REVIEW OF SCIENTIFIC INSTRUMENTS
VOLUME 71, NUMBER 7
JULY 2000
Ultrasmall volume refractive index detection using microinterferometry
Kelly Swinney, Dmitry Markov, and Darryl J. Bornhopa)
Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061
共Received 8 February 2000; accepted for publication 27 March 2000兲
A microinterferometric backscatter detector 共MIBD兲 has been developed to perform subnanoliter
volume refractive index measurements using a simple, folded optical train based on the interaction
of a laser beam and a fused silica capillary tube. Positional changes of the interference pattern
extrema 共fringes兲 allow for the determination of ⌬n at the 10⫺7 level, corresponding to 5.3 pmole
or 0.48 ng of solute, when thermal noise is controlled at 8⫻10⫺3 °C. MIBD is relatively
path-length insensitive for capillaries ranging in inner diameter from 75 to 775 ␮m, allowing a large
range of detection volumes, from 350 pL to 40 nL, to be produced. A theoretical model of the
microinterferometric backscatter detector has also been developed and evaluated and has been found
to be in agreement with experimental data. This model indicates increased sensitivity of the
instrument as the wavelength of the probe beam and the wall thickness of the capillary tube are
reduced. © 2000 American Institute of Physics. 关S0034-6748共00兲03907-1兴
co-workers.1,6–8 This device uses a HeNe laser to probe a
fused silica capillary directly and can detect changes in refractive index at 1.9 parts in 107 within a detector volume of
350 pl.1,6–8 Among the important and unique features of
MIBD are its relative path-length insensitivity for capillaries
ranging in inner diameter from 75 to 775 ␮m,6–8 its optical
simplicity, and its insensitivity to alignment. MIBD has been
shown to be capable of providing picogram concentration
detection limits in nanoliter probe volumes, is applicable
to ␮-HPLC,8 and can be used as an on-column capillary
electrophoresis detector12–14 or to perform noninvasive
thermometry.1,15
Here we describe a somewhat extensive fundamental
and theoretical study of MIBD. Included in the discussion is
a quantitative evaluation of the sensitivity of the RI detector
to temperature changes, wavelength, and capillary wall
thickness. Also a discussion on the basic principals leading
to the production of the fringe pattern and how best to detect
changes in the fringe pattern in order to perform sensitive
small volume measurements is put forth.
I. INTRODUCTION
Refractive index 共RI兲 detectors are in general bulk property, nondestructive sensors that are mass sensitive, as such,
they are potential candidates for use as microscheme universal detection. Yet miniaturizing bulk property detectors to
nanoliter volumes is inherently difficult, and therefore, refractive index measurement schemes, to date, have not been
widely used for detection in capillary-scale separations. Most
conventional RI techniques are path-length sensitive making
detection in capillaries problematic especially in the case
where on-column detection is required. In addition, the
variation in RI with temperature (dn/dT) is large for most
fluids (8⫻10⫺4 RIU/°C for water兲,1 thus small changes in
temperature result in appreciable RI signals, compromising
the signal-to-noise 共S/N兲 ratio.
Despite these difficulties, there have been many attempts
to develop refractive index detectors with volumes in the
nanoliter regime.1–11 The most successful attempts have involved some form of beam interference,1–3,5–8 which allows
for the determination of very small phase changes of coherent light. While RI detectors based on interferometry normally exhibit some level of path-length dependency,1–3,5 the
resulting sensitivity of the detector to changes in refractive
index is still high. Among the most promising approaches to
performing RI detection in capillary-scale separation
schemes is the forward scatter technique developed by Bornhop and Dovichi,2 further refined by Krattinger, Bruin, and
Bruno,3 and applied to chip-scale detection by Bruggraf
et al.9 Other novel small volume RI detectors not based on
interferometry include a fiber optic-based device put forth by
Buttry,10 and a technique based on schlieren optics introduced by Pawliszyn.11
To circumvent previous limitations in the miniaturization of the RI detector, a simple microinterferometric backscatter detector 共MIBD兲 was developed by Bornhop and
A. Optical configuration
The general block diagram for the optical configuration
is shown in Figs. 1共A兲 and 1共B兲. All components were
mounted on massive aluminum risers which were bolted to a
4 ft⫻4 ft vibrationally dampened optical bread board 共Newport Corp., CA兲. Side illumination of a fused silica capillary
tube 共PolyMicro Technologies, Phoenix, AZ兲 was provided
by a low power He–Ne laser 共5–10 mW, Melles Griot兲. The
polyimide outer coating was left intact and measures approximately 19 ␮m. The capillary tube was located 40 cm
from the laser head. By slightly tilting the capillary, the
folded optical configuration allows the backscatter radiation,
emanating from the tube in 360 °, to be directed above or
below the plane of excitation and impinge onto the detector
or imaging device, thus providing access to the fringes closest to the centroid. A detection transducer 共described in detail in the following兲 was mounted on a micrometer driven
a兲
Electronic mail: djbornhop@ttu.edu
0034-6748/2000/71(7)/2684/9/$17.00
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© 2000 American Institute of Physics
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Rev. Sci. Instrum., Vol. 71, No. 7, July 2000
Ultrasmall volume
2685
FIG. 1. 共A兲 Top view for the general block diagram of the MIBD optical
train. 共B兲 Side view for the general block diagram of the MIBD optical train.
translation stage 共Newport Corp. CA兲, and positioned directly below the illumination plane of the laser beam at a
distance of 23.0 cm from the capillary tube.
