A scanning surface plasmon resonance sensor based on the phase shift algorithm

Among various algorithms to determine the resonance angle, centroid-based methods are the most popular due to their simplicity and high sensitivity. The centroid is used to represent the resonance angle in this method.

The concept of the centroid method is shown in figure 4. A baseline is usually applied and the centroid of the area enclosed by the baseline and ATR curve is calculated as [23]

$$\begin{equation} C = \frac{{\sum\nolimits_{n = n_1 }^{n_2 } {n\left( {I_b - I_n } \right)} }}{{\sum\nolimits_{n = n_1 }^{n_2 } {\left( {I_b - I_n } \right)} }}, \end{equation} \tag{ 3 }$$

where I_n is the intensity of the ATR curve at position n, I_b is the baseline and n₁, n₂ are the crossover points between the baseline and the ATR curve. The selection of the baseline can directly affect the sensitivity and noise suppression ability, so it must be chosen carefully [26]. It has been proved that a dynamic baseline can diminish the noise from the light source shot noise [24]. However, the complex algorithm for determining the baseline is very time consuming and not suitable for real-time data process and portable equipment. A fast centroid algorithm called fixed boundary was reported and shows a higher SNR, resolution and computation efficiency [25]. Fixed start and stop positions are used to enclose an area with the ATR curve and the centroid of this area is calculated as the resonance position. Calculation complexity can be greatly reduced since no baseline needs to be determined. This method can be expressed as [25]

$$\begin{equation} C = \sum\limits_{n = n_s }^{n_e } {nI_n } \Big/ \sum\limits_{n = n_s }^{n_e } {I_n } , \end{equation} \tag{ 4 }$$

in which I_n is the intensity of ATR curve at position n, and n_s and n_e are the start and end boundaries, respectively.

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In SPR sensing, when the local refractive index of the sample varies, the resonance angle would change correspondingly. As shown in figure 3, this angle change can be considered as time delay which appears as a linear phase shift in the frequency domain. Therefore, if the signal phase can be calculated by discrete Fourier transform (DFT), the time delay can thus be obtained. The DFT calculation can be performed to an N-point digital signal x_n as

$$\begin{equation} X_k = {\mathop{\rm DFT}\nolimits} ({x_n }) = \sum\limits_{n = 0}^{N - 1} {x_n \,{\mathop{\rm e}\nolimits} ^{ - {\mathop{\rm i}\nolimits} \frac{{2\pi }}{N}nk} } , \end{equation} \tag{ 5 }$$

where k = 0, 1, 2, ..., N − 1, and i is the imaginary unit. A position shift m corresponds to adding the output X_k a linear phase change

$$\begin{equation} {\rm DFT}[ {x_{n - m} }] = X_k \,{\mathop{\rm e}\nolimits} ^{ - {\mathop{\rm i}\nolimits} \frac{{2\pi }}{N}km} . \end{equation} \tag{ 6 }$$

DFT can provide whole spectral information about amplitude and phase. In this study, only a specific frequency component is useful, so a simplified fast algorithm is developed to reduce the computation complexity. For an N-point digital signal, the frequency resolution is f_s/N (f_s is the sample frequency) and the SPR signal has a frequency of 2/T, so only X_k (k = N/N_s) needs to be calculated. The phase of the signal can be expressed as

$$\begin{equation} \theta = {\mathop{\rm arctan}\nolimits} 2\left[ {\frac{{{\mathop{\rm Im}\nolimits} \left( {X_k } \right)}}{{{\mathop{\rm Re}\nolimits} \left( {X_k } \right)}}} \right] \end{equation} \tag{ 7 }$$

in which arctan2 is the quadrant correct arctangent which can be used to determine the phase angle of a complex in the range of (−π, π], and Im and Re denote the imaginary and real parts, respectively.

Mathematic simulation is used to check the theoretical precision and computation efficiency of the phase shift, centroid method and fixed-boundary methods. Noise is generated by random series and the standard derivation of output is used to evaluate the algorithms' performance.

