Phase-contrast optical coherence tomography (PC-OCT) integrates phase-contrast techniques with optical coherence tomography. It is applicable to the mechanical characterization and testing of various biological tissues and non-biological materials. It has the potential for early disease diagnosis or early detection of damage and becomes an important direction for future functional imaging development. However, according to the Nyquist sampling theorem, the measurement range of system strain is limited by the sampling frequency of the interference signal. Reducing the sampling rate will inevitably lead to aliasing artifacts in the acquired phase images, making strain calculation difficult. Therefore, without changing the existing structure of the PC-OCT system, designing a phase reconstruction method for spectral undersampling in PC-OCT can extend the measurement system’s depth range. This significantly reduces the sampling rate requirements of the measurement system, thus enabling rapid imaging of the deep internal regions of materials. This is crucial for the early diagnosis of diseases and the detection of damage.

We present a data-driven convolutional neural network (CNN) method for phase reconstruction in spectral undersampling of PC-OCT to extend the strain depth range of PC-OCT. First, we use the self-built PC-OCT system to collect the original interference signals of various types of composite materials under different loading conditions. After pre-processing such as interpolation, we obtain simulated undersampling and oversampling interference signals. The real and imaginary parts of the undersampling signals are the inputs, while the real and imaginary parts of both undersampling and oversampling signals are the inputs and labels for training the CNN. Then, after the network training is completed, we design two new sets of experiments. We collect interference signals sorted by time frames using the self-built PC-OCT. We randomly select interference signals from two consecutive time frames for undersampling processing. These unseen data by the network are then predicted. We obtain the phase strain calculation results before and after the network prediction through the vector method. Finally, we conduct a qualitative comparison of the prediction results and a quantitative analysis using the mean square error (MSE) as the evaluation metric to validate the effectiveness of the proposed method in this study.

We construct a PC-OCT measurement system (Fig. 4) and design two sets of loading experiments under different conditions (Fig. 5) to collect the original interference signals in an oversampling state. Subsequently, we process interference signals from two randomly selected consecutive time frames through linear interpolation and other undersampling techniques to simulate the real and imaginary parts of signals under different undersampling conditions. Then we feed them into a CNN for prediction. We obtain the phase signals predicted under different undersampling conditions through phase contrast techniques. Finally, we calculate the strain results corresponding to the undersampling phases and the oversampling phases predicted using the vector method (Figs. 6 and 8). The results show that when the undersampling rate is low, that is, the phase is near aliasing, the strain results calculated by both the vector method and the CNN+vector method are quite accurate. However, as the undersampling rate increases, that is, the degree of phase aliasing intensifies, the direct use of the vector method can still calculate the strain for the non-aliased phase parts, but the aliased phase parts exhibit severe distortion. The data-driven method proposed in this study can accurately and stably reconstruct the corresponding oversampling phase for different undersampling aliased phases and can calculate the oversampling corresponding strain field well using the vector method, effectively extending the measurement range of the system by three times. Mechanical loading experiments demonstrate the method’s ability to accurately reconstruct the phase in layered samples subjected to deformation, and thermal loading experiments further confirm the robustness of the method in handling complex phase patterns caused by internal defects and uneven thermal deformation. Finally, the mean square error (MSE) consistently shows high performance at different under-sampling rates (Figs. 7 and 9), indicating the reliability and accuracy of the method.

We propose a data-driven CNN method that can reconstruct aliased phases from undersampling to oversampling phases, thereby extending the measurement range of the phase-contrast OCT system. This method does not require modifications to the optical structure or parameters of the OCT system, making it an economical and efficient solution for enhancing imaging capabilities. The data-driven approach also reduces the sampling rate requirements, enabling rapid tomographic imaging of deep tissue areas without sacrificing image resolution. Although this method requires a large amount of training data and computational resources, the proposed method offers a promising direction for the development of lightweight, unsupervised undersampling phase reconstruction models.