The flow cell 共Fig. 2兲 consisted of a capillary tube
mounted on a massive, black anodized aluminum block. The
aluminum block/capillary assembly was temperature stabilized with a peltier 共MelCor兲 thermoelectric cooler controlled
by 4 A–16 W thermistor-based temperature controller 共ILX
Lightwave, Bozeman, MT兲. The flow cell assembly was
mounted on two stacked translation stages, for ease in positioning, and was tilted at an angle 共⬃7°兲 relative to normal as
shown in Fig. 1共B兲.
FIG. 3. Cross-sectional view of the optical ray trace model for MIBD using
a diode laser with a 250-␮m-i.d., 350-␮m-o.d. capillary and a 20-␮m-thick
polyimide coating. Only three selected rays are shown with three splits.
to a change in RI within the probe volume 关Figs. 4共A兲 and
4共B兲兴. Thus, relative changes in refractive index within the
probe volume can be determined by calibrating the system
for positional changes of the fringe pattern with respect to
the change in solute concentration. As discussed in detail in
the following, positional shifts in the fringe pattern have
been measured in two ways: 共1兲 using a slit/photodetector
B. Signal generation
The high radius of curvature of the capillary, in addition
to a difference in refractive index between the capillary’s
walls and the medium within the capillary, causes the laser
light to be refracted and reflected at each optical interface
resulting in constructive and destructive interference of the
probe beam. This process is shown in the optical ray trace
model presented in Fig. 3. As a result of the tube/light and
fluid/light interaction, a 360° fan of scattered light consisting
of high contrast light and dark spots 共fringes兲 emanates from
the capillary perpendicular to the tube’s central axis. Figure
4共A兲 shows a false color reconstruction for a portion of a
typical interference fringe pattern that results from the unfocused laser beam impinging on the capillary. As the refractive index of the medium within the capillary changes, the
optical path length changes, resulting in positional changes
for the fringes at the detector plane. Upon solute introduction, the position of the backscatter fringes shifts in response
FIG. 2. Block diagram of flow cell assembly.
FIG. 4. 共A兲 False color reconstruction of the fringe pattern illustrating fringe
movement in response to changes in the refractive index of the solution in
the probe volume of the MIBD. 共B兲 The pictorial graph illustrating the
intensity change observed by the slit/photodetector assembly as a result of
fringe movement or a change in RI.
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Rev. Sci. Instrum., Vol. 71, No. 7, July 2000
Swinney, Markov, and Bornhop
assembly, where changes in the light intensity reaching the
detector from the fringe are translated into positional
changes of that fringe and 共2兲 using a charge-coupled device
共CCD兲 imaging device in communication with a laser beam
analyzer to determine positional changes of a fringe directly.
C. Effect of polarization on fringe pattern energy
distribution
The orientation of the plane of polarization of the laser
beam with respect to the central axis of the capillary affects
the intensity distribution of the backscatter fringes.16 These
intensity variations are particularly important to consider
when the backscatter fringes are evaluated with a slit/
photodetector assembly. In short and as shown in Fig. 5共A兲,
orientating the beam’s plane of polarization perpendicular
with respect to the central axis of the capillary results in a
smooth Gaussian-type intensity profile. Yet upon rotation of
the plane of polarization of the laser so that it is parallel with
respect to the central axis of the capillary 关Fig. 5共B兲兴, a series
of second-order high contrast fringes 共high frequency兲 appear within the low frequency fringes. Recall that intensity
changes are used to accurately measure positional changes
共Fig. 4兲. In practice we have found that by simply orientating
the plane of polarization of the laser perpendicular to the
central axis of the capillary, the high frequency fringe pattern
can be efficiently extinguished 关Figs. 5共A兲 and 5共B兲兴.
