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We extend our previous simulation study and we present experimental results regarding our Fast Fourier Transform method for the calculation of the resonance shifts in biosensors based on micro-ring resonators (MRRs). For the simulation study, we use a system model with a tunable laser at 850 nm, an MRR with 1.5∙104 quality factor, and a detection system with 50 dB maximum signal-to-noise ratio, and investigate the impact on the system performance of factors like the number of the resonance peaks inside the scanning window, the wavelength dependence of the laser power, and the asymmetry of the transfer functions of the MRRs. We find that the performance is improved by a factor of 2 when we go from single- to four-peak transfer functions, and that the impact of the wavelength dependence of the laser power is very low. We also find that the presence of asymmetries can lead to strong discontinuities of the transfer functions at the edges of the scanning window and can significantly increase the measurement errors, making necessary the use of techniques for their elimination. Using these conclusions, we build a system with sensing MRRs on TriPleX platform, and we experimentally validate our method using sucrose solutions with different concentrations. Involving techniques in order to exclude the noise originating from the microfluidic system, we achieve a wavelength resolution close to 0.08 pm, when the system operates with 0.5 pm scanning step. In combination with the sensitivity of the MRRs, which is measured to be equal to 93.7 nm/RIU, this wavelength resolution indicates the possibility for a limit of detection close to 8.5·10−7 RIU, which represents to the best of our knowledge a record performance for this type of optical sensors and this level of scanning steps.
© 2017 Optical Society of America
1. Introduction
Micro-ring resonators (MRRs) are optical cavities with proven potential for sensitive detection of analytes in a variety of chemical and biochemical applications [1–10]. The detection mechanism is based on the change of the refractive index (RI) in the top-cladding of the MRRs when the analytes are present in this area. This change can be sensed by the evanescent tail of the propagating optical mode, and can be translated into a wavelength shift of the resonances that are present in the transfer function (TF) of the MRRs (resonance shift) [11,12]. The sensitivity that describes the effectiveness of this translation is expressed in nanometers per refractive index unit (RIU) change [12], and depends on the exact design of the waveguiding structure and the overlap between the optical mode and the analytes. The resonance shift can be measured using either the combination of a tunable laser (TL) source with a photodiode (PD) or the combination of a broadband light source with an optical spectrometer. In either case, the final wavelength resolution of the measurement system is a very important parameter, as it represents the minimum resonance shift that can be reliably detected under the presence of noise or peak locking effects [13], and as it determines the limit of detection (LOD) in terms of actual RI change [12].
Recently, we proposed a powerful method for the processing of measurement data and the calculation of the resonance shift based on the fundamental properties of the Fast Fourier Transform (FFT) [14]. Using a model measurement system with a TL at 850 nm and a set of simulation studies involving the wavelength step of the TL, the quality factor (Q-factor) of the MRRs and the level of the measurement noise, we compared our method against the usual peak-search methods with Lorentzian fitting [15], and we showed that our method is 60 times faster, has higher performance by two orders of magnitude in terms of achievable resolution or required wavelength step, and has a preference for practical MRRs with low Q-factors around 104. Although these studies were based on the assumption of a perfectly symmetric scanning window around a single resonance peak, it was clear that the fundamental conclusions are universal and that the method is indeed powerful and well suited for low cost lab-on-chip systems.
In the present work we make a step forward and investigate in detail factors like the presence of multiple resonance peaks, the asymmetry of the scanning window and the wavelength dependence of the TL power inside this window, which are present in real measurement systems. We analyze through simulations the positive effect of the first factor and the negative effect of the other two factors on the wavelength resolution, and we describe ways for mitigating the negative effects and enabling system performance higher than that reported in [14]. More significantly, we provide a comprehensive set of experimental results that validate our method using MRRs in TriPleX technology [16] and model sucrose solutions. Specifically, using MRRs with Q-factor equal to 1.5·104 and wavelength scanning steps from 8 down to 0.5 pm, we demonstrate system resolution from 0.38 down to 0.08 pm. Taking into account the sensitivity of the particular MRRs (93.7 nm/RIU), the lower extreme of this range corresponds to a LOD close to 8.5·10−7 RIU, which represents to the best of our knowledge a record performance for this type of optical sensors. Additional measurements that compare the experimental performance of our method against the performance of Lorentzian fitting methods provide an indication of the advantage that our method can have in terms of wavelength resolution and running time efficiency.
