Anal. Chem. 1992, 64, 2885-2887
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Laser Beam Probing in Capillary lubes Frangois Maystre' and Alfred0 E. Bruno Analytical Research, Ciba-Geigy Ltd., CH-4002Basle, Switzerland
INTRODUCTION
As on-column optical detection gains acceptance in various separation techniques, capillary optics has emerged as a new field14 of importancewithin analyticalchemistry. On-column detection is particularly important for microcolumn highperformance liquid chromatography (p-HPLC) and for capillary electrophoresis (CE) because these separation techniques require detectors with volumes in the picoliter to nanoliter range. To date, on-column detectorsfor absorption? fluorescence,Sand refractive index34 have been reported, using different light sources and different optical arrangements to bring light into the capillary bore and to collect it efficiently. From the optical point of view, the main difficulty in using a round capillary is that it acts upon the incoming beam like a thick cylindrical lens with a short focal length. This cylindrical lens effect transforms circular incoming beams into stronglyellipticaloutgoingbeams, making light collection difficult. In addition, this cylindricallens effect is associated with a strong astigmatism that makes further imaging of the probing zone difficult. One way to overcome this problem is to use capillaries with square cross-sections as proposed by Zare et al.6 However,the handling of such capillariespresents increased difficulties,and manufacturing them with a narrow bore, while retaining a square cross-section with satisfactory optical quality, remains a problem. In this technical note, we present the general formalism for paraxial capillary optics using transformation matrices. The particular case of capillaries for which the lens effect vanishes is discussed in detail. For such capillaries, the intensity distribution of the light beam remains practically unchanged after interacting with the capillary, thus making the illumination and collectionoptics much simpler to design. Furthermore, experimental results show that the required geometrical conditions are satisfied for some fused-silica capillaries employed in p-HPLC and in CE. The present scheme exploits the fact that, in most practical cases, the capillary is filled with a transparent liquid (mobile phase or buffer solution) which has a refractive index smaller thanthat of the capillarywall. Thereforethe refractive powers of the outer interface (air-capillary wall) and of the inner interface (capillary wall-mobile phase) have opposite signs and act as converging and diverging lenses, respectively. By selectingthe correct geometry for a capillary, it is thus possible to suppress the lens effect of the capillary. THEORY GeometricalConfiguration. Figure 1 represents an axial (yz) and a side (zz)views of a transparent capillary tube onto which a laser beam is being focused. The optical z axis (1) Synovec, R. E. Anal. Chem. 1987,59, 2877-2884. (2) Bruno, A. E.;Gassmann, E.; Pericles, N.; Anton, K. Anal. Chem. 1989,61, 816-883. (3) Bruno,A.E.;Krattiger,B.;Maystre,F.;Widmer,H.M.Anal. Chem. 1991,63, 2689-2697. (4) Krattiger, B.; Bruno, A. E.; Widmer, H. M.; Geiser, M.; Dbdliker, R. Work done at Analytical Research, Ciba-Geigy Ltd.,CH-4002 Basle, Switzerland. Submitted for publication in Appl. Opt. (51 Amankwa,L.N.: Albin,M.;Kuhr,W. G. Trends Anal. Chem. 1992, 11,114-120. (6) Tsuda, T.;Sweedler, J.V.; Zare, R.N. Anal. Chem. 1990,62,21492152.
z
.,-
I
'
u-
Figure 1. Axial and side view of a transparent capillary tube placed on the beam waist of a focused laser beam. f l and r2 are the outer and the inner radius of the capillary whereas nl and q are the refractive Indices of the capillary wail and of the liquid in the bore, respecttveiy. T and U are the paraxial transformation matrices for each principal plane.
