Abstract

We show an interferometric method for measuring phase change with known uncertainty. Because this measurement uses the backreflection from a sample, the height is intrinsically removed, and only the phase change is measured. The uncertainty in the phase change measurement is ±3.8° and is dominated by the background subtraction method. We also investigate the effect of the phase change on the interferometric radius measurement. The theoretical worst-case error in the interferometric radius measurement due to the phase change is 30  nm.

© 2007 Optical Society of America

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References

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  1. T. L. Schmitz, A. D. Davies, and C. J. Evans, "Uncertainties in interferometric measurements of radius of curvature," in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE 4451, 432-447 (2001).
  2. T. McWaid, T. Vorburger, J. F. Song, and D. Chandler-Horowitz, "The effects of thin films on interferometric step height measurements," in Interferometry: Surface Characterization and Testing, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 2-13 (1992).
  3. M. Park and S. Kim, "Compensation of phase change on reflection in white-light interferometry for step height measurement," Opt. Lett. 26, 420-422 (2001).
    [CrossRef]
  4. D. W. Lynch and W. R. Hunter, "Metals," in Handbook of Optical Constants of Solids, E. Palik, ed. (Academic, 1998), pp. 274-368.
  5. G. Hass and L. Hadley, "Optical properties of metals," in American Institute of Physics Handbook, 3rd ed., B. H. Billings and D. E. Gray, eds., (McGraw-Hill, 1982), pp. 6.118-6.160.
  6. J. H. Weaver and H. P. R. Frederikse, "Optical properties of selected elements," in CRC Handbook of Chemistry and Physics, 84th ed., D. R. Lide, ed. (CRC Press, 2003), pp. 12.116-12.140.
  7. T. Doi, K. Toyoda, and Y. Tanimura, "Effects of phase changes on reflection and their wavelength dependence in optical profilometry," Appl. Opt. 36, 7157-7161 (1997).
    [CrossRef]
  8. J. M. Bennett, "Precise method for measuring the absolute phase change on reflection," J. Opt. Soc. Am. 54, 612-624 (1964).
    [CrossRef]
  9. J. E. Breivenkamp and J. H. Bruning, "Phase shifting interferometry," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 501-598.
  10. W. Lichten, "Precise wavelength measurements and optical phase shifts. I. General theory," J. Opt. Soc. Am. A 2, 1869-1876 (1985).
    [CrossRef]
  11. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  12. R. Liang, J. K. Erwin, and M. Mansuripur, "Measurement of the relative optical phase between amorphous and crystalline regions of the phase-change media of optical recording," Appl. Opt. 39, 2167-2173 (2000).
    [CrossRef]
  13. A. Harasaki, J. Schmit, and J. C. Wyant, "Offset of coherent envelope position due to phase change on reflection," Appl. Opt. 40, 2102-2106 (2001).
    [CrossRef]
  14. L. Ward, The Optical Constants of Bulk Materials and Films (Hilger, 1988).
  15. "Five Schott glass types," Melles Griot, 55 Science Parkway, Rochester, New York 14620, USA, http://www.mellesgriot.com/pdf/CatalogX/X_04_8-10.pdf (2006).
  16. Veeco Metrology Inc., Optical Profilers and Laser Interferometers, 2650 East Elvira Road Tucson, Ariz. 85706-7123, USA (personal communication, 2006).
  17. P. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 3rd ed. (McGraw-Hill, 2002).
  18. L. A. Selberg, "Radius measurement by interferometry," Opt. Eng. 31, 1961-1966 (1992).
    [CrossRef]
  19. C. J. Evans and R. N. Kestner, "Test optics error removal," Appl. Opt. 35, 1015-1021 (1996).
    [CrossRef] [PubMed]

2001 (3)

2000 (1)

1997 (1)

1996 (1)

1992 (2)

T. McWaid, T. Vorburger, J. F. Song, and D. Chandler-Horowitz, "The effects of thin films on interferometric step height measurements," in Interferometry: Surface Characterization and Testing, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 2-13 (1992).

L. A. Selberg, "Radius measurement by interferometry," Opt. Eng. 31, 1961-1966 (1992).
[CrossRef]

1985 (1)

1964 (1)

Bennett, J. M.

