A windowed fourier transform-based method of numerically analyzing phase shifts of SPR sensors

This study presents a simple and reliable method for numerical evaluation of the sensitivity of SPR systems. A Windowed Fourier Transform (WFT) based method is applied to extract shifts of SPR interferogram. By applying the WFT, the frequencies consisting of SPR interferogram are extracted, and phase shifts of relevant frequencies are also obtained. The normalized amplitude of the frequencies larger than 0.35 is regarded as the most prominent frequency. The summation of the phase shifts of the most prominent frequencies is regarded as an index to numerically analyzing phase shifts of SPR sensors. Through this method, the small change in the sensing surface can be monitored. By using a homemade SPR system with the proposed calculation method, it can detect the NaCl solutions ranging from 0.00003% to 0.03% (wt%), indicating its great promise for applications in fields such as medicine, food safety, and biotechnology.


Introduction
With the advancement of the biomedical and chemical fields, Surface Plasmon Resonance (SPR) has found widespread application in the realms of biology and medicine, owing to its advantages of realtime detection, label-free capabilities, and high sensitivity [1][2].SPR is based on the phenomenon of plasmon resonance on the surface of a metal film, allowing real-time monitoring of the adsorption and dissociation of biomolecules by tracking changes in the incident angle or wavelength [3].The sensitivity of an SPR sensor is a crucial performance metric, determining the sensor's ability to effectively detect low concentrations of target molecules [4][5].
Lu et al. [6] reported a fiber-optic SPR system for detecting Hg ions, achieving a detection sensitivity as low as 94 nM.Huang et al. [7] achieved the detection of microplastics in water by using an ER/SPR system, with a sensitivity reaching as low as the particle size of 20 μm.Taylor et al. [8] described a multi-channel SPR system for the identification of four bacterial species, such as Escherichia coli.The limit of detection (LOD) for each of these four bacterial species in the tested samples ranged from 3.4×103 to 1.2×105 cfu/mL.In the realm of real-time and high-efficiency SPR biosensors, their extensive applications have led to a substantial surge in data analysis demands.Traditional methods involving direct comparisons with raw data often result in subtle variations, thereby limiting the full representation of the SPR detection limits.As a response to this challenge, novel approaches in data analysis have emerged in recent years, aiming to harness the full potential of real-time and efficient SPR biosensors.These advanced methods involve intricate signal processing, statistical techniques, and machine learning algorithms, which not only enhance the sensitivity and accuracy of detection but also enable the extraction of valuable insights from the wealth of generated data.In this study, we established a differential phase SPR system and assessed its sensitivity by using a WFT-based method.The sensitivity was initially evaluated by employing a NaCl concentration ranging from 0.00003% to 0.03% (wt%), and the LOD of the proposed SPR system is 0.00003% (wt%).The results indicate that the rapid assessment of SPR system sensitivity by using NaCl and Windowed Fourier Transform holds significant potential for practical applications.

Materials
NaCl (Spectral level) was procured from Shanghai Aladdin Biochemical Technology Co., Ltd.The gold target (99.99%)was obtained from Zhongnuo New Material Technology Co., Ltd.DI water has a resistivity of 18 MΩ•cm.

Apparatus
In the course of this research, we established a surface plasmon resonance (SPR) system incorporating differential phase measurements.The system primarily consists of a halogen light source, fiber collimators (I1 and I2), linear polarizers (P1 and P2), birefringent crystals (BC), focusing lens (FL), slit, SPR sensor, fiber spectrometer, injection pump, and PC, as shown in Figure 1.The SPR bio-chip was constructed using a standard attenuated total reflectance (ATR) structure, which included a microfluidic channel surface, a triangular prism, and a BK7 glass slide.

Production of SPR chips and detection
The BK7 glass with a certain size has been cleaned by using an ultrasonic ethanol bath for 10 min.By employing thermal evaporation techniques, we successfully deposited a 50-nanometer-thick layer of gold onto the BK7 glass slide.Subsequently, utilizing a masking template, the gold film was shaped into a rectangular form with dimensions of 5 millimeters in length and 2 millimeters in width.This rectangular gold film was coupled with a microfluidic channel which was PMMA, and the total length and width are 6 mm and 2 mm, respectively.The deionized water was introduced onto the gold film surface through the microfluidic channel at a flow rate of 20 μL/min by using a syringe pump, and the spectral interferogram was collected.Subsequently, solutions of NaCl with concentrations of 0.00003%, 0.0003%, 0.003%, and 0.03% were individually introduced into the microfluidic channel at a flow rate of 20 μL/min, and the spectral interferograms were recorded.
In terms of sensor assembly, special attention is required.The coupling of the completed SPR chip with the prism necessitates the use of a custom fixture.This fixture securely holds the prism in place without obstructing the optical path.The SPR chip is then stably fixed at a specific position in the optical path through the clamping structure of the fixture.To ensure the sensor's normal operation, it is crucial to clean the prism's surface with a cleaning cloth before installing the fixture.Additionally, the gap between the well-coupled SPR chip and the prism must be filled with a matching medium of the same refractive index.It is imperative to avoid the formation of bubbles during the gap-filling process.

