Astronomy, P. J. Lena and A. Quirrenbach, eds., Proc. SPIE4006, 397–406 (2000).

Linfeld, R.

R. Linfeld, “Effects of stellar spectral types and nongeometric phase on delay estimates,” Jet Propulsion Laboratory Interoffice Memo D-32925, March, 2000; available on request to the author.

MacDonald, R.

A. J. Bronowicki, R. MacDonald, Y. Gursel, R. Goullioud, T. Neville, “Dual-stage passive vibration isolation for optical interferometer missions,” in Interferometry in Space, M. Shao, ed., Proc. SPIE4852, 753–763 (2003).

Mackay, C. D.

J. E. Baldwin, R. C. Boysen, G. C. Cox, C. A. Haniff, J. Rogers, P. J. Warner, D. M.A. Wilson, C. D. Mackay, “Design and performance of COAST,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 118–124. (1994).

Malbet, F.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

Milman, M.

M. Milman, J. Catanzarite, S. G. Turyshev, “The effect of wavenumber error on the computation of pathlength delay in white-light interferometry,” Appl. Opt. 41, 4884–4890 (2002).
[CrossRef] [PubMed]

M. Milman, M. Regehr, T. P. Shen, “White light modeling, algorithm development, and validation on the Micro-Arcsecond Metrology Testbed,” in New Frontiers in Stellar Interferometry, W. A. Traub, ed., Proc. SPIE5491, 1813–1822 (2004).

Mobley, D. W.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

Mozurkewich, D.

A. Quirrenbach, D. Mozurkewich, D. F. Buscher, C. A. Hummel, J. T. Armstrong, “Phase-referenced visibility averaging in optical long-baseline interferometry,” Astron. Astrophys. 286, 1019–1027 (1994).

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

K. A. Benson, D. Mozurkewich, S. M. Jefferies, “Active optical fringe tracking at the NPOI,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 493–496 (1998).

Neville, T.

A. J. Bronowicki, R. MacDonald, Y. Gursel, R. Goullioud, T. Neville, “Dual-stage passive vibration isolation for optical interferometer missions,” in Interferometry in Space, M. Shao, ed., Proc. SPIE4852, 753–763 (2003).

Palmer, D. L.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

Pan, X. P.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

Peryera, V.

G. H. Golub, V. Peryera, “The differentiation of pseudo-inverses and nonlinear least squares problems whose variables are separate,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 10, 413–432 (1973).
[CrossRef]

Pickles, A. J.

A. J. Pickles, “A stellar flux library: 1150-25000 A,” Astron. Soc. Pac. 110, 863–878 (1998).
[CrossRef]

Quirrenbach, A.

A. Quirrenbach, D. Mozurkewich, D. F. Buscher, C. A. Hummel, J. T. Armstrong, “Phase-referenced visibility averaging in optical long-baseline interferometry,” Astron. Astrophys. 286, 1019–1027 (1994).

Regehr, M.

M. Milman, M. Regehr, T. P. Shen, “White light modeling, algorithm development, and validation on the Micro-Arcsecond Metrology Testbed,” in New Frontiers in Stellar Interferometry, W. A. Traub, ed., Proc. SPIE5491, 1813–1822 (2004).

Rogers, J.

J. E. Baldwin, R. C. Boysen, G. C. Cox, C. A. Haniff, J. Rogers, P. J. Warner, D. M.A. Wilson, C. D. Mackay, “Design and performance of COAST,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 118–124. (1994).

Roy, M.

P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
[CrossRef]

Schmit, J.

Schnabel, R. B.

J. E. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations [SIAM (Soc. Ind. Appl. Math.), 1996].
[CrossRef]

Shao, M.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Shen, T. J.

R. Goullioud, T. J. Shen, “SIM astrometric demonstration at 24 picometers on the MAM testbed,” presented at the IEEE Aerospace Conference, March 6–13, 2004, Big Sky, Montana.

Shen, T. P.

M. Milman, M. Regehr, T. P. Shen, “White light modeling, algorithm development, and validation on the Micro-Arcsecond Metrology Testbed,” in New Frontiers in Stellar Interferometry, W. A. Traub, ed., Proc. SPIE5491, 1813–1822 (2004).

Simon, R. S.

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Staelin, D. H.

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Tango, W. J.

