Abstract

A refractive index measurement method by measuring the longitudinal displacement of a point light source (PLS) after passing through a plane-parallel-plate sample is proposed. The displacement is derived by applying two point-diffraction longitudinal shearing interferometric measurements if the distance from the PLS to the exit pupil is predetermined. With two fibers to simulate the ideal PLS, an experimental system for solid and liquid sample tests is proposed to verify the principle. The experimental results indicate that its accuracy is in the order of 104. Ways to improve the accuracy are discussed based on the detailed error analysis.

© 2013 Optical Society of America

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References

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  1. A. J. Werner, “Methods in high precision refractometry of optical Glasses,” Appl. Opt. 7, 837–844 (1968).
    [CrossRef]
  2. I. K. Ilev, “Simple autocollimation laser refractometer with highly sensitive, fiber-optic output,” Appl. Opt. 34, 1741–1743 (1995).
    [CrossRef]
  3. J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
    [CrossRef]
  4. S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
    [CrossRef]
  5. R. Ulrich and R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901–2908 (1973).
    [CrossRef]
  6. C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multisample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
    [CrossRef]
  7. S. Kim, J. Na, M. J. Kim, and B. H. Lee, “Simultaneous measurement of refractive index and thickness by combining low-coherence interferometry and confocal optics,” Opt. Express 16, 5516–5526 (2008).
    [CrossRef]
  8. K.-N. Joo and S.-W. Kim, “Refractive index measurement by spectrally resolved interferometry using a femtosecond pulse laser,” Opt. Lett. 32, 647–649 (2007).
    [CrossRef]
  9. J. Na, H. Y. Choi, E. S. Choi, and C. S. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 48, 2461–2467 (2009).
    [CrossRef]
  10. S. H. Kim, S. H. Lee, J. I. Lim, and K. H. Kim, “Absolute refractive index measurement method over a broad wavelength region based on white-light interferometry,” Appl. Opt. 49, 910–914 (2010).
    [CrossRef]
  11. M. Galli, F. Marabelli, and G. Guizzetti, “Direct measurement of refractive-index dispersion of transparent media by white-light interferometry,” Appl. Opt. 42, 3910–3914 (2003).
    [CrossRef]
  12. S. D. Nicola, P. Ferraro, A. Finizio, and P. D. Natale, “A Mach–Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
    [CrossRef]
  13. Y. Hori, A. Hirai, and K. Minoshima, “Prism-pair interferometry by homodyne interferometers with a common light source for high-accuracy measurement of the absolute refractive index of glasses,” Appl. Opt. 50, 1190–1196 (2011).
    [CrossRef]
  14. I. K. Ilev, “Fiber-optic autocollimation refractometer,” Opt. Commun. 119, 513–516 (1995).
    [CrossRef]
  15. L. Coelho, J. Kobelke, K. Schuster, J. L. Santos, and O. Frazao, “Optical refractometer based on multimode interference in a pure silica tube,” Opt. Eng. 50, 100504 (2011).
  16. W. J. Smith, Modern Optical Engineering: The Design of Optical Systems, 2nd ed. (McGraw-Hill, 1990).
  17. D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).
  18. M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl. Opt. 46, 3811–3820 (2007).
    [CrossRef]

2011 (2)

L. Coelho, J. Kobelke, K. Schuster, J. L. Santos, and O. Frazao, “Optical refractometer based on multimode interference in a pure silica tube,” Opt. Eng. 50, 100504 (2011).

Y. Hori, A. Hirai, and K. Minoshima, “Prism-pair interferometry by homodyne interferometers with a common light source for high-accuracy measurement of the absolute refractive index of glasses,” Appl. Opt. 50, 1190–1196 (2011).
[CrossRef]

2010 (1)

2009 (1)

2008 (1)

2007 (2)

2003 (1)

2002 (2)

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

S. D. Nicola, P. Ferraro, A. Finizio, and P. D. Natale, “A Mach–Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

1998 (1)

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multisample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

1997 (1)

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

1995 (2)

1973 (1)

1968 (1)

Choi, E. S.

Choi, H. Y.

Coelho, L.

L. Coelho, J. Kobelke, K. Schuster, J. L. Santos, and O. Frazao, “Optical refractometer based on multimode interference in a pure silica tube,” Opt. Eng. 50, 100504 (2011).

Daimon, M.

Ferraro, P.

S. D. Nicola, P. Ferraro, A. Finizio, and P. D. Natale, “A Mach–Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Finizio, A.

S. D. Nicola, P. Ferraro, A. Finizio, and P. D. Natale, “A Mach–Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Frazao, O.

L. Coelho, J. Kobelke, K. Schuster, J. L. Santos, and O. Frazao, “Optical refractometer based on multimode interference in a pure silica tube,” Opt. Eng. 50, 100504 (2011).

Galli, M.

Guizzetti, G.

Herzinger, C. M.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multisample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

Hirai, A.

Hori, Y.

Ilev, I. K.

Johs, B.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multisample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

Joo, K.-N.

Kim, K. H.

Kim, M. J.

Kim, S.

Kim, S. H.

Kim, S.-W.

Kobelke, J.

