In conventional spectral domain optical coherence tomography (SD-OCT), depth information is calculated by fast Fourier transform (FFT) to bring an axial resolution typically within the range of 10 μm. Sub-micrometer resolution is achieved by employing broadband light sources. Phase-sensitive SD-OCT (PSSD-OCT) provides nanometer-level precision and can be employed for film thickness measurement, displacement sensing, optical fiber Fabry-Perot sensors, quantitative phase microscopy, and surface profile imaging. Phase wrapping is an inherent issue in optical interference techniques, and various phase unwrapping algorithms have been proposed to enhance the dynamic range. The current approaches are typically to first calculate a low-precision solution by frequency estimation methods, followed by determining the phase cycle number. However, the frequency estimation methods are highly susceptible to noise, which makes them suitable only for interference spectra with high signal-to-noise ratio (SNR). Synthetic wavelength methods are widely adopted for expanding the phase dynamic range. Since the synthetic wavelength is much larger than the wavelength of the light source, it can increase the dynamic range to the synthetic wavelength size. However, when the measurement range exceeds the synthetic wavelength, phase wrapping still occurs. To improve the dynamic range of existing synthetic wavelength methods, we propose a high dynamic range synthetic wavelength (HDR-SW) phase unwrapping method. This method eliminates the phase wrapping limitation and achieves a dynamic range of millimeters. Finally, a method is provided for displacement measurements with a large dynamic range, high sensitivity, and high speed.

The experimental system mainly consists of a fiber Michelson interferometer, a SLD light source, and a spectrometer. Light from the SLD is directed into a fiber circulator. Then, it is split into reference and sample beams by a beam splitter. The beams reflected from the sample and reference arms enter a spectrometer. The spectrometer has a spectral width of 30 nm and a spectral resolution of 0.0146 nm. Both the reference and sample arms are in free space, and achromatic lenses are utilized to eliminate the dispersion mismatch between the two arms.

Firstly, the synthetic phase is calculated by splitting the interference spectrum into two sub-spectra. Then, the correct integer number of phase cycles is computed from the full-length spectrum and the half-length spectrum located in the middle of the spectrometer. The method combines the demodulation results of the interference spectra with full-length and half-length to eliminate the ±1 phase cycle jump that is easily affected by noise.

The experimental results demonstrate that the HDR-SW method enables high-sensitivity phase demodulation for a large dynamic range. Compared with the linear regression method, the HDR-SW method has higher anti-noise ability and higher precision [Fig. 2(f)-(i)]. The linear regression method conducts phase unwrapping by comparing the phase differences between adjacent points. For the case of low SNR, phase unwrapping may result in a 2π error and consequently a larger linear fitting error. In contrast, the proposed method directly calculates the unknown phase cycles. By combining the results of the spectra with full-length and half-length, the phase cycle jump can be corrected. However, when the error in the low-precision solution exceeds λc/2 with λc of the central wavelength, Eq. (7) introduces an error of λc in the high-precision solution.

Conventional SD-OCT is frequently employed for conducting imaging on multi-layer samples using FFT for optical path demodulation. Due to the inherent frequency resolution limitations of FFT, the results of the FFT method show lower precision [Fig. 4(b) and (c)]. When the proposed method is applied to multi-layer samples, it also suffers from frequency resolution limitations. The interlayer spacing must be greater than π/Δk, and the interference spectra must be separated by filtering. The theoretical sensitivity of PSSD-OCT primarily depends on the phase sensitivity. In the case of a common-path configuration, the sensitivity of this experimental system reaches the nanometer level. In the non-common-path configuration, due to the influence of environmental vibrations, the sensitivity reduces to tens of nanometers.

Phase wrapping is an inherent issue in optical interference techniques to cause a limited dynamic range in PSSD-OCT. A large dynamic range synthetic wavelength-based phase unwrapping method is proposed to improve the dynamic range in the traditional synthetic wavelength methods. By selecting the full-length interference spectrum and the half-length interference spectrum located in the middle of the spectrometer, the correct integer number of phase cycles is computed. The method combines the demodulation results of the interference spectra with full-length and half-length to eliminate the phase cycle jump that is easily affected by noise. Imaging experiments using a step calibration block, a coin, and a circuit board demonstrate that this method enables high-sensitivity displacement demodulation with a large dynamic range (millimeter-scale).