J. Davis, W. J. Tango, E. D. Thorvaldson, “Dispersion in stellar interferometry: simultaneous optimization for delay tracking and visibility measurements,” Appl. Opt. 37, 5132–5136 (1998).
[CrossRef]

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. 273, L53–L58 (1995).

W. J. Tango, “Dispersion in stellar interferometry,” Appl. Opt. 29, 516–521 (1990).
[CrossRef] [PubMed]

Thorvaldson, E.

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. 273, L53–L58 (1995).

Thorvaldson, E. D.

Traub, W. A.

W. A. Traub, “Recent results from the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 848–855 (1998).

Turyshev, S. G.

Unwin, S.

R. Danner, S. Unwin, Space Interferometry Mission, Taking the Measure of the Universe, Jet Propulsion Laboratory Pub. 400-811, March 1999.

van Belle, G. T.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

Van Loan, C. F.

G. H. Golub, C. F. Van Loan, Matrix Computations, 2nd ed. (The Johns Hopkins U. Press, 1989).

Wallace, J. K.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

Warner, P. J.

J. E. Baldwin, R. C. Boysen, G. C. Cox, C. A. Haniff, J. Rogers, P. J. Warner, D. M.A. Wilson, C. D. Mackay, “Design and performance of COAST,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 118–124. (1994).

Wilson, D. M.A.

J. E. Baldwin, R. C. Boysen, G. C. Cox, C. A. Haniff, J. Rogers, P. J. Warner, D. M.A. Wilson, C. D. Mackay, “Design and performance of COAST,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 118–124. (1994).

Wizinowich, P. L.

M. M. Colavita, P. L. Wizinowich, “Keck Interferometer: Progress report,” in Interferometry in Optical Astronomy, P. J. Lena and A. Quirrenbach, eds., Proc. SPIE4006, 310–320 (2000).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon1989).

Wyant, J. C.

Yu, J. W.

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

Appl. Opt. (6)

Astron. Astrophys. (2)

A. Quirrenbach, D. Mozurkewich, D. F. Buscher, C. A. Hummel, J. T. Armstrong, “Phase-referenced visibility averaging in optical long-baseline interferometry,” Astron. Astrophys. 286, 1019–1027 (1994).

M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).

Astron. Soc. Pac. (1)

A. J. Pickles, “A stellar flux library: 1150-25000 A,” Astron. Soc. Pac. 110, 863–878 (1998).
[CrossRef]

Astrophys. J. (1)

M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999).
[CrossRef]

J. Mod. Opt. (1)

P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
[CrossRef]

J. Opt. Soc. Am. A (1)

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

J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, E. Thorvaldson, “Atmospheric path variations for baselines up to 80m measured with the Sydney University Stellar Interferometer,” Mon. Not. R. Astron. Soc. 273, L53–L58 (1995).

Opt. Eng. (Bellingham) (1)

J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. (Bellingham) 23, 350–352 (1984).
[CrossRef]

SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. (1)

G. H. Golub, V. Peryera, “The differentiation of pseudo-inverses and nonlinear least squares problems whose variables are separate,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 10, 413–432 (1973).
[CrossRef]

Other (17)

J. E. Baldwin, R. C. Boysen, G. C. Cox, C. A. Haniff, J. Rogers, P. J. Warner, D. M.A. Wilson, C. D. Mackay, “Design and performance of COAST,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE2200, 118–124. (1994).

W. A. Traub, “Recent results from the IOTA interferometer,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 848–855 (1998).

K. A. Benson, D. Mozurkewich, S. M. Jefferies, “Active optical fringe tracking at the NPOI,” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 493–496 (1998).

M. M. Colavita, P. L. Wizinowich, “Keck Interferometer: Progress report,” in Interferometry in Optical Astronomy, P. J. Lena and A. Quirrenbach, eds., Proc. SPIE4006, 310–320 (2000).

R. Danner, S. Unwin, Space Interferometry Mission, Taking the Measure of the Universe, Jet Propulsion Laboratory Pub. 400-811, March 1999.

R. Goullioud, T. J. Shen, “SIM astrometric demonstration at 24 picometers on the MAM testbed,” presented at the IEEE Aerospace Conference, March 6–13, 2004, Big Sky, Montana.

