Abstract

The fringe pattern observed in a far field after a laser beam illuminates a fused silica capillary immersed in a refractive-index matching material and filled with an analyte fluid is exploited to develop a sensitive optical detector for capillary chemical analysis. The inner capillary interface splits the laser beam into a reflected beam fan and a refracted beam fan, which, on overlapping in the far field, lead to interferences. The intensity and the position of the fringes for capillaries with 250 μm ≥ i.d. (inner diameter) ≥ 25 μm are well reproduced by the presented model. The calculation predicts the fringe pattern for various beam/i.d. geometric configurations and is used to optimize the performance of the nanoliter–picoliter refractive-index on-column detection studied. It is found that the best contrast corresponds to a capillary that is illuminated with a beam waist of w0 ~ i.d./12, which is off-center focused with an offset of s ~ i.d./2. For a given interference pattern, the fringes that are found to be more sensitive to Δn are those that appear near the optical axis but still retain high intensity and contrast. The sensitivity increases approximately linearly with the fringe number, and the maximal fringe number increases proportionally with the i.d.

© 1993 Optical Society of America

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References

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  1. T. Braun, S. Nagydiosi-Rozsa, “Capillary electrophoresis: prospects for growth,” Trends Anal. Chem. 10, 266–268 (1991).
    [CrossRef]
  2. A. G. Ewing, R. A. Wallingford, T. M. Olefirowicz, “Capillary electrophoresis,” Anal. Chem. 61, 292A–303A (1989).
    [CrossRef] [PubMed]
  3. N. J. Dovichi, “Laser-based microchemical analysis,” Rev. Sci. Instrum. 61, 3653–3666 (1990).
    [CrossRef]
  4. E. S. Yeung, Detectors for Liquid Chromatography (Wiley, New York, 1986), Chap. 1.
  5. N. J. Dovichi, “Thermo-optical spectrometries in analytical chemistry,” Crit. Rev. Anal. Chem. 17, 357–423 (1987).
    [CrossRef]
  6. A. E. Bruno, A. Paulus, D. J. Bornhop, “Thermo-optical absorption detection in 25-μm-i.d. capillaries: capillary electrophoresis of dansylamino acids mixtures,” Appl. Spectrosc. 45, 462–467 (1991).
    [CrossRef]
  7. D. J. Bornhop, N. J. Dovichi, “Simple nanoliter refractive index detector,” Anal. Chem. 58, 504–505 (1986).
    [CrossRef]
  8. D. J. Bornhop, N. J. Dovichi, “Simultaneous laser-based refractive index and absorbance determinations within microliter diameter capillary tubes,” Anal. Chem. 59, 1632–1636 (1987).
    [CrossRef]
  9. A. E. Bruno, B. Krattiger, F. Maystre, H. M. Widmer, “On-column laser-based refractive index detector for capillary electrophoresis,” Anal. Chem. 63, 2689–2697 (1991).
    [CrossRef]
  10. D. Marcuse, Principles of Optical Fibre Measurements, 1st ed. (Academic, New York, 1981), Chap. 4.5, p. 153.
  11. L. S. Watkins, “Scattering from side-illuminated clad glass fibers for determination of fiber parameters,” J. Opt. Soc. Am. 64, 767–772 (1974).
    [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 1.5, p. 36.
  13. A. Yariv, Optical Electronics (Holt, Rinehart & Winston, New York, 1985), Chap. 2.5, p. 28.
  14. R. E. Synovec, “Refractive index effects in cylindric detector cell designs for microbore high-performance liquid chromatography,” Anal. Chem. 59, 2877–2884 (1987).
    [CrossRef]
  15. J. Pawliszin, M. F. Weber, M. J. Dignam, “Dual-beam laser deflection sensor,” Rev. Sci. Instrum. 56, 1740–1743 (1985).
    [CrossRef]
  16. A. E. Bruno, “Laser based refractive index detection in capillary tubes,” in Laser Applications to Chemical Analysis, Vol. 2 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 165.