intercepts the capillary at a right angle so that the situation corresponds to the on-axis illumination of a thick cylindrical lens. The geometry is given by the outer radius, rl, and the inner radius, rz, of the tube. Material parameters of importance are the refractive index of the capillary wall, nl, and the refractive index of the liquid within the tube, n2. The tube is in air, so that the surrounding index of refraction, no, is 1. For the mathematical description, it is convenient to place the origin of the coordinate system at the external wall of the tube. In doing so, all the refracting surfaces are on the positive side of the propagation axis. In this analysis,it is assumed that the condition for paraxial optics is satisfied? In practice, this assumption is correct if the fundamental mode of the laser beam is focused onto the capillary with a spot size a few times smaller than the bore diameter. Hence, the propagation of the beam through the tube can be described with paraxial transformation matrices8 that are calculated from the geometry of the optical layout. Transformation Matrices of the Capillary. As a detailed derivation of the transformation matrices of the capillary is beyond the scope of this paper, only the relevant results will be presented here. As shown in Figure 1,the two main radii of curvature of the optical surfaces lie in planes parallel and perpendicular to the capillary axis. Let U and T be the transformation matrices for the corresponding orthogonal components of the beam.8 The matrix U,which accounts for the transformation in the plane parallel to the (7) Klein, M. V.;Furtak,T. E. Optics, 2nded.; John Wiley: New York, 1986; pp 141-151. (8) Klein, M. V.;Furtak, T. E. Optics, 2nd ed.; John Wiley: New York, 1986; pp 151-164.
0003-2700/92/03862885$03.00/0 0 1992 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL, 64, NO. 22, NOVEMBER 15, 1992
Table I. Values for r1, n, and 6 Assuming Complete Compensation for Fused-Silica Capillaries Filled with Water (Le. n1 = 1.46 and nz = 1.33) inner diameter outer diameter astigmatism 2r2 (rm) 2r1 (rm) 6 (rm) 10
28 85
47 141
30 50 70
235 329
100
471
141 198 283
capillary axis, corresponds to a pure translation of optical path length 2u and is readily found to be (1)
with
Derivation of the matrix T, which accounts for the transformation in the plane perpendicular to the capillary axis where the curvature is strongest,involves lengthy calculations. Ultimately, it can be put in the form of (3)
with
It is important to note that by setting t = 1, the matrix T reduces to a pure translation of optical path length 2rl,namely (5)
Under this condition, eq 4 yields the desired requirement for a complete compensation of the opposite lens effects which can be written as
., r1
=n
n,-1 2
G
In most applications nl > n2,so that the right-hand term of eq 6 is positive and leads to a mathematical solution that also has a physical meaning (Le. rl > r2). To illustrate these findings, consider a fused-silica capillary filled with water. The refractive indices are then nl = 1.46 and n2 = 1.33. According to eq 6, complete compensation is obtained when rl/r2 = 4.706. For a capillary with a bore diameter of 2r2 = 75 pm, this corresponds to an outer diameter of 2rl= 353 pm. These dimensions are close to the most commonly used capillaries in CE. Other fused-silica capillaries with dimensions satisfying the complete compensation conditions when filled with water are reported in Table I. It is important to note that a t complete compensation, the ratio of both radii of the capillary is given by eq 6. Therefore the optical path in the plane of the capillary (matrix U) becomes
This value does not match the optical path in the plane perpendicular to the capillary (matrix T). For a circular incoming beam, the output beam is then also circular but
40
do
140
260
240
Inner diameter Cm] Figure 2. Eillptlctty of the output beam produced by a water-filled fused-slllca caplliary having an external diameter of 363 pm as a function of its bore diameter when a laser beam wlth a spot size of 2w0 = 32 pm Is focused on it. Open circles represent measured points for three commercially available caplllarles. The outer and inner diameters of these caplliarles are (left to right) (A) 361 pm, 50 pm: (6)362 pm, 75 pm; (C) 367 pm, 101 pm.
with a pure astigmatism. As reported in Table I, the residual astigmatic distance 6 = 2(r, - p ) (8) is of the order of a few inner capillary diameters and thus only several times larger than the laser spot size.
