F.
Purr
ab,
M.
Bassu
b,
R. D.
Lowe
b,
B.
Thürmann
a,
A.
Dietzel
*a and
T. P.
Burg
*b
aTU Braunschweig, Institute of Microtechnology, 38124 Braunschweig, Germany. E-mail: a.dietzel@tu-braunschweig.de
bMax Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany. E-mail: tburg@mpibpc.mpg.de
First published on 24th October 2017
Measuring small changes in refractive index can provide both sensitive and contactless information on molecule concentration or process conditions for a wide range of applications. However, refractive index measurements are easily perturbed by non-specific background signals, such as temperature changes or non-specific binding. Here, we present an optofluidic device for measuring refractive index with direct background subtraction within a single measurement. The device is comprised of two interdigitated arrays of nanofluidic channels designed to form an optical grating. Optical path differences between the two sets of channels can be measured directly via an intensity ratio within the diffraction pattern that forms when the grating is illuminated by a collimated laser beam. Our results show that no calibration or biasing is required if the unit cell of the grating is designed with an appropriate built-in asymmetry. In proof-of-concept experiments we attained a noise level equivalent to ∼10−5 refractive index units (30 Hz sampling rate, 4 min measurement interval). Furthermore, we show that the accumulation of biomolecules on the surface of the nanochannels can be measured in real-time. Because of its simplicity and robustness, we expect that this inherently differential measurement concept will find many applications in ultra-low volume analytical systems, biosensors, and portable devices.
Technology | Detection limit | Background cancelation/self-referencing | Size/volume | Ref. |
---|---|---|---|---|
Surface plasmon resonance | 1 × 10−7–2 × 10−5 RIU | No | 20–150 μL (ref. 24) | 24, 25 |
Young interferometer | 1.8 × 10−8 RIU (ref. 26) | Yes, reference arm | 6 μL (ref. 26) | 26–29 |
Microinterferometric backscatter detector | 6.9 × 10−9 RIU | Yes, two capillaries: fringe subtraction | 50 nL | 30 |
Ring resonator | 3.16 × 10−6 RIU (ref. 31) | Independent reference structures: multiple sensors on one chip with beam splitter33 yes, double resonator34 | 200 × 20 μm/10 μL min−1 (ref. 33) resonator cross section: 68 μm (ref. 32) | 31–34 |
3.8 × 10−8 RIU (ref. 32) | ||||
5.0 × 10−6 RIU (ref. 33) | ||||
Fiber Bragg grating | 2.2 × 10−5 RIU | No | 3.45 μm per hole | 35, 36 |
Fabry–Perot cavity | 1.7 × 10−5 RIU (ref. 37) | No | Cavity width = 24.5 μm (ref. 37) | 37–43 |
Photonic crystal: nanoscaled optofluidic sensor array (NOSA) | 7 × 10−5 RIU | Independent reference structures: multiple sensor structures on one chip with one waveguide | Hole diameter 200 nm, 250 nm deep, 8 holes per sensor | 44 |
Diffraction grating | 1.9 × 10−6 RIU (ref. 45 and 46) | I0 as reference | 50 μm thick fluid layer47 | 45–47 |
6 × 10−7 RIU (ref. 47) | ||||
Micro edge | 3 × 10−3 RIU | No | 20 μm deep; 250 μm wide | 48 |
μ-Image defocusing 3-pinhole aperture | 53.7 pixel per RIU | Self-calibration: reference fluids included on chip – one image measurement | 50 μm wide; 17–82 μm deep | 49 |
Tapered fiber | 1.42 × 10−5 RIU (ref. 50) | No | Diameter of fiber 200 μm; 6 mm long9 | 9, 50 |
For many applications, there is a need to measure small changes in refractive index that are easily overwhelmed by nonspecific background signals. For example, measurements of concentration via refractive index require accurate temperature control, and refractive index based biosensors need to be made insensitive to non-specific binding or bulk refractive index changes. Differential measurements with two devices offer a partial remedy. However, the attainable background suppression is often limited due to alignment errors, fabrication tolerances, and other differences between independent sensors.
Diffractive optical microdevices open up a path to differential sensing with direct background cancellation by the interference of light waves. One key advantage of these devices is that the signal of interest and the reference are closely integrated and lie on the same beam path. This principle has previously been used for displacement sensing in micromechanics,11–13 for chemical sensing,14–17 and for biosensing.18–20 In chemical and biological sensing, many powerful device concepts have been proposed based on micropatterning capture molecules or hydrogels into stimulus-responsive phase gratings.18,21 Binding of target molecules or swelling of the hydrogel alters the wavefront of a laser passing through the element, and this can be read out via a consequent change of the diffraction pattern in the far-field. Multiplexing is also possible by this principle if multiple gratings with different orientation are overlaid.22,23
Here, we introduce a new diffractive optofluidic device for measuring small differences in refractive index between two fluids that are guided through nanofluidic channels. The device consists of two sets of nanochannels, which are arrayed to form an interdigitated grating with an asymmetric unit cell. We show for the first time that the asymmetry enables linear optical differencing in diffractive sensors even when the optical layer thicknesses (here the nanochannel depths) are fixed and cannot be adjusted to achieve phase quadrature.
