## Simple Estimates for the Effects of Mid-spatial-Frequency Surface Errors on Image Quality

Applied Optics, Vol. 39, Issue 13, pp. 2198-2209 (2000)

http://dx.doi.org/10.1364/AO.39.002198

Acrobat PDF (2413 KB)

### Abstract

Mid-spatial-frequency surface errors can be introduced by various manufacturing processes. These errors bridge the gap between traditional figure and finish errors. Although the effects of mid-spatial-frequency errors on the imagery of an optical system can be modeled with a ray-based approach, simply tracing rays provides little insight. We present an alternative method that treats surface errors as perturbations to the nominal surface profile. This approach, combined with standard statistical methods, allows one to make simple back-of-the-envelope predictions of the effects of mid-spatial-frequency errors for various measures of optical performance. Two examples illustrating the effectiveness of this approach are presented.

© 2000 Optical Society of America

**OCIS Codes**

(080.2720) Geometric optics : Mathematical methods (general)

(080.3630) Geometric optics : Lenses

(110.3000) Imaging systems : Image quality assessment

(220.3630) Optical design and fabrication : Lenses

(240.6700) Optics at surfaces : Surfaces

**Citation**

Richard N. Youngworth and Bryan D. Stone, "Simple Estimates for the Effects of Mid-spatial-Frequency Surface Errors on Image Quality," Appl. Opt. **39**, 2198-2209 (2000)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-13-2198

Sort: Year | Journal | Reset

### References

- A. Tabenkin, “Surface finish: a machinist’s tool. A design necessity,” Modern Machine Shop, 71 (March 1999), pp. 80–88.
- Such a categorization of errors appears, for example, in W. B. Wetherell, “Effects of mirror surface ripple on image quality,” in International Conference on Advanced Technology Optical Telescopes, G. R. Burbidge and L. D. Barr, eds., Proc. SPIE 332, 335–351 (1982).
- For example, this terminology is used in Ref. 1 and in R. S. Hahn and R. P. Lindsay, “Principles of grinding … part V: grinding chatter,” Machinery Magazine (November 1971), pp. 48–53.
- J. K. Lawson, R. C. Wolfe, K. R. Manes, J. B. Trenholme, D. M. Aiken, and R. E. English, “Specification of optical components using the power spectral density function,” in Optical Manufacturing and Testing, V. J. Doherty and H. P. Stahl, eds., Proc. SPIE 2536, 38–50 (1995).
- 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,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE 2576, 281–292 (1995).
- J. E. Harvey and A. Kotha, “Scattering effects from residual optical fabrication errors,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE 2576, 155–174 (1995).
- J. E. Harvey and C. L. Vernold, “Transfer function characterization of scattering surfaces: revisited,” in Scattering and Surface Roughness, Z.-H. Gu and A. A. Maradudin, eds., Proc. SPIE 3141, 113–127 (1997).
- C. L. Vernold and J. E. Harvey, “Comparison of Harvey–Shack scatter theory with experimental measurements,” in Scattering and Surface Roughness, Z.-H. Gu and A. A. Maradudin, eds., Proc. SPIE 3141, 128–138 (1997).
- J. E. Harvey and C. L. Vernold, “Modifying the Harvey–Shack surface scatter theory,” in Scattering and Surface Roughness II, Z.-H. Gu and A. A. Maradudin, eds., Proc. SPIE 3426, 326–332 (1998).
- A description of Fermat’s principle can be found, for example, in E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), Sec. 4.2.4.
- B. D. Stone, “Perturbations of optical systems,” J. Opt. Soc. Am. A 14, 2837–2849 (1997).
- M. P. Rimmer, “Analysis of perturbed lens systems,” Appl. Opt. 9, 533–537 (1970).
- H. H. Hopkins and H. J. Tiziani, “A theoretical and experimental study of lens centring errors and their influence on optical image quality,” Brit. J. Appl. Phys. 17, 33–54 (1966).
- A discussion of the wave aberration function can be found in W. T. Welford, Aberrations of Optical Systems (Adam Hilger, New York, 1991), Chap. 7.
- R. J. Noll, “Effect of mid- and high-spatial frequencies on optical performance,” Opt. Eng. 18, 137–142 (1979).
- J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Sec. 8.3.
- See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 6.
- The expression for the PSF is treated in more detail in Refs. 15 and 16.
- The starting lens (with only spherical surfaces) is the superachromat documented in Fig. 14 of R. D. Sigler, “Glass selection for airspaced apochromats using the Buchdahl dispersion equation,” Appl. Opt. 25, 4311–4320 (1986). This lens is also described in W. J. Smith, Modern Lens Design: A Resource Manual (McGraw-Hill, New York, 1992), Fig. 10.5. For this example, aspheres were added to two of the surfaces and the lens reoptimized. During optimization, we only varied the aspheric coefficients. The figure of merit used for optimization was the mean-square wave-front error at the helium d-line (λ = 587.6 nm).
- See, for example, M. Laikin, Lens Design (Marcel Dekker, New York, 1995), Sec. 1.3.
- For a summary of this procedure, see G. H. Spencer and M. V. R. K. Murty, “General ray-tracing procedure,” J. Opt. Soc. Am. 52, 672–678 (1962).
- The lens is taken from T. P. Fjeldsted, “Four element infrared objective lens,” U.S. patent 4,380,363 (19 April 1983). This lens is also described in W. J. Smith, Modern Lens Design: A Resource Manual (McGraw-Hill, New York, 1992), Fig. 21.9.
- The phase maps used here are obtained with a commercial interferometer. They were spatial filtered to eliminate low-spatial-frequency errors and then scaled to the same rms value.
- OSLO is a registered trademark of Sinclair Optics, Inc., 6780 Palmyra Road, Fairport, N.Y. 14450.

## 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.