The development of simple, sensitive, and rapid molecular detection methods is of great importance to many fields, including medical evaluation, drug screening, and environmental applications. Molecular detection methods can provide accurate and fast drug sensitivity results, providing new tools for better understanding of drug-resistant tuberculosis (Rubin, 2018), and can also identify bacteria (Tardif et al., 2016) and detect specific micro-molecules in areas of water contamination (Dandapat et al., 2016). Hence, the molecular detection and identification methods have high application importance.

The molecular detection and identification methods can be roughly categorized into labeled methods and label-free methods. Due to high sensitivity, labeled methods, e.g., fluorescence (Sun et al., 2018; Burg et al., 2019), chemiluminescence (Jin et al., 2017; Li et al., 2017), enzyme-linked immunosorbent assay (ELISA) (Engvall and Perlmann, 1971), have been used in many sensing measurements. However, due to the complex structure and reactivity of proteins, an approach of adding additional reagents to improve the accessibility of observation could cause changes in the properties of a target molecule (MacBeath, 2002). In addition, for labeled methods, it is difficult to provide real-time insight into the molecular binding process and allow visualization of the molecular binding kinetics. Due to these disadvantages of the labeled methods, an increasing number of label-free methods have been used in biosensing applications, including optical waveguide lightmode spectroscopy (OWLS) (Orgovan et al., 2014), surface plasmon resonance (SPR) (He et al., 2016; Liu et al., 2017), ellipsometry (Demircioglu et al., 2017), and biolayer interferometry (BLI) (Sztain et al., 2021). However, these methods not only require customized and expensive substrates but also can difficultly achieve in-situ detection. For instance, SPR substrates need to be coated with an expensive gold film (Hobbs et al., 2016), whose thickness has to be precisely controlled at the nm level.

Recently, phase-sensitive interferometry (Joo et al., 2009; Chirvi et al., 2012; Ryu et al., 2014; Merryweather et al., 2021) has attracted great attention as a phase image technique. Spectral-domain phase-sensitive interferometry (SD-PSI) has been used as a quantitative phase imaging method in biosensing applications. The SD-PSI can acquire the molecular layer thickness changes caused by binding the target molecules to the probe surface in real-time. A fiber optic molecular sensor based on the SD-PSI can be used to monitor biomolecules in situ (Guo et al., 2018). Unlike other label-free detection methods, the SD-PSI does not require custom and expensive sensor substrates, such as gold-plated trigonal prisms, which are used in the SPR (Wu et al., 2010). The previous studies (Joo et al., 2009; Chirvi et al., 2012; Ryu et al., 2014) have demonstrated that laboratory-grade or off-the-shelf glass of a suitable thickness can be used as a sensor chip, and such a design is low-cost and simple to prepare. However, this technique is susceptible to disturbances induced by the temperature response of a sensor chip, non-specific binding of target molecules, and sample background. The previous experiments have required keeping the sensor and buffer solution at a constant temperature as much as possible (Chirvi et al., 2012), which increased experimental complexity and reduced experimental robustness.

The previous solutions are easily affected by different disturbances in biosensing, including temperature response and non-specific binding of target molecules. To overcome this shortcoming, this paper proposes a self-reference interference sensor based on coherence multiplexing, which can provide a differential measurement result with the phase change caused by binding of target molecules. The proposed sensor establishes referential and measuring paths with different optical path differences (OPDs) for disturbance tracking and biomolecule detection, thus realizing a self-reference measurement. The advantage of coherence multiplexing is that it allows simultaneous detection of two OPD-coded sensing signals without adding an expensive additional detection element. In addition, compared to the time-coded sequential measurement self-reference methods, the coherence multiplexing coding methods allow simultaneous biomolecule detection and disturbance dynamics tracking in both paths, thus improving detection robustness. The proposed sensor can be used as a label-free sensor with the advantages of weak temperature sensitivity, low non-specific binding, and picometer-level thickness sensitivity. In addition, the proposed sensor requires using only an ordinary optical glass as a detection substrate, which is low-cost and simple to manufacture.

The self-reference setup of the biomolecule detection method proposed in this study is presented in Figure 1. The setup is based on the SD-PSI. A super-luminescent diode provides the incident light with a central wavelength of 1,310 nm and a bandwidth of 75 nm. The two detection paths are prepared by a single-mode fiber-based 2 × 2 coupler and two sensor chips with different thicknesses. Each path can be considered as a low-coherence interferometer with a common path, where the reference light is reflected from the upper surface of a sensing chip, and the sample light is reflected from the contact surface between the sensor chip and solution. The interference signal of each path is encoded with a specific OPD, which is equal to the optical thickness of the corresponding sensor chip, i.e., the product of refractive index and thickness. The two signals were recorded by a homemade transmission grating structure-based spectrometer with a spectral resolution of 0.07 nm and a spectral measurement range of 1,240–1,380 nm, which was then decomposed from the superimposed interferometric spectra according to the difference in OPD values. The OPD between the two paths needs to be greater than the measuring range of the SD-PSI so that to avoid interference between the two paths’ beams. Sample channels are constructed by using epoxy glue to combine two different initial thicknesses of sensing chips (0.17-mm and 0.2-mm glass flakes) with a fluid chip (built-in flow channel and reaction chamber).

