Abstract

White light spectral interferometry is applied to measure the refractive index in absorbing liquids in the spectral range of 400–1000 nm. We analyze the influence of absorption on the visibility of interferometric fringes and, accordingly, on the measurement of the refractive index. Further, we show that the refractive index in the absorption band can be retrieved by a two-step process. The procedure requires the use of two samples of different thickness, the thicker one to retrieve the refractive index in the transparent region and the thinnest to obtain the data in the absorption region. First, the refractive index values are retrieved with good accuracy in the transparent region of the material for 1-mm-thick samples. Second, these refractive index values serve also to precisely calculate the thickness of a thinner sample (~150 µm) since the accuracy of the methods depends strongly on the thickness of the sample. Finally, the refractive index is recovered for the entire spectral range.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2017 (3)

Y. Arosa, E. López-Lago, and R. de la Fuente, “The phase ambiguity in dispersion measurements by white light spectral interferometry,” Opt. Laser Technol. 95, 23–28 (2017).
[Crossref]

G. Morales-Luna and A. García-Valenzuela, “Viability and fundamental limits of critical-angle refractometry of turbid colloids,” Meas. Sci. Technol. 28(12), 125203 (2017).
[Crossref]

Y. Arosa, C. D. R. Fernández, E. López Lago, A. Amigo, L. M. Varela, O. Cabeza, and R. de la Fuente, “Refractive index measurement of imidazolium based ionic liquids in the VIS-NIR,” Opt. Mater. 73, 647–657 (2017).
[Crossref]

2016 (4)

2014 (1)

Y.-M. Lee, H.-H. Cheng, J.-H. Li, K.-Y. Tsai, and Y.-T. Sheng, “Refractive index and effective thickness measurement system for the RGB color filter coatings with absorption and scattering properties,” J. Disp. Technol. 10(1), 57–70 (2014).
[Crossref]

2012 (1)

2007 (1)

2006 (1)

J. Dintinger, S. Klein, and T. W. Ebbesen, “Molecule–surface plasmon interactions in hole arrays: enhanced absorption, refractive index changes, and all-optical switching,” Adv. Mater. 18(10), 1267–1270 (2006).
[Crossref]

2003 (1)

1997 (1)

J. Rheims, J. Köser, and T. Wriedtd, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8(6), 601–605 (1997).
[Crossref]

1994 (1)

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

1989 (1)

1966 (1)

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3, and LiTaO3,” Appl. Phys. Lett. 9(1), 72–74 (1966).
[Crossref]

1963 (1)

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Nat. Bur. Stand. Sect. A 67(4), 363–377 (1963).
[Crossref]

1938 (1)

M. L. Anson, “The estimation of pepsin, trypsin, papain, and cathepsin with hemoglobin,” J. Gen. Physiol. 22(1), 79–89 (1938).
[Crossref] [PubMed]

Amigo, A.

Y. Arosa, C. D. R. Fernández, E. López Lago, A. Amigo, L. M. Varela, O. Cabeza, and R. de la Fuente, “Refractive index measurement of imidazolium based ionic liquids in the VIS-NIR,” Opt. Mater. 73, 647–657 (2017).
[Crossref]

Andrade, L. H. C.

Anson, M. L.

M. L. Anson, “The estimation of pepsin, trypsin, papain, and cathepsin with hemoglobin,” J. Gen. Physiol. 22(1), 79–89 (1938).
[Crossref] [PubMed]

Arosa, Y.

Y. Arosa, E. López-Lago, and R. de la Fuente, “The phase ambiguity in dispersion measurements by white light spectral interferometry,” Opt. Laser Technol. 95, 23–28 (2017).
[Crossref]

Y. Arosa, C. D. R. Fernández, E. López Lago, A. Amigo, L. M. Varela, O. Cabeza, and R. de la Fuente, “Refractive index measurement of imidazolium based ionic liquids in the VIS-NIR,” Opt. Mater. 73, 647–657 (2017).
[Crossref]

Y. Arosa, E. L. Lago, L. M. Varela, and R. de la Fuente, “Spectrally resolved white light interferometry to measure material dispersion over a wide spectral band in a single acquisition,” Opt. Express 24(15), 17303–17312 (2016).
[Crossref] [PubMed]

Ashkin, A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3, and LiTaO3,” Appl. Phys. Lett. 9(1), 72–74 (1966).
[Crossref]

Ballman, A. A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3, and LiTaO3,” Appl. Phys. Lett. 9(1), 72–74 (1966).
[Crossref]

Boyd, G. D.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3, and LiTaO3,” Appl. Phys. Lett. 9(1), 72–74 (1966).
[Crossref]

Cabeza, O.

