Abstract

The spectral transmission factor of liquids is currently determined by spectrophotometry for various applications, including spectrocolorimetry. Applications exist that require an accuracy of the order of 10-3 or higher in the intrinsic transmission factor. This requirement brings about the exploration of the corrections made necessary by the measuring cells’ lack of pairing, the reference liquid’s (water or solvent) spectral nonflatness, the refractive-index difference between the sample and the reference liquid, and the multiple reflections on cell walls. An analysis is conducted, and a procedure is presented for the self-correction of the cell’s lack of pairing and for the correction of systematic errors from the reference liquid’s spectral nonflatness as well as for the refractive-index discrepancies between the sample and the reference liquids and for the multiple beam reflections.

© 1998 Optical Society of America

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References

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  1. J. Ingle, S. R. Crouch, Spectrochemical Analysis (Prentice-Hall, N.J., 1988).
  2. J. D. Ingle, “Precision characteristics of simple spectrophotometers,” Ann. Chem. Acta 88, 131–139 (1977).
    [CrossRef]
  3. International Standard Organisation, International Electrotechnical Commission, Organisation International de Ḿtrologie Légal, Bureau International des Poids et Mesures, “Guide to the expression of uncertainty in measurements,” ISO/TAG 4/WG3 (International Organization for Standardization, Geneve, Switzerland, 1993).
  4. Central Bureau of Commission International de Eclairage, Colourimetry 15.2 (Vienna, Austria1986).
  5. F. M. Sogandares, E. S. Fry, “Absorption spectrum (340–640 nm) of pure water. 1. Photothermal measurements,” Appl. Opt. 36, 8699–8709 (1997).
    [CrossRef]
  6. M. Born, E. Wolf, Principle of Optics (Pergamon, Oxford, 1975).
  7. O. D. D. Soares, “Spectrocolourimetry in wines,” FV 1017-2914/230196, (Office International de la Vigne et du Vin, Paris, 1995).
  8. O. D. D. Soares, G. Mignemi, P. Barros, “Collaborative studies in wine spectrocolourimetry,” Thirty-Sixth Session, Subcommittee Analytical Methods (Office International de la Vigne et du Vin, Paris, 1996).
  9. Z. Knitte, Optics of Thin Films (Wiley, London, 1976).
  10. E. N. Grossman, D. G. McDonald, “Partially coherence transmittance of dielectric lamellae,” Opt. Eng. 34, 1289–1295 (1995).
    [CrossRef]

1997 (1)

1995 (1)

E. N. Grossman, D. G. McDonald, “Partially coherence transmittance of dielectric lamellae,” Opt. Eng. 34, 1289–1295 (1995).
[CrossRef]

1977 (1)

J. D. Ingle, “Precision characteristics of simple spectrophotometers,” Ann. Chem. Acta 88, 131–139 (1977).
[CrossRef]

Barros, P.

O. D. D. Soares, G. Mignemi, P. Barros, “Collaborative studies in wine spectrocolourimetry,” Thirty-Sixth Session, Subcommittee Analytical Methods (Office International de la Vigne et du Vin, Paris, 1996).

Born, M.

M. Born, E. Wolf, Principle of Optics (Pergamon, Oxford, 1975).

Crouch, S. R.

J. Ingle, S. R. Crouch, Spectrochemical Analysis (Prentice-Hall, N.J., 1988).

Fry, E. S.

Grossman, E. N.

E. N. Grossman, D. G. McDonald, “Partially coherence transmittance of dielectric lamellae,” Opt. Eng. 34, 1289–1295 (1995).
[CrossRef]

Ingle, J.

J. Ingle, S. R. Crouch, Spectrochemical Analysis (Prentice-Hall, N.J., 1988).

Ingle, J. D.

J. D. Ingle, “Precision characteristics of simple spectrophotometers,” Ann. Chem. Acta 88, 131–139 (1977).
[CrossRef]

Knitte, Z.

Z. Knitte, Optics of Thin Films (Wiley, London, 1976).

McDonald, D. G.

