Optical Fiber Ball Resonator Sensor Spectral Interrogation through Undersampled KLT: Application to Refractive Index Sensing and Cancer Biomarker Biosensing

Abstract

Optical fiber ball resonators based on single-mode fibers in the infrared range are an emerging technology for refractive index sensing and biosensing. These devices are easy and rapid to fabricate using a CO₂ laser splicer and yield a very low finesse reflection spectrum with a quasi-random pattern. In addition, they can be functionalized for biosensing by using a thin-film sputtering method. A common problem of this type of device is that the spectral response is substantially unknown, and poorly correlated with the size and shape of the spherical device. In this work, we propose a detection method based on Karhunen-Loeve transform (KLT), applied to the undersampled spectrum measured by an optical backscatter reflectometer. We show that this method correctly detects the response of the ball resonator in any working condition, without prior knowledge of the sensor under interrogation. First, this method for refractive index sensing of a gold-coated resonator is applied, showing 1594 RIU^-1 sensitivity; then, this concept is extended to a biofunctionalized ball resonator, detecting CD44 cancer biomarker concentration with a picomolar-level limit of detection (19.7 pM) and high specificity (30-41%).

Keywords: Karhunen−Loeve transform (KLT); ball resonator; cancer biomarker diagnostic; digital signal processing; optical fiber biosensor; optical fiber sensor; optical fiber spherical tip.

Figure 1

Photograph of the fabricated ball resonator under an optical microscope; (a) cross-section along the horizontal plane; (b) vertical plane.

Figure 2

Experimental set-up used in this study; (A) fabrication of ball resonator sensor on a CO₂ splicing machine; (B) interrogation of the sensor with optical backscatter reflectometer.

Figure 3

A flow chart of the undersampled KLT is used to demodulate the spectrum of the ball resonators.

Figure 4

Overview of the operation of the undersampled KLT applied to the spectrum of a ball resonator. (a) The reflection spectrum of the ball resonator, acquired by the OBR and processed. (b) The eigenvector corresponding to the highest rank eigenvalue, acquired over 201 samples. (c) Eigenvalue string, reporting the magnitude (in logarithmic units) of all 201 eigenvalues sorted in ascending order.

Figure 5

Performance analysis of the KLT as a function of the undersampling rate K. (a) Average computation time over 100 KLT calculations as a function of K; the horizontal line shows the limit of 10 ms computation time for rapid computing. (b) KLT output ω as a function of K; the horizontal line shows the limit of 0.1% variation of ω from the reference value computed with K = 45.

Figure 6

Refractive index sensitivity of the ball resonator interrogated with the KLT method. (a) Reflection spectra of the ball resonators, for different RI values ranging from 1.3478 to 1.3539. (b) KLT output ω as a function of the RI; the linear fit shows the sensitivity as −1593.6 RIU⁻¹.

Figure 7

Detection of CD44 protein with a biofunctionalized gold-coated ball resonator. (a) The reflection spectrum of the ball resonator for different CD44 concentrations, ranging from 6 pM to 100 nM; (b) KLT response for each concentration, reporting the standard deviation of data acquired over 10 min, the log−linear fit, and the LoD determination.

Figure 8

Evaluation of the specificity of the CD44 biosensor, using the KLT interrogation method. The chart shows the percentage change of the KLT output ω, calculated from the reference condition (6 pM, lowest concentration), for 4 different concentrations (390 pM, 1.56 nM, 25 nM, 100 nM) of the CD44 protein analyte compared to a control (IL4).

Figure 9

Comparison between KLT and feature extraction (FE) methods for demodulation of the ball resonator. The chart shows the normalized output (Y) as a function of the RI, obtained for each method. Datapoints have been interpolated with a linear fit; the R² coefficient of determination shows the quality of the agreement between measured data and the fit.

Figure 10

Comparison between KLT and feature extraction, for 5 different resonators. The charts report the normalized output Y for each method, as a function of refractive index (10 RI datapoints from 1.3478 to 1.3539). All ball resonators were fabricated using the same method based on CO₂ laser splicer, and had different diameters: (a) 290 μm; (b) 466 μm; (c) 515 μm; (d) 521 μm; (e) 532 μm.