Mitigating Surface-Roughness Effects in the BaTiO3 Top Protective Layer of a Divergence Beam Surface Plasmon Resonance Sensor Using Savitzky–Golay and Whittaker Filters

Abstract

Surface roughness in the top protective layer of a surface plasmon resonance (SPR) sensor degrades performance by introducing reflectivity fluctuations, broadening the resonance dip, and reducing the accuracy of resonance-angle estimation. In practice, obtaining a perfectly uniform barium titanate (BaTiO₃) protective coating over a commercially sized SPR chip is difficult; therefore, signal processing strategies that compensate for roughness are of practical interest. In this study, a periodic roughness profile is used to model thickness fluctuations in a 3 nm BaTiO₃ overlayer, and the resulting impact on SPR performance is analyzed theoretically using the transfer matrix method. Two digital smoothing approaches, the Savitzky–Golay (SG) filter and the Whittaker filter, are then evaluated as post-processing tools. The results show that the roughness height of 1 nm can reduce the signal-to-noise ratio (SNR) to approximately 6.4 dB and broaden the resonance feature sufficiently to compromise reliable detection. Among the tested methods, the Whittaker filter yields the most faithful recovery of the SPR curve, improving resonance-position accuracy by a factor of 119.14 relative to the rough signal, whereas the SG filter provides an improvement factor of 18.81. The Whittaker filter also increases the SNR to 26.44 dB, which signifies enhancement by 75% and preserves sensor sensitivity (390.12°/refractive index unit (RIU)), which remains close to the ideal value of 396.27°/RIU and detection accuracy more effectively than the SG filter. These findings indicate that Whittaker smoothing is a practical, low-cost computational strategy for mitigating roughness-induced degradation in high-sensitivity SPR biosensors.

Received: 11 November 2025 | Revised: 28 April 2026 | Accepted: 29 May 2026

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

The data supporting the findings of this study are available within the article, and no external dataset was generated or analyzed.

Author Contribution Statement

Jordan H. Hossea: Conceptualization, Methodology, Formal analysis, Resources, Writing – original draft, Visualization. Athuman O. Mfinanga: Software, Validation, Investigation, Writing – review & editing, Supervision.