Abstract

Transmission spectroscopy and a small number of refractometer index measurements are combined to provide refractive index measurements of transparent samples ~50 um thick at hundreds of wavelengths with absolute accuracies <1x10−4. Key to the technique is the use of independent index measurements to circumvent the need for an independent thickness measurement of the sample. The method was demonstrated on glass samples where fits to Cauchy curves had RMS accuracies <3x10−5 from 415 to 1610 nm. Issues that must be addressed to reach this level of accuracy are discussed.

© 2014 Optical Society of America

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References

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    [Crossref]

2013 (4)

R. A. Flynn, E. F. Fleet, G. Beadie, and J. S. Shirk, “Achromatic GRIN singlet lens design,” Opt. Express 21(4), 4970–4978 (2013).
[Crossref] [PubMed]

O. Cakmakci, “Optical design of a color-corrected 2.75 g visual loupe,” Opt. Eng. 52(11), 112–113 (2013).
[Crossref]

J. Ye, H. Jiao, Y. Su, and Z. Yang, “Simultaneous Measurement of Thickness and Refractive Index Based on Rotation Incidence Angle,” J. Mod. Opt. 60(11), 900–905 (2013).
[Crossref]

K. Liu and F. Yu, “Accurate Wavelength Calibration Method using System Parameters for Grating Spectrometers,” Opt. Eng. 52(1), 013603 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (3)

2008 (2)

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

N. James, N. Hilfiker, T. Singh, D. Tiwald, S. Convey, S. M. Smith, J. H. Baker, and H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).

2007 (1)

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, “New class of bioinspired lenses with a gradient refractive index,” J. Appl. Polym. Sci. 103(3), 1834–1841 (2007).
[Crossref]

2003 (1)

S. D. Poelman and P. F. Smet, “Methods for the determination of the optical constants of thin films from single transmission measurements: a critical review,” J. Phys. D Appl. Phys. 36(15), 1850–1857 (2003).
[Crossref]

2002 (1)

2001 (1)

M. Montecchi, R. A. Montereali, and E. Nichelatti, “Reflectance and transmittance of a slightly inhomogeneous thin film bounded by rough, unparallel interfaces,” Thin Solid Films 396(1-2), 264–273 (2001).
[Crossref]

1997 (1)

1995 (1)

1993 (2)

1980 (1)

1973 (1)

1971 (1)

1965 (1)

1948 (1)

A. H. Ltd and Adam Hilger Ltd, “The Hilger-Chance Refractometer,” J. Sci. Instrum. 25(1), 18 (1948).
[Crossref]

Baer, E.

Baker, J. H.

N. James, N. Hilfiker, T. Singh, D. Tiwald, S. Convey, S. M. Smith, J. H. Baker, and H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).

Balmer, T. E.

Beadie, G.

Belanger, A. M.

Bennett, J. M.

Bohn, P. W.

Cakmakci, O.

O. Cakmakci, “Optical design of a color-corrected 2.75 g visual loupe,” Opt. Eng. 52(11), 112–113 (2013).
[Crossref]

Convey, S.

N. James, N. Hilfiker, T. Singh, D. Tiwald, S. Convey, S. M. Smith, J. H. Baker, and H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).

Duparré, A.

Ferre-Borrull, J.

Fleet, E.

Fleet, E. F.

Flynn, R. A.

Ford, J. F.

Gliech, S.

Gordon, J. M.

Harrick, N. J.

Heuberger, M.

Hilfiker, N.

N. James, N. Hilfiker, T. Singh, D. Tiwald, S. Convey, S. M. Smith, J. H. Baker, and H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).

Hiltner, A.

Huibers, P. D. T.

James, N.

N. James, N. Hilfiker, T. Singh, D. Tiwald, S. Convey, S. M. Smith, J. H. Baker, and H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).

Jiao, H.

J. Ye, H. Jiao, Y. Su, and Z. Yang, “Simultaneous Measurement of Thickness and Refractive Index Based on Rotation Incidence Angle,” J. Mod. Opt. 60(11), 900–905 (2013).
[Crossref]

Jin, Y.

Kamdar, A. R.

Kazmierczak, T.

Kim, K. H.

Kim, S. H.

Kotsidas, P.

Lane, P. A.

Lee, S. H.

Lim, J. I.

Liu, K.

K. Liu and F. Yu, “Accurate Wavelength Calibration Method using System Parameters for Grating Spectrometers,” Opt. Eng. 52(1), 013603 (2013).
[Crossref]

Ltd, A. H.

A. H. Ltd and Adam Hilger Ltd, “The Hilger-Chance Refractometer,” J. Sci. Instrum. 25(1), 18 (1948).
[Crossref]

Malitson, I. H.

Mann, C. K.

Modi, V.

Montecchi, M.

M. Montecchi, R. A. Montereali, and E. Nichelatti, “Reflectance and transmittance of a slightly inhomogeneous thin film bounded by rough, unparallel interfaces,” Thin Solid Films 396(1-2), 264–273 (2001).
[Crossref]

Montereali, R. A.