From (1) and (2), the detector output is a function of the incident angle θ_i and the light source intensity I, so the form with noises can be expressed as follows:

$$\begin{equation} x_n = s( {I_0 + \Delta I_0 })R( {\theta _i + \Delta \theta _i }) + \Delta D, \end{equation} \tag{ 8 }$$

where s is a constant denoting the sensitivity of the photo detection circuit, ΔI₀ is the light intensity fluctuation, Δθ_i is the repeatability of the galvo scanner and ΔD is the quantization error.

In this simulation, the whole scanning range is from 66° to 78° and sampled into 512 points (N_s = 256). Each simulation data segment comprises four ATR curves (N = 1024). For centroid methods, these four curves are averaged into one ATR curve. The baseline for the traditional centroid method is set to the middle value of the curve. The reflectance R(θ) is calculated by Fresnel's equation of the typical prism–metal–sample system, in which the refractive index of gold is calculated by the Drude model [27]. The noise in (8) can be expressed as

$$\begin{equation} \begin{array}{l} \Delta I_0 = A_I \,{\mathop{\rm Ran}\nolimits} + A_{{\rm It}} \,{\mathop{\rm Ran}\nolimits}(t) \\ \Delta \theta _i = A_\theta \,{\mathop{\rm Ran}\nolimits}(t) \\ \end{array} \end{equation} \tag{ 9 }$$

in which Ran generates normally distributed random numbers with the mean value of 0 and standard derivation of 1/3. A_I Ran is used to simulate long-term intensity drift and it is a constant within each scanning period but varies between different periods. A_It Ran(t) is a series of numbers and used to simulate high frequency intensity noise. The maximum output of ADC is 10 V, so I₀ is chosen as 10. According to experimental measurements, the intensity noise components are chosen as A_I = 0.5%, A_It = 0.01%. A_θ is chosen as the repeatability of the galvo scanner (5 µrad). ΔD is calculated as a 16-bit ADC is used.

The relationship between the effective refractive index of the sample (n_s) and the output of the resonance angle finding algorithm is fitted by a linear model to get the regression equation. The calculation results are analyzed when n_s varies from 1.32 to 1.38, which is a typical measurement range in the biomolecular interaction analysis. The R² are 0.9993, 0.9980 and 0.9909 for the phase shift, centroid method and fixed-boundary methods, respectively, showing good linear relationship. The output of centroid-based methods is the peak position; however, the output of the phase shift method is phase in radius. In order to make their results comparable, the outputs of different methods are converted into the refractive index units (RIU) by their regression equations.

3.3.1. Precision performance

The output standard derivation of each resonance angle finding algorithm is calculated from 500 times simulation when n_s = 1.33. The results are listed in table 1. When the centroid method is used to determine the resonance angle, the area enclosed by the constant baseline and SPR resonance curve is used. As shown in the simulation results, the centroid method is very sensitive to the intensity long-term drift. For the fixed-boundary method, two constant boundaries are used. When the ATR curve shifts up and down, only a rectangle is attached or detached, so the centroid position of the shape enclosed by the curve and boundaries will not change a lot. For the phase shift method, the ATR curve is changed into the frequency domain and the long-term drift would only appear near the dc component; hence, the response can hardly be influenced. In the same way, the phase shift method has very good immunity to high frequency noise which usually has a flat frequency distribution and has a very low frequency component in the target signal frequency region. The precision performance at different n_s is shown in figure 5. The mean standard derivations are 0.39 × 10⁻⁶, 3.1 × 10⁻⁶ and 0.78 × 10⁻⁶ for the phase shift, centroid and fixed-boundary method, respectively. The simulation results show that the phase shift method has a better resolution. This method can also be applied to 2D imaging devices (CCD or PDA based SPR sensing equipment) by combining row data into a series.

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Table 1. Comparison of standard derivations of different resonance angle finding algorithms.

