Abstract

A practical measurement procedure for the determination of the complex refractive index of strongly absorbing liquids within a finite spectral range was developed. The method is based on separate measurements of reflectance and transmittance of the liquid sample, a property of dispersion and absorption, and exploitation of Fresnel’s theory. The advantage of the method is that the knowledge of the layer thickness of the light absorbing medium, which is required typically in transmittance measurements, is not needed. In addition, both measurements, the transmittance and the reflectance, were accomplished with one spectrophotometer using a home-built reflectometer and without any sample dilution. The method is validated by numerical simulation using the Lorentz model for permittivity of an insulator, and also by experimental data obtained from three strongly absorbing offset inks, namely magenta, yellow and cyan.

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References

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  1. V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig relations in Optical Materials Research (Springer, 2005).
  2. R. M. A. Azzam, “Direct relation between Fresnel’s interface reflection coefficients for the parallel and perpendicular polarizations,” J. Opt. Soc. Am. A 69(7), 1007–1016 (1979).
    [CrossRef]
  3. I. Niskanen, J. Räty, K.-E. Peiponen, H. Koivula, and M. Toivakka, “Assessment of the complex refractive index of an optically very dense solid layer: Case study offset magenta ink,” Chem. Phys. Lett. 442(4-6), 515–517 (2007).
    [CrossRef]
  4. J. S. Preston, N. J. Elton, J. C. Husband, J. Dalton, P. J. Heard, and G. C. Allen, “Investigation into the distribution of ink components on printed coated paper. Part 1. Optical and roughness considerations,” Colloids Surf. A Physicochem. Eng. Asp. 205(3), 183–198 (2002).
    [CrossRef]
  5. J. S. Preston and L. F. Gate, “The influence of colour and surface topography on the measurement of effective refractive index of offset printed coated papers,” Colloids Surf. A Physicochem. Eng. Asp. 252(2-3), 99–104 (2005).
    [CrossRef]
  6. N. J. Elton and J. C. C. Day, “A reflectometer for the combined measurement of refractive index, microroughness, macroroughness and gloss of low-extinction surfaces,” Meas. Sci. Technol. 20(2), 025309 (2009).
    [CrossRef]
  7. I. Niskanen, J. Räty, and K.-E. Peiponen, “Complex refractive index of turbid liquids,” Opt. Lett. 32(7), 862–864 (2007).
    [CrossRef] [PubMed]
  8. F. Wooten, Optical Properties of Solids (Academic Press, 1972).
  9. J. Räty, E. Keränen, and K.-E. Peiponen, “The complex refractive index measurement of liquids by a novel reflectometer apparatus for the UV-Vis spectral range,” Meas. Sci. Technol. 9(1), 95–99 (1998).
    [CrossRef]

2009

N. J. Elton and J. C. C. Day, “A reflectometer for the combined measurement of refractive index, microroughness, macroroughness and gloss of low-extinction surfaces,” Meas. Sci. Technol. 20(2), 025309 (2009).
[CrossRef]

2007

I. Niskanen, J. Räty, and K.-E. Peiponen, “Complex refractive index of turbid liquids,” Opt. Lett. 32(7), 862–864 (2007).
[CrossRef] [PubMed]

I. Niskanen, J. Räty, K.-E. Peiponen, H. Koivula, and M. Toivakka, “Assessment of the complex refractive index of an optically very dense solid layer: Case study offset magenta ink,” Chem. Phys. Lett. 442(4-6), 515–517 (2007).
[CrossRef]

2005

J. S. Preston and L. F. Gate, “The influence of colour and surface topography on the measurement of effective refractive index of offset printed coated papers,” Colloids Surf. A Physicochem. Eng. Asp. 252(2-3), 99–104 (2005).
[CrossRef]

2002

J. S. Preston, N. J. Elton, J. C. Husband, J. Dalton, P. J. Heard, and G. C. Allen, “Investigation into the distribution of ink components on printed coated paper. Part 1. Optical and roughness considerations,” Colloids Surf. A Physicochem. Eng. Asp. 205(3), 183–198 (2002).
[CrossRef]

1998

J. Räty, E. Keränen, and K.-E. Peiponen, “The complex refractive index measurement of liquids by a novel reflectometer apparatus for the UV-Vis spectral range,” Meas. Sci. Technol. 9(1), 95–99 (1998).
[CrossRef]

1979

R. M. A. Azzam, “Direct relation between Fresnel’s interface reflection coefficients for the parallel and perpendicular polarizations,” J. Opt. Soc. Am. A 69(7), 1007–1016 (1979).
[CrossRef]

Allen, G. C.

