Evaluation of a simple PC-based quadrature detection method at very low SNR for luminescence spectroscopy

Sensors and Actuators B 192 (2014) 334–340

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Sensors and Actuators B: Chemical journal homepage: www.elsevier.com/locate/snb

Evaluation of a simple PC-based quadrature detection method at very low SNR for luminescence spectroscopy Santiago Medina-Rodríguez a,b,∗ , Ángel de la Torre-Vega a , Jorge Fernando Fernández-Sánchez b,∗∗ , Alberto Fernández-Gutiérrez b a b

Department of Signal Theory, Networking and Communications, CITIC-UGR, University of Granada, C/ Periodista Rafael Gómez 2, E-18071 Granada, Spain Department of Analytical Chemistry, Faculty of Sciences, University of Granada, Avda. Fuentenueva s/n, E-18071 Granada, Spain

a r t i c l e

i n f o

Article history: Received 4 August 2013 Received in revised form 31 October 2013 Accepted 31 October 2013 Available online 8 November 2013 Keywords: Optical sensor Photoluminescence Digital lock-in detection Quadrature detection Phase-resolved Spectroscopy

a b s t r a c t We developed a PC-based phase measuring system based on the principles of quadrature detection with ideal features for accurately determining the amplitude and phase of a sinusoidal signal, even in the presence of very high noise levels. This detection technique was implemented via software on a personal computer (PC), and its response was analyzed using experimental tests under different noise conditions using 1 s test signals. Additionally, this technique was implemented and was subsequently evaluated using a real measurement system (a versatile and low-cost optical-fiber measurement system for optically detecting oxygen in the gas phase) under different lighting conditions. The results demonstrate the robustness of the proposed technique to noise and its computational efficiency; these results were similar to those obtained using a measuring instrument commonly used in research laboratories (a commercially available digital lock-in amplifier (LIA)). © 2013 Elsevier B.V. All rights reserved.

1. Introduction During the last two decades, there has been considerable interest and tremendous research activity in the field of optical sensing, specifically in real-time monitoring. This attention is justified because optical sensors are important in various areas, including analytical chemistry, environmental sensing, biochemistry, clinical chemistry, and industrial applications [1–7]. Most optical sensors are based on measurements of the luminescence emission intensity [2,4,8–10]. Unfortunately, although they are relatively simple and accurate to conduct in the laboratory, they are often inadequate for real applications because the emission intensity is highly influenced by external perturbations [11–13], such as the intensity fluctuations of the exciting light, detector drift, degradation or leaching of the dye, light losses in the optical path, orientation and location of the sensor, concentration of the luminophore, and optical surface quality [12,14]. Furthermore, another disadvantage of intensity-based measurements is that they

∗ Corresponding author at: Department of Signal Theory, Networking and Communications, CITIC-UGR, University of Granada, C/ Periodista Rafael Gómez 2, E-18071 Granada, Spain. Tel.: +34 958 240842. ∗∗ Corresponding author. Tel.: +34 958 240451; fax: +34 958243328. E-mail addresses: [email protected] (S. Medina-Rodríguez), [email protected] (J.F. Fernández-Sánchez). 0925-4005/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.snb.2013.10.131

are often performed with expensive and bulky instrumentation (typical for luminescence spectrometers used in laboratory measurements [8]) or with portable but equally expensive and specific measuring instruments, such as fiber optic photometers [10] and charge-coupled device (CCD) cameras [3]. These difficulties can be minimized by measuring the luminescence lifetime [15] because it is an intrinsic property of the luminophore. Therefore, lifetime measurements are often preferable when designing reliable and robust optical luminescence sensors [11,14,16]. The phase-modulation methods using the phase as analytical signal are the preferred techniques for measuring the luminescence lifetime in the frequency domain [4,13,16] because they allow detecting the low-level, slowly varying optical signals that are common in many optical measurement situations (e.g., optical sensors), even when high-level, low frequency optical interference and low frequency (1/f) noise are present [17]. Therefore, intensitymodulated optical sources and lock-in detection systems (known as quadrature detection systems) are commonly used to measure lifetime. To date, various measurement systems based on digital lockin detection techniques have been reported with ideal features for working with modulated signals at simple or multiple modulation frequencies [12,18]. Some systems allow better phase resolution and stability [12,19,20], fast amplitude and phase computations [18], reduced device size [17], greater versatility [12,21,22], and a notable cost reduction [12,17,23]. However, very few of these

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measurement systems have been exhaustively analyzed using real scenarios with different noise conditions, and even fewer have been implemented or evaluated in real-world applications under weak lighting conditions. In this work, we use a single-frequency digital phase measuring technique (known as the I/Q method) based on the principles of quadrature detection, with ideal features for accurately determining the amplitude and phase of a sinusoidal signal when high noise levels are present. This quadrature detection method is implemented entirely using software on a personal computer, and because all of the signal processing occurs on a computer, full control over the acquired signals and error statistics during every processing stage is possible. This method has been evaluated under different noise conditions using numerically generated analog signals. In addition, we also describe the implementation and evaluation of the I/Q detection method in a versatile and lowcost optical-fiber measurement system to detect oxygen in the gas phase under different lighting conditions as a typical real application. The results from the I/Q method have been compared with those obtained using a commercially available lock-in amplifier (LIA) as a reference under the same experimental conditions.