2. Resonance shift estimation method and simulation study
Our processing method is based on the well-known property of the Fourier transform that associates a delay between two identical functions in the time domain with a phase difference in the frequency domain [14,17]. If this phase change can be precisely calculated, it is possible to go back to the time domain and estimate the delay with a similar degree of precision. Since the terms time domain and frequency domain are only conventions, this property is not limited to the actual functions of time, but concerns all physical functions, including the TF of an MRR, which describes the transmitted power at the drop port of the MRR as a function of the operating wavelength. In this particular case, the possible delay that is observed between two transfer functions T1(λ) and T2(λ) is identical to the sought resonance shift in the sensing applications of our interest. In practice, the method is based on the processing of two sampled TFs T1(λj) and T2(λj) from two wavelength scans with the same scanning window and the same wavelength vector λj, assuming that these signals are cyclic and already in steady state. Working with scanning windows around a single resonance peak and using various combinations of the wavelength step, the Q-factor and the measurement noise, we showed through simulations in [14] that the phase difference in the frequency domain can be calculated indeed with ultra-high precision, allowing for the estimation of the resonance shift with accuracy much higher than the wavelength step and much higher than the accuracy achieved with techniques performed exclusively in the time domain.
2.1 Effect of number of resonance peaks inside the wavelength scanning window
Without loss of generality, we focus now on a realistic set of parameters and study the effect of the presence of additional resonance peaks on our method. We use a model measurement system with 50 dB maximum signal-to-noise ratio (SNRmax) [14] and a model MRR design with a Q-factor of 1.5·104, a round-trip amplitude transmission of 0.9 [11,14], a round-trip length of 872 µm, and an effective refractive index of 1.65. These parameters result in a free spectral range (FSR) of 505 pm at 855 nm. We assume that this effective refractive index is constant across our scanning window. Although this assumption is not completely true due to the dispersion effects, which are always present in waveguiding systems, it is a safe and meaningful simplification in the case of the FFT method due to the tolerance of the method to these effects. This tolerance originates from the handling of the total waveform inside the scanning window as a single block and the calculation of a unique wavelength shift. Thiscalculation is a result of a sample averaging and weighting process, which is inherent to the method and can eliminate the wavelength shift variations across the scanning window due to the dispersion effects. For our first study, we take as an example the case of a moderate effective RI change of the propagating mode inside the MRR equal to 10−6 RIU, and we perform a series of Monte-Carlo simulations with 10000 runs for each combination of scanning step and number of resonance peaks. The system resolution for each combination is extracted through the mean error and the standard deviation in the estimation of the actual resonance shift between the initial and the shifted TF, as per the analysis in [14]. For the calculation of these statistical parameters, we have pre-calculated the theoretical resonance shift for the specific effective RI change with ultra-high precision (0.56030487 pm). In order to make this pre-calculation, we temporarily removed any source of measurement noise, and used the peak search method with an unrealistically short scanning step (0.00390625 pm).
As illustrated in Fig. 1, our study involves the use of three different scanning windows that contain exactly one, two or four complete periods of the initial and the shifted TF. The resonance peaks reside symmetrically inside these windows, and are sampled with seven different scanning steps (0.125, 0.25, 0.5, 1, 2, 4 and 8 pm). Figures 2(a) and 2(b) presents the results of the study in terms of mean error and 3σ standard deviation, respectively, revealing that the presence of additional peaks in the processed parts of the TFs can average out the noise and improve the accuracy of the FFT method in a noisy environment. As the mean error remains negligible in all cases, the improvement is more evident in the 3σ standard deviation, which drops by almost a factor of 2 for all scanning steps, when we switch from single-peak to four-peak operation. It is noted, however, that this improvement is achieved at the expense of a broader scanning range, which entails higher complexity for the TL and the driving electronics and longer duration for the scanning process.
Fig. 1 Typical pair of initial and wavelength shifted TF of an MRR with Q-factor equal to 104 and ɑ equal to 0.9 for an effective RI change of 10−6: (a) Options for a symmetric scanning window with one, two or four resonance peaks, and (b) Zoom-in on the rightmost resonance peaks of the two TFs.
Fig. 2 System performance using the FFT method as a function of the number of resonance peaks and the scanning step: (a) Mean error, and (b) 3σ standard deviation in the calculation of the resonance shift. The results refer to Monte Carlo simulations with 10.000 runs for each point in the two contour plots. The simulations were made for an effective RI change equal to 10−6, using an MRR with Q-factor = 104and ɑ = 0.9. The model measurement system has both amplitude (SNRmax = 50 dB) and spectral noise (σλ = 0.4·Δλ).