Bevington, P.

P. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 3rd ed. (McGraw-Hill, 2002).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Breivenkamp, J. E.

J. E. Breivenkamp and J. H. Bruning, "Phase shifting interferometry," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 501-598.

Bruning, J. H.

J. E. Breivenkamp and J. H. Bruning, "Phase shifting interferometry," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 501-598.

Chandler-Horowitz, D.

T. McWaid, T. Vorburger, J. F. Song, and D. Chandler-Horowitz, "The effects of thin films on interferometric step height measurements," in Interferometry: Surface Characterization and Testing, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 2-13 (1992).

Davies, A. D.

T. L. Schmitz, A. D. Davies, and C. J. Evans, "Uncertainties in interferometric measurements of radius of curvature," in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE 4451, 432-447 (2001).

Doi, T.

Erwin, J. K.

Evans, C. J.

T. L. Schmitz, A. D. Davies, and C. J. Evans, "Uncertainties in interferometric measurements of radius of curvature," in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE 4451, 432-447 (2001).

C. J. Evans and R. N. Kestner, "Test optics error removal," Appl. Opt. 35, 1015-1021 (1996).
[CrossRef] [PubMed]

Frederikse, H. P. R.

J. H. Weaver and H. P. R. Frederikse, "Optical properties of selected elements," in CRC Handbook of Chemistry and Physics, 84th ed., D. R. Lide, ed. (CRC Press, 2003), pp. 12.116-12.140.

Hadley, L.

G. Hass and L. Hadley, "Optical properties of metals," in American Institute of Physics Handbook, 3rd ed., B. H. Billings and D. E. Gray, eds., (McGraw-Hill, 1982), pp. 6.118-6.160.

Harasaki, A.

Hass, G.

G. Hass and L. Hadley, "Optical properties of metals," in American Institute of Physics Handbook, 3rd ed., B. H. Billings and D. E. Gray, eds., (McGraw-Hill, 1982), pp. 6.118-6.160.

Hunter, W. R.

D. W. Lynch and W. R. Hunter, "Metals," in Handbook of Optical Constants of Solids, E. Palik, ed. (Academic, 1998), pp. 274-368.

Kestner, R. N.

Kim, S.

Liang, R.

Lichten, W.

Lynch, D. W.

D. W. Lynch and W. R. Hunter, "Metals," in Handbook of Optical Constants of Solids, E. Palik, ed. (Academic, 1998), pp. 274-368.

Mansuripur, M.

McWaid, T.

T. McWaid, T. Vorburger, J. F. Song, and D. Chandler-Horowitz, "The effects of thin films on interferometric step height measurements," in Interferometry: Surface Characterization and Testing, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 2-13 (1992).

Park, M.

Robinson, D. K.

P. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 3rd ed. (McGraw-Hill, 2002).

Schmit, J.

Schmitz, T. L.

T. L. Schmitz, A. D. Davies, and C. J. Evans, "Uncertainties in interferometric measurements of radius of curvature," in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE 4451, 432-447 (2001).

Selberg, L. A.

L. A. Selberg, "Radius measurement by interferometry," Opt. Eng. 31, 1961-1966 (1992).
[CrossRef]

Song, J. F.

T. McWaid, T. Vorburger, J. F. Song, and D. Chandler-Horowitz, "The effects of thin films on interferometric step height measurements," in Interferometry: Surface Characterization and Testing, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 2-13 (1992).

Tanimura, Y.

Toyoda, K.

Vorburger, T.

T. McWaid, T. Vorburger, J. F. Song, and D. Chandler-Horowitz, "The effects of thin films on interferometric step height measurements," in Interferometry: Surface Characterization and Testing, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 2-13 (1992).

Ward, L.

L. Ward, The Optical Constants of Bulk Materials and Films (Hilger, 1988).

Weaver, J. H.

J. H. Weaver and H. P. R. Frederikse, "Optical properties of selected elements," in CRC Handbook of Chemistry and Physics, 84th ed., D. R. Lide, ed. (CRC Press, 2003), pp. 12.116-12.140.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Wyant, J. C.