of the processing unit. The numerical generation of these reference signals is advantageous because they have no noise (with the exception of the numerical precision errors); however, if the source modulation hardware and the sampling of the ADC are not synchronized, a slight frequency mismatch may occur [18,20]. The discrete reference signals (cosine and sine) are multiplied by the discrete measured signal (M[n]) to yield the ‘in phase’ and ‘quadrature’ components, which are also commonly called the I[n] and Q[n] signals [18,28]. The measured amplitude (Am ) and the phase (ϕm ) of the signal (M[n]) can be calculated from the dc terms, I and Q, by filtering I[n] and Q[n] with a low-pass filter (hL [n]). The low-pass filtered versions of I[n] and Q[n] are often called the real (X) and imaginary (Y) parts of the measured sinusoid [18,28]. The amplitude and phase of the measured sinusoid can be calculated using the real and imaginary parts as follows [18,28]:

2. Theory

2.2. Proposed phase measuring technique (I/Q method)

2.1. Standard digital lock-in detection (LIA)

The proposed phase measuring technique (I/Q method) is based on quadrature detection [12,29], which is well known in the field of digital communications [30]. This technique is relatively simple to implement using a computer [12,18] and is less expensive than the commercial measurement equipment used in measuring laboratories to determine the amplitude and phase of a sinusoidal signal measured relative to a reference signal. The I/Q method is a simplified version of the standard digital lock-in detection implemented in most commercial digital lock-in amplifiers; the projections of the input sinusoidal signal on the reference in-phase and quadrature components are calculated using simple arithmetic operations without applying any digital filters. The details and theoretical background of the I/Q detection technique used for simultaneously measuring the amplitude and phase of single and multi-frequency signals have been previously developed by Medina-Rodríguez et al. [12]. In the present work, we are only interested in single-frequency detection, and the X and Y terms for the digital measured signal (M[n]) can be calculated using the following expressions [12]:

In general, for lock-in detection [18–28], there is a source signal (R(t)) used as a reference input signal in the lock-in detector. This signal contains a periodic signal of amplitude (As ), a modulation frequency (fm ), a phase angle (ϕs ), and a dc component (dcs ). R(t) = dcs + As cos(2fm t + ϕs )

(1)

This source signal is used as the excitation signal for a system that yields a measurable response (M(t)) that is attenuated in the amplitude and phase shifted according to the following: M(t) = dcm + Am cos(2fm t + ϕm ) + noise

(2)

where dcm is the dc term, Am is the amplitude, fm is the modulation frequency (which is known), ϕm is the phase, and noise is an additive noise term. Essentially, a lock-in detector takes a periodic reference signal R(t) and a noisy input signal M(t) and uses a phase-sensitive detector (PSD) to extract only the portion of the output signal whose frequency matches the reference [28]. Typically, to gain some information about a measured system, the instrument provides the amplitude and the phase. In contrast, the dcm term is usually not useful because it is contaminated with unwanted environmental and/or systematic distortions [18]. When the signal’s phase is unknown for the quantity of interest, quadrature detection is used, requiring two reference signals in quadrature (i.e., cosine and sine signals) [18]. During digital lock-in detection [19–23,25–28], an analog-to-digital converter (ADC) is used to digitize the analog signals. The ADC takes Ns samples of M(t) at a sampling frequency (fs ), yielding the digital signal: M[n] = dcm + Am cos

 2f n  m fs



+ ϕm + noise [n]

(3)

where n is the index of the nth sample (with 0 ≤ n ≤ Ns − 1). The time required to take Ns samples is the measurement time (Tm ) and is given by Tm = Ns /fs ; it may also be viewed as the settling time for the lock-in filter [18,28]. The data sampled by the ADC are transferred to a digital processing unit where the computations for the digital lock-in detection are performed [18,28]. Digital lock-in techniques require digital signals for the cosine and sine waves at the modulation frequency (fm ) [18] that are generally obtained from a numerically generated reference signal stored in the memory

Am =



X2 + Y 2

ϕm = tan−1

X=

(4)

Y 

(5)

X

Ns −1 Ns −1 M[n]C[n] M[n] cos[(2fm n/fs )] n=0 =  n=0 Ns −1 2 Ns −1 2 n=0

C[n]

n=0

Ns −1 Ns −1 M[n]S[n] M[n] sin[(2fm n/fs )] n=0 Y=  = n=0 Ns −1  N 2 2 s −1 n=0

S[n]

n=0

(6)

cos [(2fm n/fs )]

(7)

sin [(2fm n/fs )]