2.2 Effect of power dependence of the tunable laser source on the wavelength
Using the same MRR design and the same effective RI change, we study next the effect of the wavelength dependence of the laser output power on the performance of the FFT method and the final system resolution. Since the TL in this type of sensors is usually a vertical cavity surface emitting laser (VCSEL) at 850 nm, the wavelength scanning is based on the strong adiabatic chirp of the VCSEL, and can be realized through a corresponding scanning of the injection current. Figure 3(a) presents a realistic model of the optical power as a function of the emission wavelength, assuming that the wavelength dependence is linear within the 4-peak scanning window with total range of 2.02 nm, and that the output optical power at the lower end of this window is only 35% of the optical power at the upper end. In order to assess the effect of the power dependence, we compare the system accuracy in the case of one, two or four resonance peaks under the presence or absence of this dependence. In all cases, we define the individual scanning windows taking from the total range of 2.02 nm, the corresponding number of rightmost resonance peaks, as shown in Fig. 3(a), in order to retain the optical power levels as high as possible. Since the mean error in the estimation of the actual resonance shift remains negligible in all cases, we base our comparison again on the study of the corresponding 3σ standard deviations. Figure 3(b) presents the simulation results and reveals the high tolerance of the FFT method. More specifically, the diagram shows that the power dependence has practically no effect in the case of a single peak, has a very weak effect in the case of two peaks, and a larger but still weak effect in the case of four peaks. The mechanism of this effect does not relate to the fundamental properties of the FFT method, but rather to the lower optical power levels at the leftmost part of the scanning window. Since the method uses the samples from all parts of the TFs in order to extract the resonance shift,these lower power parts make the measurement noisier, increasing in this way the 3σ standard deviation.
Fig. 3 (a) Initial and wavelength shifted TF of our model MRR in the presence of wavelength dependence of the laser output power, and options for a symmetric scanning window with one, two or four resonance peaks. (b) 3σ standard deviation in the calculation of the resonance shift using the FFT method as a function of the scanning step in the case of presence or absence of wavelength dependence of the laser output power.
2.3 Effect of relative position of transfer functions inside the scanning window
So far, we have assumed that the range of the scanning window is a multiple of the FSR. In the absence of any laser power dependence, this assumption is sufficient to ensure that the TFs, which are mathematically treated by the FFT as cyclic functions, do not present any discontinuity at the edges of the scanning window. Moreover, we have also assumed that the scanning window is always symmetrical with respect to the resonance peaks of each TF, which ensures in turn that the values of the TF at the edges of the scanning window are the minimum ones, and that the possible discontinuity of the TF remains negligible even in the presence of laser power dependence. This fact is very important, since the presence of any large discontinuity can lead to a false mathematical calculation of a strong high-frequency component in the spectrum of the TF, and can result in significant error in the phase calculation of the Fourier transform. We now go further, and investigate the actual impact of this type of discontinuity on a real measurement, working with a system that features both laser power dependence and asymmetry between the scanning window and the resonance peaks. We take as an example the 2.02 nm scanning window, which is four times as wide as the FSR of our model MRR, and assume that the same noise level and the same laser power dependence as before are present. Figure 4(a) presents five cases with different relative positions of the TF inside the scanning window, and Fig. 4(b) provides a zoom-in on the lower and the upper edge of the scanning window, revealing the level of discontinuity in each case. As observed, the third case corresponds to the perfect symmetry, whereas the other cases correspond to various degrees of asymmetry between the scanning window and the resonance peaks, resulting in different degrees of edge discontinuity.
Fig. 4 (a) Five different TFs of our model MRR corresponding to five different relative positions inside a scanning window with range equal to four times the FSR. (b) Zoom-in on the lower and the upper edge of the scanning window revealing the edge discontinuity for each one of the five cases.
Figures 5(a) and 5(b) present the impact of these variations on the final performance of the system in terms of mean error and standard deviation in the estimation of the resonance shift for an effective RI change of 10−6. As observed, the asymmetry does not affect the standard deviation of the simulation runs, but can affect the mean error of the measurement in a critical way, degrading the actual resolution and reliability of the system. More specifically, as shown in Fig. 5(a), the mean error increases together with the edge discontinuity, and almost irrespectively of the scanning step. Since the use of windowing techniques based on Gaussian, tapered cosine or Chebyshev windows [18] cannot sufficiently resolve this problem, it is evident that the elimination of the edge discontinuity is necessary for reliable measurements. In practice, this can be easily achieved by using a larger scanning window, and selecting for further processing out of this window a smaller one that is a multiple of the FSR and symmetric with respect to the resonance peaks. This approach has been successfully used in the experimental part of our work, and is presented in the next section.