E. N. Grossman, D. G. McDonald, “Partially coherence transmittance of dielectric lamellae,” Opt. Eng. 34, 1289–1295 (1995).
[CrossRef]

Mignemi, G.

O. D. D. Soares, G. Mignemi, P. Barros, “Collaborative studies in wine spectrocolourimetry,” Thirty-Sixth Session, Subcommittee Analytical Methods (Office International de la Vigne et du Vin, Paris, 1996).

Soares, O. D. D.

O. D. D. Soares, “Spectrocolourimetry in wines,” FV 1017-2914/230196, (Office International de la Vigne et du Vin, Paris, 1995).

O. D. D. Soares, G. Mignemi, P. Barros, “Collaborative studies in wine spectrocolourimetry,” Thirty-Sixth Session, Subcommittee Analytical Methods (Office International de la Vigne et du Vin, Paris, 1996).

Sogandares, F. M.

Wolf, E.

M. Born, E. Wolf, Principle of Optics (Pergamon, Oxford, 1975).

Ann. Chem. Acta (1)

J. D. Ingle, “Precision characteristics of simple spectrophotometers,” Ann. Chem. Acta 88, 131–139 (1977).
[CrossRef]

Appl. Opt. (1)

Opt. Eng. (1)

E. N. Grossman, D. G. McDonald, “Partially coherence transmittance of dielectric lamellae,” Opt. Eng. 34, 1289–1295 (1995).
[CrossRef]

Other (7)

J. Ingle, S. R. Crouch, Spectrochemical Analysis (Prentice-Hall, N.J., 1988).

International Standard Organisation, International Electrotechnical Commission, Organisation International de Ḿtrologie Légal, Bureau International des Poids et Mesures, “Guide to the expression of uncertainty in measurements,” ISO/TAG 4/WG3 (International Organization for Standardization, Geneve, Switzerland, 1993).

Central Bureau of Commission International de Eclairage, Colourimetry 15.2 (Vienna, Austria1986).

M. Born, E. Wolf, Principle of Optics (Pergamon, Oxford, 1975).

O. D. D. Soares, “Spectrocolourimetry in wines,” FV 1017-2914/230196, (Office International de la Vigne et du Vin, Paris, 1995).

O. D. D. Soares, G. Mignemi, P. Barros, “Collaborative studies in wine spectrocolourimetry,” Thirty-Sixth Session, Subcommittee Analytical Methods (Office International de la Vigne et du Vin, Paris, 1996).

Z. Knitte, Optics of Thin Films (Wiley, London, 1976).

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Figures (9)

Fig. 1
Fig. 1

Measurement of the cells, pairing discrepancies in liquid samples’ spectrophotometry. (a) Reference reading without cells, S r ; (b) test reading to compute S c with both cells inserted and filled with distilled water; (c) spectral transmission factor measurement and computation of S s .

Fig. 2
Fig. 2

Example of verification of the degree of pairing of the measuring cells for the reference and the sample beam: S r , spectral scanning of beam ratio without cells introduced (transmission reference line); S c , spectral scanning of beam ratio with reference and sample beam going through the pair of cells filled with distilled water.

Fig. 3
Fig. 3

Flux budget through a measuring cell. The flux Φ a sees four interfaces ①, ②, ③ and ④. The refractive index varies by steps, following the sequence n 0, n q , n s , n q , and n 0 where n s is the sample-liquid refractive index and T s is the internal transmission factor of the sample-liquid film in the sample cell. The n 0 and the n q are the refractive indices of the air and the quartz, the assumed cell material.

Fig. 4
Fig. 4

Plot of the fractional correction factor ε to be applied to the spectral scan ratio S s to yield the internal transmission factor of a sample-liquid film for a measuring cell in quartz (lower curves, n q ) and in glass, (upper curves, n g ); solid curves, for the measuring procedure of Fig. 1 and Eq. (8), as described in the text (assumed T w = 1); dashed curves, for the corresponding values for the correction factor δ, from Eq. (24).