D. Detection of RI signal
1. Intensity measurement
Because the backscatter fringes are essentially Gaussian
共under the proper conditions兲, a simple approach to measure
the positional shift of the pattern related to the change in RI
is to place a slit/photodetector assembly on the edge of a
fringe 关Fringe 4共B兲兴. Using such an arrangement, a change in
refractive index of the solution in the probe volume produces
a change in the amount of light reaching the active surface of
the photodetector, which is masked by the slit. As the fringe
shifts from a change in refractive index (⌬n) the output from
the detector is observed as a change in voltage. The fringe
shift 共Fig. 5兲 has previously been found to be proportional to
analyte concentration and is generally linear over three
decades.7,8 This simple intensity-based detection method is
inexpensive and easy to implement, yet ultimately limits the
dynamic operation range to a refractive index change equal
to a distance that corresponds to 2␴ for the fringe being
interrogated 共e.g., once the fringe ‘‘maxima’’ or ‘‘minima’’
approaches the slit, nonlinear operation ensues兲.
The slit/photodetector used for observing positional
shifts of the fringe pattern consisted of a pin photodiode
integrated with a 632.8 nm interference filter 共CoherentEaling兲 wired with a simple current to voltage conversion
circuit. The output of the photodiode is conditioned with a
current-to-voltage converter, consisting of a JFET operational amplifier, wired with a 10 M⍀ feedback resistor in
parallel with a 0.01 pF capacitor. A 50 ␮m precision air slit
共Melles Griot兲 was mounted vertically in the center of the
active surface area of the photodetector. The slit/
FIG. 5. 共A兲 False color representation of a typical backscatter fringe when
the plane of polarization of the laser beam is orientated perpendicular with
respect to the central axis of the capillary. Notice the Gaussian-type intensity profile of the fringe. 共B兲 False color representation of a series of backscatter fringes that emerge when the plane of polarization of the laser beam
is orientated parallel with respect the central axis of the capillary. Observed
is a second set of fringes 共high frequency fringes兲 contained or carried by a
set of low frequency fringes. White represents saturation of the CCD camera
while black corresponds to little or no photon flux.
photodetector assembly was housed in a 6 cm⫻2.5 cm
⫻2 cm aluminum dye cast box 共ITT Pomona Electronics兲,
bolted to the aluminum optical bench between the laser and
the capillary, and aligned on the edge of a fringe 关Fig. 4共B兲兴.
The detector is then placed so that a small voltage output is
observed. This position corresponds to the edge of the sloping intensity gradient of the working fringe and is located at
about I⫽1/e 2 of the essentially Gaussian intensity distribution 关Fig. 4共B兲兴. The voltage output from the detector was
amplified by an instrumentation amplifier built in-house
(gain⫽10). Then the analog signal was digitized with an
external DAQ board 共PPIO-AIO8, CyberResearch, Branford,
CT兲 and displayed on a PC computer running a digital stripchart recorder 共LABTECH For Windows兲.
2. Position measurements
The shift of the fringes, in response to changes in refractive index, can also be detected using a position sensor such
as a CCD camera in communication with a laser beam analyzer 共LBA兲. The advantage of position measurements based
on array detection is that they are inherently insensitive to
the nonuniform intensity profile of a single fringe. Further,
fringe movement can be tracked over large distances facilitating enhanced operating dynamic range because detection
is not limited by the width and slope of the fringe. Here,
positional measurements were obtained by employing a 9
␮m pixel CCD camera 共COHU, San Diego, CA兲 based laser
beam analyzer 共LBA兲 共Spiricon, Logan, UT兲. The centroid
determination function of the LBA, which functions by locating the X – Y coordinate pair that corresponds to the center
of the backscatter fringe of interest, was used to measure/
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Rev. Sci. Instrum., Vol. 71, No. 7, July 2000
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quantify the positional shifts of the imaged fringe pattern.
All fringe shift measurements were determined relative to the
initial position of the fringe for the blank solution.
E. Temperature sensitivity: The major source of noise
In measurements of refractive index (n), the primary
source of noise is thermal perturbations. For most fluids, n
has a relatively high thermal coefficient (dn/dT), requiring
very precise temperature stabilization of the system. As an
example, dn/dT for H2O is on the order of 8⫻10⫺4 °C, so
at an analytically useful detection limit for ⌬n of one part in
106 , the temperature-induced signal corresponds to a change
in T of 1.25⫻10⫺2 °C. Therefore, thermal stability of the
system must be maintained to a millidegree centigrade or
better, to determine n at a level of one part in 108 in an
aqueous environment. In the past, we have shown that using
the flow cell depicted in Fig. 2, thermal stability better than
5.0⫻10⫺3 °C over a 30 min period is achievable, allowing
for detection limits of approximately 2 parts in 107 ⌬n. 1 This
flow cell was thermostated with active control using a Peltier
thermoelectric cooling chip 共Melcore, Trenton, NJ兲 controlled by a power supply 共ILX Lightwave, Bozeman, MT兲
wired in feedback from a calibrated thermocouple.