Fig. 5 System performance using the FFT method in the five cases of the relative position of the TF of our model MRR inside the scanning window: (a) Mean error, and (b) 3σ standard deviation in the calculation of the resonance shift as a function of the scanning step for an effective RI change of 10−6.
3. Experimental study and discussion
The experimental demonstration of our processing method is based on the detection of the bulk RI changes in the sensing area of the MRRs, when sucrose solutions of different concentrations are brought inside this area. More specifically, the demonstration is based on a photonic circuit with MRRs that has been fabricated on the TriPleX photonic integration platform [16]. Figure 6 presents the layout of the circuit and the cross-section of its waveguiding structure for single-mode operation at 850 nm. It comprises a Mach-Zehnder interferometer (MZI) for calibration purposes, a reference MRR without sensing window, and a 6-fold array of sensing MRRs with a common sensing window that has been engineered by locally removing the top-cladding silicon oxide layer above the silicon nitride strip. For 850 nm operation, the Q-factor, the round-trip length and the FSR of the MRRs are 1.5·104, 872 µm and 390 pm, respectively, in accordance with the values in the simulation study. A multi-mode interference (MMI) coupler [19] splits on-chip the input light into eight parts in order to feed the MZI and the MRRs. After these elements, the signals are forwarded to the output waveguides that form together with the input waveguide an 8-fold array with 250 µm pitch.
Fig. 6 Layout of the photonic integrated circuit on TriPleX platform for the experimental validation of our method. The circuit comprises one MZI, one reference MRR and six sensing MRRs that share a common sensing window. The cross-section of the waveguiding structure is shown in the inset. It is based on a single strip of silicon nitride surrounded by silicon oxide and supports single mode operation at 850 nm.
3.1 Experimental setup
Figure 7 presents the experimental setup for the use of the TriPleX chip and the implementation of our sensing system. For the coupling of light in and out of the integrated circuit, we use a fiber array unit with one polarization maintaining (PM) fiber and 7 single-mode fibers at 850 nm. Light from a single-mode VCSEL with transverse electric (TE) polarization is transported through the PM fiber and is coupled into the chip. The VCSEL is biased above its lasing threshold, and is driven by a sawtooth injection current waveform with 4 mA amplitude. This driving signal enables the repetitive wavelength scanning of a spectral range of 1.86 nm around 855.105 nm. During operation, the temperature of the VCSEL is kept at 30°C using active cooling. The optical signals at the output port of the MZI and the drop ports of the MRRs are coupled out of the chip using the single-mode fibers of the fiber array unit. Five specific fibers that carry the signal from the MZI, the signal from the reference MRR, and the signals from three sensing MRRs are further connected to a 5-fold array of silicon photodiodes for detection. A low noise transimpedance amplifier (TIA) array with adjustable gains is also used at the back end of the photodiodes in order to amplify thegenerated photocurrents and adjust their levels within the operating range of the data acquisition system. The latter is based on a board with digital-to-analog converters (DACs) and analog-to-digital converters (ADCs) that are responsible for the generation of the driving waveform and the synchronous sampling of the detected signals. The maximum sampling rate of the board and the resolution of the converters are 1MS/s and 16 bits, respectively. Using a DAC with this resolution and an additional voltage-to-current conversion circuit, it is possible to generate the sawtooth waveform with high precision and adjust the scanning step to sizes down to 0.5 pm. Using the ADCs on the other hand, it is possible to sample the five detected signals and reconstruct with high fidelity the TFs of the corresponding optical structures that fall within the 1.86 nm scanning range. Although the maximum sampling rate of the board can support scanning frequencies up to several hundreds of Hz, the scanning frequency in ourexperiments is set to 1 Hz irrespectively of the scanning step. Given the dynamics of our biochemical system, this frequency is sufficient for detecting and tracking all transient effects.