Method	Galvo repeatability, Δθ0 (µRIU)	Intensity long-term drift, AI Ran (µRIU)	High-frequency intensity noise, AIt Ran(t) (µRIU)	Quantization error, ΔD (µRIU)
Phase shift	0.08	ε	0.39	ε
Centroid	0.14	2.97	0.09	ε
Fixed boundary	0.09	ε	0.71	ε

All standard derivations are calculated from 500 times simulation. The value of ε is about 10⁻¹⁰–10⁻¹⁵ (RIU).

3.3.2. Calculation speed

Two syringe pumps (C3000) with 120° 3-port valve were purchased from Tricontinent. An HPLC-like loop flow is built by a 6-port distribution valve (HVXL6–6) purchased from Hamilton. Fisherfinest BK7 glass slides purchased from Thermo Fisher Scientific were used as the substrates of SPR sensing chips. ACS reagent ≥99% glycerol was purchased from Sigma-Aldrich and glycerol solutions are prepared with Millipore water.

The SPR sensing chips are made by the flowing procedure. First, the glass slides are totally immersed into piranha solution (a mixture of 98% H₂SO₄ and 30% H₂O₂, 7:3, v/v) for at least 1 h and then washed with Millipore water. After being dried under nitrogen, they are cleaned by a plasma cleaner immediately before the deposition. A 50 nm thick Au film is deposited on the substrates by sputtering and 1 nm Cr is used as the adhesion layer. Sensing chips are also cleaned by piranha solution before every experiment.

The reflected intensity is measured to check the quality of the ATR curve. The data are collected in a scanning period when Millipore water fills the flow chamber. The light source intensity distribution as a function of the scanning position, which corresponds to the incident angle, is shown in figure 6(a) by the dashed line and the ATR curve of flow channel 1 is shown in figure 6(a) by the solid line. The normalized ATR curve is shown in figure 6(b). The latter half period of the ATR curve in a scanning period is reversed as shown in figure 6(c).

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There is a good linear relationship between the concentration and refractive index of the glycerol solution [28], so it can be used to evaluate the performance of the SPR setup. All solutions are handled by two syringe pumps in the PTFE tube (1.5 mm OD, 0.5 mm ID) at a flow rate of 50 µl min⁻¹. 4%, 8%, 12%, 16%, 20% 24%, 28%, 32%, 36% and 40% glycerol solutions are injected and Millipore water is used to purge the channel after every glycerol solution injection. The refractive index of glycerol solutions is tested by an Abbe refractometer. The collected data are processed by the phase shift, centroid and fixed-boundary methods, respectively, and the sensorgrams are shown in figures 7(a)–(c). The responses of different methods to the refractive index of glycerol solutions are also fitted by the linear regression model as shown in figures 7(d)–(f).

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The baseline characteristic is analyzed to evaluate the resolution. Millipore water is applied to both channels at a flow rate of 50 µl min⁻¹ for about 30 min. Because there is no temperature regulator for the flow chamber, one of the two channels is used as a reference to compensate for the temperature drift. The real-time chart of baseline calculated by the phase shift, centroid and fixed-boundary methods are illustrated in figures 8(a)–(c). The compensated baselines are shown in figures 8(d)–(f).

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0.05% glycerol dilute solution is prepared to check the resolution directly. The dilute solution is injected in channel 1 at 50 µl min⁻¹ and Millipore water is applied in channel 2 as a reference. This process is repeated three times. The real-time sensorgrams processed by the phase shift, centroid and fixed-boundary methods are shown in figures 9(a)–(c), respectively.

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As shown in figure 6, it can be clearly seen that there is no interference noise contained in the ATR curve. The scanning optical geometry can avoid the SNR reduction caused by the interference noise.

The incident beam cannot be ideally focused into a line, so the light source intensity just has an approximate uniform distribution while scanning as shown in figure 6(a). The small distortion of light source distribution can be considered as the fixed pattern noise and may vary with different SPR sensing chips. This noise can also be seen on the ATR curve as shown in figure 6(a). The ATR curve is normalized by the light source distribution to reduce the fixed pattern noise. As shown in figure 6(b), a smooth ATR curve can be acquired and a contrast better than 80% also indicates a clean sensing surface.