From the X and Y terms, the amplitude (Am ) and phase (ϕm ) of the measured signal (M[n]) can be calculated as depicted in (4) and (5). The discrete signals for the cosine and sine (i.e., C[n] and S[n], respectively) are obtained from a numerically generated reference signal stored on a computer. All discrete signals are sampled at an identical rate (fs ) while having the same length (i.e., a total number of samples equal to Ns ) and frequency (fm ) (which is known a priori). The I/Q method should behave correctly in most cases; however, if the source modulation hardware and the ADC sampling are not synchronized (or if there is frequency drift in the reference source), there may be a slight frequency mismatch, leading to large errors in the signal’s phase measurements (M[n]), which is a disadvantage relative to commercial LIAs (i.e., lock-in detection technique) in which a PLL (Phase-Locked Loop) is used to engage the frequency of the input signal in real time. Nevertheless, a simple solution to

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this problem might also be digitally implemented during the I/Q method, although those details are beyond the scope of this work. The main advantage of the I/Q method versus LIA is its simplicity and flexibility because a very narrow bandwidth for the measured signal M[n] can be achieved (on the order of 1/Tm , where Tm is the time duration of the signal) without applying any low-pass filtering with optimum parameters dependent on Tm . The phase measurement is obtained using a single frequency (i.e., from in-phase and quadrature signal’s projections on the reference frequency of interest fm ) while ignoring the noise from other frequencies. Therefore, only the noise added to the relevant bandwidth of the signal M[n] affects the phase measurement, achieving a very high SNR.

duration, respectively) were added to prevent sample loss during the subsequent data acquisition process using an oscilloscope. These stored digital signals were converted to analog signals using a digital-to-analog converter (DAC) and they were used to validate the I/Q method under different noise levels. In addition, these results were compared with those obtained using a commercial dual-phase digital lock-in amplifier (SR830, Stanford Research Systems, www.thinksrs.com). Electronic Supporting Information (ESI) shows further information about the protocol used for validating the I/Q method by using analog signals.

3. Experimental

The control over oxygen concentration and phase-shift measurements was carried out using an ad hoc measurement system designed and built in our laboratory. Fig. 1 displays a schematic diagram of the optical-fiber measurement system for sensing oxygen using phase-shift measurements. In this scheme, the PtTFPP-containing sensing film was excited with an ultraviolet LED (peak 395 nm, angle of illumination 15◦ , LED diameter 5 mm, luminous power 25 ␮W into a 600 ␮m optical-fiber, model LS-450 LED-395, Ocean Optics, www.oceanoptics.com) filtered through an optical bandpass filter (OF-1) (central 390 nm, FWHM 18 nm, model MF390-18, Thorlabs GmbH, www.thorlabs.com). The UV-LED light source was sinusoidally modulated at an optimal frequency of 5145 Hz [12]. The numerically generated digital signals were extracted using two analog output channels on an AD/DA board (model NI PCIe-6363/BNC-2120, National Instruments, www.ni.com) at 100 kS/s. One of the channels was used to modulate the current of the LED light source in the LED driving circuit, and the other one was used as an external reference signal for the data acquisition device. A bifurcated fiber bundle (wavelength range 200–800 nm UVVIS, 12 illumination fibers 200 ␮m core diameter, 1 read fiber 600 ␮m core diameter, N.A. 0.22, model FCR-7xx200-2, Avantes Inc., www.avantes.com) was used to guide the excitation light toward the sensing film and to guide the luminescence emission back to the detector after passing through an optical bandpass filter (OF-2) (central 630 nm, FWHM 60 nm, model A10033-03, Hamamatsu Photonics, www.hamamatsu.com). The luminescence was detected with a photomultiplier tube (PMT) (BW DC-1 MHz, model H10723-20, Hamamatsu Photonics). The voltage signal provided by the PMT (only a few tens of millivolts) was amplified with a commercially available low-noise programmable voltage preamplifier (model SIM911 BJT, Stanford Research Systems) and subsequently filtered with a three-stage passive-RC low-pass filter (with filter cut-off frequencies of 20, 27 and 33 kHz for each of the stages, respectively) before being subjected to the data acquisition device: (1) a commercial dual-phase digital lock-in amplifier (model SR830, Stanford Research Systems) and (2) a digital oscilloscope (model WaveRunner 604Zi, LeCroy, www.lecroy.com). For the oscilloscope-based acquisition system, both the excitation signal (the reference) and the emission signal from the sensing film were simultaneously digitized using the digital oscilloscope at 100 kS/s. Signals 1 s in duration (i.e., a 100 kS data buffer) were recorded and transferred via Ethernet from the oscilloscope to the PC. An ad hoc Matlab program was used to digitally process the signals (i.e., calculate the phase-shift between the excitation signal and the emission signal). The average processing time for each phase-shift measurement using the I/Q method was less than 200 ms. Therefore, because the average acquisition time for the signals using the oscilloscope was less than 1.5 s (including the data transfer time from the oscilloscope to the PC), an average total measuring time of less than 1.7 s was necessary to provide each phase-shift measurement; therefore, this system can be used to measure oxygen concentrations in real time.

