Abstract

Optical designs often specify both surface form and centering (tilt and lateral displacement) tolerances on aspheric surfaces. In contrast to spherical surfaces, form and centering errors are coupled for aspheric surfaces. Current standards do not specify how to interpret such tolerances, and in particular they do not define the position of an aspheric surface that has form errors. The straightforward definition that uses the best-fit surface position that minimizes rms error has subtle problems. The best-fit surface position for aspheric surfaces is influenced by power error and can be highly sensitive to surface form errors when the derivative of aspheric departure is small. We analyze the conditions under which form and centering tolerances may be considered compatible when the best-fit surface-position definition is used. We propose alternative definitions of surface position that do not suffer from the same problems and consider their consequences for optical design and metrology.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. International Organization for Standardization , “Optics and optical instruments—preparation of drawings for optical elements and systems,” Standard ISO 10110-1:1996(E) (International Organization for Standardization, Geneva, 1996).
  2. R. H. Wilson, R. C. Brost, D. R. Strip, R. J. Sudol, R. N. Youngworth, P. O. McLaughlin, “Considerations for metrology of aspheric optical components,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 133–134.
  3. R. E. Hopkins, Mil-Hdbk 141, Military Standardization Handbook, Optical Design (U.S. Department of Defense, Washington, D.C., 1962), Sect. 5.5.2.
  4. G. P. Adams, “Tolerancing of optical systems,” Ph.D. dissertation (University of London, London, 1987).
  5. ISO Standard 10110 uses the British spelling “centring.”
  6. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1997), App. VII.
  7. Ref. 6, Chap. 9.
  8. H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, 1970, Dover, New York, 1993), Sect. 40.
  9. D. P. Feder, “Automatic optical design,” Appl. Opt. 2, 1209–1226 (1963).
    [CrossRef]
  10. Matsushita Electrical Industrial Company , “Ultrahigh accurate 3-D profilometer—UA3P for Windows,” operating instructions (Matsushita Electric Industrial Co., Ltd., Osaka, Japan, 1998).
  11. International Organization for Standardization , “Technical drawings—geometrical tolerancing—tolerancing of form, orientation, location and run-out—generalities, definitions, symbols, indications on drawings,” Standard ISO 1101:1983 (International Organization for Standardization, Geneva, 1983).
  12. American Society of Mechanical Engineers , “Dimensioning and Tolerancing,” Standard ANSI Y14.5M-1982 (American Society of Mechanical Engineers, New York, 1982).
  13. A. A. G. Requicha, “Toward a theory of geometric tolerancing,” Int. J. Robotics Res. 2, 45–60 (1983).
    [CrossRef]
  14. A. A. G. Requicha, “Representation of tolerances in solid modeling: issues and alternative approaches,” in Solid Modeling by Computers: From Theory to Applications, M. S. Pickett, J. W. Boyse, eds. (Plenum, New York, 1984), pp. 3–22.
    [CrossRef]
  15. D. Heshmaty-Manesh, G. Y. Haig, “Lens tolerancing by desk-top computer,” Appl. Opt. 25, 1268–1270 (1986).
    [CrossRef] [PubMed]
  16. Optical Research Associates , Code V Reference Manual (Optical Research Associates, Pasadena, California, 1996), Vol. 2, Chap. 6.
  17. Sinclair Optics , OSLO Version 5 Optics Reference (Sinclair Optics, Fairport, New York, 1996), Chap. 8.
  18. Focus SoftwareZemax Optical Design Program, user’s guide, V. 10.0 (Focus Software, San Diego, Calif., 2001), Chap. 15.

1986 (1)

1983 (1)

A. A. G. Requicha, “Toward a theory of geometric tolerancing,” Int. J. Robotics Res. 2, 45–60 (1983).
[CrossRef]

1963 (1)

Adams, G. P.

G. P. Adams, “Tolerancing of optical systems,” Ph.D. dissertation (University of London, London, 1987).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1997), App. VII.

Brost, R. C.

R. H. Wilson, R. C. Brost, D. R. Strip, R. J. Sudol, R. N. Youngworth, P. O. McLaughlin, “Considerations for metrology of aspheric optical components,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 133–134.

Buchdahl, H. A.

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, 1970, Dover, New York, 1993), Sect. 40.

Feder, D. P.

Haig, G. Y.

Heshmaty-Manesh, D.

Hopkins, R. E.

R. E. Hopkins, Mil-Hdbk 141, Military Standardization Handbook, Optical Design (U.S. Department of Defense, Washington, D.C., 1962), Sect. 5.5.2.

McLaughlin, P. O.

R. H. Wilson, R. C. Brost, D. R. Strip, R. J. Sudol, R. N. Youngworth, P. O. McLaughlin, “Considerations for metrology of aspheric optical components,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 133–134.

Requicha, A. A. G.

A. A. G. Requicha, “Toward a theory of geometric tolerancing,” Int. J. Robotics Res. 2, 45–60 (1983).
[CrossRef]

A. A. G. Requicha, “Representation of tolerances in solid modeling: issues and alternative approaches,” in Solid Modeling by Computers: From Theory to Applications, M. S. Pickett, J. W. Boyse, eds. (Plenum, New York, 1984), pp. 3–22.
[CrossRef]

Strip, D. R.