Fig. 7 Experimental setup for the validation of the FFT method. It is based on the use of the TriPleX chip of Fig. 6 and a microfluidic system that delivers sucrose solutions with different concentrations inside the sensing window of the MRRs. The bulk RI change due to the sucrose solutions is estimated through the resonance shift of the MRRs, which is calculated using the FFT method. The photograph in the upper right part shows the holder that holds together the TriPleX and the microfluidic chip.
In our actual measurements, we use double-distilled (dd) water with 1.3290 RI, and four aqueous solutions of sucrose with mass-to-mass concentrations of 1% w/w, 2% w/w, 4% w/w and 8% w/w. The estimated RI of the first solution is 1.3372, whereas the RI change of the second, third, and fourth solution compared to the first one is 1.6·10−3, 4.8·10−3 and 1.12·10−2, respectively. The liquids are hold in glass containers and are transferred to the sensing window of the chip via a microfluidic system. This system comprises a number of port valves, a peristaltic pump and proper tubing that interconnects the individual elements and ends at the input port of a chip holder [20]. The latter provides a means for the physical interfacing between the photonic and the microfluidic part, and facilitates the actual access of the liquids to the sensing window of the sensing MRRs. During the measurements, the flow rate of the peristaltic pump is kept constant at 2 micro-liters per second (µl/s). The data acquisition system and the microfluidic system are controlled via a proper software platform (LabVIEW) running on a personal computer. The FFT processing algorithm and the method for the selection of a proper scanning window out of a broader one have been incorporated into this platform in order to perform the signal processing in real-time using the same software environment. The time evolution of the calculated resonance shift of each sensing MRR is visualized also in real time, using either the absolute value of the shift or the relative value of the shift compared to the reference MRR or compared to a different sensing MRR (differential measurement).
3.2 Experimental results and discussion
Figure 8(a) presents an indicative snapshot of our measurement process showing the TFs of the reference and the sensing MRRs in the spectral window from 854.175 to 856.035 nm. In this exemplary case, the liquid brought inside the sensing window of the MRRs is water and the wavelength step of the VCSEL is 0.5 pm. The time for the scanning of the spectral window and the extraction of the TFs is only one second. In the next snapshot, the TFs are re-extracted and their possible wavelength shift compared to the previous snapshot is calculated using the FFT method. Since the peaks of each TF are not symmetrical within the scanning window, the calculation of the corresponding wavelength shift is based on a part of the window as per the description in our simulation study. Figure 8(b) presents as an example the case of the reference MRR. The part of the window we use for further processing is twice as large as the FSR of the reference MRR and starts from a point that corresponds to a minimum of the TF. Among the possible intervals that satisfy these conditions for each TF, we always take the right-most one in order to maximize the signal-to-noise ratio. The inset in Fig. 8(b) presents a zoom-in on the right-most peak of the TF within the selected interval, and reveals the amplitude perturbation that is present in our measurement. Using fitting algorithms, it is possible to estimate the standard deviation of this perturbation and conclude that the maximum signal-to-noise ratio (SNRmax) of our system is close to 50 dB, remaining in good agreement with the value we used in our simulation study.
Fig. 8 (a) Indicative snapshot of the measurement process, showing the TFs of the reference and the sensing MRRs inside the scanning window from 854.175 to 856.035 nm. (b) Algorithm for the selection of a smaller window for data processing out of the initial scanning window in the case of the reference MRR. The data processing window is symmetrical and has a width twice as large as the FSR of the MRR. The inset in Fig. 8(b) presents a zoom-in on the TF peak.
Figure 9 presents indicative results from the operation with the four sucrose solutions. The measurement protocol includes four steps, each one with flow of the corresponding solution over the sensing MRRs. Each step lasts 300 sec and is followed by a washing step of the same duration with flow of double distilled water over the MRRs. The measurement of the resonance shifts is made with 1 Hz repetition rate. Figure 9(a) illustrates the time evolution of the cumulative resonance shifts that correspond to the reference and the three sensing MRRs over a total period of 2600 sec. All measurements composing the four curves in the particular diagram have been carried out using a scanning step of 0.5 pm. However, the same measurements have been also repeated with scanning steps of 1, 2, 4 and 8 pm. Figure 9(b) depicts in fact the execution of the same protocol with a scanning step of 8 pm. As observed in the two diagrams, the evolution of the cumulative resonance shift is very similar for the three sensing MRRs and the two scanning steps, revealing the homogeneity of the sensing MRRs on the TriPleX chip, and the potential of the FFT method to provide reliable results even in the case of coarse scanning steps. On the other hand, the resonance shift of the reference MRR remains in both cases below the noise level, as the liquids have not access to the cladding area of the particular MRR and do not affect the resonance conditions.