1991 (3)

T. Braun, S. Nagydiosi-Rozsa, “Capillary electrophoresis: prospects for growth,” Trends Anal. Chem. 10, 266–268 (1991).
[CrossRef]

A. E. Bruno, B. Krattiger, F. Maystre, H. M. Widmer, “On-column laser-based refractive index detector for capillary electrophoresis,” Anal. Chem. 63, 2689–2697 (1991).
[CrossRef]

A. E. Bruno, A. Paulus, D. J. Bornhop, “Thermo-optical absorption detection in 25-μm-i.d. capillaries: capillary electrophoresis of dansylamino acids mixtures,” Appl. Spectrosc. 45, 462–467 (1991).
[CrossRef]

1990 (1)

N. J. Dovichi, “Laser-based microchemical analysis,” Rev. Sci. Instrum. 61, 3653–3666 (1990).
[CrossRef]

1989 (1)

A. G. Ewing, R. A. Wallingford, T. M. Olefirowicz, “Capillary electrophoresis,” Anal. Chem. 61, 292A–303A (1989).
[CrossRef] [PubMed]

1987 (3)

N. J. Dovichi, “Thermo-optical spectrometries in analytical chemistry,” Crit. Rev. Anal. Chem. 17, 357–423 (1987).
[CrossRef]

R. E. Synovec, “Refractive index effects in cylindric detector cell designs for microbore high-performance liquid chromatography,” Anal. Chem. 59, 2877–2884 (1987).
[CrossRef]

D. J. Bornhop, N. J. Dovichi, “Simultaneous laser-based refractive index and absorbance determinations within microliter diameter capillary tubes,” Anal. Chem. 59, 1632–1636 (1987).
[CrossRef]

1986 (1)

D. J. Bornhop, N. J. Dovichi, “Simple nanoliter refractive index detector,” Anal. Chem. 58, 504–505 (1986).
[CrossRef]

1985 (1)

J. Pawliszin, M. F. Weber, M. J. Dignam, “Dual-beam laser deflection sensor,” Rev. Sci. Instrum. 56, 1740–1743 (1985).
[CrossRef]

1974 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 1.5, p. 36.

Bornhop, D. J.

A. E. Bruno, A. Paulus, D. J. Bornhop, “Thermo-optical absorption detection in 25-μm-i.d. capillaries: capillary electrophoresis of dansylamino acids mixtures,” Appl. Spectrosc. 45, 462–467 (1991).
[CrossRef]

D. J. Bornhop, N. J. Dovichi, “Simultaneous laser-based refractive index and absorbance determinations within microliter diameter capillary tubes,” Anal. Chem. 59, 1632–1636 (1987).
[CrossRef]

D. J. Bornhop, N. J. Dovichi, “Simple nanoliter refractive index detector,” Anal. Chem. 58, 504–505 (1986).
[CrossRef]

Braun, T.

T. Braun, S. Nagydiosi-Rozsa, “Capillary electrophoresis: prospects for growth,” Trends Anal. Chem. 10, 266–268 (1991).
[CrossRef]

Bruno, A. E.

A. E. Bruno, A. Paulus, D. J. Bornhop, “Thermo-optical absorption detection in 25-μm-i.d. capillaries: capillary electrophoresis of dansylamino acids mixtures,” Appl. Spectrosc. 45, 462–467 (1991).
[CrossRef]

A. E. Bruno, B. Krattiger, F. Maystre, H. M. Widmer, “On-column laser-based refractive index detector for capillary electrophoresis,” Anal. Chem. 63, 2689–2697 (1991).
[CrossRef]

A. E. Bruno, “Laser based refractive index detection in capillary tubes,” in Laser Applications to Chemical Analysis, Vol. 2 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 165.

Dignam, M. J.

J. Pawliszin, M. F. Weber, M. J. Dignam, “Dual-beam laser deflection sensor,” Rev. Sci. Instrum. 56, 1740–1743 (1985).
[CrossRef]

Dovichi, N. J.

N. J. Dovichi, “Laser-based microchemical analysis,” Rev. Sci. Instrum. 61, 3653–3666 (1990).
[CrossRef]

N. J. Dovichi, “Thermo-optical spectrometries in analytical chemistry,” Crit. Rev. Anal. Chem. 17, 357–423 (1987).
[CrossRef]

D. J. Bornhop, N. J. Dovichi, “Simultaneous laser-based refractive index and absorbance determinations within microliter diameter capillary tubes,” Anal. Chem. 59, 1632–1636 (1987).
[CrossRef]

D. J. Bornhop, N. J. Dovichi, “Simple nanoliter refractive index detector,” Anal. Chem. 58, 504–505 (1986).
[CrossRef]

Ewing, A. G.