M. Montecchi, R. A. Montereali, and E. Nichelatti, “Reflectance and transmittance of a slightly inhomogeneous thin film bounded by rough, unparallel interfaces,” Thin Solid Films 396(1-2), 264–273 (2001).
[Crossref]

Moore, D. T.

Nichelatti, E.

M. Montecchi, R. A. Montereali, and E. Nichelatti, “Reflectance and transmittance of a slightly inhomogeneous thin film bounded by rough, unparallel interfaces,” Thin Solid Films 396(1-2), 264–273 (2001).
[Crossref]

Notni, G.

Offersgaard, J. F.

Perret, E.

Poelman, S. D.

S. D. Poelman and P. F. Smet, “Methods for the determination of the optical constants of thin films from single transmission measurements: a critical review,” J. Phys. D Appl. Phys. 36(15), 1850–1857 (2003).
[Crossref]

Ponting, M.

Rosenberg, A.

Shirk, J. S.

Simmons, S. M.

Singh, T.

N. James, N. Hilfiker, T. Singh, D. Tiwald, S. Convey, S. M. Smith, J. H. Baker, and H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).

Smet, P. F.

S. D. Poelman and P. F. Smet, “Methods for the determination of the optical constants of thin films from single transmission measurements: a critical review,” J. Phys. D Appl. Phys. 36(15), 1850–1857 (2003).
[Crossref]

Smith, S. M.

N. James, N. Hilfiker, T. Singh, D. Tiwald, S. Convey, S. M. Smith, J. H. Baker, and H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).

Steinert, J.

Su, Y.

J. Ye, H. Jiao, Y. Su, and Z. Yang, “Simultaneous Measurement of Thickness and Refractive Index Based on Rotation Incidence Angle,” J. Mod. Opt. 60(11), 900–905 (2013).
[Crossref]

Tai, H.

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, “New class of bioinspired lenses with a gradient refractive index,” J. Appl. Polym. Sci. 103(3), 1834–1841 (2007).
[Crossref]

Tiwald, D.

N. James, N. Hilfiker, T. Singh, D. Tiwald, S. Convey, S. M. Smith, J. H. Baker, and H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).

Tompkins, H. G.

N. James, N. Hilfiker, T. Singh, D. Tiwald, S. Convey, S. M. Smith, J. H. Baker, and H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).

Torge, R.

Tseng, C.-H.

Ulrich, R.

Vickers, T. J.

Wollman, S. T.

Yang, Y.

Yang, Z.

J. Ye, H. Jiao, Y. Su, and Z. Yang, “Simultaneous Measurement of Thickness and Refractive Index Based on Rotation Incidence Angle,” J. Mod. Opt. 60(11), 900–905 (2013).
[Crossref]

Ye, J.

J. Ye, H. Jiao, Y. Su, and Z. Yang, “Simultaneous Measurement of Thickness and Refractive Index Based on Rotation Incidence Angle,” J. Mod. Opt. 60(11), 900–905 (2013).
[Crossref]

Youngquist, R. C.

Yu, F.

K. Liu and F. Yu, “Accurate Wavelength Calibration Method using System Parameters for Grating Spectrometers,” Opt. Eng. 52(1), 013603 (2013).
[Crossref]

Appl. Opt. (6)

Appl. Spectrosc. (3)

J. Appl. Polym. Sci. (1)

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, “New class of bioinspired lenses with a gradient refractive index,” J. Appl. Polym. Sci. 103(3), 1834–1841 (2007).
[Crossref]

J. Mod. Opt. (1)

J. Ye, H. Jiao, Y. Su, and Z. Yang, “Simultaneous Measurement of Thickness and Refractive Index Based on Rotation Incidence Angle,” J. Mod. Opt. 60(11), 900–905 (2013).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Phys. D Appl. Phys. (1)

S. D. Poelman and P. F. Smet, “Methods for the determination of the optical constants of thin films from single transmission measurements: a critical review,” J. Phys. D Appl. Phys. 36(15), 1850–1857 (2003).
[Crossref]

J. Sci. Instrum. (1)

A. H. Ltd and Adam Hilger Ltd, “The Hilger-Chance Refractometer,” J. Sci. Instrum. 25(1), 18 (1948).
[Crossref]

Opt. Eng. (2)

K. Liu and F. Yu, “Accurate Wavelength Calibration Method using System Parameters for Grating Spectrometers,” Opt. Eng. 52(1), 013603 (2013).
[Crossref]

O. Cakmakci, “Optical design of a color-corrected 2.75 g visual loupe,” Opt. Eng. 52(11), 112–113 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Thin Solid Films (2)

M. Montecchi, R. A. Montereali, and E. Nichelatti, “Reflectance and transmittance of a slightly inhomogeneous thin film bounded by rough, unparallel interfaces,” Thin Solid Films 396(1-2), 264–273 (2001).
[Crossref]

N. James, N. Hilfiker, T. Singh, D. Tiwald, S. Convey, S. M. Smith, J. H. Baker, and H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).

Other (5)

Application Note “Bulk Material or Thick Film Index/Birefringence Measurement,” Metricon Corporation, Pennington, New Jersey 08534.