Results and discussion
Figure 2 (A1, A2, A3, and A4) presents the spectral interferogram of 0.03%~0.00003%NaCl solution detected by using the SPR sensor for calculating SPR sensing results.Figure 2 (B1, B2, B3, and B4) presents the calculated frequencies and phase shifts for each frequency.Frequencies with a normalized amplitude greater than 0.35 are selected, and the summation of phase shifts for these frequencies (Iops) is used as a detection metric.The Iops greater than the machine response is considered a reliable phase shift in subsequent analysis.The summation of phase for Iops was calculated as follows: where  represents the phase shift in degrees obtained for each frequency greater than 0.35 by using the WFT.The SPR biosensor can be influenced by various factors such as light stability, spectrometer stability, and temperature fluctuations.To obtain reliable detection results, 10 measurements were conducted by using deionized water as a reference.The data was divided into two groups of 5 measurements each, and the error calculation is shown in Figure 2. In the first group, Iops was 39°, and in the second group, Iops was 28°.The maximum value of 39° was taken as the error.The process of calculating the errors in the sensing system involves a systematic correction procedure.It is essential to note that, due to the significant impact of subtle vibrations on the optical path, the entire system needs to be installed on a stable optical platform.Simultaneously, precautions must be taken to prevent environmental light interference during experiments, and the entire optical path should be situated in a dark environment.During experimentation, it was observed that the movement of the optical fiber also had a substantial impact on the results.To address this, the optical fiber should be securely fixed using a ribbon, and throughout the experimental process, the sensor surface must remain bubble-free.Prior to each measurement, air bubbles should be purged.
In addition, the occurrence of bubble-induced vibrations during the detection process can significantly compromise the authenticity of experimental results.In such instances, it is imperative to clean the sensor with deionized (DI) water and initiate the experimental procedure anew.Only through these measures can reliable and accurate results be attained.
The total phase shift results for various concentrations of NaCl solutions and DI water are obtained by summing the phases of prominent frequencies in Figure 3.In the above context, (A1), (A2), (A3), and (A4) represent spectral interferograms captured at the SPR resonance wavelength for both deionized water and NaCl concentrations spanning from 0.00003% to 0.03%.The phase shift results were computed by analyzing the spectral interferograms.Among them, Iops at 0.00003% is 108°, Iops at 0.0003% is 236°, Iops at 0.003% is 441°, and Iops at 0.03% is 772°.The results of our detection are presented in Figure 4. From the experimental results, it can be observed that within the margin of error, the minimum detection limit of this SPR system for NaCl is 0.00003%.

Conclusion
In summary, we have successfully introduced and validated a method based on the WFT for analyzing the detection results of SPR systems.The application of the WFT method involves extracting frequency domain results from SPR spectral interferograms and determining phase shifts corresponding to each frequency.A numerical index, derived from the cumulative sum of phase shifts at prominent frequencies, is employed to portray and reflect the detected outcomes.Using NaCl as the analyte, the detection limit for NaCl solutions ranging from 0.00003% to 0.03% (wt%) was determined to be 0.00003% (wt%).The results of this study provide an effective computational method for discerning subtle shifts and hold practical application value in assessing the sensitivity of SPR systems.
Moreover, the versatility and robustness of the WFT-based analysis method make it a valuable tool for a wide range of applications.This approach not only enhances our understanding of SPR spectral interferograms but also offers insights into the detection limits for various analytes.Beyond its application with NaCl, this method can be extended to other compounds and complex mixtures, showcasing its potential for use in fields such as environmental monitoring, medical diagnostics, and biochemistry.As the demand for sensitive and accurate detection methods continues to grow, the WFTbased approach presented in this study holds promise as a valuable resource for researchers and practitioners in the realm of surface plasmon resonance technology.

Figure 1 .
Figure 1.Schematic diagram of the differential phase SPR system.

Figure 2 .
Figure 2. DI water as the detection target exhibiting spectral interference patterns along with the corresponding frequency domain plot and computed phase map.

Figure 4 .
Figure 4. Detection of phase shift in NaCl solutions ranging from 0.00003% to 0.03% in DI water.