Fig. 9 (a) Time evolution of the cumulative resonance shifts corresponding to the reference and the three sensing MRRs during the execution of our main microfluidic protocol with a total duration of 2600 sec. The measurements have been performed using our FFT method with 1 Hz scanning frequency and 0.5 pm scanning step. (b) Results from the execution of the same protocol with a scanning step of 8 pm.
Figure 10(a) presents the analysis of the measurements concerning the sensitivity of the three sensing MRRs. The diagram presents six sets of points, which correspond to the three MRRs and the two extreme scanning steps (0.5 and 8 pm) in our system. Nine more sets of points that correspond to the intermediate scanning steps (1, 2 and 4 pm) have been also extracted, but are not shown in the diagram in order to keep it clear, since they have practically a perfect overlap with the illustrated data. Each point associates the difference of the second, third and fourth plateau from the level of the first plateau (in pm) with the RI change of the second, third and fourth sucrose solution compared to the first one (in RIU). For each set of points, the estimation for the sensitivity can be made through the calculation of theslope of the fitted linear curve, as shown in Fig. 10(a). It is noting that the estimated value in all cases presented in the diagram is around 93.7 nm/RIU with standard deviation smaller than 0.1 nm/RIU.
Fig. 10 (a) Extraction of the sensitivity of each MRR based on the resonance shift difference of the second, third and fourth plateau from the first one, and the difference in the RI of the corresponding sucrose solutions. The sensitivity is extracted from the slope of the fitted curves for the different MRRs and scanning steps. (b) Dependence of the wavelength resolution (given as the 3σ standard deviation of the measurements) on the scanning step in the case of operation with constant microfluidic flow (2 µl/s) and the case of stagnant sucrose solutions on the MRRs. In the case of stagnant solutions, the processing of the measurements has been made both with the FFT method and with two veriations of the Lorentzian fitting method. The theoretical curve according to the simulations in Fig. 3(b) is also presented as a reference.
Figure 10(b) presents in turn an analysis of the standard deviation of the measurements, providing an estimation of the wavelength resolution of the system. As a reference for the evaluation of our results we use the blue curve, which corresponds to the simulation results of Fig. 3(b) for TFs with two resonance peaks and power dependence. The black curve in Fig. 10(b) refers to experimental data from the run of our microfluidic protocol with different scanning step, and shows the dependence of the 3σ standard deviation of the resonance shifts on this step. The measurements that are taken into account for this calculation include all measurements at the four plateaus of each protocol run. In order to ensure that the transients at the rising and the falling edge of each plateau will not disturb the calculation, we use only the measurements that fall within the time interval between 100 and 250 seconds after the start of each protocol step with flow of a sucrose solution. Moreover, for the same calculation we do not employ the absolute resonance shifts, but rather the relative ones by subtracting the absolute values of the first sensing MRR from the absolute values of the second one. This differential scheme is necessary in order to eliminate the measurement noise from the perturbations of the VCSEL source and the fluctuations of the ambient temperature, which are always present in the measurement system [10]. Compared to the use of the reference MRR as the reference in this scheme, the use of a second sensing MRR is highly preferable, since it can eliminate the temperature noise much more efficiently. The reason for this is that the two sensing MRRs have the same structure and are affected in the same way by the changes in the ambient temperature. On the contrary, the silicon-oxide layer that serves as top cladding in the reference MRR has a thermo-optic coefficient with opposite sign compared to the aqueous solutions that have the same role in a sensing MRR, leading inevitably to different behaviors.
As shown in the black curve of Fig. 10(b), the standard deviation using the conventions and the techniques described above, remains relatively large (0.6 pm) even in the case of a short scanning step (0.5 pm). We believe that this deviation from the theoretical values is associated with the presence of pressure fluctuations on the surface of the sensing MRRs. These pressure fluctuations originate from the microfluidic components in our system and can lead to perturbations of the TFs. These perturbations can be detrimental, since they do not shift together with the TFs, when there is a change in the effective refractive index of the sensing MRRs. Hence, they can affect the center of gravity of the Lorentzian resonances, deforming the shape of the TFs and reducing the accuracy in the calculation of the actual resonance shifts. A possible solution can be the use of digital band-stop filters in order to filter out the spectral components of the perturbations without affecting the useful part of the signals. This type of digital filtering can be applied prior to the FFT in order to improve the tolerance of our method to this type of non-random noise. Work to this direction is ongoing and involves the spectral analysis of the pressure-induced perturbations, the interrelation of this spectral profile with the flow rate and the micro-mechanical properties of the microfluidic chip, and the cancellation of the noise using proper filter designs. It is noted that the same approach can be also used for the cancellation of other non-random patterns in the TFs, like for example the periodic patterns from Fabry-Perot cavities that can be formed in the optical path of the system. Although such patterns are not evident in our experimental results, in principle they can be present in similar experimental setups deteriorating the system accuracy.