Y. Arosa, C. D. R. Fernández, E. López Lago, A. Amigo, L. M. Varela, O. Cabeza, and R. de la Fuente, “Refractive index measurement of imidazolium based ionic liquids in the VIS-NIR,” Opt. Mater. 73, 647–657 (2017).
[Crossref]

Calatroni, J.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

Cheng, H.-H.

Y.-M. Lee, H.-H. Cheng, J.-H. Li, K.-Y. Tsai, and Y.-T. Sheng, “Refractive index and effective thickness measurement system for the RGB color filter coatings with absorption and scattering properties,” J. Disp. Technol. 10(1), 57–70 (2014).
[Crossref]

Contreras-Tello, H.

A. Nahmad-Rohen, H. Contreras-Tello, G. Morales-Luna, and A. García-Valenzuela, “On the refractive index of blood,” Phys. Scr. 91(1), 015503 (2016).
[Crossref]

Costantino, S.

Daimon, M.

de la Fuente, R.

Y. Arosa, C. D. R. Fernández, E. López Lago, A. Amigo, L. M. Varela, O. Cabeza, and R. de la Fuente, “Refractive index measurement of imidazolium based ionic liquids in the VIS-NIR,” Opt. Mater. 73, 647–657 (2017).
[Crossref]

Y. Arosa, E. López-Lago, and R. de la Fuente, “The phase ambiguity in dispersion measurements by white light spectral interferometry,” Opt. Laser Technol. 95, 23–28 (2017).
[Crossref]

Y. Arosa, E. L. Lago, L. M. Varela, and R. de la Fuente, “Spectrally resolved white light interferometry to measure material dispersion over a wide spectral band in a single acquisition,” Opt. Express 24(15), 17303–17312 (2016).
[Crossref] [PubMed]

Dintinger, J.

J. Dintinger, S. Klein, and T. W. Ebbesen, “Molecule–surface plasmon interactions in hole arrays: enhanced absorption, refractive index changes, and all-optical switching,” Adv. Mater. 18(10), 1267–1270 (2006).
[Crossref]

Dobson, C. C.

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3, and LiTaO3,” Appl. Phys. Lett. 9(1), 72–74 (1966).
[Crossref]

Ebbesen, T. W.

J. Dintinger, S. Klein, and T. W. Ebbesen, “Molecule–surface plasmon interactions in hole arrays: enhanced absorption, refractive index changes, and all-optical switching,” Adv. Mater. 18(10), 1267–1270 (2006).
[Crossref]

Escalona, R.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

Fernández, C. D. R.

Y. Arosa, C. D. R. Fernández, E. López Lago, A. Amigo, L. M. Varela, O. Cabeza, and R. de la Fuente, “Refractive index measurement of imidazolium based ionic liquids in the VIS-NIR,” Opt. Mater. 73, 647–657 (2017).
[Crossref]

García-Valenzuela, A.

G. Morales-Luna and A. García-Valenzuela, “Viability and fundamental limits of critical-angle refractometry of turbid colloids,” Meas. Sci. Technol. 28(12), 125203 (2017).
[Crossref]

A. Nahmad-Rohen, H. Contreras-Tello, G. Morales-Luna, and A. García-Valenzuela, “On the refractive index of blood,” Phys. Scr. 91(1), 015503 (2016).
[Crossref]

Habel, F.

Jourdain, P.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

Kante, B.

Klein, S.

J. Dintinger, S. Klein, and T. W. Ebbesen, “Molecule–surface plasmon interactions in hole arrays: enhanced absorption, refractive index changes, and all-optical switching,” Adv. Mater. 18(10), 1267–1270 (2006).
[Crossref]

Köser, J.

J. Rheims, J. Köser, and T. Wriedtd, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8(6), 601–605 (1997).
[Crossref]

Lago, E. L.

Lanzillotti-Kimura, N. D.

Lee, Y.-M.

Y.-M. Lee, H.-H. Cheng, J.-H. Li, K.-Y. Tsai, and Y.-T. Sheng, “Refractive index and effective thickness measurement system for the RGB color filter coatings with absorption and scattering properties,” J. Disp. Technol. 10(1), 57–70 (2014).
[Crossref]

Levinstein, J. J.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3, and LiTaO3,” Appl. Phys. Lett. 9(1), 72–74 (1966).
[Crossref]

Li, J.-H.

Y.-M. Lee, H.-H. Cheng, J.-H. Li, K.-Y. Tsai, and Y.-T. Sheng, “Refractive index and effective thickness measurement system for the RGB color filter coatings with absorption and scattering properties,” J. Disp. Technol. 10(1), 57–70 (2014).
[Crossref]

Lima, S. M.