R. Laskin, “The Space Interferometry Mission (SIM)- technology completion and transition to flight,” in New Frontiers in Stellar Interferometry, W. Traub, ed., Proc. SPIE5491, 334–352 (2004).

K. Creath, “Phase-measurement interferometery techniques,” in Progress in Optics, Vol. XXVI, E. Wolf, ed. (Elsevier, 1988), pp. 350–393.

P. R. Lawson, M. M. Colavita, P. J. Dumont, B. F. Lane, “Least squares estimation and group delay in astrometric interferometers,” in Interferometry in Optical Astronomy, P. J. Lena and A. Quirrenbach, eds., Proc. SPIE4006, 397–406 (2000).

A. F. Boden, “Elementary theory of interferometry,” in Principles of Long Baseline Stellar Interferometry, P. R. Lawson, ed., Course Notes from the 1999 Michelson Interferometry Summer School, Jet Propulsion Laboratory Pasadena, Calif., August 15–19, 1999.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon1989).

G. H. Golub, C. F. Van Loan, Matrix Computations, 2nd ed. (The Johns Hopkins U. Press, 1989).

T. Kato, Perturbation Theory for Linear Operators (Springer-Verlag, 1980).

R. Linfeld, “Effects of stellar spectral types and nongeometric phase on delay estimates,” Jet Propulsion Laboratory Interoffice Memo D-32925, March, 2000; available on request to the author.

J. E. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations [SIAM (Soc. Ind. Appl. Math.), 1996].
[CrossRef]

M. Milman, M. Regehr, T. P. Shen, “White light modeling, algorithm development, and validation on the Micro-Arcsecond Metrology Testbed,” in New Frontiers in Stellar Interferometry, W. A. Traub, ed., Proc. SPIE5491, 1813–1822 (2004).

A. J. Bronowicki, R. MacDonald, Y. Gursel, R. Goullioud, T. Neville, “Dual-stage passive vibration isolation for optical interferometer missions,” in Interferometry in Space, M. Shao, ed., Proc. SPIE4852, 753–763 (2003).

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Figures (15)

Fig. 1
Fig. 1

Comparison of delay error for monochromatic versus polychromatic estimators.

Fig. 2
Fig. 2

Comparison of delay error for monochromatic estimators with different assumed wavelengths.

Fig. 3
Fig. 3

First eight singular values for 1 μ m stroke.

Fig. 4
Fig. 4

First three shape functions for 778–900 nm channel case.

Fig. 5
Fig. 5

First three shape functions for 400–900 nm channel case.

Fig. 6
Fig. 6

Smoothness of the function Q ( x ) T y 2 .

Fig. 7
Fig. 7

Shape change when noise is added to the observation vector.

Fig. 8
Fig. 8

Effect of changing number of spectral coefficients on rectangular bandpass problem.

Fig. 9
Fig. 9

Estimation error with a monochromatic spectrum.

Fig. 10
Fig. 10

Estimation performance with a two-line spectrum.

Fig. 11
Fig. 11

Spectrum of representative M star.

Fig. 12
Fig. 12

Error in four spectral channels using mean wavenumber (left) and weighted mean wavenumber (right).

Fig. 13
Fig. 13

Error in eight spectral channels using mean wavenumber (left) and weighted mean wavenumber (right).

Fig. 14
Fig. 14

Error in delay estimate on M star spectrum using spectral estimator with three-spectral-coefficient model.

Fig. 15
Fig. 15

Error in four spectral channels using spectral estimator with shift error in spectrometer.

Tables (2)

Tables Icon

Table 1 Mean Wavelengths in Four Channels

Tables Icon

Table 2 Mean Wavelengths in Eight Channels

Equations (42)