EXPERIMENTAL SECTION Experimental Setup. A set of commercially available fusedsilicacapillarieswith different diameters (PolimicroTechnologies, Phoenix,AZ) were prepared by removingthe polyimide protective coating over a few millimetres and filling with HPLC-gradewater. The beam of a 2-mW linearly polarized HeNe laser (Uniphase No. 1103P) was focused at a right angle on the capillary using a spherical lens with a focal length off = 30 mm. The lens was mounted on a three-axis translation stage to facilitate the positioning of the laser beam with respect to the capillary. The spot size was measured without capillary to be 2w0 = 32 pm. The ellipticity(i.e. the ratio between the long axis and the short axis) of the cross-section of the output beam was measured with a ruler on a screen placed at a distance d = 300 mm away from the capillary.
RESULTS AND DISCUSSION The experimental results for three capillaries with approximately the same outer diameters but different bore diameters are shown in Figure 2. For comparison, the ellipticity of the output beam was computed9 using eqs 1 and 3, as shown in the Appendix. The measured values show good agreement with the theoretical curve, in particular if one takes into consideration the accuracy of the measurement procedure employed. As predicted by the theory, the capillary where rllr2 = 4.8 and which is labeled B in Figure 2 best approximates the value for complete compensation (Le. rllr2 = 4.7), and practically no ellipticity is observed in the output beam. It is important to note that the theoretical curve has a relatively flat minimum and therefore the tolerances on the dimensions of the capillary are fairly large. For a capillary specified to minimize ellipticity at a given refractive index value of the buffer, the tolerances on the refractive index are also fairly large. As an example, a capillary with outer and inner diameters of 353 and 75 pm, respectively (i.e. optimized for n2 = 1.33 or water), produces an ellipticity of less than 1.07 over a refractive index range from 1.32 to 1.34. This indicates that refractive index changes due to eluting peaks, the use of different buffer solutions or the use (9)Yariv, A. Optical Electronics, 3rd ed.; Holt-Saundera: New York, 1985;pp 32-34.
ANALYTICAL CHEMISTRY, VOL. 64, NO. 22, NOVEMBER 15, 1992
of a gradient elution techniques will have little effect on the ellipticity. Polyacrylamide gel-filled capillaries were also tested and displayed results close to water-filled capillaries, indicating that this gel has optical properties much like those of water.
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Such cells constitute a good way of boosting the sensitivity of detectors and will be of particular significance when very narrow bore capillaries (e.g. with inner diameter smaller than 50 ctm) become standard in capillary electrophoresis. ACKNOWLEDGMENT
CONCLUSIONS
The possibility of passing a laser beam perpendicularly through a transparent capillary tube without introducing ellipticity has been demonstrated. The important parameters are the ratio of the outer to inner diameters of the capillary and the refractive indices of the capillary wall and of the liquid in the bore. Using these findings, it is possible to design an on-column detection cell in which the light beam remains collimated within the bore. This results in a better defined probing volume with a well-controlled optical path length compared to what is obtained with conventional on-column cells.10 For cells designed accordingto the above geometrical considerations,a substantial reduction of distorting refractive index effects and light scattering is also expected. This would allow for the development of more reliable fluorescence detectors with improved detection limits. On-column multipass absorption cells with increased sensitivity11 can be constructed using the described method. (10) Stewart, J. E.Appl. Opt. 1981,20,654-659. (11) Wang,T.;Aiken, J. H.; Huie, C. W.; Hartwick, R. A. Anal. Chem. 1991,63, 1372-1376.
We would like to thank H. M. Widmer for supporting this research and E. Verpoorte for critically reviewing the manuscript. APPENDIX
Ellipticity of the Output Beam. With the propagation matrices given in eqs 1and 3, the cross-section of the output beam is readily computed. In general, this cross-section is elliptical and the ratio between the long axis a and the short axis b is
where k = 2u/X is the free space wave number and 2w0 is the spot size (diameter) of the incoming laser beam.
RECEIVED for review May
20, 1992.
1992.
Registry No. Silica, 60676-86-0.
Accepted August 12,