Using this device, it is possible to measure small differences in the bulk refractive index of two solutions in the presence of large common-mode fluctuations. Alternatively, the device can measure optical path differences caused by different surface-adsorbed layers. This effect is significant due to the small height of our nanofluidic channels. We envision that the inherently differential measurement and the efficient surface-directed transport of molecules in the nanofluidic channels render this concept interesting for label-free biosensing applications.
For a correct signal processing, we calculate here the dependence of the intensity distribution of the diffraction pattern produced by the asymmetric grating for small Δn.
When a collimated laser beam is reflected off the device, the reflected light intensity in the Fraunhofer approximation at a distance D from the chip is given by:11,51
![]() | (1) |
g(u,v) = f(u,v)·ejφ(u), | (2) |
![]() | (3) |
![]() | (4) |
Inserting eqn (2) into eqn (1) and using the convolution theorem, we find the diffraction pattern to be a linear array of peaks located at positions . If f(u,v) is a Gaussian beam of waist diameter W0 ≫ P, then all the peaks are also Gaussian in shape, well separated, and non-interfering.
The peak intensities are proportional to the magnitudes of the coefficients am:
Im ∼ |am|2. | (5) |
Here we define the signal of our measurement for a pair of modes m ≠ 0 as
![]() | (6) |
This is a non-linear function of the refractive indices of the fluids inside the detection and the reference channels. Expanding to the first order in Δφ reveals that, for small optical path differences,
![]() | (7) |
Importantly, Sm is independent of the absolute optical path length in the reference and detection channels provided that Δφ ≪ 1. Also note that, to first order, the sensitivity is independent of the channel width. This is due to the normalization by the total mode intensity Im + I−m which tends towards zero for w → 0. Analogously, the optical path φ3 through the wall between the channels does not enter into the linear approximation of the normalized signal. Note that the parameters w and φ3 can still be used to optimize the amount of light diverted from the central peak (m = 0) to higher order modes. While the divergence of the tangent in eqn (7) for arguments approaching odd multiples of
suggests a very large sensitivity at these points, there is a trade-off in signal-to-noise ratio, for the net mode intensity tends towards zero at the same time, as revealed by eqn (4).
Of particular interest is that and the channel depth h are the only design parameters entering into eqn (7). For a symmetric arrangement
of reference and detection channels in the array we find
for all even values of m. In this special case, the diffraction pattern is symmetric about the origin. Each diffracted mode is then either at a maximum or at a minimum of intensity when Δφ = 0 due to complete constructive or destructive interference between the light reflected off the reference and the detection channels, respectively. For all other values of l, the operating point of the interferometer acquires a desirable bias away from these points of zero sensitivity. This is critical for many sensing applications that require the measurement of rather small differences in refractive index around Δn = 0.
For the lateral dimensions of the nanochannels, we selected two combinations: (1) w = 3 μm, l = 7 μm, P = 18 μm and (2) w = μm, l = 6 μm, P = 18 μm. These dimensions were chosen to obtain high sensitivity to bulk refractive index changes and to surface-adsorption while maintaining safe tolerances during fabrication. The grating layout consisted of 25 reference and detection nanochannels, respectively, for a total of 50 channels per grating, and each channel was 320 μm in length. Vias (3 μm in diameter) on each end of the nanochannels were opened by deep reactive ion etching (DRIE) through the silicon device layer of the SOI followed by BHF to open the buried oxide (Fig. 3A).
Subsequently, a 210 μm thick Borofloat 33 wafer was bonded to the top side of the silicon wafer to seal the nanofluidic grating. The silicon wafer was then ground to a thickness of 50 μm and polished. After the silicon was thinned down, microfluidic channels were etched from the back side by DRIE to connect to the vias previously fabricated from the top side. After bonding, a thin residual oxide diaphragm that sometimes remained in the vias was cleared by a vapor-phase HF etch. Thinning the silicon served a dual role in the above process. First, the depth and aspect ratio of the DRIE step was significantly reduced; thus, the etch could be stopped uniformly and with minimal footing on the buried oxide layer of the SOI. Second, the volume of the microfluidic channels connecting to the nanochannels could be kept small in this way.
