Abstract

The accuracy of interferometric measurements made with a nonnull configuration is degraded by test-dependent aberrations. Calibration of the data can be done with reverse optimization methods. An iterative reverse optimization process that improves efficiency and eliminates sensitive merit function weighting issues is described. The process is shown to calibrate a nonnull interferometric measurement of a wave front with more than 200 waves of departure to an accuracy of 0.16 waves peak to valley and 0.02 waves rms.

© 2004 Optical Society of America

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References

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  1. A. E. Lowman, J. E. Greivenkamp, “Interferometer errors due to the presence of fringes,” Appl. Opt. 35, 6826–6828 (1996).
    [Crossref] [PubMed]
  2. C. J. Evans, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” Int. Inst. Prod. Res. Ann. 42, 577–580 (1993).
  3. H. J. Jeong, G. N. Lawrence, “Simultaneous determination of misalignment and mirror surface figure error of a three mirror off-axis telescope by end-to-end measurements and reverse optimization: numerical analysis and simulation,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 341–353 (1988).
    [Crossref]
  4. I. Powell, “Employment of reverse optimization to relax manufacturing tolerances imposed on system constructional parameters associated with complex optical systems,” Appl. Opt. 39, 2174–2183 (2000).
    [Crossref]
  5. A. E. Lowman, J. E. Greivenkamp, “Interferometer induced wavefront errors when testing in a non-null configuration,” Interferometry VI: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. O. Jueptner, eds., Proc. SPIE2004, 173–181 (1993).
    [Crossref]
  6. R. Jozwicki, “Influence of aberrations of Fizeau interferometer elements on measurement errors,” Appl. Opt. 30, 3126–3132 (1991).
    [Crossref]
  7. J. M. Geary, “Retrace error: a case study,” in Interferometry: Surface Characterization and Testing, K. Creath, J. Greivenkamp, eds., Proc. SPIE1776, 98–105 (1992).
    [Crossref]
  8. R. Gappinger, G. A. Williby, J. E. Greivenkamp, J. M. Sasian, “Design of afocal components for optical metrology systems,” in Optical Fabrication and Testing, Vol. 42 of Trends OSA In Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 115–117.
  9. J. E. Greivenkamp, R. O. Gappinger, “Design of a nonnull interferometer for aspheric wave fronts,” Appl. Opt. 43, 5143–5151 (2004).
    [Crossref] [PubMed]
  10. R. R. Shannon, The Art and Science of Optical Design (Cambridge U. Press, New York, 1997).
    [Crossref]
  11. A. E. Lowman, “Calibration of a non-null interferometer for aspheric testing,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1995).
  12. R. R. Shannon, “Overview of conformal optics,” in Window and Dome Technologies and Materials VI, R. W. Tustisoni, ed., Proc. SPIE3705, 180–188 (1999).
    [Crossref]
  13. J. E. Greivenkamp, “Sub-Nyquist interferometery,” Appl. Opt. 26, 5245–5258 (1987).
    [Crossref] [PubMed]

2004 (1)

2000 (1)

1996 (1)

1993 (1)

C. J. Evans, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” Int. Inst. Prod. Res. Ann. 42, 577–580 (1993).

1991 (1)

1987 (1)

Evans, C. J.

C. J. Evans, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” Int. Inst. Prod. Res. Ann. 42, 577–580 (1993).

Gappinger, R.

R. Gappinger, G. A. Williby, J. E. Greivenkamp, J. M. Sasian, “Design of afocal components for optical metrology systems,” in Optical Fabrication and Testing, Vol. 42 of Trends OSA In Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 115–117.

Gappinger, R. O.

Geary, J. M.

J. M. Geary, “Retrace error: a case study,” in Interferometry: Surface Characterization and Testing, K. Creath, J. Greivenkamp, eds., Proc. SPIE1776, 98–105 (1992).
[Crossref]

Greivenkamp, J. E.

J. E. Greivenkamp, R. O. Gappinger, “Design of a nonnull interferometer for aspheric wave fronts,” Appl. Opt. 43, 5143–5151 (2004).
[Crossref] [PubMed]

A. E. Lowman, J. E. Greivenkamp, “Interferometer errors due to the presence of fringes,” Appl. Opt. 35, 6826–6828 (1996).
[Crossref] [PubMed]

J. E. Greivenkamp, “Sub-Nyquist interferometery,” Appl. Opt. 26, 5245–5258 (1987).
[Crossref] [PubMed]

R. Gappinger, G. A. Williby, J. E. Greivenkamp, J. M. Sasian, “Design of afocal components for optical metrology systems,” in Optical Fabrication and Testing, Vol. 42 of Trends OSA In Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 115–117.