3.1. Materials and chemicals The oxygen-sensitive luminescent dye, platinum(II) 5,10,15,20meso-tetrakis-(2,3,4,5,6-pentafluorophenyl)-porphyrin (PtTFPP), was obtained from Frontier Scientific Inc. (www.frontiersci.com, UT, USA) and immobilized in a transparent, oxygen-permeable polystyrene matrix (PS; Scientific Polymer Products Inc., www.scientificpolymer.com, Ontario, NY, USA). All components were dissolved in chloroform, which was used for its ability to dissolve both the luminescent dye and polymer [8,12]. The chloroform was obtained from Sigma–Aldrich (www.sigmaaldrich.com, Química S.A., Madrid, Spain). For the gas mixture, nitrogen and oxygen (99.999% purity) were obtained from Air Liquide ˜ S.A., Madrid, Spain). (www.airliquide.com, AL Air Liquide Espana 3.2. Preparation of the oxygen-sensitive film The cocktail necessary to obtain the sensing film was prepared by dissolving 3 mg of PtTFPP and 198 mg of PS in 2 mL of chloroform (dye concentration of 1.5 mg/mL) [8,12]. The mixture was shaken with an IKA-Vibramax-VXR (IKA-Labortechnik, Staufen, Germany) until all components had completely dissolved. The oxygensensitive membrane was obtained with a Laurell spin-coater (WS400B-6NPP/LITE, Laurell Technologies, www.laurell.com, North Wales, PA, USA): 200 ␮L of the cocktail was injected onto a rotating glass support spinning at 700 rpm. The PtTFPP/PS membrane obtained after the deposition process was a soft reddish color and allowed visible light to pass through it. The resulting layer was approximately 4 ␮m thick and was modulated by the viscosity of the cocktail and the spin-coater’s rotation speed [8,12]. 3.3. Evaluation of the I/Q method using numerically generated analog signals A personal computer (Intel(R) Core(TM)2 Quad CPU Q9400 at 2.66 GHz, equipped with the numerical computing environment, Matlab 7.10 (MathWorks, www.mathworks.com, Natick, MA, USA)) was used to implement the I/Q method and generate the required digital signals. Two discrete reference signals (cosine and sine) were numerically generated and stored on the computer with the following parameters: dc = 0, A = 1, fm = 5145 Hz, fs = 100 kHz, ϕ = 0◦ , noise = 0, signal duration = 1 s, and Ns = 100 kS. In addition, digital test signals with identical lengths (Ns ), sampling frequencies (fs ) and modulation frequencies (fm ) but with amplitude of 0.15, randomly phase between 0 and −180◦ and different levels of additive white Gaussian noise (AWGN) were also generated and stored on the computer. All signals were 1 s in duration. This value was arbitrarily assigned to reduce the processing time and the size of the signal data while remaining long enough to ensure that there was a sufficient number of signal cycles for processing. Additionally, bursts of zeros at the beginning and end of the signals (of 3 s and 1 s

3.4. Measurement system

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Fig. 1. Schematic diagram of the experimental setup designed for measuring the phase-shifts using two different data acquisition devices: (1) a commercial dual-phase lock-in amplifier and (2) a digital oscilloscope connected to a personal computer for further data processing using the I/Q method.

The additional phase-shift value (i.e., instrumental bias) introduced by the hardware components of the measurement system (AD/DA board, LED driver, PMT, voltage preamplifier, passive-RC low-pass filter, data acquisition device, etc.) was previously estimated for each experimental setup using a red reference LED (peak 660 nm, angle of illumination 50◦ , LED diameter 5 mm, luminous intensity 2000 mcd typ./20 mA, model L2-0-R5TH50, LED Supply, www.ledsupply.com) in the same spectral range as the sensing film. Subtracting this phaseshift value from the experimental data allowed us to calculate the specific phase-shift value introduced only by the sensing film. To characterize, calibrate, and evaluate the oxygen-sensitive film in the gas phase, a flow-through cell was specifically designed to hold the sensing film. It was made of black polytetrafluoroethylene (PTFE) to prevent stray reflections and to ensure that the system was chemically inert. Different mixtures of nitrogen and oxygen at a constant flow of 200 mL/min were passed through the flow cell to calibrate (and evaluate) the sensing film. To mix the gases, two mass-flow controllers (MFCs) (EL-FLOW Select F-201CV, Bronkhorst High-Tech, www.bronkhorst.com, Ruurlo, Netherlands) were connected, using copper and stainless steel tubing, to the flow-through cell. The N2 /O2 -gas station was controlled from a PC using an ad hoc computer program developed in LabVIEW 8.5 and Matlab 7. The PC was connected to a Flow-Bus Interface (Bronkhorst High-Tech) to control the MFCs via a RS-232 serial port. Finally, both the flow-through cell and the PMT were housed in a dark room (XE25C1, Thorlabs GmbH) to prevent interference from stray light. All the measurements were performed at room temperature (21 ◦ C). The temperature was continuously monitored using a commercial temperature sensor (MicroLite, Fourtec-Fourier

