Phase-contrast optical coherence elastography (PC-OCE) measurements involve collecting interference spectra before and after sample deformation, performing Fourier transforms, and conducting differential analysis to obtain wrapped phase containing deformation information. Strain calculations typically employ vector methods or deep learning approaches. However, excessive sample deformation can cause speckle decorrelation, which submerges the PC-OCE phase in noise and significantly complicates strain calculations. To address this challenge, researchers developed a time-domain tracking-based strain increment calculation method. This approach collects sequential interferometric spectra during deformation, selects appropriate inter-frame spacing, and divides large deformations into multiple smaller ones for separate strain calculations, followed by cumulative reconstruction. While recent PC-OCE strain adaptive incremental calculation methods utilize noise thresholds for frame spacing selection and vector-based strain calculation, limitations persist. These methods indirectly assess strain quality through wrapped phase noise levels, resulting in smaller inter-frame spacing and increased cumulative error when speckle noise is strong and unevenly distributed. Consequently, there is a need to develop an improved PC-OCE strain increment calculation method capable of handling complex and intense speckle noise conditions.

This paper proposes an adaptive incremental approach integrating Bayesian neural networks with incremental computation methods for temporal tracking. The method requires pre-training a Bayesian neural network to establish an end-to-end mapping from wrapped phase to strain. The trained network predicts strain while generating uncertainty distributions to evaluate strain quality. These uncertainty measurements guide inter-frame interval selection during incremental computation. Following the establishment of an uncertainty threshold, the optical coherence tomography (OCT) system captures sequential interference spectra during object deformation. The network performs strain prediction and generates corresponding uncertainty distributions, with the calculated average uncertainty optimizing inter-frame spacing adaptively. This process enables high signal-to-noise ratio strain calculation under phase speckle decorrelation conditions.

The method's effectiveness is evaluated using an OCT system to calculate strain under speckle decorrelation phase for both uniform and non-uniform deformation conditions. Experiment 1 involved uniform compression loading of a silicone film sample, as illustrated in Fig. 4. Figure 4(a) displays the wrapped phase obtained through Eq. (3) during compression loading, with Fig. 4(a-1) to Fig. 4(a-5) corresponding to mechanical loads of 3, 5, 7, 9, and 11 μm, respectively. Increasing loads resulted in greater film deformation and denser phase fringes. Speckle decorrelation emerged at the sample edge, as shown in Fig. 4(a-3), progressively expanding until phase fringes were substantially submerged, as evident in Fig. 4(a-5). Figure 4(c) presents strain results from the noise threshold-based adaptive incremental method, while Fig. 4(e) shows results from the Bayesian neural network-based approach. The strain distributions in Fig. 4(d-1) to Fig. 4(d-3) align with their corresponding Fig. 4(e-1) to Fig. 4(e-3) counterparts. This consistency occurs because the average uncertainty of direct Bayesian neural network strain calculations falls below the incremental method's preset threshold, resulting in single strain accumulation. Comparatively, the traditional method requires multiple accumulations, potentially increasing error propagation and reducing imaging signal-to-noise ratio. Experimental results demonstrate signal-to-noise ratio improvements of 28.2% and 74.3% for uniform and non-uniform deformation cases, respectively, compared to traditional methods.

Excessive sample deformation causes speckle decorrelation in PC-OCE, significantly complicating strain calculation. This paper introduces a novel Bayesian neural network-based strain increment calculation method with two key features: 1) Bayesian network uncertainty directly reflects strain quality, enabling adaptive and efficient frame spacing optimization while reducing cumulative errors common in traditional calculations; 2) following threshold establishment, the method requires no additional parameter settings and achieves automatic processing.