Two-dimensional phase unwrapping based on U2-Net in complex noise environment

Phase unwrapping algorithm based on phase diversity wavefront reconstruction and virtual Hartmann-Shack technology

Phase unwrapping (PU) algorithms play a crucial role in various phase measurement techniques. Traditional algorithms cannot work well in strong noise environments, which makes it very difficult to obtain the accurate absolute phase from the noisy wrapped phase. In this Letter, we introduce a novel, to the best of our knowledge, phase unwrapping algorithm named PD-VHS. This algorithm innovatively employs point spread function (PSF) filtering to eliminate noise from the wrapped phase. Furthermore, it combines a phase diversity (PD) wavefront reconstruction technology with a virtual Hartmann-Shack (VHS) technology for phase reconstruction and phase unwrapping of the filtered PSFs. In simulations, hundreds of random noise wrapped phases, containing the first 45 Zernike polynomials (excluding piston and the two tilt terms) and the wavefront RMS = 0.5λ and 1λ, are used to compare the classical quality-map guided algorithm, the VHS algorithm with decent noise immunity, with our PD-VHS algorithm. When signal-to-noise ratio (SNR) drops to just 2 dB, the mean root mean square errors (RMSEs) of the residual wavefront between the unwrapped result and the absolute phase of the quality-map guided algorithm and the VHS algorithm are up to 3.99λ, 0.44λ, 4.29λ, and 0.85λ, respectively; however, our algorithm RMSEs are low: 0.11λ and 0.17λ. Simulation results demonstrated that the PD-VHS algorithm significantly outperforms the quality-map guided algorithm and the VHS algorithm under large-scale noise conditions.

Efficient and robust phase unwrapping method based on SFNet

Phase unwrapping is a crucial step in obtaining the final physical information in the field of optical metrology. Although good at dealing with phase with discontinuity and noise, most deep learning-based spatial phase unwrapping methods suffer from the complex model and unsatisfactory performance, partially due to simple noise type for training datasets and limited interpretability. This paper proposes a highly efficient and robust spatial phase unwrapping method based on an improved SegFormer network, SFNet. The SFNet structure uses a hierarchical encoder without positional encoding and a decoder based on a lightweight fully connected multilayer perceptron. The proposed method utilizes the self-attention mechanism of the Transformer to better capture the global relationship of phase changes and reduce errors in the phase unwrapping process. It has a lower parameter count, speeding up the phase unwrapping. The network is trained on a simulated dataset containing various types of noise and phase discontinuity. This paper compares the proposed method with several state-of-the-art deep learning-based and traditional methods in terms of important evaluation indices, such as RMSE and PFS, highlighting its structural stability, robustness to noise, and generalization.

Improved spatial speckle contrast model for tissue blood flow imaging: effects of spatial correlation among neighboring camera pixels

Significance

Speckle contrast analysis is the basis of laser speckle imaging (LSI), a simple, inexpensive, noninvasive technique used in various fields of medicine and engineering. A common application of LSI is the measurement of tissue blood flow. Accurate measurement of speckle contrast is essential to correctly measure blood flow. Variables, such as speckle grain size and camera pixel size, affect the speckle pattern and thus the speckle contrast.

Aim

We studied the effects of spatial correlation among adjacent camera pixels on the resulting speckle contrast values.

Approach

We derived a model that accounts for the potential correlation of intensity values in the common experimental situation where the speckle grain size is larger than the camera pixel size. In vitro phantom experiments were performed to test the model.

Results

Our spatial correlation model predicts that speckle contrast first increases, then decreases as the speckle grain size increases relative to the pixel size. This decreasing trend opposes what is observed with a standard speckle contrast model that does not consider spatial correlation. Experimental data are in good agreement with the predictions of our spatial correlation model.

Conclusions

We present a spatial correlation model that provides a more accurate measurement of speckle contrast, which should lead to improved accuracy in tissue blood flow measurements. The associated correlation factors only need to be calculated once, and open-source software is provided to assist with the calculation.

Performance of a U2-net model for phase unwrapping

Phase unwrapping plays a pivotal role in optics and is a key step in obtaining phase information. Recently, owing to the rapid development of artificial intelligence, a series of deep-learning-based phase-unwrapping methods has garnered considerable attention. Among these, a representative deep-learning model called U 2-net has shown potential for various phase-unwrapping applications. This study proposes a U 2-net-based phase-unwrapping model to explore the performance differences between the U 2-net and U-net. To this end, first, the U-net, U 2-net, and U 2-net-lite models are trained simultaneously, then their prediction accuracy, noise resistance, generalization capability, and model weight size are compared. The results show that the U 2-net model outperformed the U-net model. In particular, the U 2-net-lite model achieved the same performance as that of the U 2-net model while reducing the model weight size to 6.8% of the original U 2-net model, thereby realizing a lightweight model.