A. E. Lowman, J. E. Greivenkamp, “Interferometer induced wavefront errors when testing in a non-null configuration,” Interferometry VI: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. O. Jueptner, eds., Proc. SPIE2004, 173–181 (1993).
[Crossref]

Jeong, H. J.

H. J. Jeong, G. N. Lawrence, “Simultaneous determination of misalignment and mirror surface figure error of a three mirror off-axis telescope by end-to-end measurements and reverse optimization: numerical analysis and simulation,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 341–353 (1988).
[Crossref]

Jozwicki, R.

Lawrence, G. N.

H. J. Jeong, G. N. Lawrence, “Simultaneous determination of misalignment and mirror surface figure error of a three mirror off-axis telescope by end-to-end measurements and reverse optimization: numerical analysis and simulation,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 341–353 (1988).
[Crossref]

Lowman, A. E.

A. E. Lowman, J. E. Greivenkamp, “Interferometer errors due to the presence of fringes,” Appl. Opt. 35, 6826–6828 (1996).
[Crossref] [PubMed]

A. E. Lowman, J. E. Greivenkamp, “Interferometer induced wavefront errors when testing in a non-null configuration,” Interferometry VI: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. O. Jueptner, eds., Proc. SPIE2004, 173–181 (1993).
[Crossref]

A. E. Lowman, “Calibration of a non-null interferometer for aspheric testing,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1995).

Powell, I.

Sasian, J. M.

R. Gappinger, G. A. Williby, J. E. Greivenkamp, J. M. Sasian, “Design of afocal components for optical metrology systems,” in Optical Fabrication and Testing, Vol. 42 of Trends OSA In Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 115–117.

Shannon, R. R.

R. R. Shannon, The Art and Science of Optical Design (Cambridge U. Press, New York, 1997).
[Crossref]

R. R. Shannon, “Overview of conformal optics,” in Window and Dome Technologies and Materials VI, R. W. Tustisoni, ed., Proc. SPIE3705, 180–188 (1999).
[Crossref]

Williby, G. A.

R. Gappinger, G. A. Williby, J. E. Greivenkamp, J. M. Sasian, “Design of afocal components for optical metrology systems,” in Optical Fabrication and Testing, Vol. 42 of Trends OSA In Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 115–117.

Appl. Opt. (5)

Int. Inst. Prod. Res. Ann. (1)

C. J. Evans, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” Int. Inst. Prod. Res. Ann. 42, 577–580 (1993).

Other (7)

H. J. Jeong, G. N. Lawrence, “Simultaneous determination of misalignment and mirror surface figure error of a three mirror off-axis telescope by end-to-end measurements and reverse optimization: numerical analysis and simulation,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 341–353 (1988).
[Crossref]

A. E. Lowman, J. E. Greivenkamp, “Interferometer induced wavefront errors when testing in a non-null configuration,” Interferometry VI: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. O. Jueptner, eds., Proc. SPIE2004, 173–181 (1993).
[Crossref]

R. R. Shannon, The Art and Science of Optical Design (Cambridge U. Press, New York, 1997).
[Crossref]

A. E. Lowman, “Calibration of a non-null interferometer for aspheric testing,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1995).

R. R. Shannon, “Overview of conformal optics,” in Window and Dome Technologies and Materials VI, R. W. Tustisoni, ed., Proc. SPIE3705, 180–188 (1999).
[Crossref]

J. M. Geary, “Retrace error: a case study,” in Interferometry: Surface Characterization and Testing, K. Creath, J. Greivenkamp, eds., Proc. SPIE1776, 98–105 (1992).
[Crossref]

R. Gappinger, G. A. Williby, J. E. Greivenkamp, J. M. Sasian, “Design of afocal components for optical metrology systems,” in Optical Fabrication and Testing, Vol. 42 of Trends OSA In Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 115–117.

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Figures (6)

Fig. 1
Fig. 1

Physical path models for (a) a 25-mm aperture system and (b) a 150-mm aperture system. PZTs, piezoelectric transmitters.

Fig. 2
Fig. 2

Optical path models for (a) a 25-mm system, (b) a 150-mm system reference arm, and (c) a 150-mm system test arm.

Fig. 3
Fig. 3

Transmitted wave front for a plano–convex lens.

Fig. 4
Fig. 4

Calibration test flow chart. Iter Rev Opt, Iterative Reverse Optimization.

Fig. 5
Fig. 5

Difference wave front for a plano–convex lens.

Fig. 6
Fig. 6

Induced aberration removed by reverse optimization.

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