Feasibility Using a Compact Fiber Optic Sagnac Interferometer for Non-Contact Soft Tissue Surface Mechanical Wave Speed Detection

Compact Fiber Optic Sagnac Interferometer

Exploring the Potential of Fiber Optic Sagnac Interferometer in Non-Contact Elasticity Characterization of Soft Tissues

Introduction

The mechanical properties of soft tissues are critical to modern medicine and biomedical research. Understanding these properties provides significant insights into structural integrity and potential pathological conditions. However, traditional methods for assessing tissue elasticity often require direct contact, which can cause discomfort, especially in sensitive areas such as ophthalmology. Additionally, direct contact may lead to tissue contamination or introduce artifacts, which can compromise measurement accuracy. Thus, developing non-contact methods for measuring the mechanical attributes of soft tissues is essential.

Recently, optical techniques such as Fourier Domain Optical Coherence Tomography (FD-OCT) have emerged as a popular approach for detecting mechanical waves in soft tissues. However, FD-OCT has limitations, including restricted detection bandwidth, complex post-data processing, and significant noise. In contrast, the Sagnac interferometer directly detects vibration velocity, eliminating the need for post-processing, reducing noise, and offering superior frequency range adjustability.

To address these challenges, Gui Chen and Professor Jinjun Xia from Lawrence Technological University proposed an integrated system combining an air-coupled PZT (Lead Zirconate Titanate, Pb-Zr-Ti) ultrasound transducer and a compact fiber optic Sagnac interferometer. This system was presented in a study published in Biomedical Optics Express in February 2025, demonstrating its feasibility and potential applications in characterizing the elastic properties of soft tissues.


Methodology

Experimental Workflow

The study involved the following key steps:

1. Design of the Air-Coupled PZT Transducer for Surface Wave Excitation

A line-focused air-coupled PZT transducer was developed for generating mechanical waves based on the principle of radiation force. Specifically, transient focused ultrasound waves impinging on the surface of soft tissues generate low-frequency shear oscillations that propagate through the tissue. To optimize radiation force, a 1 MHz line-focused ultrasound longitudinal wave was obliquely incident on the sample surface to enhance momentum transfer.

2. Development of the Compact Fiber Optic Sagnac Interferometer

The study developed a compact fiber optic Sagnac interferometer to detect surface waves generated by the air-coupled transducer. In a Sagnac interferometer, two light beams alternately pass through identical optical paths. When the sample surface is stationary, no optical path difference exists; when the surface vibrates, the interference signal transforms into a vibration velocity signal. A 50-meter polarization-maintaining single-mode optical fiber was used as the delay line to adjust the detectable frequency range.

3. Tissue-Mimicking Phantom Selection and Preparation

To simulate real biological tissues, gelatin-based tissue-mimicking phantoms were used. The stiffness of these phantoms was controlled by varying gelatin concentrations. Phantoms with 6% and 8% gelatin concentrations were prepared, incorporating titanium dioxide (TiO2) as a light scatterer to emulate skin’s optical scattering properties. The samples were fabricated in cylindrical shapes with a height of 15 mm and a diameter of 100 mm.

4. Surface Wave Velocity Measurement and Time-Delay Estimation

To accurately calculate surface wave velocities, the ultrasound RF signals were converted into analytical signals using the Hilbert transform, and the time delay (\Delta t) was estimated using the cross-correlation coefficient function. Given the known distance (\Delta d) between the excitation and detection points, surface wave velocity was calculated using (\Delta d/\Delta t). Both group velocity and phase velocity were measured to validate consistency.


Data Analysis and Algorithm Description

1. Time-Delay Estimation Method

Time-delay estimation was based on cross-correlation calculations, with the Cramér-Rao lower bound formula used to assess system error. The study specifically analyzed the effects of Signal-to-Noise Ratio (SNR), peak correlation coefficients, and bandwidth on time-delay estimation errors.

2. Group and Phase Velocity Calculations

Group velocity was determined by analyzing waveform frequency attenuation and phase delays using Fourier transform. Phase velocity was calculated at the center frequency (1 kHz) and two frequencies close to the 6 dB down points to ensure data representativeness and consistency.


Experimental Results

1. Detection of Surface Waves

The compact fiber optic Sagnac interferometer successfully detected low-frequency surface waves in tissue-mimicking phantoms. In the 8% gelatin phantom, the group and phase velocities were measured as 3.32 m/s and 3.39 m/s, respectively. In contrast, for the 6% gelatin phantom, these velocities were 2.05 m/s and 2.11 m/s.

2. Young’s Modulus Calculation

Based on classical elasticity theory, the study calculated the Young’s modulus for the phantoms. The results were 14.5 ± 3.44 kPa for the 6% phantom and 37.44 ± 18.11 kPa for the 8% phantom. These findings align with standard mechanical testing results, validating the method’s reliability.

3. Error Analysis

For the 8% phantom, the minimum time-delay estimation error was 15.94 µs, with a relative error of 1.6%. For the 6% phantom, the error was 49.98 µs, with a relative error of 5%. Even when considering correlation coefficient decay, the errors remained within acceptable limits.


Conclusion and Significance

Study Conclusions

  1. This study demonstrated that the compact fiber optic Sagnac interferometer can successfully detect low-frequency surface waves, offering a potential method for non-contact mechanical characterization of soft tissues.
  2. The consistent group and phase velocity results confirmed the reliability of the Young’s modulus calculations.

Research Implications

  1. The study addresses technical challenges related to weak optical reflection signals in non-contact methods for biological soft tissue characterization.
  2. The system holds significant potential for clinical applications, especially in fields like ophthalmology where non-contact methods are essential.

Study Highlights

  1. Methodological Innovation: The combination of an air-coupled PZT transducer and the Sagnac interferometer is groundbreaking, reducing signal processing noise and errors.
  2. Versatility: The Sagnac system’s tunable frequency range enhances its adaptability.
  3. Reliability: Experimental results align with classical elasticity theory, bridging the gap between theory and practice.

Future Outlook

The research team plans to enhance the Sagnac system by incorporating an optical scanning mechanism to accelerate data collection. Additionally, they intend to validate the system using real biological tissues and compare it with FD-OCT systems to fully elucidate the advantages and limitations of the two approaches, setting a direction for future research in non-contact soft tissue mechanical characterization.