A. G. Ewing, R. A. Wallingford, T. M. Olefirowicz, “Capillary electrophoresis,” Anal. Chem. 61, 292A–303A (1989).
[CrossRef] [PubMed]

Krattiger, B.

A. E. Bruno, B. Krattiger, F. Maystre, H. M. Widmer, “On-column laser-based refractive index detector for capillary electrophoresis,” Anal. Chem. 63, 2689–2697 (1991).
[CrossRef]

Marcuse, D.

D. Marcuse, Principles of Optical Fibre Measurements, 1st ed. (Academic, New York, 1981), Chap. 4.5, p. 153.

Maystre, F.

A. E. Bruno, B. Krattiger, F. Maystre, H. M. Widmer, “On-column laser-based refractive index detector for capillary electrophoresis,” Anal. Chem. 63, 2689–2697 (1991).
[CrossRef]

Nagydiosi-Rozsa, S.

T. Braun, S. Nagydiosi-Rozsa, “Capillary electrophoresis: prospects for growth,” Trends Anal. Chem. 10, 266–268 (1991).
[CrossRef]

Olefirowicz, T. M.

A. G. Ewing, R. A. Wallingford, T. M. Olefirowicz, “Capillary electrophoresis,” Anal. Chem. 61, 292A–303A (1989).
[CrossRef] [PubMed]

Paulus, A.

Pawliszin, J.

J. Pawliszin, M. F. Weber, M. J. Dignam, “Dual-beam laser deflection sensor,” Rev. Sci. Instrum. 56, 1740–1743 (1985).
[CrossRef]

Synovec, R. E.

R. E. Synovec, “Refractive index effects in cylindric detector cell designs for microbore high-performance liquid chromatography,” Anal. Chem. 59, 2877–2884 (1987).
[CrossRef]

Wallingford, R. A.

A. G. Ewing, R. A. Wallingford, T. M. Olefirowicz, “Capillary electrophoresis,” Anal. Chem. 61, 292A–303A (1989).
[CrossRef] [PubMed]

Watkins, L. S.

Weber, M. F.

J. Pawliszin, M. F. Weber, M. J. Dignam, “Dual-beam laser deflection sensor,” Rev. Sci. Instrum. 56, 1740–1743 (1985).
[CrossRef]

Widmer, H. M.

A. E. Bruno, B. Krattiger, F. Maystre, H. M. Widmer, “On-column laser-based refractive index detector for capillary electrophoresis,” Anal. Chem. 63, 2689–2697 (1991).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 1.5, p. 36.

Yariv, A.

A. Yariv, Optical Electronics (Holt, Rinehart & Winston, New York, 1985), Chap. 2.5, p. 28.

Yeung, E. S.

E. S. Yeung, Detectors for Liquid Chromatography (Wiley, New York, 1986), Chap. 1.

Anal. Chem. (5)

A. G. Ewing, R. A. Wallingford, T. M. Olefirowicz, “Capillary electrophoresis,” Anal. Chem. 61, 292A–303A (1989).
[CrossRef] [PubMed]

D. J. Bornhop, N. J. Dovichi, “Simple nanoliter refractive index detector,” Anal. Chem. 58, 504–505 (1986).
[CrossRef]

D. J. Bornhop, N. J. Dovichi, “Simultaneous laser-based refractive index and absorbance determinations within microliter diameter capillary tubes,” Anal. Chem. 59, 1632–1636 (1987).
[CrossRef]

A. E. Bruno, B. Krattiger, F. Maystre, H. M. Widmer, “On-column laser-based refractive index detector for capillary electrophoresis,” Anal. Chem. 63, 2689–2697 (1991).
[CrossRef]

R. E. Synovec, “Refractive index effects in cylindric detector cell designs for microbore high-performance liquid chromatography,” Anal. Chem. 59, 2877–2884 (1987).
[CrossRef]