Conversely, the ‘‘noise’’ in RI measurements can be
used to the advantage of the analyst. For example, thermal
sensitivity can be used to determine minute temperature
changes in small-volume following streams, noninvasive
process stream monitoring, and even protein folding.15 The
relationship between dn and dT is linear.8,15,17 Previous results have shown that when all conditions are optimized the
dn/dT response for the MIBD is 1.7⫻10⫺3 RIU °C and a
temperature change of 5.9⫻10⫺5 °C 共or 50 microdegrees C兲
can be detected for the fluid contained or flowing through a
probe volume 2.6 nL 共defined by the inner diameter of the
capillary and the diameter of the probe beam兲.1 Typically,
MIBD can be used to measure thermal changes at the level
of a few millidegrees centigrade noninvasively and to determine dn/dT for fluids, which must be contained or constrained to a small volume.
FIG. 6. Reproducible calibration curve for MIBD using a CCD camera in
communication with a laser beam analyzer 共LBA兲. Plotted is fringe position
or response vs glycerol concentration. Note: Error bars are included in the
graph but fall within the size of each data point.
source兲 did not experience any retardation or interference
with the incoming light. This configuration eliminates capillary tilting in order to gain access to the first fringes. It also
produces a representative configuration, because experimentally little change in the fringe pattern is observed when tilting the tube by 7°. During the tracing step, each ray was
allowed no more than seven splits at each optical interface.
This model was created in such a way that it allows for
modification of any parameter in the system, such as capillary dimensions, wavelength, detector and source locations,
etc., in order to accommodate a particular experimental
setup. Also, the model provides the options of displaying
results in the detector plane as a contour, three dimensional,
or profile plot. By varying the calculation window it is also
possible to display the whole picture or zoom in on a particular fringe. Figure 3 shows a simulation cross section produced by the above-described model for a 250/360 ␮m capillary with a 20-␮m-thick polyimide coating 共selected rays
only兲 illuminated with HeNe laser (␭⫽632.8 nm).
II. RESULTS AND DISCUSSION
F. Model
To further investigate the unique properties of MIBD
and its RI sensitivity, an optical model was constructed using
a sophisticated optical modeling program ASAP 6.5 共BRO Research, Inc.兲. Using built-in functions, the fused silica capillary with a polyimide coating was created with selectable
inner and outer diameters and coating thickness. The long
axis of the capillary symmetry coincides with the x axis of
the local coordinate system. The capillary was illuminated
with a coherent light source consisting of seven base rays
with each ray accompanied by eight parabasal rays, all centered around the z axis at some distance away from the capillary. The resulting backscattered intensity distribution was
observed in the detector plane that was placed along the z
axis at a distance of 23 cm behind the light source. Since the
laser in this model did not have any optical properties except
for the emitted wavelength, the backscattered light traveling
from the capillary toward the detector 共literally through the
A. Detection
1. Position measurements
A calibration curve of fringe position versus glycerol
concentration was generated using the CCD/LBA assembly
to determine the RI sensitivity of MIBD 共Fig. 6兲. A linear
relationship exists between solute concentration and relative
positional shift of the selected backscatter fringe 共third fringe
from centroid兲. Based on the positional response of the
fringe to RI changes, the mass limit of detection for MIBD is
5.28 pmole or 1.02 ng using a 5 nL probe volume and corresponds to a ⌬n⫽1.38⫻10⫺5 RIU. The low resolution of
the integrating software for the CCD imager significantly
limits the sensitivity of the system to positional shifts in the
fringe pattern to 9 ␮m, resulting in poorer detection limits
than those previously reported.4,6,7,11–13 Regardless of the
poorer detection limits produced by a 9 ␮m limiting resolution, the LBA does allow convenient analysis of the fringes
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Rev. Sci. Instrum., Vol. 71, No. 7, July 2000
FIG. 7. Reproducible refractive index calibration curve of fringe position
for the third and sixth fringe right of the centroid vs glycerol concentration.
Error bars are included in the graph but are smaller than the size of the data
points.
and evaluation of their movement in response to change in
refractive index when refractive index changes greater than
the detection limit (⌬n⫽1.38⫻10⫺5 RIU) are produced.
To answer the question of which fringe in the interference pattern is most sensitive to small changes in RI and to
evaluate fringe number versus RI sensitivity, two representative fringes were compared: one near the centroid 共No. 3兲
and an ‘‘outer’’ fringe 共No. 6兲. Figure 7 shows the experimentally reproducible calibration curves of fringe movement
versus glycerol concentration for the two fringes 共third and
sixth兲 chosen for signal interrogation. The slope of the calibration curve for the sixth fringe 共24.8 ␮m/mM兲 is identical
共within experimental error兲 to that of the response produced
from using the third fringe 共24.9 ␮m/mM兲. These data suggest that when using position sensing techniques such as the
CCD/LBA detection method interference fringes located as
far out as the sixth fringe appear to respond to changes in RI
with the same level of sensitivity. Consequently, it is not
necessary to choose one direct backscatter fringe 共first to
sixth兲 over another when the LBA or other position sensitive
methodology is used for detecting fringe movement. Thus,
fringe selection constraints are considerably relaxed when
using array-sensing methodologies.