The binding of a molecule to be detected to the probe molecule on the sensing chip surface changes the sensing chip thickness, which causes a phase shift of the interference signal. Disturbances of a sensing chip, including non-specific binding and temperature response, can also induce changes in the interference signal phase. The two detection paths in the self-reference system, denoted as path 1 (P1) and path 2 (P2), are used to detect phase variations induced by the biomolecule detection and disturbances during the biomolecule detection process, respectively. Finally, the self-reference molecule detection is achieved by performing the difference operation between the phases of the two OPD-encoded signals. The basic principle of the self-reference interference sensor based on coherence multiplexing is shown in Figure 2.

In the proposed sensor design, a differential-path modification method for sensing chips is shown in Figure 2A, which is described in detail in the next section, is used. The two superimposed interferometric spectra signals detected by a spectrometer are shown in Figure 2B, which can be expressed as follows: I ( k ) = 2 β S ( k ) R r R s cos ( 2 k ( Z 10 + Z 20 ) + ϕ 1 ′ ( t ) + ϕ 2 ′ ( t ) ) (1) where k is the wavenumber, β is the beam splitting ratio of the fiber coupler, and S(k) is the spectral density of the Gaussian-type light source; R r and R s are the reflectance values of the upper surface of the sensing chip and the sample layer, respectively; Z 10 and Z 20 are the initial optical thicknesses of the sensing chips, corresponding to the encoded signals; ϕ 1 ′ ( t ) is the phase induced by the biomolecule detection in molecular detection path P1 due to the true specific molecular binding, as well as temperature and non-specific disturbances; ϕ 2 ′ ( t ) is the phase induced by temperature and non-specific disturbances in disturbances tracking path P2.

Since paths P1 and P2 have different OPDs, their signal peaks can be obtained, as shown in Figure 2C, after performing the fast Fourier transform algorithm on the two superimposed interferometric spectra. The phases of the space-domain interference signals at these two peaks, which also include phase variations induced by biomolecule detection and disturbances, can be calculated by: ϕ c = 1,2 ( t ) = tan − 1 { I m ( I c = 1,2 ( Z ) ) R e ( I c = 1,2 ( Z ) ) } = ϕ c = 1,2 T ( t ) + ϕ B c = 1,2 ( t ) (2) where ϕ c = 1,2 T ( t ) is the phase change induced by the temperature response of the sensor chips in paths P1 and P2, and it is in line with the initial optical thickness of the sensing chips and temperature and can be approximately expressed as ϕ c = 1,2 T ( t ) ≈ T Z c = 1,20 .

Thus, the temperature response of the molecular detection path P1 can be calculated by linearly fitting the temperature response of the disturbances tracking path P2, which can be expressed as follows: ϕ 1 T ( t ) = a ϕ 2 T ( t ) + b (3) where a denotes the temperature correction factor, and b is the temperature compensation factor.

Different modification processes are used in different thickness chips of the proposed sensor; the difference of these processes is that the referential path does not modify the probe molecule. The proposed design allows tracking the total phase change ϕ B 1 ( t ) due to specific binding and non-specific disturbance in P1, while the non-specific disturbance ϕ B 2 ( t ) is simultaneously tracked in P2. Then, ϕ B c = 1,2 ( t ) is differenced in real-time to obtain the corrected specific binding by: Z c o r r e c t e d = ϕ B 1 ( t ) − ϕ B 2 ( t ) 2 k 0 =   ϕ 1 ( t ) − ϕ 2 ( t ) − ( a − 1 ) ϕ 2 T ( t ) − b 2 k 0 (4) where k 0 is the central wavenumber of the light source, and it is given by k 0 = 2 π / λ 0 , where λ 0 is the central wavelength of the broadband light source.

In the experiment, ϕ c = 1,2 T ( t ) denotes the average phase change calculated from the stable data before performing molecular detection; ϕ c = 1,2 T ( t ) is used in Eq. 3 to obtain a and b .

This paper presents a sensor based on coherence multiplexing, which can be used to resist different disturbances in biosensing applications, including temperature and non-specific binding disturbances. The proposed sensor has two reaction chambers and sensing chips of different thicknesses, which define two interferometric paths with different OPDs. This allows the proposed sensor to achieve self-reference based on coherent multiplexing. The proposed sensor is suitable for applications that require large-scale testing of biomolecular interactions, such as drug screening. Using fiber optic-based glass as a sensor chip reduces the cost of the proposed sensor. This technology can also be used in other sensing applications, such as multi-channel pressure sensing systems.