An overview of power spectral density (PSD) calculations

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5869, Issue , 2005, Pages 1-11

  Youngworth, Richard N ^a   Gallagher, Benjamin B ^a   Stamper, Brian L ^a  

^a BALL AEROSPACE AND TECHNOLOGIES CORP   (United States)

Author keywords

Optical metrology; Optical specifications; Optical surface; Power spectral density

Indexed keywords

OPTICAL METROLOGY; OPTICAL SPECIFICATIONS; OPTICAL SURFACES; POWER SPECTRAL DENSITY;

OPTICS; POLYNOMIALS;

OPTICAL MATERIALS;

EID: 29144458025     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.618478     Document Type: Conference Paper

References (27)

1. E.A. Avallone and T. Baumeister III, Marks' Standard Handbook for Mechanical Engineers, McGraw-Hill, Tenth Edition, New York, 1996.
2. R. Martin, "Noise Power Spectral Density Estimation Based on Optimal Smoothing and Minimum Statistics", IEEE Transactions on Speech and Audio Processing 9(5), pp. 504-512, 2001.
3. J.Merle Elson and Jean M. Bennett, "Calculation of the power spectral density from surface profile data," Applied Optics 34, pp. 201-208, 1995.
4. nd Ed., Washington, 1999.
5. J. M. Bennett, "Surface Roughness" in Encyclopedia of Optical Engineering, Marcel-Dekker, New York, 2003.
6. J. C. Stover, Optical Scattering, McGraw-Hill, New York, 1990.
7. H. Toebben, G. Ringel, F. Kratz, and D. Schmitt, "Use of Power Spectral Density (PSD) to specify optical surfaces," Proc. SPIE 2775, pp. 240-50, 1996.
8. A. Duparré, J. Ferre-Borrull, S. Gliech, G. Notni, J. Steinert, J. Bennett, "Surface characterization techniques for determining the root-mean-square roughness and power spectral densities of optical components," Applied Optics 41, pp. 154-171, 2002.
9. C. L. Vernold and J. E. Harvey, "'Effective' surface PSD for bare hot isostatic pressed (HIP) beryllium mirrors", SPIE 1530, 1991.
10. D. M. Aikens, "The origin and evolution of the optics specifications for the National Ignition Facility" Proc. SPIE 2536, pp. 2-12, 1995.
11. J. K. Lawson, C. R. Wolfe, K. R. Manes, J. B. Trenholme, D. M. Aikens, and R. E. English, Jr., "Specification of optical components using the power spectral density function," Proc. SPIE 2536, pp. 38-50, 1995.
12. D. M. Aikens, C. R. Wolfe, and J. K. Lawson, "The use of Power Spectral Density (PSD) functions in specifying optics for the National Ignition Facility," Proc. SPIE 2576, pp. 281-292, 1995.
13. J.K. Lawson, D.M. Aikens, R.E. English, Jr., and C.R. Wolfe, "Power spectral density specifications for high-power laser systems," Proc. SPIE 2775, pp. 345-356, 1996.
14. E. L. Church and P. Z. Takacs, "Specification of glancing- and normal -incidence x-ray mirrors," Optical Engineering 34, pp. 353-359, 1995.
15. C. J. Walsh, A. J. Leistner, J. Seckold, B. F. Oreb, and D. I. Farrant, "Fabrication and Measurement of Optics fo the Gravitational Wave Observatory," Applied Optics 38, pp. 2870-2879, 1999.
16. C. J. Walsh, A. J. Leistner, and B. F. Oreb, "Power Spectral Density Analysis of Optical Substrates for gravitational-wave interferometry," Applied Optics 38, pp. 4790-4801, 1999.
17. J. W. Goodman, Statistical Optics, John Wiley & Sons, Inc, New York, 1985.
18. E. C. Titchmarsh, "A Contribution to the Theory of Fourier Transforms," Proc. Lond. Math. Soc. 23, 279 (1924).
19. rd Ed., New York, 2000.
20. *(v) is the complex conjugate of U(v).
21. J. Hayes, "Fast Fourier Transforms and Their Applications," Ch. 2 in Applied Optics and Optical Engineering, Vol. 11, Academic Press, New York, 1992.
22. Note that the argument for a 2-dimensional PSD also can be extended for volumes and thus 3-dimensional PSD functions. These would be useful in applications like metrology and certification of transmissive materials.
23. The integrated PSD can also be calculated by converting the spectrum to polar coordinates and summing for different v around 2π for the azimuth angle. Note that this method adds a factor proportional to π into the integrated PSD.
24. R. E. Parks, "Optical Specifications and Tolerances for Large Optics," Proc. SPIE 406, pp 98-105, 1983.
25. J. E. Harvey and A. Kotha, "Scattering effects from residual optical fabrication errors", Proc. SPIE 2576, pp. 155-174 (1995).
26. R. N. Youngworth and B. D. Stone, "Simple estimates for the effects of mid-spatial-frequency surface errors on image quality", Applied Optics 39(13), 2198-2209 (2000).
27. C. Progler and A. Wong, "Zernike coefficients: are they really enough?", Proc. SPIE 4000, pp. 40-52 (2000).