2. Intensity measurements
Another method for sensing RI changes in MIBD is
based on a fixed photodetector whose active surface area is
masked by an air slit. This configuration allows for the measurement of fringe movement as a function of the light intensity impinging upon the fixed photodetector as the fringe
moves across the face of the detector. While using a CCD
allows detection to be indifferent to the intensity distribution
of an individual fringe, here fringe selection is critical. Success is dependent upon choosing a fringe with a uniform
intensity profile. As shown in Fig. 8, the theoretical model of
the MIBD-RI detector indicates that although the peak intensity of individual fringes varies throughout the whole interference pattern, the fringes located closest to the centroid
have the highest photon fluxes. It is these fringes that con-
Swinney, Markov, and Bornhop
FIG. 8. Theoretically generated intensity profiles of the backscatter fringe
pattern for two capillaries 共250 i.d./330 o.d. ␮m --- and 250 i.d./290 o.d. ␮m
– – –兲. Glycerol concentration⫽20 mM.
sistently provide larger changes in intensity for the small
positional changes induced by minute refractive index signals. Therefore, these fringes are most suitable when using a
slit/photodetector assembly. Although it has been shown that
when using position detection method 共i.e., CCD/LBA兲 the
third and sixth fringes from the centroid have similar position sensitivity to changes in RI 共third fringe slope
⫽24.92 ␮ m/mM; sixth fringe slope⫽24.75␮ m/mM) 共Fig.
7兲, the total integrated and peak intensities of the two fringes
are quite different. Quantitatively the integrated intensity ratio of the third:sixth fringe is 2.80:1, while the peak intensity
ratio of the third:sixth fringe is 1.88:1. Therefore selecting
the third fringe is preferable for the RI measurements using a
slit/photodetector assembly since the overall intensity and
photon flux on the sloping part of the intensity distribution is
greater. In short, the steeper intensity profiles of the fringes
located closest to the central fringe 共first to third fringes兲
provide larger signals for small changes in refractive index.
Given the difference in the detection limits for the CCD/
LBA and the slit/photodetector assembly and previously observed values,1,7 an evaluation of resolution for the 50 ␮m
slit system was performed. First a theoretical fringe was obtained from our theoretical model. The sloping part of the
slope fringe was then fit with a straight line producing the
relationship between the position and the output voltage of
Y 共 mV兲 ⫽6.248X 共 ␮ m兲 .
共1兲
For simplicity the y intercept in Eq. 共1兲 was left out since it
cancels out during the calculations and does not contribute to
the result. Next, the noise in the system was measured experimentally using a HP54603B digital oscilloscope
equipped with a data storage and processing module (V noise
⫽7 mVrms). In practice, when the signal-to-noise ratio is
greater than or equal to 1.5, a quantifiable signal is measured
with a corresponding detectable signal being 10.5 mV or
higher. Upon substitution of this minimum signal value into
Eq. 共1兲, we found the minimum detectable displacement of
the fringe to be d min⫽1.68 ␮ m. Thus, the resolving power
for the 50 ␮m slit/photodetector assembly for a Gaussian
fringe 共theoretical兲 with similar properties to an experimental
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Rev. Sci. Instrum., Vol. 71, No. 7, July 2000
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␮-HPLC.1 It also shows promise for small volume
thermometry/calorimetry,15 as a detector for CEC and as an
on-chip 共planar format兲 detector where probe volumes and
channel dimensions are more constrained 共⬍100 ␮m兲 with
detection volumes in the picoliter regime typically being
used.
C. RI sensitivity as a function of the capillary wall
thickness
FIG. 9. Reproducible calibration curve of fringe response vs refractive index for a series of glycerol solutions with known refractive indexes.
fringe is 1.68 ␮m. The corresponding ⌬RI detection limit
was then found by substituting d min into the line equation of
the 共experimental兲 calibration curve shown in Fig. 9 and was
calculated to be 4.147⫻10⫺7 ⌬n. This refractive index
change is 2.4 times higher than earlier reported detection
limits of MIBD.1,7 Here however, no reference detector and
only moderate thermal control was used leading to a system
with higher noise.