Technologies, www.fouriersystems.com) placed at a point close to the flow cell. 3.5. Characterization and test of the oxygen-sensitive film The spectroscopic behavior of the oxygen-sensitive film (i.e., luminescence excitation and emission spectra in the absence and presence of oxygen) was determined with a Varian Cary-Eclipse luminescence spectrometer (Agilent Technologies, www.home.agilent.com, CA, USA). The parameter settings for the spectroscopic characterization were as follows: exc = 394 nm, em = 650 nm, slit-widthexc/em = 10/10 nm, delay time 0.1 ms, gate time 5 ms, flow rate 200 mL/min, and detector voltage 550 V. All measurements were performed at room temperature (21 ◦ C). Phase-shift measurements at different oxygen partial pressures between 0 and 50 kPa O2 (or 0–50% O2 (v/v)) were taken with the two experimental setups illustrated in Fig. 1. The phase-shift measurements versus oxygen concentration were used to obtain a typical calibration curve for the sensing film (i.e., Stern–Volmer Plot (SVP)). The fits were performed using Matlab. In addition, the overall responses of the measurement systems were also evaluated under different lighting conditions. For it, the amplitude of the sinusoidal signal used to modulate the current for the LED light source was varied, and then phase-shift measurements at different oxygen concentrations were recorded for each lighting condition (see ESI for further information). 4. Results and discussion 4.1. Validation of the I/Q method using analog signals To validate the I/Q method, experimental tests were performed using analog signals with different noise levels and these results

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Table 1 Statistical results of the validation of the IQ method using analog signals with different SNR levels. SNR (dB)

−18 −12 −6 0 6 12 18 24 30 36 a

I/Q method

LIA

Mean (◦ )

Sdev (◦ )

Max (◦ )

RMSE (◦ )

Outliersa (%)

Mean (◦ )

Sdev (◦ )

Max (◦ )

RMSE (◦ )

Outliersa (%)

1.1122 0.5688 0.3019 0.1453 0.0750 0.0413 0.0222 0.0158 0.0142 0.0139

1.4101 0.7113 0.3636 0.1836 0.0926 0.0487 0.0276 0.0192 0.0177 0.0173

4.2590 2.1029 1.0895 0.5520 0.2830 0.1482 0.0840 0.0615 0.0547 0.0510

1.4115 0.7210 0.3798 0.1837 0.0941 0.0518 0.0277 0.0196 0.0178 0.0172

0.2 0.2 0 0 0 0 0 0 0 0

1.9036 1.0047 0.4825 0.2339 0.1183 0.0623 0.0349 0.0255 0.0210 0.0186

2.3234 1.1580 0.5862 0.2912 0.1492 0.0780 0.0437 0.0313 0.0260 0.0224

7.5514 3.7744 1.9108 0.8611 0.4264 0.2304 0.1289 0.0898 0.0763 0.0664

2.4047 1.2641 0.6109 0.2933 0.1492 0.0780 0.0438 0.0313 0.0260 0.0229

0.8 0.6 0.6 0.4 0 0 0 0 0 0

Percentage of outliers deleted from the dataset including 500 error measurements (criterion: ei > 3 · Sdev (dataset)).

were compared to those obtained with LIA (used as reference method). All the configuration parameters of the LIA were previously optimized to obtain the best response for the phase-shift measurement using signals only 1 s in duration: time constant (TC) of 100 ms, lowpass filter with a slope of 12 dB/octave, AC couple, 1 V sensitivity, low noise reserve, 50/60 Hz Notch filter, sine reference input, and float ground. ESI shows the selection of the TC value. Table 1 and ESI (see Fig. ESI-5) show the statistical results of the absolute phase errors for the experimental tests using the I/Q method and the LIA for a total of 500 statistically independent phase-shift measurements at different signal-to-noise ratio (SNR) conditions. The absolute phase errors are defined as ei = |ϕi − ϕ ˆ i| with i = 1, 2, 3,. . ., 500, where ϕi is the theoretical phase value (known a priori) and ϕ ˆ i is the estimated phase value. It is possible to conclude that both methods provided similar results, although these results appeared to be slightly better for the I/Q method in all cases (i.e., a lower RMS phase error for the different noise conditions tested). For example, for SNRs <18 dB, the I/Q method provided an RMS phase error equivalent to that of the LIA for SNR values that were approximately 4.5 dB lower. For SNRs >18 dB, the RMS phase error stagnated due to the electrical noise introduced by the measurement system’s hardware components. The results demonstrate the robustness of the quadrature detection technique toward noise in very low SNR situations, confirming that this detection technique is suitable for measuring the phase of a sinusoidal signal in the presence of high noise levels.