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

y i = k k + I 0 ( k ) [ 1 + V ( k ) cos ( k u i + k d ) ] d k .
y i = I 0 { 1 + γ ( x ) cos [ k ¯ x + α ( x ) ] } , x = u i + d ,
y i = I 0 [ 1 + V sinc ( Δ u i 2 + Δ d 2 ) cos ( k ¯ u i + k ¯ d ) ] ,
y = A x , A = [ 1 sinc [ Δ ( u 1 + d ) 2 ] cos ( k ¯ u 1 ) sinc [ Δ ( u 1 + d ) 2 ] sin ( k ¯ u 1 ) 1 sinc [ Δ ( u N + d ) 2 ] cos ( k ¯ u N ) sinc [ Δ ( u N + d ) 2 ] sin ( k ¯ u N ) ] , x = [ I 0 I 0 V cos ( k ¯ d ) I 0 V sin ( k ¯ d ) ] .
cos ( k u i + k d ) = cos ( k u i + k ¯ d ) sin ( k u i + k ¯ d ) ( k k ¯ ) d + O ( δ k 2 d 2 ) ,
cos ( k u i + k ¯ d ) = cos ( k u i ) cos ( k ¯ d ) sin ( k u i ) sin ( k ¯ d ) ,
sin ( k u i + k ¯ d ) = sin ( k u i ) cos ( k ¯ d ) + cos ( k u i ) sin ( k ¯ d ) ,
cos ( k u i + k d ) = cos ( k u i ) cos ( k ¯ d ) sin ( k u i ) sin ( k ¯ d ) d ( k k ¯ ) cos ( k u i ) sin ( k ¯ d ) d ( k k ¯ ) sin ( k u i ) cos ( k ¯ d ) .
cos ( k u i + k d ) = cos ( k u i ) cos ( x ) sin ( k u i ) sin ( x ) ( k k ¯ ) k ¯ cos ( k u i ) x sin ( x ) ( k k ¯ ) k ¯ sin ( k u i ) x cos ( x ) .
y i = N 0 + k k + F ( k ) cos ( k u i ) d k cos ( x ) k k + F ( k ) sin ( k u i ) d k sin ( x ) k k + F ( k ) k k ¯ k ¯ cos ( k u i ) d k x sin ( x ) k k + F ( k ) k k ¯ k ¯ sin ( k u i ) d k x cos ( x ) ,
N 0 = k k + I 0 ( k ) d k .
X = span { cos ( k u i ) , sin ( k u i ) , ( k k ¯ ) k ¯ cos ( k u i ) , ( k k ¯ ) k ¯ sin ( k u i ) } i = 1 N .
f , g L 2 = k k + f ( k ) g ( k ) d k .
y i = N 0 + F , f i L 2 cos ( x ) F , f N + i L 2 sin ( x ) F , f 2 N + i L 2 x sin ( x ) F , f 3 N + i L 2 x cos ( x ) .
a , b = i 4 N a i b i .
H x = i = 1 4 N σ i U i V i , x ,
H r x = i = 1 r σ i U i V i , x .
f j = i = 1 4 N σ i v i j U i ,
F = i = 1 4 N α i U i + i = 4 N + 1 α i U i ,
F , f j L 2 = i = 1 4 N α i σ i v i j ,
F , H e j H r e j L 2 σ r + 1 F .
F , f i L 2 = j = 1 r α j k k + U j ( k ) f i ( k ) d k , i = 1 , , 4 N ,
H * f , x = f , H x L 2 ,
H * f = [ f , f 1 L 2 f , f 4 N L 2 ] .
H H i j * = l f i , f l L 2 f j , f l L 2 .
U i = j x i ( j ) f j
y i = α 0 + i = 1 r α j C i j cos ( x ) i = 1 r α j S i j sin ( x ) i = 1 r α j C ̃ i j x sin ( x ) i = 1 r α j S ̃ i j x cos ( x ) ,
C i j = k k + U j ( k ) cos ( k u i ) d k , S i j = k k + U j ( k ) sin ( k u i ) d k ,
C ̃ i j = k k + U j ( k ) k k ¯ k ¯ cos ( k u i ) d k ,
S ̃ i j = k k + U j ( k ) k k ¯ k ¯ sin ( k u i ) d k .
y = M ( x ) α ,
M ( x ) = [ 1 M 0 ( x ) 1 ] ,
M 0 ( x ) = C cos ( x ) S sin ( x ) C ̃ x sin ( x ) S ̃ x cos ( x ) ,
min x , α y M ( x ) α 2 ,
α 0 = M ( x 0 ) y .
min x y M ( x ) M ( x ) y 2 ,
max x Q T ( x ) y 2 .
y = M ( x 0 ) α 0 .
min δ x , δ α y + η M ( x 0 + δ x ) ( α 0 + α x ) 2 .
[ δ x δ α ] = J η ,
J = [ M ( x 0 ) α 0 M ( x 0 ) ] .
Q = J Q η [ J ] T ,

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