R. H. Wilson, R. C. Brost, D. R. Strip, R. J. Sudol, R. N. Youngworth, P. O. McLaughlin, “Considerations for metrology of aspheric optical components,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 133–134.

Sudol, R. J.

R. H. Wilson, R. C. Brost, D. R. Strip, R. J. Sudol, R. N. Youngworth, P. O. McLaughlin, “Considerations for metrology of aspheric optical components,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 133–134.

Wilson, R. H.

R. H. Wilson, R. C. Brost, D. R. Strip, R. J. Sudol, R. N. Youngworth, P. O. McLaughlin, “Considerations for metrology of aspheric optical components,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 133–134.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1997), App. VII.

Youngworth, R. N.

R. H. Wilson, R. C. Brost, D. R. Strip, R. J. Sudol, R. N. Youngworth, P. O. McLaughlin, “Considerations for metrology of aspheric optical components,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 133–134.

Appl. Opt. (2)

Int. J. Robotics Res. (1)

A. A. G. Requicha, “Toward a theory of geometric tolerancing,” Int. J. Robotics Res. 2, 45–60 (1983).
[CrossRef]

Other (15)

A. A. G. Requicha, “Representation of tolerances in solid modeling: issues and alternative approaches,” in Solid Modeling by Computers: From Theory to Applications, M. S. Pickett, J. W. Boyse, eds. (Plenum, New York, 1984), pp. 3–22.
[CrossRef]

Optical Research Associates , Code V Reference Manual (Optical Research Associates, Pasadena, California, 1996), Vol. 2, Chap. 6.

Sinclair Optics , OSLO Version 5 Optics Reference (Sinclair Optics, Fairport, New York, 1996), Chap. 8.

Focus SoftwareZemax Optical Design Program, user’s guide, V. 10.0 (Focus Software, San Diego, Calif., 2001), Chap. 15.

International Organization for Standardization , “Optics and optical instruments—preparation of drawings for optical elements and systems,” Standard ISO 10110-1:1996(E) (International Organization for Standardization, Geneva, 1996).

R. H. Wilson, R. C. Brost, D. R. Strip, R. J. Sudol, R. N. Youngworth, P. O. McLaughlin, “Considerations for metrology of aspheric optical components,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 133–134.

R. E. Hopkins, Mil-Hdbk 141, Military Standardization Handbook, Optical Design (U.S. Department of Defense, Washington, D.C., 1962), Sect. 5.5.2.

G. P. Adams, “Tolerancing of optical systems,” Ph.D. dissertation (University of London, London, 1987).

ISO Standard 10110 uses the British spelling “centring.”

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1997), App. VII.

Ref. 6, Chap. 9.

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, 1970, Dover, New York, 1993), Sect. 40.

Matsushita Electrical Industrial Company , “Ultrahigh accurate 3-D profilometer—UA3P for Windows,” operating instructions (Matsushita Electric Industrial Co., Ltd., Osaka, Japan, 1998).

International Organization for Standardization , “Technical drawings—geometrical tolerancing—tolerancing of form, orientation, location and run-out—generalities, definitions, symbols, indications on drawings,” Standard ISO 1101:1983 (International Organization for Standardization, Geneva, 1983).

American Society of Mechanical Engineers , “Dimensioning and Tolerancing,” Standard ANSI Y14.5M-1982 (American Society of Mechanical Engineers, New York, 1982).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

(a) Aspheric optical surface and measured surface with sagittal error and (b) best-fit surface position. This example also demonstrates that multiple best-fit positions are possible. A second best-fit surface position exists where the surface is tilted up instead of down.

Fig. 2
Fig. 2

Lateral displacement of the best-fit surface position as a function of sagittal error on an example surface, when c is held constant and is not fitted (solid line) and when c is fitted as well (dotted line).

Fig. 3
Fig. 3

Aspheric surface and measured points that indicate combined tilt and lateral displacement.

Fig. 4
Fig. 4

Close-up of measured point p near the aspheric surface.

Fig. 5
Fig. 5

Trade-off between surface position and form error for a surface with a small derivative of aspheric departure (top) and a larger derivative of aspheric departure (bottom). Solid curves, rms error; dashed curves, P-V error.

Fig. 6
Fig. 6

Example of a telecommunications lens. The left aspheric surface has a centering tolerance of 4 min of tilt relative to the planar right surface.

Fig. 7
Fig. 7

Trade-off between surface position and form error of an example lens. The shaded region indicates surface positions and form errors that satisfy the tolerance specification. Point a is the best-fit position to minimize rms error, b minimizes rms error subject to the centering tolerance, and c minimizes tilt subject to the form tolerance. Solid curve, rms error; dashed curve, P-V error.

Tables (1)

Tables Icon

Table 1 Effect of Coma on Best-Fit Surface Position as a Function of Derivative of Aspheric Departure A

Equations (11)

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

z=cr21+1-1+κc2r21/2+a4r4+a6r6+,
g=Rθ,
gg2+f2=ef.
A=dAds=fg
f=Ag.
gg2+g2A2=eAg, g=eA1+A2.
g=eA.
g=10eA=100.0680.05=13.6 μm,
θ=gR=0.01362.5=0.00544 rad,
g=eA=0.020.05=0.4 μm
θ=gR=0.00042.5=0.00016 rad,

Metrics