Appl. Spectrosc. (1)

Crit. Rev. Anal. Chem. (1)

N. J. Dovichi, “Thermo-optical spectrometries in analytical chemistry,” Crit. Rev. Anal. Chem. 17, 357–423 (1987).
[CrossRef]

J. Opt. Soc. Am. (1)

Rev. Sci. Instrum. (2)

J. Pawliszin, M. F. Weber, M. J. Dignam, “Dual-beam laser deflection sensor,” Rev. Sci. Instrum. 56, 1740–1743 (1985).
[CrossRef]

N. J. Dovichi, “Laser-based microchemical analysis,” Rev. Sci. Instrum. 61, 3653–3666 (1990).
[CrossRef]

Trends Anal. Chem. (1)

T. Braun, S. Nagydiosi-Rozsa, “Capillary electrophoresis: prospects for growth,” Trends Anal. Chem. 10, 266–268 (1991).
[CrossRef]

Other (5)

E. S. Yeung, Detectors for Liquid Chromatography (Wiley, New York, 1986), Chap. 1.

D. Marcuse, Principles of Optical Fibre Measurements, 1st ed. (Academic, New York, 1981), Chap. 4.5, p. 153.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 1.5, p. 36.

A. Yariv, Optical Electronics (Holt, Rinehart & Winston, New York, 1985), Chap. 2.5, p. 28.

A. E. Bruno, “Laser based refractive index detection in capillary tubes,” in Laser Applications to Chemical Analysis, Vol. 2 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 165.

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Figures (12)

Fig. 1
Fig. 1

Illustration of the optical arrangement of the refractive-index detector for CE, which resembles a Young double-slit interferometric arrangement. The fringes, which are formed by the coherent addition of the exiting TP and TIR rays, are represented as moiré structures in the figure.

Fig. 2
Fig. 2

Geometric parameters used to describe the paths of the TIR and the TP rays.

Fig. 3
Fig. 3

Ideal fringe pattern (equal intensities of interfering rays) versus scattering angle α for a water-filled capillary with i.d. = 100 μm and N = 0.914.

Fig. 4
Fig. 4

Sensitivity S as a function of scattering angle α for a 100-μm-i.d. water-filled capillary. S is maximum for axial rays, where the longest possible optical path through the sample occurs. RIU, refractive-index unit.

Fig. 5
Fig. 5

Intensity attenuation that is due to the curvature of the inner capillary wall.

Fig. 6
Fig. 6

Fringe pattern simulation for a 100-μm-i.d. fused silica capillary filled with water, illuminated by a beam with a waist of w0 = 8.4 μm and an offset of s = 48 μm. The individual intensity contributions of the TIR and TP rays are given as dotted curves. Maximum fringe contrast is observed for equal intensities at α = 12° and α = 28°.

Fig. 7
Fig. 7

Fringe pattern simulations for 100-μm-i.d. capillary illuminated by a beam with a waist w0 = 8.4 μm for various beam offsets ranging from s = 0 μm to s = 60 μm.

Fig. 8
Fig. 8

Experimental setup used to record the fringe patterns. The capillary, which is immersed in RIMF, is concentric to the cell tube and the x-axis translation corresponds to the beam offset s.

Fig. 9
Fig. 9

Experimental (solid curve) and simulated (dotted curve) fringe patterns. Best fit is achieved for a simulation with i.d. = 105 μm, which is slightly outside production tolerance of the capillary (error probably caused by imperfection of the cell window).

Fig. 10
Fig. 10

Recorded and simulated fringe patterns for capillaries with i.d. = 50, 25, 15, and 5 μm illuminated by a beam with a waist of w0 = 22 μm and beam offsets of s = 36, 21, 19, and 0 μm, respectively.

Fig. 11
Fig. 11

Sensitivity calculation performed with two fringe patterns for a 100-μm-i.d. tube illuminated by a beam with w0 = 8.4 μm for Δn = 1.0 × 10−3 refractive-index units. The first derivative of the fringe pattern simulation is used to determine the points of maximum intensity, and is shown in the lower trace.

Fig. 12
Fig. 12

Fringe sensitivity Gf as a function of fringe number m for various capillaries (data from Table 1). The larger capillaries display more fringes and, for equivalent fringes, higher sensitivities. The fringe number dependence can also be interpreted as the path-length dependence of Gf.