B. Detection limits as a function of capillary inner
diameter
Because of the path-length sensitivity of previously developed RI detectors2–4,5,9 it has been problematic to use
them with small diameter capillaries and for small volume
separations. In the past to determine the path-length sensitivity of MIBD, the refractive index detection limits as a function of capillary inner diameter were determined with a flow
injection analysis experiment for a series of capillaries with
varying inner diameter 共75, 100, 250, 775 ␮m兲.1 Calibration
curves obtained experimentally of RI signal versus concentration were generated for each capillary using a series of
glycerol solutions 共0.004–0.4% wt/v兲. Detection limits 共for
various inner diameters兲 were calculated based on the shortterm noise 共voltage signal variation in a 10 s period兲 of the
RI signal and applying the accepted relationship of DL
⫽3 ␴ /slope. At 3␴, the minimal detectable quantity of glycerol for a capillary with an inner diameter of 100 ␮m was
determined to be 1.24⫻10⫺6 g/mL, corresponding to 1.89
⫻10⫺7 ⌬n 1 . At the calculated detection limit, in a probed
volume of ⬃2.6⫻10⫺9 L 共2.6 nL兲, approximately 3.2 pg of
glycerol is present. From those experiments it was concluded
that MIBD was relatively path-length insensitive over the
capillary inner diameter range examined since the detection
limits did not vary significantly from one inner diameter to
another ( ␴ 2 ⫽0.15⫻10⫺7 ⌬n). 1 This observation can be further understood by examining Fig. 3 and noting that while
the probe volume is constrained for a particular capillary
inner diameter, the optical path length is actually many times
longer than that of the inner diameter 共i.d.兲. As a result,
MIBD has proven to be very useful as a detector for CE,12–14
To further understand the unique optical properties of
MIBD, the RI sensitivity as a function of wall thickness was
evaluated. Using the above-described theoretical model, a
capillary with 250 ␮m inner diameter and with outer diameters ranging from 290 to 530 ␮m in 20 ␮m increments was
created. These parameters correspond to wall thickness between 10 and 130 ␮m with 10 ␮m increments. The outer
wall of the capillary was always covered with 10-␮m-thick
polyimide coating. Sequentially, for every inner/outer diameter capillary dimension, the RI of the fluid in the model
experiment was changed to mimic the introduction of a series of glycerol solutions at various concentrations 共0, 10, 20,
40, 60, and 80 mM兲. Intensity profiles were then obtained for
each capillary with each solution and then measurements of
fringe position were made.
These simulations produced several important results.
First, by increasing the wall thickness of the capillary, the
quality of the fringe pattern diminishes 共Fig. 8兲. The
Gaussian-type profile of the fringes appear to develop jagged
sides which may significantly complicate the RI measurement and definitely will lead to the erroneous measurements
for the slit/photodetector assembly unless some signal processing is applied. Second, upon comparison of the intensity
profiles of the fringe pattern produced by the capillaries with
various outer diameters it was noticed that the fourth fringe
appears to be less influenced by shape irregularities 共Fig. 8兲.
Since this fringe’s shape tends to stay close to Gaussian, it
was chosen as a ‘‘token’’ fringe for the positional measurements and construction of the solute calibration curves.
Third, it was noticed that capillaries with thinner walls produce more sensitive measurements than those with thicker
walls.
The calibration curves for different glycerol concentrations and various outer diameters 共same inner diameter兲 were
obtained using the ‘‘token’’ fringe. The results of these measurements are depicted in Fig. 10 and tabulated in Table I.
One can see that there is a measurable difference in the
slopes for the calibration curves for capillaries with thin
walls compared to those with thicker walls, indicating that
capillaries with the thinner walls render more sensitive measurements 共when all other parameters are fixed兲. One of the
possible explanations for this observation is that with thinner
walled tubes less light is trapped inside the silica substrate,
leading to a higher degree of interaction between the light
and the fluid inside the capillary. A similar explanation can
be proposed for the highly irregular shapes of some of the
fringes for particular inner and outer diameter ratios. It is
possible that a larger proportion of the light rays are trapped
inside the capillary wall, do not interact with the fluid, and
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2690
Rev. Sci. Instrum., Vol. 71, No. 7, July 2000
Swinney, Markov, and Bornhop
FIG. 11. Theoretical 共circle兲 and experimental 共triangle兲 results obtained for
MIBD sensitivity vs capillary wall thickness.
FIG. 10. Theoretical generated calibration curves of fringe position 共RI
response兲 vs glycerol concentration for a series of capillaries with various
inner diameter–outer diameter ratios. Inner diameter is constant at 250 ␮m
while outer diameter varies from 290, 390, 410, and 530 ␮m.
experience much higher phase delays than the rays that
propagate through the fluid and silica. This phase difference
may result in some irregularities in the resulting fringe pattern observed at the detector plane. This hypothesis is currently under investigation and a more detailed explanation
will be produced in the future.