4.2. Response of the phase measuring system during a real-world application (oxygen sensor) A further analysis of the I/Q method was carried out by implementing and evaluating this method using a real measurement system (i.e., a versatile and low-cost optical-fiber measurement system for optically detecting oxygen in the gas phase). The response of the proposed measurement system was assessed by characterizing, calibrating and evaluating a known oxygen-sensitive membrane (PtTFPP/PS) under different lighting conditions. Additionally, these results were also compared to those obtained on the same membrane using a standard measurement system based on a commercial LIA. Fig. 2 displays the Stern–Volmer plots (i.e., ϕ0 /ϕ versus oxygen concentration) obtained for the same oxygen-sensitive film by using I/Q and LIA methods. This figure also reveals the fitting of experimental data according to the widely used Demas model [12,31]. This model assumes that the indicator is localized in two regions of different microenvironments, explaining the deviation from the linearity in the Stern–Volmer plot. Its mathematical expression is given as follows [8,12]: ϕ0 = ϕ



x2 x1 + 1 + KSV 1 [O2 ] 1 + KSV 2 [O2 ]

−1 (8)

where ϕ0 and ϕ are the unquenched and quenched phase-shift values (i.e., in the absence and in the presence of oxygen, respectively), [O2 ] is the oxygen concentration, x1 and x2 are the fractions of the total emission for each site (with x1 + x2 = 1), and KSV1 and KSV2

N

Fig. 2. Calibration of the oxygen-sensitive film (PtTFPP/PS) using the proposed I/Q method (, black bars) and LIA (, white bars). (a) Phase-shift variation versus oxygen concentration. Each point in the figure represents the average of N = 10 phase-shift measurements with its error (ϕ ± error; where ϕ = (1/N) ·

indicate the 95% confidence intervals based on Student’s t-distribution). (b) Stern–Volmer plots fitted according to the Demas model (solid line).

n=1

ϕn , and the error bars

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concentration at higher amplitudes of the LED excitation signal (i.e., for better lighting conditions) was observed, due to the higher SNR level (or optical power) of the emission signal received by the detector. Therefore, for 0.25–45% O2 (v/v), the average RMSE values of 0.16 and 0.31 (in % O2 (v/v)) were obtained for the I/Q-based and LIA-based systems, respectively, under the most favorable lighting condition studied in this work (1000 mV amplitude); the average RMSE values of 5.72 and 7.34 were obtained for these systems under the worst lighting condition studied (22 mV amplitude). ESI (see Fig. ESI-6) compares the oxygen concentration values measured with the MFCs [O2 ]n,MFCs (taken as reference values) and their correˆ 2 ]n,A under all sponding estimated oxygen concentration values [O i

Fig. 3. Average RMSE values (expressed in units of % O2 (v/v)) obtained under different lighting conditions using the I/Q method (black bars) and LIA system (white bars).

are the Stern–Volmer quenching constants for each microenvironment. ESI (see Table ESI-2) summarizes the fitting parameters for the two setups under study. It is possible to conclude that both measurement setups provided similar calibration curves for the sensing film (after an earlier calibration process to compensate for the instrumental bias). Furthermore, the t95 response times for the sensing film were also determined [8,12], revealing a response time under 10 s when changing from 0 to 50% O2 (v/v) and under 18 s when changing from 50 to 0% O2 (v/v). To study the effect of the noise level on the accuracy of the oxygen determination using both systems, several experiments were carried out under different lighting conditions (22, 31, 44, 62, 88, 124, 176, 249, 353, 499, 707 and 1000 mV of amplitude for the LED excitation signal) while assuming a constant 1000 mbar environmental pressure and a 200 mL/min total gas flow at 21 ◦ C. Each oxygen concentration was maintained for 15 min before the measurements, and subsequently, 10 phase-shift measurements were registered for each oxygen concentration and lighting condition with both setups. Using the calibration curves for the sensing film (see Fig. 2b), the estimated values for the oxygen concentraˆ 2 ]) could be calculated from the phase-shift measurements tion ([O taken with both measurement setups. From these estimated % O2 (v/v) values (10 values for each of the 9 oxygen concentrations tested), the average RMS error while estimating the oxygen concentration under the different lighting conditions (RMSEAi ) was determined:



RMSEAi =

2 1 N ˆ 2 ]n,A − [O2 ]n,MFCs ) ([O i N n=1

(9)

where the subscript Ai denotes a particular lighting condition (or amplitude of the LED excitation signal), N is the total number of ˆ 2 ]n,A is the estimated value measurements (90 in this case), [O i for a given oxygen concentration, and [O2 ]n,MFCs is the true value for the estimated oxygen concentration (provided by the MFCs’ control software). The RMSEAi value (expressed in units of % O2 (v/v)) was used as a statistic parameter for comparing the response of both measurement setups (see Fig. 3). A trend similar to that already observed in the experimental tests using analog signals was obtained for both setups. Slightly higher RMSE values were obtained for the LIA-based oxygen measurement system under all lighting conditions (the average RMSE value was approximately 1.5 times higher than for the I/Q-based measurement system). In all cases, a decrease in the RMSE value for the estimated oxygen