Tables (1)

Tables Icon

Table 1 Computed Fringe Sensitivities Gf As Defined in Eq. (19) for the Most Important Fringes for Capillaries with 25 μm ≤ i.d. ≤ 250 μm

Equations (30)

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N = n i n e 1 ,
H TP = x TP R ,             0 H TP H max ,
H TIR = x TIR R ,             H max H TIR 1 ,
H TIR = 1 N [ ( N 2 - H TP 2 ) 1 / 2 ( 1 - H TP 2 ) 1 / 2 + H TP 2 ] .
α ( H TP ) = 2 [ arcsin ( H TP / N ) - arcsin ( H TP ) ] .
OP TIR ( N , H TP ) = 2 R n e N [ ( N - H TP ) ( 1 - H TP 2 ) 1 / 2 + H TP ( N 2 - H TP 2 ) 1 / 2 ] ,
OP TP ( N , H TP ) = 2 R n e ( N 2 - H TP 2 ) 1 / 2 .
Φ p = - 2 arctan ( 1 N 2 { N 2 ( 1 - N 2 ) H TP 2 [ ( 1 - N 2 ) 1 / 2 - ( N 2 - H TP 2 ) 1 / 2 ] 2 - 1 } 1 / 2 ) ,
Φ s = - 2 arctan ( { N 2 ( 1 - N 2 ) H TP 2 [ ( 1 - N 2 ) 1 / 2 - ( N 2 - H TP 2 ) 1 / 2 ] 2 - 1 } 1 / 2 ) ,
Ψ ( H TP , N ) = 2 π λ ( OP TP - OP TIR ) - Φ p , s ,
Ψ ( H TP , N ) = 4 π R n e λ H TP - N N × [ ( 1 - H TP 2 ) 1 / 2 - ( N 2 - H TP 2 ) 1 / 2 ] - Φ p , s .
m = Ψ 2 π ,
H max = N .
m max = Ψ max 2 π = 2 R ( n i - n e ) + 0.5 λ λ .
S = 1 π Ψ n i = 1 π n e Ψ N .
S = 4 R λ { H TP N 2 [ ( N 2 - H TP 2 ) 1 / 2 - ( 1 - H TP 2 ) 1 / 2 ] + ( N - H TP ) ( N 2 - H TP 2 ) 1 / 2 } .
S max = 4 R λ ,
T p ( H TP ) = 4 N 2 ( N 2 - H TP 2 ) 1 / 2 ( 1 - H TP 2 ) 1 / 2 [ ( N 2 - H TP 2 ) 1 / 2 + N 2 ( 1 - H TP 2 ) 1 / 2 ] 2 ,
T s ( H TP ) = 4 ( N 2 - H TP 2 ) 1 / 2 ( 1 - H TP 2 ) 1 / 2 [ ( N 2 - H TP 2 ) 1 / 2 + ( 1 - H TP 2 ) 1 / 2 ] 2 .
I in Δ x Δ y = I out ( Δ α u ) Δ y .
D TP 2 ( H TP ) = I out I in = | 1 u x TP α | ,
D TIR 2 ( H TP ) = I out I in = | 1 u x TIR α | .
D TP 2 ( H TP ) = R 2 u ( 1 - H TP 2 ) 1 / 2 ( N 2 - H TP 2 ) 1 / 2 ( 1 - H TP 2 ) 1 / 2 - ( N 2 - H TP 2 ) 1 / 2 ,
D TIR 2 ( H TP ) = ( 1 - H TP 2 ) 1 / 2 u .
A TP = T ( H TP ) D TP ( H TP ) exp [ i OP TP ( H TP ) ] ,
A TIR = D TIR ( H TP ) exp [ i OP TIR ( H TP ) ] .
I ( N , H TP ) = A TP + A TIR 2 = ( A TP ) 2 + ( A TIR ) 2 + 2 A TP A TIR cos Ψ ( N , H TP ) ,
A G ( H ) = A 0 exp [ - ( H R - s w 0 ) 2 ] ,
G f = Δ α Δ n i σ .
G f = - S .

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