J. S. Preston, N. J. Elton, J. C. Husband, J. Dalton, P. J. Heard, and G. C. Allen, “Investigation into the distribution of ink components on printed coated paper. Part 1. Optical and roughness considerations,” Colloids Surf. A Physicochem. Eng. Asp. 205(3), 183–198 (2002).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, “Direct relation between Fresnel’s interface reflection coefficients for the parallel and perpendicular polarizations,” J. Opt. Soc. Am. A 69(7), 1007–1016 (1979).
[CrossRef]

Dalton, J.

J. S. Preston, N. J. Elton, J. C. Husband, J. Dalton, P. J. Heard, and G. C. Allen, “Investigation into the distribution of ink components on printed coated paper. Part 1. Optical and roughness considerations,” Colloids Surf. A Physicochem. Eng. Asp. 205(3), 183–198 (2002).
[CrossRef]

Day, J. C. C.

N. J. Elton and J. C. C. Day, “A reflectometer for the combined measurement of refractive index, microroughness, macroroughness and gloss of low-extinction surfaces,” Meas. Sci. Technol. 20(2), 025309 (2009).
[CrossRef]

Elton, N. J.

N. J. Elton and J. C. C. Day, “A reflectometer for the combined measurement of refractive index, microroughness, macroroughness and gloss of low-extinction surfaces,” Meas. Sci. Technol. 20(2), 025309 (2009).
[CrossRef]

J. S. Preston, N. J. Elton, J. C. Husband, J. Dalton, P. J. Heard, and G. C. Allen, “Investigation into the distribution of ink components on printed coated paper. Part 1. Optical and roughness considerations,” Colloids Surf. A Physicochem. Eng. Asp. 205(3), 183–198 (2002).
[CrossRef]

Gate, L. F.

J. S. Preston and L. F. Gate, “The influence of colour and surface topography on the measurement of effective refractive index of offset printed coated papers,” Colloids Surf. A Physicochem. Eng. Asp. 252(2-3), 99–104 (2005).
[CrossRef]

Heard, P. J.

J. S. Preston, N. J. Elton, J. C. Husband, J. Dalton, P. J. Heard, and G. C. Allen, “Investigation into the distribution of ink components on printed coated paper. Part 1. Optical and roughness considerations,” Colloids Surf. A Physicochem. Eng. Asp. 205(3), 183–198 (2002).
[CrossRef]

Husband, J. C.

J. S. Preston, N. J. Elton, J. C. Husband, J. Dalton, P. J. Heard, and G. C. Allen, “Investigation into the distribution of ink components on printed coated paper. Part 1. Optical and roughness considerations,” Colloids Surf. A Physicochem. Eng. Asp. 205(3), 183–198 (2002).
[CrossRef]

Keränen, E.

J. Räty, E. Keränen, and K.-E. Peiponen, “The complex refractive index measurement of liquids by a novel reflectometer apparatus for the UV-Vis spectral range,” Meas. Sci. Technol. 9(1), 95–99 (1998).
[CrossRef]

Koivula, H.

I. Niskanen, J. Räty, K.-E. Peiponen, H. Koivula, and M. Toivakka, “Assessment of the complex refractive index of an optically very dense solid layer: Case study offset magenta ink,” Chem. Phys. Lett. 442(4-6), 515–517 (2007).
[CrossRef]

Niskanen, I.

I. Niskanen, J. Räty, K.-E. Peiponen, H. Koivula, and M. Toivakka, “Assessment of the complex refractive index of an optically very dense solid layer: Case study offset magenta ink,” Chem. Phys. Lett. 442(4-6), 515–517 (2007).
[CrossRef]

I. Niskanen, J. Räty, and K.-E. Peiponen, “Complex refractive index of turbid liquids,” Opt. Lett. 32(7), 862–864 (2007).
[CrossRef] [PubMed]

Peiponen, K.-E.

I. Niskanen, J. Räty, and K.-E. Peiponen, “Complex refractive index of turbid liquids,” Opt. Lett. 32(7), 862–864 (2007).
[CrossRef] [PubMed]

I. Niskanen, J. Räty, K.-E. Peiponen, H. Koivula, and M. Toivakka, “Assessment of the complex refractive index of an optically very dense solid layer: Case study offset magenta ink,” Chem. Phys. Lett. 442(4-6), 515–517 (2007).
[CrossRef]

J. Räty, E. Keränen, and K.-E. Peiponen, “The complex refractive index measurement of liquids by a novel reflectometer apparatus for the UV-Vis spectral range,” Meas. Sci. Technol. 9(1), 95–99 (1998).
[CrossRef]

Preston, J. S.

J. S. Preston and L. F. Gate, “The influence of colour and surface topography on the measurement of effective refractive index of offset printed coated papers,” Colloids Surf. A Physicochem. Eng. Asp. 252(2-3), 99–104 (2005).
[CrossRef]

J. S. Preston, N. J. Elton, J. C. Husband, J. Dalton, P. J. Heard, and G. C. Allen, “Investigation into the distribution of ink components on printed coated paper. Part 1. Optical and roughness considerations,” Colloids Surf. A Physicochem. Eng. Asp. 205(3), 183–198 (2002).
[CrossRef]

Räty, J.