Because the galvo scans in a back and forth way, the reflectance in a single scanning period is symmetric. The latter half scanning period is reversed to meet the requirement of the resonance angle finding methods.

The small step response of the galvo is 150 µs and the data sample consumes about 40 µs. Therefore, 200 µs is adequate to finish a scanning step. One ATR curve comprises 256 scanning steps and four ATR curves generate one sensing point. That is to say the maximum sampling rate is about 5 Hz.

The real-time sensorgrams and fitting results of measurement on different glycerol solutions are shown in figure 7. The mass percentage of glycerol in water varies from 0% to 40% at a step of 4%. The response of glycerol solutions is calculated by three different resonance angle finding algorithms. The relationship between the response and the refractive index of the glycerol solutions is linearly fitted as shown in figures 7(d)–(f). The fitting results show that this SPR setup has a wide refractive index measurement range from 1.33 to 1.385 with the normally used BK7 glass sides. The R² are 0.9997, 0.9922 and 0.9962 for the phase shift, centroid and fixed-boundary methods, respectively. The curve generated by the phase shift method shows the best linearity over the whole measurement range. The linearity of the fixed-boundary method is good when the measurement range is within 1.37, but it will degrade dramatically when the resonance angle is close to the end boundary.

The baselines of two flow channels are measured for about 30 min and collected data are processed by three different resonance angle finding algorithms as shown in figure 8. The actual baseline character is evaluated after compensation between two channels to reduce the temperature drift. It should be noted that there is a phase bias between these two channels. This bias is caused by the imperfect optical alignment. If the focus line on the sensing gold surface was perfectly perpendicular to the channels, there would be no bias between two channels. In practice, SPR biosensing is a relative measurement. This bias would not affect the system performance.

For the phase shift method, the regression equation from the measurement on glycerol solutions is P = 67.4n−89.9 as shown in figure 7(d), so 1 rad phase shift is equivalent to a refractive index change of 0.015 RIU. The standard derivation of baseline obtained by the phase shift method is 4 × 10⁻⁵ rad as shown in figure 8(d). Hence, this SPR setup with the phase shift algorithm can distinguish a phase change of 1.2 × 10⁻⁴ rad (3 standard derivations) which is equivalent to 1.8 × 10⁻⁶ RIU. The standard derivations of baselines calculated by the centroid and fixed-boundary methods are 0.0045 and 0.0012, respectively. The detection limits can thus be determined as 4.4 × 10⁻⁶ RIU and 3.2 × 10⁻⁶ RIU. This result shows that the phase shift algorithm can enhance the SPR setup performance remarkably.

From figure 8, it can be seen clearly that the baseline drift cannot be fully canceled out by the reference channel. A possible reason is that the temperature drift of different channels is not identical. If a temperature-stabilized flow chamber can be utilized, the resolution can be further enhanced.

The performances of the phase shift and fixed-boundary methods have good agreement with the simulated result. The centroid method shows a better result than the simulated result, because this method can be remarkably influenced by the noise characteristics and the noise may not have a completely random distribution as in the simulation.

The resonance angle finding algorithm performance can also be checked by measurement on dilute solutions. By linearly fitting the relationship between the refractive index and concentration of the dilute glycerol solution, the regression equation can be obtained as n = 0.11C + 1.33, where n is the refractive index and C is the concentration of the glycerol solution [28]. Therefore, 0.05% glycerol solution would cause a phase change of about 0.0037 for the phase shift method, and position changes of 0.17 and 0.06 for the centroid and fixed-boundary method, theoretically. The actual responses in figure 9 are 0.0035, 0.1648 and 0.056, which are close to the theoretical values. By comparing the response and baseline noise, it can be clearly seen that the phase shift algorithm has a better performance.