Abstract

Inspection of the refractive-index distribution in fused silica is very sensitive to thermally induced measurement errors. A model is derived for the estimation and interpretation of thermal errors applicable to interferometric homogeneity investigations. The outlines of the model are supported by experimental investigations and numerical calculations. The results state a mandatory temperature stability of ΔT = 0.02 K for a required reproducibility of σ(Δn) ≤ 1 × 10-7 and a lower sensitivity of higher-order Zernike terms. Requirements of the interferometer environment include spatial and temporal stability. Only a small part of the frequency spectrum of temporal instabilities contributes significantly to the measurement error and is therefore critical for the system. Experimental values are given for different environmental conditions.

© 2003 Optical Society of America

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References

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  1. J. M. Huntley, “Suppression of phase errors from vibration in phase-shifting interferometry,” J. Opt. Soc. Am. A 15, 2233–2241 (1998).
    [Crossref]
  2. P. de Groot, “Measurement of transparent plates with wavelength-tuned phase-shifting interferometry,” Appl. Opt. 39, 2658–2663 (2000).
    [Crossref]
  3. B. Dörband, “High precision testing of optical components,” in International Optical Design Conference, L. R. Gardner, K. P. Thompson, eds., Proc. SPIE3482, 484–489 (1998).
  4. G. E. Sommargren, “Diffraction methods raise interferometer accuracy,” Laser Focus World61–71 (August1996).
  5. V. Greco, G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7, 1341–1346 (1998).
    [Crossref]
  6. D. Schoenfeld, B. Kuehn, A. Steinert, R. Takke, “How to measure sub-ppm optical homogeneity in fused silica: impact of temperature on accuracy and reproducibility,” in Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, A. Duparré, B. Singh, eds., Proc. SPIE4449, 102–110 (2001).
    [Crossref]
  7. P. Hartmann, R. Mackh, H. Kohlmann, “Advances in homogeneity measurements of optical glass at the Schott 20-inch Fizeau Interferometer,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee, J.-F. Houée, eds., Proc. SPIE2775, 108–114 (1996).
    [Crossref]
  8. “Product data sheet: “Quarzglas für die Optik, Daten und Eigenschaften,” (Heraeus Quarzglas, Hanau, Germany, 1994).
  9. J. Y. Wang, D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. 19, 1510–1518 (1980).
    [Crossref] [PubMed]
  10. O. S. Narayanaswamy, “Tempering glass spheres and related topics,” Glastech. Ber. 71 (5), 120–128 (1998).
  11. S. Callard, G. Tallarida, A. Borghesi, L. Zanotti, “Thermal conductivity of SiO2 films by scanning thermal microscopy,” J. Non-Cryst. Solids 245, 203–209 (1999).
    [Crossref]
  12. C. Kittel, H. Krömer, Physik der Wärme (Oldenbourg-Verlag, 3. Auflage, 1989), p. 415.
  13. PDEase2D Pro v2.3 (Macsyma Inc., Arlington, Mass.).

2000 (1)

1999 (1)

S. Callard, G. Tallarida, A. Borghesi, L. Zanotti, “Thermal conductivity of SiO2 films by scanning thermal microscopy,” J. Non-Cryst. Solids 245, 203–209 (1999).
[Crossref]

1998 (3)

J. M. Huntley, “Suppression of phase errors from vibration in phase-shifting interferometry,” J. Opt. Soc. Am. A 15, 2233–2241 (1998).
[Crossref]

V. Greco, G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7, 1341–1346 (1998).
[Crossref]

O. S. Narayanaswamy, “Tempering glass spheres and related topics,” Glastech. Ber. 71 (5), 120–128 (1998).

1996 (1)

G. E. Sommargren, “Diffraction methods raise interferometer accuracy,” Laser Focus World61–71 (August1996).

1980 (1)

Borghesi, A.

S. Callard, G. Tallarida, A. Borghesi, L. Zanotti, “Thermal conductivity of SiO2 films by scanning thermal microscopy,” J. Non-Cryst. Solids 245, 203–209 (1999).
[Crossref]

Callard, S.