López Lago, E.

Y. Arosa, C. D. R. Fernández, E. López Lago, A. Amigo, L. M. Varela, O. Cabeza, and R. de la Fuente, “Refractive index measurement of imidazolium based ionic liquids in the VIS-NIR,” Opt. Mater. 73, 647–657 (2017).
[Crossref]

López-Lago, E.

Y. Arosa, E. López-Lago, and R. de la Fuente, “The phase ambiguity in dispersion measurements by white light spectral interferometry,” Opt. Laser Technol. 95, 23–28 (2017).
[Crossref]

Martínez, O.

Masumura, A.

McCrackin, F. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Nat. Bur. Stand. Sect. A 67(4), 363–377 (1963).
[Crossref]

Morales-Luna, G.

G. Morales-Luna and A. García-Valenzuela, “Viability and fundamental limits of critical-angle refractometry of turbid colloids,” Meas. Sci. Technol. 28(12), 125203 (2017).
[Crossref]

A. Nahmad-Rohen, H. Contreras-Tello, G. Morales-Luna, and A. García-Valenzuela, “On the refractive index of blood,” Phys. Scr. 91(1), 015503 (2016).
[Crossref]

Nahmad-Rohen, A.

A. Nahmad-Rohen, H. Contreras-Tello, G. Morales-Luna, and A. García-Valenzuela, “On the refractive index of blood,” Phys. Scr. 91(1), 015503 (2016).
[Crossref]

Nassau, K.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3, and LiTaO3,” Appl. Phys. Lett. 9(1), 72–74 (1966).
[Crossref]

Nunes, L. A. O.

O’Brien, K.

Park, Y.

Passaglia, E.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Nat. Bur. Stand. Sect. A 67(4), 363–377 (1963).
[Crossref]

Pervak, V.

Rheims, J.

J. Rheims, J. Köser, and T. Wriedtd, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8(6), 601–605 (1997).
[Crossref]

Rocha, A. C. P.

Sáinz, C.

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

Sheng, Y.-T.

Y.-M. Lee, H.-H. Cheng, J.-H. Li, K.-Y. Tsai, and Y.-T. Sheng, “Refractive index and effective thickness measurement system for the RGB color filter coatings with absorption and scattering properties,” J. Disp. Technol. 10(1), 57–70 (2014).
[Crossref]

Silva, J. R.

Smith, L. M.

Smith, R. G.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3, and LiTaO3,” Appl. Phys. Lett. 9(1), 72–74 (1966).
[Crossref]

Steinberg, H. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Nat. Bur. Stand. Sect. A 67(4), 363–377 (1963).
[Crossref]

Stromberg, R. R.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Nat. Bur. Stand. Sect. A 67(4), 363–377 (1963).
[Crossref]

Suchowski, H.

Torga, J.

Trubetskov, M.

Tsai, K.-Y.

Y.-M. Lee, H.-H. Cheng, J.-H. Li, K.-Y. Tsai, and Y.-T. Sheng, “Refractive index and effective thickness measurement system for the RGB color filter coatings with absorption and scattering properties,” J. Disp. Technol. 10(1), 57–70 (2014).
[Crossref]

Varela, L. M.

Y. Arosa, C. D. R. Fernández, E. López Lago, A. Amigo, L. M. Varela, O. Cabeza, and R. de la Fuente, “Refractive index measurement of imidazolium based ionic liquids in the VIS-NIR,” Opt. Mater. 73, 647–657 (2017).
[Crossref]

Y. Arosa, E. L. Lago, L. M. Varela, and R. de la Fuente, “Spectrally resolved white light interferometry to measure material dispersion over a wide spectral band in a single acquisition,” Opt. Express 24(15), 17303–17312 (2016).
[Crossref] [PubMed]

Wriedtd, T.

J. Rheims, J. Köser, and T. Wriedtd, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8(6), 601–605 (1997).
[Crossref]

Yin, X.

Zhang, X.

Adv. Mater. (1)

J. Dintinger, S. Klein, and T. W. Ebbesen, “Molecule–surface plasmon interactions in hole arrays: enhanced absorption, refractive index changes, and all-optical switching,” Adv. Mater. 18(10), 1267–1270 (2006).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3, and LiTaO3,” Appl. Phys. Lett. 9(1), 72–74 (1966).
[Crossref]

J. Disp. Technol. (1)

Y.-M. Lee, H.-H. Cheng, J.-H. Li, K.-Y. Tsai, and Y.-T. Sheng, “Refractive index and effective thickness measurement system for the RGB color filter coatings with absorption and scattering properties,” J. Disp. Technol. 10(1), 57–70 (2014).
[Crossref]