L. Coelho, J. Kobelke, K. Schuster, J. L. Santos, and O. Frazao, “Optical refractometer based on multimode interference in a pure silica tube,” Opt. Eng. 50, 100504 (2011).

Köser, J.

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Lee, B. H.

Lee, C. S.

Lee, S. H.

Lim, J. I.

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

Marabelli, F.

Masumura, A.

McGahan, W. A.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multisample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

Minoshima, K.

Na, J.

Natale, P. D.

S. D. Nicola, P. Ferraro, A. Finizio, and P. D. Natale, “A Mach–Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Nicola, S. D.

S. D. Nicola, P. Ferraro, A. Finizio, and P. D. Natale, “A Mach–Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Paulson, W.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multisample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

Rheims, J.

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Santos, J. L.

L. Coelho, J. Kobelke, K. Schuster, J. L. Santos, and O. Frazao, “Optical refractometer based on multimode interference in a pure silica tube,” Opt. Eng. 50, 100504 (2011).

Schuster, K.

L. Coelho, J. Kobelke, K. Schuster, J. L. Santos, and O. Frazao, “Optical refractometer based on multimode interference in a pure silica tube,” Opt. Eng. 50, 100504 (2011).

Singh, S.

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems, 2nd ed. (McGraw-Hill, 1990).

Torge, R.

Ulrich, R.

Werner, A. J.

Woollam, J. A.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multisample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

Wriedt, T.

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Appl. Opt. (8)

J. Appl. Phys. (1)

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multisample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

Meas. Sci. Technol. (1)

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Opt. Commun. (2)

S. D. Nicola, P. Ferraro, A. Finizio, and P. D. Natale, “A Mach–Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

I. K. Ilev, “Fiber-optic autocollimation refractometer,” Opt. Commun. 119, 513–516 (1995).
[CrossRef]

Opt. Eng. (1)

L. Coelho, J. Kobelke, K. Schuster, J. L. Santos, and O. Frazao, “Optical refractometer based on multimode interference in a pure silica tube,” Opt. Eng. 50, 100504 (2011).

Opt. Express (1)

Opt. Lett. (1)

Phys. Scr. (1)

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

Other (2)

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems, 2nd ed. (McGraw-Hill, 1990).

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

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Figures (7)

Fig. 1.
Fig. 1.

Wavefront of a point source at the exit pupil.

Fig. 2.
Fig. 2.

Wavefront difference of two point sources at the exit pupil.

Fig. 3.
Fig. 3.

Wavefront difference of two point sources after displacement.

Fig. 4.
Fig. 4.

PLS’s longitudinal displacement after passing through a plane parallel plate.

Fig. 5.
Fig. 5.

Experiment system for RI measurement.

Fig. 6.
Fig. 6.

(a) Shape and the nominal size of the cuvette. (b) Empty cuvette. (c) Cuvette filled with liquid sample. (d) Fringe patterns of the empty cuvette. (e) Fringe patterns of the cuvette filled with the distilled water.

Fig. 7.
Fig. 7.

Contact measurement of the RI of the wedge sample.

Tables (2)

Tables Icon

Table 1. RI Measurement Results at the Wavelength of 532 nm

Tables Icon

Table 2. Requirements for R, d and Δk1 to Acquire RI Accuracy Better Than 1×104

Equations (16)

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

w(x,y)=z=rr2(x2+y2).
Δw(x,y)=RR2(x2+y2)[rr2(x2+y2)]=RR1(x2+y2)/R2[rr1(x2+y2)/r2]RR[1x2+y22R2(x2+y2)28R4]{rr[1x2+y22r2(x2+y2)28r4]}=x2+y22Rx2+y22r+(x2+y2)28R3(x2+y2)28r3=k1(x2+y2)+k2(x2+y2)2,
Δw(x,y)=RΔR(RΔR)2(x2+y2)[rr2(x2+y2)]x2+y22(RΔR)x2+y22r+(x2+y2)28(RΔR)3(x2+y2)28r3=k1(x2+y2)+k2(x2+y2)2,
Δk1=k1k1=12(RΔR)12R=12R(11ΔR/R1)ΔR2R2[1+ΔRR+(ΔRR)2].
ΔR=(11n)d.
n=ddΔR.
Δk1ΔR2R2.
ΔR=2R2Δk1.
n=ddΔR=dd2R2Δk1.
nd=2R2Δk1(d2R2Δk1)2,nR=4dRΔk1(d2R2Δk1)2,nΔk1=2dR2(d2R2Δk1)2.
n=2R2Δk1(d2R2Δk1)2d=2dR2Δk1(d2R2Δk1)2dd,
n=4dRΔk1(d2R2Δk1)2R=4dR2Δk1(d2R2Δk1)2RR,
n=2dR2(d2R2Δk1)2Δk1=2dR2Δk1(d2R2Δk1)2Δk1Δk1.
n=dΔR(dΔR)2dd=1dΔR2+ΔRddd=d/dnn12+n1n=n(n1)dd,
n=2dΔR(dΔR)2RR=2dΔR2+ΔRdRR=2R/Rnn12+n1n=2n(n1)RR,
n=dΔR(dΔR)2Δk1Δk1=1dΔR2+ΔRdΔk1Δk1=Δk1/Δk1nn12+n1n=n(n1)Δk1Δk1.

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