S. Callard, G. Tallarida, A. Borghesi, L. Zanotti, “Thermal conductivity of SiO2 films by scanning thermal microscopy,” J. Non-Cryst. Solids 245, 203–209 (1999).
[Crossref]

de Groot, P.

Dörband, B.

B. Dörband, “High precision testing of optical components,” in International Optical Design Conference, L. R. Gardner, K. P. Thompson, eds., Proc. SPIE3482, 484–489 (1998).

Greco, V.

V. Greco, G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7, 1341–1346 (1998).
[Crossref]

Hartmann, P.

P. Hartmann, R. Mackh, H. Kohlmann, “Advances in homogeneity measurements of optical glass at the Schott 20-inch Fizeau Interferometer,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee, J.-F. Houée, eds., Proc. SPIE2775, 108–114 (1996).
[Crossref]

Huntley, J. M.

Kittel, C.

C. Kittel, H. Krömer, Physik der Wärme (Oldenbourg-Verlag, 3. Auflage, 1989), p. 415.

Kohlmann, H.

P. Hartmann, R. Mackh, H. Kohlmann, “Advances in homogeneity measurements of optical glass at the Schott 20-inch Fizeau Interferometer,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee, J.-F. Houée, eds., Proc. SPIE2775, 108–114 (1996).
[Crossref]

Krömer, H.

C. Kittel, H. Krömer, Physik der Wärme (Oldenbourg-Verlag, 3. Auflage, 1989), p. 415.

Kuehn, B.

D. Schoenfeld, B. Kuehn, A. Steinert, R. Takke, “How to measure sub-ppm optical homogeneity in fused silica: impact of temperature on accuracy and reproducibility,” in Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, A. Duparré, B. Singh, eds., Proc. SPIE4449, 102–110 (2001).
[Crossref]

Mackh, R.

P. Hartmann, R. Mackh, H. Kohlmann, “Advances in homogeneity measurements of optical glass at the Schott 20-inch Fizeau Interferometer,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee, J.-F. Houée, eds., Proc. SPIE2775, 108–114 (1996).
[Crossref]

Molesini, G.

V. Greco, G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7, 1341–1346 (1998).
[Crossref]

S. Narayanaswamy, O.

O. S. Narayanaswamy, “Tempering glass spheres and related topics,” Glastech. Ber. 71 (5), 120–128 (1998).

Schoenfeld, D.

D. Schoenfeld, B. Kuehn, A. Steinert, R. Takke, “How to measure sub-ppm optical homogeneity in fused silica: impact of temperature on accuracy and reproducibility,” in Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, A. Duparré, B. Singh, eds., Proc. SPIE4449, 102–110 (2001).
[Crossref]

Silva, D. E.

Sommargren, G. E.

G. E. Sommargren, “Diffraction methods raise interferometer accuracy,” Laser Focus World61–71 (August1996).

Steinert, A.

D. Schoenfeld, B. Kuehn, A. Steinert, R. Takke, “How to measure sub-ppm optical homogeneity in fused silica: impact of temperature on accuracy and reproducibility,” in Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, A. Duparré, B. Singh, eds., Proc. SPIE4449, 102–110 (2001).
[Crossref]

Takke, R.

D. Schoenfeld, B. Kuehn, A. Steinert, R. Takke, “How to measure sub-ppm optical homogeneity in fused silica: impact of temperature on accuracy and reproducibility,” in Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, A. Duparré, B. Singh, eds., Proc. SPIE4449, 102–110 (2001).
[Crossref]

Tallarida, G.

S. Callard, G. Tallarida, A. Borghesi, L. Zanotti, “Thermal conductivity of SiO2 films by scanning thermal microscopy,” J. Non-Cryst. Solids 245, 203–209 (1999).
[Crossref]

Wang, J. Y.

Zanotti, L.