In order to experimentally validate our explanation for the deviation between the measurements and the theoretical values of the standard deviation, we have repeated the measurements with a modified protocol, pausing temporarily the flow of the liquids at each plateau, and taking into account for the calculation of the standard deviation only the points that correspond to the time intervals with stagnant sucrose solutions on the sensing MRRs. The red curve in Fig. 10(b) presents the corresponding results and shows that without the impact of the microfluidic noise, they are very close to the theoretical ones. More specifically, the 3σ standard deviation for 8 pm step is 0.38 pm, whereas for 0.5 pm step is only 0.08 pm, validating the efficiency of the FFT method and indicating that the achievable LOD of our system can be only 8.5·10−7 RIU. Since our differential scheme is based on the use of two sensing MRRs, the actual demonstration of this ambitious LOD can be realized using either a different photonic chip with separate sensing windows and different solutions flowing over the different groups of MRRs, or using the same chip with a single sensing window and surface functionalization of selected MRRs in order to selectively capture the target analytes. The implementation of either approach was not within the scope of the present work. The second approach, however, is the main one for the detection of small biomolecules in various biochemical applications, and will be the subject of our future works.
Finally, in order to experimentally validate the advantage of the FFT method over the Lorentzian fitting in terms of accuracy, we have re-processed off-line the data from the wavelength scans that correspond to the time intervals with stagnant solutions, using Lorentzian fitting. The Lorentzian function, which the measured TFs should fit to, is as follows:
where and are the parameters that are iteratively optimized. In this study, we have used the same data processing window as before [see Fig. 8(b)], and have employed two different ways for the optimization of the fitting process. The first one takes into account only the right-most resonance peak inside the data processing window and uses a single Lorentzian function for the fitting of the TF in the area around this peak. The second way takes into account both peaks inside the data processing window and uses the superposition of two Lorentzian functions for the fitting process. The green and purple curves in Fig. 10(b) present the standard deviation of the differential resonance shift that is obtained with either way, and can be directly compared to the red curve, which presents the corresponding results with the FFT method. As observed in Fig. 10(b), the superposition of two functions appears to improve the accuracy of the Lorentzian fitting in a way similar to the way that a larger number of peaks improve the accuracy of the FFT method (see Fig. 2). Nevertheless, even with this improvement, it is clear that the FFT method has a big advantage compared to the Lorentzian fitting, especially for operation with coarse scanning steps.Interestingly, this higher accuracy of the FFT method comes with a huge advantage also in terms of computation resources and script running speed. More specifically, the execution of our FFT script takes in our LabVIEW platform less than 1 ms. On the other hand, our single-peak Lorentzian fitting script based on the Levenberg-Marquardt method takes almost 1365 ms, prohibiting the data processing in real-time for a scanning rate of 1 Hz. Although certain that our Lorentzian fitting script is not optimum in terms of speed and that the actual running time difference between the two methods can be closer to 100 rather than to 1000, the difference in the running time of the two scripts observed in our platform is indicative for the time and resource efficiency of our FFT method.
4. Conclusions
We have extended our previous simulation study in [14] regarding the accuracy of our FFT method for the calculation of the resonance shift in MRR-based biosensors. We have investigated in particular the impact of factors like the number of the resonance peaks, the wavelength dependence of the laser power and the asymmetry of the TFs. We have assessed and quantified the positive impact of the first factor, the negative impact of the second factor, and we have proposed a technique for the compensation of the third factor in real systems, since it can result in significant measurement errors if it is left uncompensated. Moreover, we have built a measurement system with a microfluidic part and a photonic sensing part with MRRs on TriPleX platform with 1.5∙104 Q-factor, and we have experimentally validated our method using sucrose solutions with different concentrations. Using the absolute resonance shifts of the MRRs, we have estimated that their sensitivity is close to 93.7 nm/RIU. Using the relative resonance shifts on the other hand and excluding the noise from the microfluidic part, we have confirmed that the wavelength resolution of the measurement system can be 0.38 pm for a coarse scanning step of 8 pm and only 0.08 pm for a finer step of 0.5 pm. In combination with the sensitivity of the MRRs, this wavelength resolution indicates the possibility for a limit of detection close to 8.5·10−7 RIU, which represents to the best of our knowledge a record performance for this type of optical sensors and level of scanning steps.