I. Niskanen, J. Räty, K.-E. Peiponen, H. Koivula, and M. Toivakka, “Assessment of the complex refractive index of an optically very dense solid layer: Case study offset magenta ink,” Chem. Phys. Lett. 442(4-6), 515–517 (2007).
[CrossRef]

I. Niskanen, J. Räty, and K.-E. Peiponen, “Complex refractive index of turbid liquids,” Opt. Lett. 32(7), 862–864 (2007).
[CrossRef] [PubMed]

J. Räty, E. Keränen, and K.-E. Peiponen, “The complex refractive index measurement of liquids by a novel reflectometer apparatus for the UV-Vis spectral range,” Meas. Sci. Technol. 9(1), 95–99 (1998).
[CrossRef]

Toivakka, M.

I. Niskanen, J. Räty, K.-E. Peiponen, H. Koivula, and M. Toivakka, “Assessment of the complex refractive index of an optically very dense solid layer: Case study offset magenta ink,” Chem. Phys. Lett. 442(4-6), 515–517 (2007).
[CrossRef]

Chem. Phys. Lett.

I. Niskanen, J. Räty, K.-E. Peiponen, H. Koivula, and M. Toivakka, “Assessment of the complex refractive index of an optically very dense solid layer: Case study offset magenta ink,” Chem. Phys. Lett. 442(4-6), 515–517 (2007).
[CrossRef]

Colloids Surf. A Physicochem. Eng. Asp.

J. S. Preston, N. J. Elton, J. C. Husband, J. Dalton, P. J. Heard, and G. C. Allen, “Investigation into the distribution of ink components on printed coated paper. Part 1. Optical and roughness considerations,” Colloids Surf. A Physicochem. Eng. Asp. 205(3), 183–198 (2002).
[CrossRef]

J. S. Preston and L. F. Gate, “The influence of colour and surface topography on the measurement of effective refractive index of offset printed coated papers,” Colloids Surf. A Physicochem. Eng. Asp. 252(2-3), 99–104 (2005).
[CrossRef]

J. Opt. Soc. Am. A

R. M. A. Azzam, “Direct relation between Fresnel’s interface reflection coefficients for the parallel and perpendicular polarizations,” J. Opt. Soc. Am. A 69(7), 1007–1016 (1979).
[CrossRef]

Meas. Sci. Technol.

J. Räty, E. Keränen, and K.-E. Peiponen, “The complex refractive index measurement of liquids by a novel reflectometer apparatus for the UV-Vis spectral range,” Meas. Sci. Technol. 9(1), 95–99 (1998).
[CrossRef]

N. J. Elton and J. C. C. Day, “A reflectometer for the combined measurement of refractive index, microroughness, macroroughness and gloss of low-extinction surfaces,” Meas. Sci. Technol. 20(2), 025309 (2009).
[CrossRef]

Opt. Lett.

Other

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig relations in Optical Materials Research (Springer, 2005).

F. Wooten, Optical Properties of Solids (Academic Press, 1972).

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Figures (4)

Fig. 1
Fig. 1

Lorentzian simulation of a substance which has two absoprtion bands located at 600 and 180 nm. The latter absorption band, being much stronger than the other one and located outside of the visible spectral range, is not shown in the figure. Vertical dashed line represents the baseline correction. λlo and λhi isolates the absorption band and defines the operational wavelength range for the procedure.

Fig. 2
Fig. 2

Flowchart of the procedure.

Fig. 3
Fig. 3

Schematic illustration of REM reflectometer. Besides the reflection detecting mode, a liquid cuvette or holder for solid materials can be installed into the system for the transmission measurements.

Fig. 4
Fig. 4

Refractive index (red curve) and extinction coefficient (blue curve) of a) magenta, b) yellow and c) cyan offset ink. Vertical lines show λlo and λhi for each ink.

Tables (1)

Tables Icon

Table 1 Layer thicknesses (μm) retrieved from the method and from the reference measurement. Uncertainties in the interferometric measurement refers to 95% level of confidence.

Equations (4)

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

T(λ)=exp(α( λ )d)=exp( 4π λ k( λ )d).
r s = cos(θ) n r 2 sin (θ) 2 cos(θ)+ n r 2 sin (θ) 2 r p = n r 2 cos(θ) n r 2 sin (θ) 2 n r 2 cos(θ)+ n r 2 sin (θ) 2 ,
Re{ ε r (ω) }=1+A ω 0 2 ω 2 ( ω 0 2 ω 2 ) 2 + Γ 2 ω 2 Im{ ε r (ω) }=A Γω ( ω 0 2 ω 2 ) 2 + Γ 2 ω 2 ,
n(ω') n = 2 π P 0 ωk(ω)dω ω 2 ω' 2 ,

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