To further verify the above-noted results, a set of additional modeling exercises and experiments was conducted
using capillaries with various wall thickness. Experimental
calibration curves were obtained for the same concentration
of glycerol solutions contained in fused silica capillaries with
100 ␮m inner diameter and 160, 240, and 360 ␮m outer
diameters. The slopes of these calibration curves represent
the sensitivity of our detection scheme to changes in concentration for a given solution and, as expected, are linearly
proportional to the variations in the index of refraction of the
solution. Figure 11 shows the relationship between the sensitivity and capillary wall thickness and allows for a comparison between experimental and theoretical results. The
lower plot was obtained experimentally, while the top plot
was obtained theoretically for similar capillaries using the
above-described model 共capillary dimensions in the model
were modified appropriately to be the same as those used in
the experiment兲. As one can see the experimental results are
in good accordance with the theory, which leads to the conclusion that capillaries with thinner walls are more suitable
for sensitive RI measurements than capillaries with thicker
walls. The shift or displacement along the y axis between
theoretical and experimental curves in Fig. 11 can be attrib-
uted to a number of reasons such as use of nonideal detectors
or capillaries with small imperfections.
D. RI sensitivity as a function of wavelength
Shown in Fig. 12共A兲 are the false color reconstruction
images of backscatter fringe patterns produced experimentally by MIBD for water at various wavelengths 共488, 514.5,
632.8, and 670 nm兲. For comparison Fig. 12共B兲 shows the
theoretical results at the same wavelengths. Two observations can be extracted as expected. First, the shorter wavelengths produce fringe patterns with higher spatial frequencies than those at longer wavelengths. Second, the intensity
profiles depicted in Fig. 12 for the shorter wavelength 共e.g.,
488 nm兲 do not vary significantly from the central fringe,
while for the longer wavelengths such as 632.8 nm, the central fringes 共centroid to the third fringe兲 are most intense
共higher photon flux兲, e.g., the intensity of the fringes decreases with distance from the centroid. Consequently, such
an effect on intensity profile influences the type of measurement used to track fringe movement. While intensity profiles
inherently have less influence when array detection and
fringe counting schemes are used for MIBD, the intensity
nonuniformities of the backscatter fringes do play a significant role when an air/slit photodetector is employed.
Refractive index sensitivity of MIBD as a function of
wavelength was determined at four wavelengths 共488, 514.5,
632.8, and 670 nm兲. Calibration curves of fringe position 共RI
signal兲 versus concentration were generated at each wavelength using a series of glycerol solutions prepared in deionized water 共10, 20, 40, 60, 80, and 100 mM兲. At each
wavelength, each glycerol solution was injected into the capillary, allowed to temperature and pressure stabilize, and
TABLE I. Slopes of calibration curves for glycerol solutions as a function of capillary wall thickness.a
Thickness
10
20
30
40
50
60
70
80
90
100
110
120
130
共␮m兲
Slope
47.35 45.31 42.77 42.39 40.85 40.64 36.19 36.82 35.30 34.01 33.34 29.64 31.11
共␮m/mM兲
These slopes were obtained using the model described in the text for a 250-␮m-i.d. capillary with 10 ␮m
polyimide coating.
a
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Rev. Sci. Instrum., Vol. 71, No. 7, July 2000
Ultrasmall volume
2691
FIG. 13. Reproducible calibration curves of fringe position vs glycerol concentration at four different wavelengths 共488, 514.5, 632.8, and 670 nm兲.
关 DL(488 nm):⌬n⫽9.74⫻10⫺6 RIU or 29.8⫻10⫺12 mole
(2.75⫻10⫺9 g); DL(670 nm):⌬n⫽1.39⫻10⫺5 RIU or 42.6
⫻10⫺12 mole(3.92⫻10⫺9 g)兴. However, one must take into
consideration that although shorter wavelengths produce
more sensitive RI measurements in MIBD, few molecules
absorb light at 633 nm yet, at 488 nm, some molecules have
appreciable absorption coefficients and these absorption effects will likely interfere with RI measurements. Furthermore, silicon photodetectors have considerably higher quantum efficiencies at longer wavelengths making detection of
low light levels easier. The combined effect of these considerations indicate that either a 632.8 nm HeNe or diode laser
with a wavelength between 630 and 700 nm are preferred for
the practical implementation of MIBD.
E. Detection limits of MIBD
FIG. 12. 共A兲 Experimental false color reconstruction of the backscatter
fringe pattern at four different wavelengths 共488, 514.5, 632.8, and 670 nm兲.
共B兲 Theoretical false color reconstruction of the backscatter fringe pattern at
four different wavelengths 共488, 514.5, 632.8, and 670 nm兲.
sampled for positional shift in the fringe pattern using the
CCD based LBA. This procedure was repeated in triplicate
at each of the four different wavelengths to access the reproducibility of the measurement and to ensure the data are
statistically significant.