5. Funding
The work was supported by the European Commissioned-funded project FP7-ICT-BIOFOS (Contract No. 611528).
References and links
1. A. Yalcin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, V. Oliver King, Van, D. Sai Chu, M. Gill, M. S. Anthes-Washburn, Unlu, and B. B. Goldberg, “Optical sensing of biomolecules using microring resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 148–155 (2006). [CrossRef]
2. H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15(15), 9139–9146 (2007). [CrossRef] [PubMed]
3. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007). [CrossRef] [PubMed]
4. N. A. Yebo, P. Lommens, Z. Hens, and R. Baets, “An integrated optic ethanol vapor sensor based on a silicon-on-insulator microring resonator coated with a porous ZnO film,” Opt. Express 18(11), 11859–11866 (2010). [CrossRef] [PubMed]
5. M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, and J. E. Bowers, “Ultra-high quality factor planar Si3N4 ring resonators on Si substrates,” Opt. Express 19(14), 13551–13556 (2011). [CrossRef] [PubMed]
6. C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006). [CrossRef]
7. C. Ciminelli, C. M. Campanella, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Label-free optical resonant sensors for biochemical applications,” Prog. Quantum Electron. 37(2), 51–107 (2013). [CrossRef]
8. R. Guider, D. Gandolfi, T. Chalyan, L. Pasquardini, A. Samusenko, G. Pucker, C. Pederzolli, and L. Pavesi, “Design and optimization of SiON ring resonator-based biosensors for aflatoxin M1 detection,” Sensors (Basel) 15(7), 17300–17312 (2015). [CrossRef] [PubMed]
9. J. Hu, X. Sun, A. Agarwal, and L. C. Kimerling, “Design guidelines for optical resonator biochemical sensors,” J. Opt. Soc. Am. B 26(5), 1032–1041 (2009). [CrossRef]
10. R. Heideman, M. Hoekman, and E. Schreuder, “TriPleX-based integrated optical ring resonators for lab-on-a- chip and environmental detection,” IEEE J. Sel. Top. Quantum Electron. 18(5), 1583–1596 (2012). [CrossRef]
11. W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012). [CrossRef]
12. I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16(2), 1020–1028 (2008). [CrossRef] [PubMed]
13. L. Gui and S. T. Wereley, “A correlation-based continuous window-shift technique to reduce the peaklocking in digital PIV evaluation,” Exp. Fluids 32(4), 506–517 (2002). [CrossRef]
14. L. Gounaridis, P. Groumas, E. Schreuder, R. Heideman, H. Avramopoulos, and C. Kouloumentas, “New set of design rules for resonant refractive index sensors enabled by FFT based processing of the measurement data,” Opt. Express 24(7), 7611–7632 (2016). [CrossRef] [PubMed]
15. M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010). [CrossRef]
16. K. Wörhoff, R. G. Heideman, A. Leinse, and M. Hoekman, “TriPleX: a versatile dielectric photonic platform,” Adv. Opt. Technol. 4(2), 189–207 (2015).
17. A. Lamberti, S. Vanlanduit, B. De Pauw, and F. Berghmans, “A novel fast phase correlation algorithm for peak wavelength detection of Fiber Bragg Grating sensors,” Opt. Express 22(6), 7099–7112 (2014). [CrossRef] [PubMed]
18. F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66(1), 51–83 (1978). [CrossRef]
19. L. Gounaridis, P. Groumas, E. Schreuder, R. Heideman, V. Katopodis, C. Kouloumentas, and H. Avramopoulos, “Design of grating couplers and MMI couplers on the TriPleX platform enabling ultra-compact photonic-based biosensors,” Sensor Actuat. Biol. Chem. 209, 1057 (2015).
20. G. A. J. Besselink, R. Heideman, E. Schreuder, L. S. Wevers, F. Falke, and H. H. Van den Vlekkert, “Performance of arrayed microring resonator sensors with the TriPleX platform,” J. Biosensors Bioelectronics 7(2), 209 (2016).