lighting conditions using the two proposed measurement systems; the mean and standard deviation of 120 points for each oxygen concentration (10 values for each lighting condition) as well as the best-fitting line (i.e., the least squares regression line) through the data for both systems are displayed. The typical oxygen measurement range for the I/Q-based measurement system was from 0 to 50% O2 (v/v) (or from 0 to 50 kPa), with a measurement accuracy of <1% O2 (v/v) (or <1 kPa) across the entire measurement range for the 1000 mV amplitude and <13.96% O2 (v/v) for the 22 mV amplitude. However, a higher accuracy was obtained at lower oxygen concentrations; the measurement accuracy for <0.2% O2 (v/v) (or <0.2 kPa) was reached over the measurement range of 0–20% O2 (v/v) (or 0–20 kPa) for the 1000 mV amplitude and <3% O2 (v/v) for the 22 mV amplitude. The limit of detection (LOD) for the I/Q-based oxygen sensor was 0.01% O2 (v/v) (or 0.01 kPa) under the best lighting condition; LOD was estimated as the oxygen concentration that produced an analytical signal three times the standard deviation of ten blank injections (0% oxygen (v/v) in this case) [12].

5. Conclusions We presented a single-frequency measurement technique (known as the I/Q method) based on the principles of quadrature detection with ideal features for accurately determining the phase of a sinusoidal signal, even when very high noise levels were present (i.e., under conditions of very low SNR). This detection technique was implemented using only software on a personal computer. To verify the proposed phase estimation method, tests using analog signals 1 s in duration with different SNR levels were carried out and successfully compared to those obtained with a standard measuring instrument used in research laboratories (a commercial digital lock-in amplifier). It can be concluded that the I/Q method is robust toward noise, confirming that the quadrature detection technique is suitable for measuring the phase of a sinusoidally modulated signal even with very low SNR levels. In addition, the I/Q method was expanded by implementing and evaluating the technique in a real world measurement system (i.e., a versatile and low-cost optical-fiber measurement system for gas phase oxygen sensing), obtaining satisfactory results even when detecting low-level optical signals. Due to the I/Q method can be efficiently implemented using software, miniaturization and portability of the measuring system may be attainable (for example, using an AD/DA board). However, the main advantages over commercial equipment (LIA) are: (1) the ease of use because no parameter settings are necessary (unlike most commercial equipment, where a parameter optimization process is essential for obtaining the best response under each experimental condition) and (2) the low-cost, computational efficiency and flexibility of digital implementation, as well as the full availability of the signals involved in the measuring process. This last feature allows offline signal processing for continuous measurement of the phase over time. This capability might be useful in real-time systems or in