The calibration curves generated experimentally for
fringe shift 共RI response兲 versus glycerol concentration for
each wavelength are shown in Fig. 13. The results from the
investigation of MIBD RI sensitivity as a function of wavelength indicates that the response is directly related to the
wavelength of light chosen for illumination. As expected
from scattering theory, the sensitivity of MIBD to changes in
RI increases with decreasing wavelength. Thus, as shown in
Fig. 13, the steeper slope of the 488 nm calibration curve,
leads to a RI sensitivity that is 1.43 times greater than that at
670 nm. Quantitatively, the RI sensitivity decreases from
36.14 ␮m/mM for 488 nm to 25.34 ␮m/mM for 670 nm
Mass detection limits of femtomole 共picogram兲 are
achievable for MIBD-RI detection. The detection limits for a
series of solutes are listed in Table II. These mass detection
limits are achievable for flowing stream analyses in capillary
dimensions.8,12–14 The detection limits are determined using
the short-term noise 共voltage signal variation in a 25 s peTABLE II. MIBD-RI detection limits for flowing streams.
Solute
identity
Potassium (K⫹) b
Barium (Ba⫹2) b
Sodium (Na⫹) b
Lithium (Li⫹) b
Bromothymol bluec
Thymol bluec
Bromocresol greenc
Caffeined
Glycerole
Concentration
DLa 共M兲
2.11⫻10⫺4
5.35⫻10⫺5
2.38⫻10⫺5
1.90⫻10⫺4
4.66⫻10⫺7
1.12⫻10⫺6
7.23⫻10⫺7
2.33⫻10⫺6
1.35⫻10⫺5
Injected mass
DLa
22.4
19.5
1.5
3.5
1.4
2.5
2.4
2.2
3.3
pg
pg
pg
pg
pg
pg
pg
pg
pg
or
or
or
or
or
or
or
or
or
559 fmol
142 fmol
63.0 fmol
504 fmol
2.19 fmol
5.3 fmol
3.4 fmol
10.9 fmol
35.8 fmol
Detection
volume 共nL兲
2.65
2.65
2.65
2.65
4.7
4.7
4.7
4.7
2.65
Calculated at 3␴.
Reference 12.
Reference 13.
d
Reference 14.
e
Reference 8.
a
b
c
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2692
Rev. Sci. Instrum., Vol. 71, No. 7, July 2000
riod兲 and applying the accepted relationship of DL
⫽3 ␴ /slope. The mass detection limits are calculated using
the cylindrical probe volume of the detector, which is related
to the diameter of the probe beam 共0.6 mm兲 and the inner
diameter radius of the capillary. For example, the probe volume of a 100-␮m-i.d. capillary is estimated to be 4.7 nL.
Since femtomole 共picogram兲 mass detection limits are
achievable in nanoliter volumes, it allows MIBD to be used
as a detection scheme for capillary-scale separations that require sensitive measurements within small volumes. More
important, when compared to current commercial RI detectors, the sensitivity of MIBD-RI detection is unsurpassed.
For example, the best commercial RI detector is reported to
have nanogram detection limits but requires a large probe
volume, 8 ␮l.18 Thus, MIBD-RI is three orders of magnitude
more sensitive than the most sensitive commercial RI detector 共HP 1100兲, and achieves this sensitivity in a probe volume three orders of magnitude smaller.
Theoretical modeling of the MIBD optical configuration
predicts detection limits considerably better than ⌬n
⫽10⫺8. 1,7,8 Currently, the MIBD-RI detection limits are 2
⫻10⫺7 ⌬n. Theoretically predicted detection limits should
be achievable if experimental noise such as electronic noise,
detector shot noise, thermal perturbations of the fluid
(dn/dT), and environmental effects such as air currents are
significantly reduced. First, reduction of 1/f noise can be
achieved by using an electronic filter. Currently, no electronic filters have been incorporated to condition the output
signal of the detector. The incorporation of a low pass filter
for the output signal would improve S/N. Second, the incorporation of thermal control in the 0.001 °C range will reduce
the major source of noise 共thermal noise⫽8⫻10⫺4 °C⫺1). In
fact, it is no coincidence that when the current limit of detection for MIBD-RI measurements are expressed in terms of
⌬T, the value corresponds to the current Peltier control performance level of approximately 1.0⫻10⫺2 °C. Therefore
by improving the Peltier-based thermal control system and
flow cell technology to thermally control the fluid to
⫾0.001 °C, a detection limit of approximately 10⫺8 ⌬n will
Swinney, Markov, and Bornhop
be achievable. Finally, by doing some instrumentation engineering like isolating the entire experiment from its environment to minimize temperature fluctuations in air currents,
such improvements will be possible.19
ACKNOWLEDGMENTS
The authors would like to acknowledge the support provided by National Science Foundation 共DBI-9876839兲 and
by Welch Foundation 共D1312兲. Breault Research of Tucson,
AZ is acknowledged for donating the ASAP Optical Modeling Program.
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19
See EPAPS Document No. E-RSINAK-71-039007 for five files of color
versions of Figures 3, 4, 5, 8, and 12. This document may be retrieved via
the EPAPS homepage 共http://www.aip.org/pubservs/epaps.html兲 or from
ftp.aip.org in the directory/epaps/. See the EPAPS homepage for more
information.
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