OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 38, Iss. 22 — Aug. 1, 1999
  • pp: 4790–4801

Power spectral density analysis of optical substrates for gravitational-wave interferometry

Christopher J. Walsh, Achim J. Leistner, and Bozenko F. Oreb  »View Author Affiliations

Applied Optics, Vol. 38, Issue 22, pp. 4790-4801 (1999)

View Full Text Article

Enhanced HTML    Acrobat PDF (519 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The power spectral density of surface-relief variations on polished optical surfaces across microscopic through to macroscopic spatial scales is calculated from measurements on substrates that are being produced for the Laser Interferometer Gravitational-Wave Observatory (LIGO). These spectra give a guide to the scattering properties of the surface, which in turn critically influence the performance of LIGO. Measurements obtained by use of a full-aperture interferometer and an interference microscope with two different objectives are combined to produce one-dimensional power spectral density representations of the surfaces across spatial frequencies ranging from 0.1 to 8000 cm-1. These measurements from different instruments are in good agreement with an analytic power spectrum that varies as ν-1.5, where ν is the spatial frequency. Some anomalies in the power spectral density spectra can be related to aspects of the polishing process.

© 1999 Optical Society of America

OCIS Codes
(030.5770) Coherence and statistical optics : Roughness
(120.4800) Instrumentation, measurement, and metrology : Optical standards and testing
(120.6660) Instrumentation, measurement, and metrology : Surface measurements, roughness
(220.4840) Optical design and fabrication : Testing
(220.5450) Optical design and fabrication : Polishing
(240.5770) Optics at surfaces : Roughness

Original Manuscript: January 4, 1999
Revised Manuscript: April 29, 1999
Published: August 1, 1999

