## Accurately computing the optical pathlength difference for a Michelson interferometer with minimal knowledge of the source spectrum

JOSA A, Vol. 22, Issue 12, pp. 2774-2785 (2005)

http://dx.doi.org/10.1364/JOSAA.22.002774

Acrobat PDF (179 KB)

### 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

**OCIS Codes**

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(120.5060) Instrumentation, measurement, and metrology : Phase modulation

**ToC Category:**

Instrumentation, Measurement, and Metrology

**Citation**

Mark H. Milman, "Accurately computing the optical pathlength difference for a Michelson interferometer with minimal knowledge of the source spectrum," J. Opt. Soc. Am. A **22**, 2774-2785 (2005)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-12-2774

Sort: Year | Journal | Reset

### References

- R. Danner and S. Unwin, Space Interferometry Mission, Taking the Measure of the Universe, Jet Propulsion Laboratory Pub. 400-811, March 1999.
- R. Goullioud and 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. SPIE 5491, 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, and 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. SPIE 4006, 397-406 (2000).
- 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, and G. H. Kaplan, "The Mark III stellar interferometer," Astron. Astrophys. 193, 357-371 (1988).
- J. Davis, P. R. Lawson, A. J. Booth, W. J. Tango, and 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).
- K. A. Benson, D. Mozurkewich, and S. M. Jefferies, "Active optical fringe tracking at the NPOI," in Astronomical Interferometry, R.D.Reasenberg, ed., Proc. SPIE 3350, 493-496 (1998).
- 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, and G. T. van Belle, "The Palomar Testbed Interferometer," Astrophys. J. 510, 505-521 (1999).
- M. M. Colavita and P. L. Wizinowich, "Keck Interferometer: Progress report," in Interferometry in Optical Astronomy, P.J.Lena and A.Quirrenbach, eds., Proc. SPIE 4006, 310-320 (2000).
- A. Quirrenbach, D. Mozurkewich, D. F. Buscher, C. A. Hummel, and J. T. Armstrong, "Phase-referenced visibility averaging in optical long-baseline interferometry," Astron. Astrophys. 286, 1019-1027 (1994).
- J. E. Baldwin, R. C. Boysen, G. C. Cox, C. A. Haniff, J. Rogers, P. J. Warner, D. M. A. Wilson, and C. D. Mackay, "Design and performance of COAST," in Amplitude and Intensity Spatial Interferometry II, J.B.Breckinridge, ed., Proc. SPIE 2200, 118-124. (1994).
- W. A. Traub, "Recent results from the IOTA interferometer," in Astronomical Interferometry, R.D.Reasenberg, ed., Proc. SPIE 3350, 848-855 (1998).
- S. S. C. Chim and G. S. Kino, "Phase measurements using the Mirau correlation microscope," Appl. Opt. 30, 2197-2201 (1991).
- P. Hariharan and M. Roy, "White-light phase-stepping interferometry: measurement of the fractional interference order," J. Mod. Opt. 42, 2357-2360 (1995).
- A. Harasaki, J. Schmit, and J. C. Wyant, "Improved vertical-scanning interferometry," Appl. Opt. 39, 2107-2115 (2000).
- K. G. Larkin, "Effective nonlinear algorithm for envelope detection in white light interferometry," J. Opt. Soc. Am. A 13, 832-843 (1996).
- S. G. Turyshev, "Analytical modeling of the white-light fringe," Appl. Opt. 42, 71-90 (2003).
- G. H. Golub and 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).
- J. E. Greivenkamp, "Generalized data reduction for heterodyne interferometry," Opt. Eng. (Bellingham) 23, 350-352 (1984).
- 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 and E. Wolf, Principles of Optics, 6th ed. (Pergamon1989).
- G. H. Golub and 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 and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations [SIAM (Soc. Ind. Appl. Math.), 1996].
- M. Milman, J. Catanzarite, and S. G. Turyshev, "The effect of wavenumber error on the computation of pathlength delay in white-light interferometry," Appl. Opt. 41, 4884-4890 (2002).
- A. J. Pickles, "A stellar flux library: 1150-25000 A," Astron. Soc. Pac. 110, 863-878 (1998).
- M. Milman, M. Regehr, and 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. SPIE 5491, 1813-1822 (2004).
- A. J. Bronowicki, R. MacDonald, Y. Gursel, R. Goullioud, and T. Neville, "Dual-stage passive vibration isolation for optical interferometer missions," in Interferometry in Space, M.Shao, ed., Proc. SPIE 4852, 753-763 (2003).
- W. J. Tango, "Dispersion in stellar interferometry," Appl. Opt. 29, 516-521 (1990).
- J. Davis, W. J. Tango, and E. D. Thorvaldson, "Dispersion in stellar interferometry: simultaneous optimization for delay tracking and visibility measurements," Appl. Opt. 37, 5132-5136 (1998).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.