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applications where very rapid phase changes must be accurately measured. Finally, the I/Q method could be also easily extended to detect amplitude and/or phase at multiple frequencies simultaneously. Thus, this method is ideal for applications using multiple modulation frequencies, including optical chemical sensors, as well as optical and electrical impedance spectroscopy and tomography applications. Acknowledgments The authors gratefully acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness (Project CTQ2011-25316 and Medina-Rodríguez’s grant reference BES2009-026919). Additionally, the authors are grateful to M. Marín-Suárez and F.J. Sainz-Gonzalo for their help during the preparation of the oxygen-sensitive film. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.snb.2013.10.131. References ´ [1] J. Janata, M. Josowicz, P. Vanysek, D.M. DeVaney, Chemical sensors, Analytical Chemistry 70 (1998) 179–208. [2] D.B. Papkovsky, T.C. O’Riordan, Emerging applications of phosphorescent metalloporphyrins, Journal of Fluorescence 15 (2005) 569–584. [3] M. Schäferling, The art of fluorescence imaging with chemical sensors, Angewandte Chemie International Edition 51 (2012) 3532–3554. [4] J.R. Lakowicz, Principles of Fluorescence Spectroscopy, 2nd ed., Kluwer Academic, New York, 1999. [5] J. Dakin, B. Culshaw, Optical Fiber Sensors: Applications, Analysis, and Future Trends, Artech House, 1997. [6] J.F. Fernández-Sánchez, T. Nezel, R. Steiger, U.E. Spichiger-Keller, Novel optical NO2 -selective sensor based on phthalocyaninato-iron(II) incorporated into a nanostructured matrix, Sensors and Actuators B: Chemical 113 (2006) 630–638. [7] O.S. Wolfbeis, B.M. Weidgans, F. Baldini, A.N. Chester, J. Homola, S. Martellucci, Fiber Optic Chemical Sensors and Biosensors: A View Back Optical Chemical Sensors, Springer, The Netherlands, 2006, pp. 17–44. [8] M. Marín-Suárez del Toro, J.F. Fernández-Sánchez, E. Baranoff, M.K. Nazeeruddin, M. Gräetzel, A. Fernández-Gutiérrez, Novel luminescent Ir(III) dyes for developing highly sensitive oxygen sensing films, Talanta 82 (2010) 620–626. [9] C. McDonagh, C.S. Burke, B.D. MacCraith, Optical chemical sensors, Chemical Reviews 108 (2008) 400–422. [10] F.J. Sainz-Gonzalo, C. Elosua, J.F. Fernández-Sánchez, C. Popovici, I. Fernández, F.L. Ortiz, et al., A novel luminescent optical fibre probe based on immobilized tridentate bis(phosphinic amide)-phosphine oxide for europium(III) ion aqueous detection in situ, Sensors and Actuators B: Chemical 173 (2012) 254–261. [11] M. Valledor, J.C. Campo, I. Sánchez-Barragán, J.M. Costa-Fernández, J.C. Álvarez, A. Sanz-Medel, Determination of phosphorescence lifetimes in the presence of high background signals using phase-shift measurements, Sensors and Actuators B: Chemical 113 (2006) 249–258. [12] S. Medina-Rodríguez, A. de la Torre-Vega, J.F. Fernández-Sánchez, A. FernándezGutiérrez, An open and low-cost optical-fiber measurement system for the optical detection of oxygen using a multifrequency phase-resolved method, Sensors and Actuators B: Chemical 176 (2013) 1110–1120. [13] H. Szmacinski, J.R. Lakowicz, Measurement of the intensity of long-lifetime luminophores in the presence of background signals using phase-modulation fluorometry, Applied Spectroscopy 53 (1999) 1490–1495. [14] C. McDonagh, C. Kolle, A.K. McEvoy, D.L. Dowling, A.A. Cafolla, S.J. Cullen, et al., Phase fluorometric dissolved oxygen sensor, Sensors and Actuators B: Chemical 74 (2001) 124–130. [15] H. Szmacinski, J. Lakowicz, Lifetime-based sensing, in: C.D. Geddes, J.R. Lakowicz (Eds.), Topics in Fluorescence Spectroscopy, Springer, USA, 2002, pp. 295–334. [16] D. Andrzejewski, I. Klimant, H. Podbielska, Method for lifetime-based chemical sensing using the demodulation of the luminescence signal, Sensors and Actuators B: Chemical 84 (2002) 160–166. [17] A.A. Dorrington, R. Künnemeyer, A Simple microcontroller based digital lock-in amplifier for the detection of low level optical signals, in: Proceedings of the First IEEE International Workshop on Electronic Design, Test and Applications (DELTA’02), IEEE Computer Society, 2002, p. 486.

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Biographies Santiago Medina Rodríguez was born in Granada (Spain) in 1985. He received the BS and MSc degree in Telecommunications Engineering from the University of Granada (Granada, Spain) in 2008 and 2009, respectively. He was granted a PhD fellowship by the Spanish Ministry of Economy and Competitiveness in September 2009, and since then he has been working toward his PhD degree in the Department of Signal Theory, Networking and Communications (TSTC) and the Department of Analytical Chemistry at the University of Granada. His research interests include optical sensor systems and signal processing. Ángel de la Torre Vega received the MSc and PhD degrees in Physics from the University of Granada (UGR) (Granada, Spain), in 1994 and 1999, respectively. Since 1994, he has been with the Research Group on Signals, Networking and Communications, Department of Signal Theory, Networking and Communications (TSTC, UGR). In 2000, he joined the PAROLE Group, Laboratoire RFIA du LORIA, Nancy, France, as a Postdoctoral Researcher in the field of robust speech recognition, and the Institut für Angewandte Physik, Innsbruck, Austria, as a Postdoctoral Researcher in the field of cochlear implants. Since 2003, he has been an Associate Professor with the University of Granada. His research interests are in the field of signal processing, and particularly robust speech recognition, speech processing in noise conditions, signal processing for cochlear implants, processing of seismic signals, acquisition and processing of electrophysiological responses in audiology, and processing of mass spectrometry data. He is reviewer for several scientific journals. Jorge Fernando Fernández Sánchez is Associate Professor in the Department of Analytical Chemistry at the University of Granada (Granada, Spain). He received his MS (2001) and PhD (2003) in Analytical Chemistry from the University of Granada. Between 2004 and 2006 he was working at the Swiss Federal Institute of Zurich, and since 2006 he is co-heading the optical sensor research line of the Prof. FernándezGutiérrez’s research group. He has coauthored more than 60 book chapters, journal and conference papers related to optical sensors and nanotechnology applied to the development of optical sensing films. Alberto Fernández Gutiérrez is Full Professor in the Department of Analytical Chemistry at the University of Granada (Granada, Spain). He founded the Environmental, Biochemical and Foodstuffs Analytical Control research group twenty years ago. Since then, he has been its director. From 1969 to 1974 he was assistant lecturer at the University of Granada, from 1974 to 1982 lecturer at the University of Extremadura, during 1983 guest lecturer at the University of Florida (USA) and in 1984 he returned to the University of Granada as associate professor. He has published over 250 papers in international journals, and about 25 books and chapters of books. He has supervised 17 PhD theses, 37 dissertations and more than 50 research contracts and projects.