Finally, a 700 μm thick Borofloat 33 wafer was bonded onto the back side of the wafer to ensure the robustness of the fabricated devices. Before bonding, through-holes (800 μm in diameter) were opened on the back side Borofloat 33 wafer by femtosecond laser ablation to allow fluid delivery into the nanofluidic system.
The use of silicon and glass as substrate results in the fabrication of robust and chemically resistant chips. This, on the other hand, requires a relatively expensive fabrication technology. An alternative could be the use of thermoplastic materials and hot embossing that would allow fabricating disposable devices more suitable for point-of-care applications.
A pressure-driven fluidic system was used to introduce fluids into all channels. The reference and detection nanochannels can be supplied with different fluids through separate microfluidic supply channels (Fig. 1 and 3C), enabling selective functionalization and avoiding contamination between the channels. The fluids are guided through the nanochannels by controlling the pressures on either side.
Additional details regarding the optical and fluidic setup are described in the ESI.†
For each measurement, a baseline was determined by flushing all channels with the reference solution (water or PBS for these studies) for five minutes. At the five minute interval, the pressure difference was switched to introduce the sample solution into only the detection channel and reference solution was maintained in the reference channel. Following the measurement, all channels in the grating were again filled with the reference solution. To avoid clogging of the nanochannels, all solutions were passed through a 300 kDa cutoff filter before use.
The same procedure was then repeated in triplicate for every concentration of glycerol, thus demonstrating the repeatability of the measurements and stability of the system. In all measurements the same baseline was recovered when water was again introduced into the detection channels.
Values of S2 are plotted as a function of the independently measured Δn in Fig. 4B. For comparison, Fig. 4B also shows the theoretical prediction calculated according to eqn (7). The slope s = ∂S2/∂Δn corresponds to the sensitivity of our device. Based on the geometry and the wavelength we find s = 2.408 RIU−1. Importantly, the linear response of the sensor corresponds accurately with the analytical solution for the entire range of Δn measured. Linear regression on the data shown in Fig. 4B yields a slope ŝ = 2.416 ± 0.01926 RIU−1 (correlation coefficient of R = 0.99954). This is in good agreement with the analytical prediction.
The noise floor is dominated by low-frequency fluctuations. Over the first four minutes of measurement, the refractive index equivalent of the standard deviation in S2 is σΔn = 1.3 × 10−5 RIU. For comparison with other methods that are summarized in Table 1, our limit of detection taken as three standard deviations above the noise corresponds to ∼4 × 10−5 RIU.
Phosphate buffered saline (1× PBS) was used as the reference and wash solution. After 5 minutes of acquiring a baseline, the solution in the detection channel was exchanged to water in order to verify that the system was correctly responding to bulk solution changes. After another 5 minutes, PBS was again flowed through all channels and the baseline signal was recovered. To confirm the ability of the device to sequentially measure changes in refractive index of multiple solutions, 2% glycerol was then introduced. As expected, the signal increased. Next, PBS was again introduced to all channels and the baseline signal was recovered.
Avidin adsorption was measured by flowing a solution of avidin in PBS (0.5 mg mL−1 avidin in PBS) through the detection channel for 5 minutes and subsequently rinsing with PBS for 10 minutes to remove any loosely bound protein. It is important to note that after the 10 minute rinse, the baseline signal was not recovered, suggesting the avidin molecules adhered tightly to the channel wall. We expect that significantly lower concentrations of protein can be measured provided that the accumulation time is extended or the flow rate is increased.
We expect that our nanofluidic grating sensor could be functionalized with different affinity reagents for the label-free detection of specific biomolecules. For sensitive detection, the large surface-to-volume ratio of these channels should provide distinct advantages, as molecules would have a high capture probability on their passage through the channel. At the same time, the large number of parallel nanochannels provides a large effective capture area, so that rare molecules could be efficiently concentrated in the sensing area.
The differential design of our system allows measurements that are inherently compensated for common mode variations. Here, we have shown that common mode refractive index changes due to temperature fluctuations can be suppressed by at least a factor of 10 in the differential signal. The noise floor of the device in our current setup is limited by low-frequency fluctuations to 1.3 × 10−5 RIU (standard deviation over 4 minutes). Although the sensitivity achieved with our method is currently lower compared to other methods employing microfluidic devices, we expect that this can be significantly improved through both optimization of channel alignment and external measurement components. Moreover, our optofluidic method is superior regarding simplicity and robustness to disturbances.
The separate fluidic addressing of reference and detection channels allows a specific immobilization of molecules in just the detection channels. The capability of quantifying thin adsorbed protein layers in combination with the above described common mode rejection provides the potential for detecting biomolecules label-free with a uniquely simple, robust, and inherently differential sensor. Future applications as a point-of-care device are therefore very attractive.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7lc00929a |
This journal is © The Royal Society of Chemistry 2017 |