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

L. A. Selberg, "Radius measurement by interferometry," Opt. Eng. 31, 1961-1966 (1992).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

T. McWaid, T. Vorburger, J. F. Song, and D. Chandler-Horowitz, "The effects of thin films on interferometric step height measurements," in Interferometry: Surface Characterization and Testing, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 2-13 (1992).

Other (10)

T. L. Schmitz, A. D. Davies, and C. J. Evans, "Uncertainties in interferometric measurements of radius of curvature," in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE 4451, 432-447 (2001).

J. E. Breivenkamp and J. H. Bruning, "Phase shifting interferometry," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 501-598.

D. W. Lynch and W. R. Hunter, "Metals," in Handbook of Optical Constants of Solids, E. Palik, ed. (Academic, 1998), pp. 274-368.

G. Hass and L. Hadley, "Optical properties of metals," in American Institute of Physics Handbook, 3rd ed., B. H. Billings and D. E. Gray, eds., (McGraw-Hill, 1982), pp. 6.118-6.160.

J. H. Weaver and H. P. R. Frederikse, "Optical properties of selected elements," in CRC Handbook of Chemistry and Physics, 84th ed., D. R. Lide, ed. (CRC Press, 2003), pp. 12.116-12.140.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

L. Ward, The Optical Constants of Bulk Materials and Films (Hilger, 1988).

"Five Schott glass types," Melles Griot, 55 Science Parkway, Rochester, New York 14620, USA, http://www.mellesgriot.com/pdf/CatalogX/X_04_8-10.pdf (2006).

Veeco Metrology Inc., Optical Profilers and Laser Interferometers, 2650 East Elvira Road Tucson, Ariz. 85706-7123, USA (personal communication, 2006).

P. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 3rd ed. (McGraw-Hill, 2002).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the interferometric phase change measurement where step height is intrinsically removed from measurement result.

Fig. 2
Fig. 2

Phase change, Eq. (1), at glass–gold interface and air–gold interface for varying incident angles.

Fig. 3
Fig. 3

Samples with the deposited metal.

Fig. 4
Fig. 4

PSI measurement of the normal angle of incidence postbackground subtraction for a glass to gold sample. (a) Full measurement showing the glass–gold and glass–air interfaces and (b) cross section where the phase change (in height) is the average distance between the glass–gold and the glass–air interfaces.

Fig. 5
Fig. 5

Schematic of the interferometric radius measurement. At confocal, all rays are incident at 90° and at cat's-eye, the incident angle of the rays varies.

Fig. 6
Fig. 6

Theoretical height error due to phase change at the air–gold interface for TM mode showing the fit parameters for NA = 0.7.

Fig. 7
Fig. 7

Apparent height error maps due to phase change at varying NA and the corresponding Zernike defocus term.

Fig. 8
Fig. 8

Example data set demonstrating the artificial test optic position shift toward the interferometer caused by the phase change on reflection. The amount of shift shown is the worst-case scenario, approximately 2 .1   nm .

Fig. 9
Fig. 9

Schematic of the polarization state at the cat's-eye reflection. (a) Before reflection, (b) TM mode (parallel to plane of incidence), (c) TE mode (perpendicular to plane of incidence), and (d) TE and TM modes.

Tables (3)

Tables Icon

Table 1 Measured and Calculated a Phase Changes at Normal Incidence

Tables Icon

Table 2 Demonstration of the Uncertainty in the Phase Change in the Background Subtraction Process a

Tables Icon

Table 3 Worst-Case Offset Values Due to Phase Change

Equations (7)

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

r TE = p TE e ϕ TE = n 1 cos θ 1 + n ^ 2 cos θ 2 n 1 cos θ 1 + n ^ 2 cos θ 2 ,
r TM = p TM e ϕ TM = n ^ 2 cos θ 1 + n 1 cos θ 2 n ^ 2 cos θ 1 + n 1 cos θ 2 ,
r = p e ϕ = n 1 + n 2 i k 2 n 1 + n 2 i k 2 ,
tan ϕ = 2 k 2 n 1 n 1 2 + n 2 2 + k 2 2 .
ϕ = 4 π h λ .
Position Offset = a 20   Phase Change Slope .
Slope   [ nm nm ] = 1 1 NA 2 .

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