Fig. 1. LBS method framework. (a) The reconstruction process for the experimental 3D particle field. (b) The training data preparation for the U-Net. P is the parameter to be optimized, and P* is the optimal parameter.

Fig. 2. HCS framework.

Fig. 3. (a) In-line holography experimental setup and data preparation. (b) OCE framework.

Fig. 4. Modified U-Net framework with the training input and label.

Fig. 5. (a) Two transformed reconstructed images with additional name labels, with the ppp concentration is 1.36×10−1. The solid red box marks all the in-focus particles and the dashed blue box marks several out-of-focus particles. (b) Location comparison between the prediction result and the ground-truth.

Fig. 6. Reconstruction comparison among the normal simulation data, better synthetic data, and real experimental data under different reconstruction distances.

Fig. 7. Training results for the three types of training datasets: loss during training, and JI, ER, and point metrics for validation.

Fig. 8. Comparison of particle locations between the reconstruction and the reference results for the three types of training datasets. The reconstructed particles are categorized as true positive (TP), false negative (FN), and false positive (FP).