S. Callard, G. Tallarida, A. Borghesi, L. Zanotti, “Thermal conductivity of SiO2 films by scanning thermal microscopy,” J. Non-Cryst. Solids 245, 203–209 (1999).
[Crossref]

Appl. Opt. (2)

Glastech. Ber. (1)

O. S. Narayanaswamy, “Tempering glass spheres and related topics,” Glastech. Ber. 71 (5), 120–128 (1998).

J. Non-Cryst. Solids (1)

S. Callard, G. Tallarida, A. Borghesi, L. Zanotti, “Thermal conductivity of SiO2 films by scanning thermal microscopy,” J. Non-Cryst. Solids 245, 203–209 (1999).
[Crossref]

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

Laser Focus World (1)

G. E. Sommargren, “Diffraction methods raise interferometer accuracy,” Laser Focus World61–71 (August1996).

Pure Appl. Opt. (1)

V. Greco, G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7, 1341–1346 (1998).
[Crossref]

Other (6)

D. Schoenfeld, B. Kuehn, A. Steinert, R. Takke, “How to measure sub-ppm optical homogeneity in fused silica: impact of temperature on accuracy and reproducibility,” in Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, A. Duparré, B. Singh, eds., Proc. SPIE4449, 102–110 (2001).
[Crossref]

P. Hartmann, R. Mackh, H. Kohlmann, “Advances in homogeneity measurements of optical glass at the Schott 20-inch Fizeau Interferometer,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee, J.-F. Houée, eds., Proc. SPIE2775, 108–114 (1996).
[Crossref]

“Product data sheet: “Quarzglas für die Optik, Daten und Eigenschaften,” (Heraeus Quarzglas, Hanau, Germany, 1994).

C. Kittel, H. Krömer, Physik der Wärme (Oldenbourg-Verlag, 3. Auflage, 1989), p. 415.

PDEase2D Pro v2.3 (Macsyma Inc., Arlington, Mass.).

B. Dörband, “High precision testing of optical components,” in International Optical Design Conference, L. R. Gardner, K. P. Thompson, eds., Proc. SPIE3482, 484–489 (1998).

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Figures (12)

Fig. 1
Fig. 1

One-dimensional projection of the Fourier components F k on the rotational Zernike functions C j .

Fig. 2
Fig. 2

Effective thermal conductivity k eff and relaxation time.

Fig. 3
Fig. 3

Measurement of the temporal development of the C3 term of samples with a nonadapted temperature: CA, sample clear aperture over which the interferograms are evaluated.

Fig. 4
Fig. 4

Temporal decay of the Zernike components after a misadjustment of ΔT = 1.4 K. A comparison of experimental and numerical results is shown.

Fig. 5
Fig. 5

Temperature distribution inside a test sample and the resulting wave-front distortion.

Fig. 6
Fig. 6

Calculation of adaption time, with and without an interface, and experimental data.

Fig. 7
Fig. 7

Temporal behavior of Zernike term 3 during unusually high system instability. The measured C3 versus the calculated C3 is shown.

Fig. 8
Fig. 8

Temporal behavior of Zernike term 3 during unusually high system instability. The measured C3 versus the calculated C3 is shown.

Fig. 9
Fig. 9

Temporal behavior of spherical Zernike terms C3 and C8 and the peak-to-valley (PV) value of a polished sample: clear aperture, 190 mm; temperature mismatch, ΔT ≈ 0.02 K.

Fig. 10
Fig. 10

Measurement error induced by a temperature fluctuation of ΔT(t, T) = 0.1Ksin(2πt/ T) in a fused silica sample with a diameter of 330 mm and thickness d = 180 mm, depending on frequency: CA, 90% of the sample diameter.

Fig. 11
Fig. 11

Measurement error induced by a temperature fluctuation of ΔT = 0.1 K, regarding resonance time in a quartz glass sample with a diameter of 330 mm, depending on sample thickness.

Fig. 12
Fig. 12

Temperature development over several days in the interferometer: A and B are opposite corners in the interferometer setup.

Equations (8)

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

D 2Tz, tz2-Tz, tt=0,
Tz, t=T0+m=1 amsinmπzLFmexp-m2tτ with τ=L2π2D, m=1, 2, ,
Tz, tT0+a1 sinπzLexp-tτ with t>τ.
Δtτ lnΔTt=0ΔTt=Δt.
h13 Wm2K
h1301300 Wm2K.
dkeff=dk+R with R=1h,
D=keffcv,

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