M. Born and E. Wolf, Principles of Optics (Pergammon Press, 1980), 6th ed., p. 323.

T. S. Moss, Optical Properties of Semiconductors (Butterworths Scientific Publications, 1959).

J. M. Bennett and L. Mattson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Wash. D.C. 1999) Chap. 3.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, Inc., 1991).

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Figures (7)

Fig. 1
Fig. 1 Fringe spectrometer. White light transmitted through a thin sample is coupled into four static grating high resolution spectrometers by dichroic beam splitters and mirrors.
Fig. 2
Fig. 2 How index values are found from Metricon measurements and fringe spectra. (a) Plot of Mrel vs 1/λ (black dots), the fringe peak “ruler,” from which the relative optical path lengths M rel of each Metricon (n, λ) pair are interpolated (red circles). (b) Sample thickness D is estimated by slope of Metricon M rel vs n/λ. (c) Absolute mode order of fringe peaks Mabs is found from D and an (n, λ) pair. (d) Index data are calculated at each fringe peak from Mabs and λ, using the local thickness D per spectrometer. Peak and index values in (b) are representative of a 50 um thick BK7 sample. Actual fringe peaks are more closely spaced in λ.
Fig. 3
Fig. 3 Plot of representative set of raw refractive index errors for 4 different glass samples, after the system was calibrated using FSilica 1.
Fig. 4
Fig. 4 Plot of Cauchy fits subtracted from reference curves for the index data used to generate Fig. 3. The RMS error in index was <3x10−5, the maximum discrepancy was < 1x10−4.
Fig. 5
Fig. 5 Illustration of sample and illumination geometry for simulations of thickness effects on retrieved index data. The top contour plots show the topography of two wedged samples, plotted over a (2x2) mm2 area. On the LHS the wedge is perfectly linear with a slope of 0.1 um/mm. On the RHS, the “wedge” is curved, according to the equation given in the inset. The illumination profile is Gaussian with a 1/e2 intensity half width of 0.6 mm (FWHM of 0.71 mm).
Fig. 6
Fig. 6 Histograms of intensity-normalized thickness distributions from the sample geometries of Fig. 5. Histograms computed from numerical sampling of (2x2) mm2 areas shown in Fig. 5, sampled across 301x301 points. The peak-to-valley thickness difference for each histogram is identical, at 233 nm.
Fig. 7
Fig. 7 Retrieved index errors from fringe spectra simulated with the histograms of Fig. 6, as approximated by asymmetric Gaussian functions and sampled at 101 evenly spaced intervals for each one. While the straight wedge allows for accurate index retrieval, the modified wedge results in fringe peak positions distorted across the spectra which result in systematic errors in recovered index.

Tables (2)

Tables Icon

Table 1 Schott reference material index data for our BK7 etalons; measured in air at 22.0°C.

Tables Icon

Table 2 Thickness, minimum and maximum wavelength, number of peaks and Cauchy fit standard deviation (σ) of refractive index data generated from spectra of our etalons. Fused Silica 1, italicized, was used to calibrate the spectrometers.

Equations (18)

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λ = ( 2 D ) n ( λ ) cos ( θ ) M
M = 2 n ( λ ) D λ
n = v 0 + v 1 λ 2 + v 2 λ 2 + v 3 λ 4 + v 4 λ 6 + v 5 λ 8
λ M = ( 2 D ) n ( λ M ) cos ( θ ) M
λ M = ( 2 D ) n ( λ M ) 2 sin 2 ( θ e x t ) M
n ( λ M ) = ( M λ M 2 D ) 2 + sin 2 ( θ e x t )
n ( λ M ) = M λ M 2 ( D o + δ D ) = n o ( λ M ) ( 1 δ D D o )
n ( λ M ) = ( M λ M 2 D o ) 2 + sin 2 ( θ e x t o + δ θ )
n ( λ M ) = n o ( λ M ) [ 1 + 1 2 ( δ θ n o ( λ M ) ) 2 ]
D 1 2 n m κ m ( M j + κ m κ j κ j + 1 κ j )
δ D D ( δ n m n m ) 2 + ( δ κ j κ j ( 1 Δ M ) ) 2 + ( δ κ j + 1 κ j + 1 Δ M ) 2
δ D D o = ( 2 n + κ m n ) 32 ( D o ) 2 κ m n m 3
n ( κ ) = n m + ( κ κ m ) n + 1 2 ( κ κ m ) 2 n
D = 1 2 n m κ m ( 2 n j κ j D o 1 sin 2 ( δ θ ) n j 2 + κ m κ j κ j + 1 κ j )
D = D o ( 1 1 2 n m κ m κ j sin 2 ( δ θ ) n j ) = D o ( 1 λ m 2 n m n j λ j δ θ 2 )
n o ( λ k ) = ( M k λ k 2 D o ) 2 + sin 2 ( δ θ )
n ( λ k ) = M k λ k 2 D
n ( λ k ) n o ( λ k ) = n k δ θ 2 2 [ λ m n m n j λ j 1 n k 2 ]

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