Christopher J. Walsh, Achim J. Leistner, and Bozenko F. Oreb, "Power spectral density analysis of optical substrates for gravitational-wave interferometry," Appl. Opt. 38, 4790-4801 (1999)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992). [CrossRef] [PubMed]
  2. C. J. Walsh, A. J. Leistner, J. Seckold, B. F. Oreb, D. I. Farrant, “Fabrication and measurement of optics for LIGO,” Appl. Opt. 38, 2870–2879 (1999). [CrossRef]
  3. J. M. Bennett, L. Mattson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).
  4. J. E. Harvey, K. L. Lewotsky, A. Kotha, “Performance predictions of a Schwarzschild imaging microscope for soft x-ray applications,” Opt. Eng. 35, 2423–2436 (1996). [CrossRef]
  5. E. L. Church, “Fractal surface finish,” Appl. Opt. 27, 1518–1526 (1988). [CrossRef] [PubMed]
  6. H. Toebben, G. Ringel, F. Kratz, D.-R. Schmitt, “Use of power spectral density (PSD) to specify optical surfaces,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee, J. Houee, eds., Proc. SPIE2775, 240–250 (1996). [CrossRef]
  7. J. K. Lawson, D. M. Aikens, R. E. English, C. R. Wolfe, “Power spectral density specifications for high-power laser systems,” in Specifications, Production, and Testing of Optical Components and Systems, A. E. Gee, J. Houee, eds., Proc. SPIE2775, 345–356 (1996). [CrossRef]
  8. G. M. Jenkins, D. G. Watts, Spectral Analysis and Its Applications (Holden-Day, San Francisco, Calif., 1969).
  9. E. Spiller, R. A. McCorkle, J. S. Wilczynski, L. Golub, G. Nystrom, P. Z. Takacs, C. Welch, “Normal-incidence soft x-ray telescopes,” Opt. Eng. 30, 1109–1115 (1991). [CrossRef]
  10. V. T. Vorburger, C. J. Evans, V. W. Tsai, J. Fu, E. C. Williams, R. G. Dixson, P. J. Sullivan, T. McWaid, “Finish and figure metrology for soft x-ray optics,” in Proceedings of Japan Society for Precision Engineering U.S.-Japan Workshop on Soft X-ray Optics: Technical Challenges, T. Namioka, H. Kinoshita, K. Ito, eds. (Japan Society for Precision Engineering, Tokyo, 1997), p. 298.
  11. W. Wong, D. Wang, R. T. Benoit, P. Berthol, “A comparison of low scatter PSD derived from multiple wavelength BRDF’s and WYKO profilometer data,” in Optical Scatter: Applications, Measurement, and Theory, J. C. Stover, ed., Proc. SPIE1530, 86–103 (1991).
  12. E. Marx, I. J. Malik, Y. E. Strauser, T. C. Bristow, N. S. Poduje, J. C. Stover, “Round robin determination of power spectral densities of different Si wafer surfaces,” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, J. C. Stover, ed., Proc. SPIE3275, 26–36 (1998). [CrossRef]
  13. R. Weiss, “Spectral analysis of coated optics phase maps,” (Laser Interferometer Gravitational-wave Observatory, California Institute of Technology, Pasadena, Calif., 1997); this report is available from the LIGO on-line document index at http://www.ligo.caltech.edu .
  14. P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, Y. Gilliand, C. H. Freund, A. J. Leistner, J. A. Seckold, C. J. Walsh, “A 300-mm aperture phase shifting fizeau interferometer,” Opt. Eng. (to be published).
  15. vision software, Version 1.8 [Veeco Corporation (formerly WYKO Corporation), East Elvira Road, Tucson, Ariz., 1996). Mention of this product does not constitute endorsement by CSIRO.
  16. J. C. Wyant, C. L. Koliopolous, B. Bhushan, D. Basila, “Development of a three-dimensional noncontact optical profiler,” J. Tribol. 108, 1–8 (1986). The TOPO instrument is manufactured by WYKO Corporation, East Elvira Road, Tucson, Arizona. Mention of this product does not constitute endorsement by CSIRO. [CrossRef]
  17. “Standard practice for estimating the power spectral density function and related finish parameters from surface profile data,” (American Society for Testing and Materials, Pittsburgh, Pa., 1998).
  18. J. M. Elson, J. M. Bennett, “Calculation of the power spectral density from surface-profile data,” Appl. Opt. 34, 201–208 (1995). [CrossRef] [PubMed]
  19. W. H. Press, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).
  20. E. L. Church, P. Z. Takacs, “The optimal estimation of finish parameters,” in Optical Scatter: Applications, Measurements, and Theory, J. C. Stover, ed., Proc. SPIE1530, 71–86 (1991).
  21. W. D. Dixon, F. J. Massey, Introduction to Statistical Analysis (McGraw-Hill, New York, 1957).
  22. J. C. Wyant, K. Creath, “Basic wave-front theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1992), Vol. 11, pp. 1–53.
  23. E. L. Church, P. Z. Takacs, “Use of an optical-profiling instrument for the measurement of figure and finish of optical quality surfaces,” Wear 109, 241–257 (1986). [CrossRef]
  24. Talysurf (Rank Taylor Hobson Pty. Ltd., Leicester, UK). Mention of this product does not constitute endorsement by CSIRO.
  25. K. Creath, “Error sources in phase measuring interferometry,” in International Symposium on Optical Fabrication, Testing, and Surface Evaluation, J. Tsujiuchi, eds., Proc. SPIE1720, 428–435 (1992). [CrossRef]
  26. A. J. Leistner, “Teflon polishers: their manufacture and use,” Appl. Opt. 15, 293–298 (1976).
  27. S. Whitcomb, G. Billingsley, J. Carri, A. Golovitser, D. Jungwirth, W. Kells, H. Yamamoto, B. Bochner, Y. Hefetz, P. Saha, R. Weiss, “Optics development for LIGO,” paper presented at the TAMA Workshop on Gravitational Wave Detection, Saitama, Japan, 11–12 November 1996; also published as . (Laser Interferometry Gravitational-Wave Observatory, California Institute of Technology, Pasadena, Calif., 1996).

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.

CrossCheck Deposited