J. Gen. Physiol. (1)

M. L. Anson, “The estimation of pepsin, trypsin, papain, and cathepsin with hemoglobin,” J. Gen. Physiol. 22(1), 79–89 (1938).
[Crossref] [PubMed]

J. Res. Nat. Bur. Stand. Sect. A (1)

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Nat. Bur. Stand. Sect. A 67(4), 363–377 (1963).
[Crossref]

Meas. Sci. Technol. (2)

J. Rheims, J. Köser, and T. Wriedtd, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8(6), 601–605 (1997).
[Crossref]

G. Morales-Luna and A. García-Valenzuela, “Viability and fundamental limits of critical-angle refractometry of turbid colloids,” Meas. Sci. Technol. 28(12), 125203 (2017).
[Crossref]

Opt. Commun. (1)

C. Sáinz, P. Jourdain, R. Escalona, and J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 111(5-6), 632–641 (1994).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (1)

Y. Arosa, E. López-Lago, and R. de la Fuente, “The phase ambiguity in dispersion measurements by white light spectral interferometry,” Opt. Laser Technol. 95, 23–28 (2017).
[Crossref]

Opt. Lett. (1)

Opt. Mater. (1)

Y. Arosa, C. D. R. Fernández, E. López Lago, A. Amigo, L. M. Varela, O. Cabeza, and R. de la Fuente, “Refractive index measurement of imidazolium based ionic liquids in the VIS-NIR,” Opt. Mater. 73, 647–657 (2017).
[Crossref]

Phys. Scr. (1)

A. Nahmad-Rohen, H. Contreras-Tello, G. Morales-Luna, and A. García-Valenzuela, “On the refractive index of blood,” Phys. Scr. 91(1), 015503 (2016).
[Crossref]

Other (1)

B. Welz, Atomic Absorption Spectrometry (Wiley, 1999).

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Figures (6)

Fig. 1
Fig. 1 (a) Absorbance of solutions of CR39 dye in deionized water, A = −logT = 0.433αd with d = 2 mm; the circles correspond to the cut-off wavelengths (see Table 2 and the related text). (b) Absorptivity, ε = α/c. (c) Photographs of samples 1, 3, 6, 9, and 12 inside a 1-mm-thick cell.
Fig. 2
Fig. 2 Interferograms for pure deionized water (blue line) and for solution 11 (green line) after subtraction of the background irradiance.
Fig. 3
Fig. 3 Relation between visibility, normalized background irradiance, and absorbance. The circles and triangles indicate the values obtained from the interferograms, while the continuous curves represent theory.
Fig. 4
Fig. 4 a) Phases obtained for different solutions; b) difference of the obtained phases with that obtained for the deionized water sample.
Fig. 5
Fig. 5 Refractive indices for solution 14. The cells used are 1-mm thick (blue line) and 150-µm thick (green line).
Fig. 6
Fig. 6 (a) Absorbance of [BMIM]3[Cu(SCN)4] for a 10-µm-thick cell, (b) refractive index obtained with a 1-mm-thick cell (red), refractive index measured using microscope cover slips (blue), and fitted refractive index (green); the spectral range used to extract d is the one between the circles; (c) difference between the refractive index given by Eq. (10) and the experimental refractive index obtained with a 150-μm-thick cell.

Tables (3)

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Table 1 Sample Concentrations

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Table 2 Cut-off Wavelength, Corresponding Absorbance, and Visibility of the Interferogram

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Table 3 Values of k obtained from Linear Fitting, Rounded Values, and Final Fitted Thicknesses of the Thin Samples

Equations (10)

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I( λ )= I 1 ( λ )+ I 2 ( λ )+2 I 1 I 2 v s ( λ )cosφ( λ ),
I 1 = 1 2 ( I 0 ΔI ) e 2αd I 2 = 1 2 ( I 0 +ΔI ),
φ( λ )= 4π λ [ d( n1 )L ],
I( λ )= I B ( λ )[ 1+v( λ )cosφ( λ ) ],
I B ( λ )= I 1 ( λ )+ I 2 ( λ ) = I 0 ( λ ) e αd [ cosh( αd )+Δsinh( αd ) ],
v( λ )= 1 Δ 2 v s ( λ ) cosh( αd )+Δsinh( αd ) ,
φ exp ( λ )=φ( λ )2kπ= 4π λ [ d( n1 )L ]2kπ.
λ c Δφ( λ c ) 4πd = 10 4 .
φ exp ( λ ) 2π 2L λ =2d ( n1 ) λ k.
n 2 1=1.5 10 3 / λ 4 +2.08 10 2 / λ 2 +1.39017.6 10 3 λ 2 +2.3 10 3 λ 4 ,

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