Fig. 5
Fig. 5

Modulation effect on the transmission factor of a quartz cell filled with distilled water for an internal path of 2 mm.

Fig. 6
Fig. 6

Determination of the spectral transmission factor of water, T w , after corrections for multiple beam reflections.

Fig. 7
Fig. 7

Cycle of measurements for dark signal correction (spectrophotometer set at optical zero).

Fig. 8
Fig. 8

Dispersion curves of n q (λ), measuring cells wall material (fused quartz); n w (λ), distilled water; and n s (λ) = Port Wine 97/00121/01 Tinto Aloirado.

Fig. 9
Fig. 9

Measured spectra S s (λ) of the sample Port Wine 97/00121/01 Tinto Aloirado with a quartz cell of 2-mm thickness for the liquid film and of T w (λ), the internal spectral transmission factor of the distilled water film inside of the same cell when filled with distilled water.

Tables (2)

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Table 1 Effect of Systematic Errors on the Color Coordinates Evaluated for the Port Wine 97/00121/01 Tinto Aloirado a

Tables Icon

Table 2 Color Difference between Color Evaluation Results Considering and Ignoring the Described Corrections

Equations (24)

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S m λ = S c S r = T ca T cr ,
S m λ = T ca / T cr = 1 ± 2 μ T cr .
S s λ = T cas / T ca ,
T c = T s 1 - ρ oq 2 1 - ρ qs 2 exp - a d + d ,
ρ oq = n 0 - n q n 0 + n q 2 ,     ρ qs = n s - n q n s + n q 2 ,
S s λ = T s T w 1 - ρ qs 1 - ρ qw 2 = T s T w n s n w 2 n q + n w n q + n s 4 ,
1 ε = 1 T w n s n w 2 n q + n w n q + n s 4 .
1 ε = n s n w 2 n q + n w n q + n s 4 ,     T w = 1 .
n q 2 = n s n w ,
n s = n w .
n s = n w + Δ ,     Δ < 1 ,
1 ε 1 + 2 Δ   n q - n w n w n q + n w .
S w λ = T w T a n w n a 2 n q + n a n q + n w 4 ,
T c = 1 - r 0 q 2 2 1 - r qs 2 2 1 + r 0 q 2 r qs 2 + 2 r 0 q r qs cos   ϕ d 1 + r 0 q 2 r qs 2 + 2 r 0 q r qs cos   ϕ d   T s exp - a d + d ,
r 0 q = n 0 - n q n 0 + n q ,     r qs = n q - n s n q + n s ,
ϕ d = 4 π λ 0   n q d   cos   θ d + 2 ψ d , ϕ d = 4 π λ 0   n q d   cos   θ d + 2 ψ d ,
T c T s exp - a d + d 1 - 2 r 0 q 2 + r qs 2 - 4 r 0 q r qs cos ϕ d + ϕ d 2 cos ϕ d - ϕ d 2 + .
ϕ d - ϕ d 2 2 π λ 0   n q - d   n s 2 2 n q 2 2 θ s α + α 2 + γ 1 - n s 2 2 n q 2 θ s + α 2 + 2 ψ d - ψ d ,
Δ λ 0 = λ 0 2 c - λ 0 ,
c = n q - d   n s 2 2 n q 2 2 θ s   α + α 2 + γ 1 - n s 2 2 n q 2 θ s + α 2 .
T w = S w 1 - 4 r 0 q 2 1 - 2 r 0 q 2 + r qw 2 ,
S s * λ = S ¯ s λ - S ¯ 0 λ S ¯ c λ - S ¯ 0 λ ,
σ 2 S s * = 1 S c - S 0 2 σ 2 S s + 1 S c - S 0 2 × S s - S c 2 σ 2 S 0 + S s - S 0 2 σ 2 S c .
T s = S s λ T w 1 - 2 r 0 q 2 + r qs 2 1 - 2 r 0 q 2 + r qw 2 , δ = 1 - 2 r 0 q 2 + r qw 2 1 - 2 r 0 q 2 + r qs 2 .

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